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University M icrofilm s International 300 North Zeeb Road Ann Arbor, Michigan 46106 USA SI. John's Road, Tyler's Green High Wycombe, Bucks, England HP10 6HR I f 77-11,690 OSTEEN, Craig Dennis, AN APPLICATION OF A TO SPATIAL PLANNING THE KALAMAZOO RIVER 1949LINEAR PROGRAMMING MODEL OF FOREST RESOURCES IN BASIN OF MICHIGAN. Michigan S ta te U n iv e rs ity , P h .D ., 1976 Economics, a g ric u ltu r a l Xerox University Microfilms, Ann Arbor, Michigan 48106 AN APPLICATION OF A LINEAR PROGRAMMING MODEL TO SPATIAL PLANNING OF FOREST RESOURCES IN THE KALAMAZOO RIVER BASIN OF MICHIGAN By Craig Dennis Osteen A DISSERTATION Submitted to Michigan S tate U n iv e rs ity in p a r tia l f u lf illm e n t o f th e requirements fo r the degree o f DOCTOR OF PHILOSOPHY Department o f Resource Development 1976 ABSTRACT AN APPLICATION OF A LINEAR PROGRAMMING MODEL TO SPATIAL PLANNING OF FOREST RESOURCES IN THE KALAMAZOO RIVER BASIN OF MICHIGAN By Craig Dennis Osteen The U.S. Forest Service is in te re s te d in developing an in te g rate d land inventory and evalu atio n system useful fo r r iv e r basin planning. The system is c a lle d the M u ltip le Use Management Sim ulator (MUMS). The o b je c tiv e o f the study is to examine the f e a s i b i l i t y o f b u ild in g an in ­ teg rated land inven tory and evalu atio n system fo r r iv e r basin planning s tu d ie s . The lo c a tio n aspect o f the model is emphasized. Important issues considered in co n ceptu alizin g the system include the s p a tia l and time aspects o f demand, production, and environmental impacts; the openness o f the r iv e r basin economy; and the tr a n s fe r o f goods through the economy. o f components. The conceptualized system consists o f a set The f i r s t component is the land evalu atio n system which generates acreages o f land management s tr a te g ie s , which are combinations o f land p ractices which produce goods, to meet various requirements fo r goods a t d if f e r e n t lo c a tio n s . and t h e ir outputs in space. This component also locates s tra te g ie s This component consists o f a psuedo-dynamic regional lin e a r programming model w ith tra n s p o rta tio n and environmental d iffu s io n components incorporated In to the production component. This model a llo c a te s production requirements among regions and generates p a t- Craig Dennis Osteen terns o f land management. A m u ltip le land use assignment model a l l o ­ cates management s tra te g ie s among g rid c e lls which make up a region. The second component is the land Inventory component which stores inform ation needed by the land evalu atio n system. raw resource d ata, and resource classes are sto red. Location in fo rm atio n , The th ir d compon­ ent is the c o n s tra in t generator which constrains the land evalu atio n system w ith decisions made outside o f the system. A lte rn a tiv e flow charts are presented. The fo urth component is goals fo r outputs and land use. component includes land management s tra te g y data. The f i f t h Inform ation is gener­ ated by re la tio n s h ip s based on resource d ata, land p ra c tic e s , and tim e. The s ix th component consists o f displays which include tab les and maps produced by computer graphics. A p ortio n o f the system was te s te d . A pseudo-dynamic regional l i n ­ ear programming model w ith the tra n s p o rt component incorporated was con­ stru cted fo r the fo re s t secto r o f the Kalamazoo R iver Basin. Six time perio ds, fo u r commodities, fo u r regions in s id e the r iv e r b as in , and e ig h t regions outside o f the r iv e r basin were considered. system connects the regions. over tim e. ated . A tra n s p o rt Requirements fo r the goods were estimated Production in regions outside o f the r iv e r basin was estim ­ Im porting and exporting was included in the model. tra n s p o rt costs were estim ated. Production and The model minimizes production and tra n s ­ p o rta tio n costs su b ject to land c o n s tra in ts and requirements fo r goods a t d if f e r e n t lo c a tio n s . Five computer runs were completed. Assumptions associated with these runs were as fo llo w s: A. No growth' in tim ber and hunterday requirements over tim e. Craig Dennis Osteen B. Growth in tim ber requirements in regions w ith p u lp m ills . C. Growth in tim ber and hunterday requirements. D. Growth in hunterday requirements and a higher ra te o f growth o f tim ber requirements. E. Growth in hunterdays and no growth in tim ber requirem ents. Land management p a tte rn s , le v e ls o f production, q u a n titie s re ­ ceived a t d if fe r e n t lo c a tio n s , and flows between regions were discussed. I t was found th a t a l l lands capable o f producing tim ber during the time period o f an alysis should be converted to in te n s iv e management as soon as p o s sib le , given the assumptions and o b jec tiv es o f the model. non-tim ber producing lands in the adequate co n dition A ll class should be converted to in te n s iv e management as soon as possible. Non-timber pro­ ducing lands in the non-adequate co n dition classes have the lowest p r i ­ o r it y fo r in te n s iv e management. Important fac to rs a ffe c tin g a llo c a tio n o f land management s tra te g ie s inclu d e: 1) le v e ls o f requirements fo r goods produced, 2) tra d e -o ffs between investments in land to increase outputs and tra n s p o rta tio n and im porting costs to bring goods in to a re ­ gion, 3) time d is trib u tio n o f production, and 4) time period o f an alysis* OBERS demands fo r the r iv e r basin fo r the present and 1990 cannot be met given the assumptions o f th is model. P o s s ib ilitie s f o r growth o f tim ber-using in d u s trie s are lim ite d by small amounts o f commercial fo re s t lan d , conversion o f fo re s t land to urban use, and the dispersed, p riv a te ownership o f fo re s t land. Problems w ith the model are discussed. The assumptions o f lin e a r programming, assumptions concerning behavior o f social and natural sys­ tems, and assumptions th a t reduce data needs make the model sim pler than r e a lity . The model does not seem to be w ell su ited to p re d ic tin g land Craig Dennis Osteen use patterns in the Kalamazoo R iver Basin which is made up o f sm all, s c a tte re d , privately-ow ned tra c ts o f land. The model appears to be b e t­ t e r s u ite d to planning management o f publicly-owned land o r fo r s e ttin g g u idelin es fo r management p ractices to be encouraged through extension programs. Im portant management options were not included in the model. Bias could be introduced in to the so lu tio n as a r e s u lt. Including the dimensions o f time and space g re a tly increase the size o f the tableau and costs o f solving the model. I t is fe a s ib le to construct a lin e a r programming model o f the f o r ­ e s t resource o f a r iv e r basin which includes s p a tia l and temporal ecolo g ic and economic dimensions. d i f f i c u l t to c o n stru c t. However, i t is c o s tly to operate and I t is d i f f i c u l t to lin k the tested model to the c u rre n tly used USDA model. Data in the Kalamazoo R ive r Basin are not precise enough in s p a tia l and management terms to support a gridded data system. Data th a t could be used in demand and supply p ro je c tio n models are also scarce. documented. Data submitted by the U.S. Forest Service were poorly More documentation o f these data is d e s ira b le . PREFACE This d is s e rta tio n is the fin a l re p o rt o f a research p ro je c t funded by the Northeastern Area, S ta te and P riv a te F o re s try , Forest S e rvic e, U.S.D.A The research study was c a lle d the " M u ltip le Use Sim ulator (MUMS)." The problem statem ent, study o b je c tiv e s , research approach, and d e s c rip tio n o f the study area are presented in Chapter I . is conceptualized in Chapter I I . The model which tested and the data c o lle c te d fo r the model are discussed in Chapter I I I . cusses the re s u lts o f te s tin g . The ideal model Chapter IV d is ­ The model is c r it ic iz e d in Chapter V. Chapter VI contains the summary, conclusions, and recommendations. d ix AA contains flo w c h a rt symbols. Appendices B through CC contain i n ­ form ation used as in p u t to the model. re s u lts o f te s tin g the model. Appen­ Appendices CC through FF contain Appendix GG is a glossary o f terms. TABLE OF CONTENTS Page LIST OF TABLES....................................................................................................... v11 LIST OF F IG U R E S ................................................................................................... x iv CHAPTER I. II. III. INTRODUCTION ...................................................................................... 1 Statement o f th e Problem .................................................... Study O b je c t iv e s ..................................................................... Research Approach ................................................................. D escriptio n o f Study Area ................................................ 1 5 6 7 CONCEPTUAL BASIS OF THE S Y S T E M ................................................ 31 Issues Considered by The System ................................... Components o f The MUMS S y s t e m ....................................... D efin in g The Ideal Model fo r The Land Evaluation System ........................................................ Land Management S trateg y Inform ation .......................... Goals f o r Land Use M a n a g e m e n t....................................... Linking The Land Evaluation System to The Land Inform ation System .................................................... Linking a C o n stra in t G enerator to The Land Evaluation System ......................................................... M a p p in g ....................................................................................... S u m m a ry ....................................................................................... 31 35 101 102 109 MODEL TO BE TESTED AND DATA U S E D ............................................ 112 S tru ctu re o f The Model to be Tested .......................... C a lc u la tin g Requirements fo r Roundwood ...................... Roundwood Production Outside o f The R ive r Basin A v a ila b le f o r Use in The R iver Basin . . . . C a lc u la tin g Requirements fo r llu n t e r d a y s .................. Supplies o f Hunterdays in Regions Outside o f The R iver B a s i n ............................................................. D efin in g R e g io n s ...................................................................... C a lc u la tin g T ra n s fe r C o s t s ................................................ Generating Forest Production A c t iv itie s .................. S u m m a ry ....................................................................................... 115 119 * * .* n i 38 86 86 87 126 129 134 138 139 153 171 iv CHAPTER IV . Page ANALYSIS AND R E S U LTS ........................................................................... 173 Types o f Computer Runs M a d e ........................................173 Discussion and Analysis o f Land Management R e s u lt s ..........................................................................174 Receipts o f G o o d s ............................................................. 189 P ro d u c tio n .............................................................................. 190 Flows o f Goods Between R e g io n s ................................... 195 C o s t s .......................................................................................207 Recommendations f o r Land Management .......................... 210 D iscussionof Problems Encountered During Testing . 215 Costs o f M o d e llin g ............................................................. 218 Changes Recommended fo r The Model A fte r Testing . 219 S u m m a ry ...................................................................................220 V. CRITICAL ANALYSIS OF THE MODEL FOR POLICY ANALYSIS AND ITS USEFULNESS TO LAND USE PLANNING............................... 222 A Review o f The Problems o f The c u rre n t USDA A p p ro ach .......................................................................... 223 C ritic is m o f The Ideal Model ........................................... C ritic is m o f The S p e c ific A p p lic a tio n ...................... Usefulness o f The Model to P o lic y Analysis . . . . Final Assessment o f The S u it a b i l it y o f TheModel . V I. 226 236 243 245 SUMMARY AND CONCLUSIONS............................................................... 248 S u m m a ry ................................................................................... 248 Needs fo r Further R e s e a rc h ............................................ 260 Conclusions and Recommendations ................................... 262 APPENDICES A. FLOWCHART SYMBOLS ............................................................................... B. PURCHASES OF SAWLOGS AND VENEER L O G S ................................. 271 C. PROPORTIONS OF COUNTY CONSUMPTION ALLOCATED TO REGIONS............................................................................................ 272 D. DEMAND MULTIPLIERS USING TREND OF FIRST DERIVATIVE . . 273 E. REQUIREMENTS FOR SAWLOGS, VENEER LOGS, AND PULPWOOD . . 274 F. ROUNDWOOD REQUIREMENTS G. PROPORTIONS OF COUNTY TIMBER PRODUCTION ALLOCATED TO R E G IO N S .................................................................................... 277 H. SAWLOG PRODUCTION IN OUTSIDE REGIONS 270 .................................................................. ................................... 276 278 V APPENDICES Page I. VENEER LOG PRODUCTION IN OUTSIDE REGIONS ............................ 279 J. EXCESS SUPPLIES OF TIMBER .............................................................. 280 K. REQUIREMENTS FOR DEER HUNTERDAYS, 1970 281 L. REQUIREMENTS FOR HUNTERDAYS .......................................................... 282 M. GAME KILLS IN REGIONS OUTSIDE OF THE RIVER BASIN 283 N. HUNTERDAYS SUPPLIED IN REGIONS OUTSIDE OF THE RIVER BASIN, 1970 ...................................................................................... 284 0. EXCESS PRODUCTION OF HUNTERDAYS BY OUTSIDE REGION . . . 285 P. MILES TRAVELLED ON EACH CLASS OF ROAD IN EACH REGION 286 Q. MILEAGE TRAVELLED ON THE TRANSPORTATION NETWORK IN EACH R E G IO N ....................................................................................................287 R. TIMBER TRANSFER COSTS BETWEEN REGIONS, 1970 ....................... S. WEIGHTS ON EACH YEAR'S CAR C L A S S ..................................................290 T. PROPORTIONS OF EACH CAR CLASS PRODUCED..................................... 291 U. TRANSFER COSTS FOR BIG AND SMALL GAME HUNTERDAYS, 1970 292 V. RANGES OF FIBER PRODUCTION 294 W. AGE DISTRIBUTION OF FOREST TYPES IN THE SOUTHERN LOWER PENINSULA................................................................................................296 X. ACRES OF COMMERCIAL FOREST LAND BY STAND SIZE CLASS IN THE SOUTHERN LOWER PENINSULA ................................................ 297 Y. PRODUCTION ACTIVITIES ...................................................................... 298 Z. MULTIPLIERS FOR PRODUCT COEFFICIENTS 300 . . . . .......................................................... .................................... 288 AA. AGE CLASS AS A PROPORTION OF STAND SIZE CLASS BY ECOSYSTEM................................................................................................306 BB. COSTS OF PRODUCTION ACTIVITIES, 1970 308 CC. QUANTITIES OF GOODS PRODUCED OUTSIDE OF THE MODEL . . . 314 DD. ACREAGES ALLOCATED TO MANAGEMENT STRATEGIES IN LINEAR PROGRAMMING SOLUTIONS ................................................................. 316 vi APPENDICES Page EE. SURPLUSES AND D E F IC IT S ........................................................................... 323 FF. RIVER BASIN PRODUCTION...........................................................................324 GG. DEFINITION OF TERMS................................................................................... 325 LITERATURE CITED............................................................................................................327 LIST OF TABLES TABLE 1 -1 . Page Population Figures fo r 1960 and 1970 and Percentage Change fo r Counties in the Kalamazoo R iver Basin . . 11 1 -2 . 1970 Population f o r the Hydrological R iver Basin . . . 11 1 -3 . Urban-Rural Population D is tr ib u tio n , 1970 12 1 -4 . Urban Population in Sub-basins o f the Kalamazoo R iver Basin, 1970 12 1 -5 . Population o f Incorporated C it ie s , 1970 13 1 -6 . Populations o f Regions Outside o f the R iver Basin, 1970 ................................................................................................... 14 Total Earnings and Percentage C ontributions from Each Sector in 1969 .............................................................................. 15 Value Added by Manufacturing and Wood Products Manu­ fa c tu rin g and Value o f Roundwood in 1970 ...................... 16 1 -9 . Primary Wood Using Plants in Each County in 1974 . . . 17 1-1 0 . Per Capita Income fo r Counties in the R iver Basin, 1970 1-1 1 . Value o f Wood Production in Counties Outside o f the R iver Basin in 1970 18 Primary Wood-Using Plants in Counties Outside o f the R iver Basin, 1974 19 1 -7 . 1 -8 . 1-12. 1 -1 3 . 1-1 4 . Percentages o f County Land in Each Land Use, 1970 . . . 18 20 Acres o f Each Ecosystem in Each Region in the R iver Basin, 1966 21 1 -1 5 . Net Volume o f Growing Stock and Sawtimber, 1966 22 1 -1 6 . Public Ownership o f Land in the R ive r Basin, 1974 . . 23 1-1 7. Acreage o f Each Forest S o il Group in the R iver Basin, 1974 ................................................................................................... 30 vi i . . . vi ii TABLE 2 -1 . Page Rating o f A lte rn a tiv e s fo r the Land Evaluation S y s te m .............................................................................................. 63 2 -2 . Rating o f A lte rn a tiv e Model Structures ................................ 71 2 -3 . Rating Grid Cell S i z e .................................................................. 94 3 -1 . Estimated Pulpwood Consumption by the Menasha Corpor­ a tio n and the Warren Company in Time Period 1 . . . 121 3 -2 . Requirements fo r Sawlogs and Veneer Logs by Region in Time Period 1 .............................................................................. 124 3 -3 . Estimates o f Pulpwood Production in Outside Regions 3 -4 . Estimated Sawlog Production in Outside Regions . . . . 128 3 -5 . Estimated Veneer Log Production in Outside Regions . . 129 3 -6 . Hunters per Person, Hunterdays per Hunter, and Hunterdays per Person fo r Each DNR Z o n e ........................................130 3 -7 . Requirements fo r Deer Hunterdays in Each Region in Time Period 1 ...................................................................................131 3 -8 . Hunters per Person, Hunterdays per Hunter, and Hunter­ days per Person by S p e c ie s ......................................................... 132 3 -9 . Requirements fo r Small Game Hunterdays by Region in Time Period 1 . 127 133 3 -1 0 . Population M u ltip lie r s fo r Each Time P e r i o d ....................... 133 3-11. Deer K ills per A c r e ........................................................................... 135 3-1 2 . Supplies o f Hunterdays in Regions Outside o f the R iver B a s i n ....................................................................................... 136 3-1 3 . Small Game K ills per Acre in DNR Region I I I 3-1 4 . Estimates o f Hunters per K i l l , Hunterdays per Hunter, and Hunterdays per K ill fo r Each Small Game S p e c i e s ................................................................................................137 3-15. Estimates o f Small Game Hunterdays Supplied by Regions Outside o f the R iver B a s i n ......................................................... 137 3-1 6 . R epresentative Demand Points in the R ive r Basin 3-17. R epresentative Demand Points f o r Regions Outside o f the R ive r B a s i n ...............................................................................140 ....................... 136 . . . 139 ix TABLE Page 3-1 8 . Hauling Costs fo r Timber in M ichigan, 1975 ........................ 147 3-19. Costs per M ile Figures fo r Operating an Automobile . . 150 3-20. Costs per M ile per Hunterday fo r Each Class o f Car . . 152 3-21. Aggregation o f S o il Groups and Condition Classes . . . 155 3-22. R otation Age and Time Periods in Each Stand Size C l a s s .................................................................................................... 157 3-23. C a lc u la tin g Growing Stock Harvest/Growing Stock V olum e.................................................................................................... 162 3-2 4 . Merchantable Volume/Growing Stock H arvest, 1966 . . . 162 3-25. Merchantable Volume/Growing Stock H arvest, 1972 . . . 162 3-26. Merchantable Volume/Total F ib e r Volume ............................... 164 3-2 7 . Conversion o f Forest Land to Urban Use by Region . 168 3 -2 8 . Projected Percentage o f 1967 Forest Land Converted Through Each Time P e r i o d ......................................................... 170 3-2 9 . Extra Supplies o f Goods A v a ila b le to Each Region from Outside the 12 Region Area o f A n a l y s i s ........................... 171 4 -1 . Ranking o f Runs fo r Production o f Commodities in the Kalamazoo R ive r Basin ............................................................. . . 191 4 -2 . Ranking o f Total R ive r Basin Production fo r Each Commodity............................................................................................191 4 -3 . Ranking o f Big Game Hunterday Production by Run in Each Time P e r i o d .......................................................................... 192 4 -4 . Ranking o f O verall Big Game Hunterday Production by Run fo r Each R e g io n ...................................................................... 192 4 -5 . Ranking o f Small Game Hunterday Production by Region fo r Each Time P e r i o d ..................................................................193 4 -6 . Ranking o f Small Game Hunterday Production Over A ll Time Periods fo r Each R e g i o n .................................................193 4 -7 . Ranking o f Production o f Erosion by Run in Each Time P e r i o d ................................................................................................ 194 4 -8 . Ranking o f Production o f Erosion Over A ll Time Periods fo r Each Run in Each R e g io n ..................................................... 194 X TABLE Page 4 -9 . OBERS Demands and R iver Basin Production in the In fe a s ib le R u n .................................................................................. 195 4 -1 0 . R iver Basin Timber Production in Time Periods 1, 3, and 6 f o r Runs A Through E .......................................................... 195 4 -1 1 . Exports and Imports o f Timber fo r Run A ............................... 196 4 -1 2 . Changes in Imports and Exports 4 -1 3 . Changes in Imports and Exports o f Timber in Run C ....................................................................................................198 4 -1 4 . Changes in Exports and Imports o f Time in Run D ....................................................................................................199 4 -1 5 . Big Game Hunterday 4 -1 6 . Changes in Imports and Exports o f Big Game Hunterdays Brought About by Run B ..................................................................200 4 -1 7 . Changes in Imports and Exports o f Hunterdays Brought About by Run C ...................................................................................201 4 -1 8 . Changes in Imports and Exports o f Big Game Hunterdays Caused by Run D ...............................................................................202 4 -1 9 . Changes in Imports and Exports o f Big Game Hunterdays Caused by Run E .............................................................................. 203 4 -2 0 . Imports and Exports o f Small Game Hunterdays in Run A .................................................................................................... 203 4 -2 1 . Changes in the P attern o f Imports and Exports o f Small Game Hunterdays Caused by Run B ............................................ 204 4 -2 2 . Changes in the P attern o f Imports and Exports o f Small Game Hunterdays Caused by Run C ............................................ 205 4 -2 3 . Changes in the P a tte rn o f Imports and Exports o f Small Game Hunterdays Caused by Run D ............................................ 205 4 -2 4 . Changes in the P a tte rn o f Imports and Exports o f Small Game Hunterdays Caused by Run E ............................................ 206 4 -2 5 . Costs Incurred in the R iver Basin fo r Each Run . . . . 207 B - l. Purchases o f Veneer Logs and Sawlogs by County (Mcf) . 271 C -l. Proportions o f County Consumption A llo c ate d to R e g io n .................................................................................................... 272 o f Timber in Run B . . Imports and Exports in Run A . . . 197 200 xi TABLE Page D -l. Demand M u ltip lie r s a t 1970 P r i c e s ............................................ 273 D-2. Demand M u ltip lie r s a t R ising R e la tiv e P r i c e s .......................273 D-3. Demand M u ltip lie r s a t R e la tiv e Prices Above 1970 . . . 273 E -l. Requirements fo r Sawlogs and Veneer Logs w ith 1970 R e la tiv e Prices (Mcf) ............................................................ 274 Requirements fo r Sawlogs and Veneer Logs w ith Rising R e la tiv e Prices (Mcf) ............................................................. 274 E-2. E -3. Pulpwwod Requirements w ith 1970 R e la tiv e Prices (C c f). 275 E-4. Pulpwood Requirements w ith R ising R e la tiv e Prices ( C c f ) ....................................................................................................275 F -l. Roundwood Requirements w ith 1970 R e la tiv e Prices (Mcf) ....................................................................................................276 F-2. Roundwood Requirements w ith Rising R e la tiv e Prices . . G -l. Proportions o f County Timber Production A llocated to R e g i o n s ................................................................................................277 H - l. Sawlog Production from Outside Regions by County ( M c f ) .................................................................................................... 278 1 -1 . Veneer Log Production by Region and County (Mcf) . . . J -l. Excess Supplies o f Timber w ith 1970 R e la tiv e Prices ( M c f ) .................................................................................................... 280 J -2 . Excess Supplies o f Timber w ith Rising R e la tiv e Prices (Mcf) .................................................................................. 280 Requirements fo r Deer Hunterdays by County and Region, 1970 ................................................................................................... 281 K -l. 276 279 L -l. Requirements fo r Deer H u n te rd a y s .................................................. 282 L -2 . Requirements fo r Small Game Hunterdays ................................ M - l. Game K ills Per County in Regions Outside o f the R iver B a s i n .................................................................................................... 283 N -l. Hunterdays Supplied by Counties in Regions Outside o f the Basin, 1970 284 0 -1 . Excess Production o f Deer Hunterdays .................................... 285 0 -2 . Excess Production o f Small Game Hunterdays ....................... 285 282 x ii TABLE Page P -l. M iles T ra v e lle d on Each Class o f Road in EachRegion . 286 Q - l. Mileage T ra v e lle d on the Transportation Network in Each R e g i o n .............................................................................. 287 R -l. Timber T ran s fe r Costs Between Regions ($ /C c f), 1970 S -l. Weight's on Each Year's Car C l a s s ............................................. 290 T -l. Proportions o f Each Car Class P ro d u c ed .................................... 291 U -l. T ran sfer Costs o f Big and Small Game Hunterdays, 1970 . V -l. Ranges o f F ib er Production by Resource C lass, Manage­ ment S trategy and Stand Size C l a s s 294 W -l. Age D is trib u tio n o f Forest Types in the Southern Lower Peninsula (1000 A c r e s ) ......................................................... 296 X -l. Acres o f Commercial Forest Land by Stand Size Class in .................. the Southern Lower Peninsula (1000 Acres) . 288 292 297 Z -l. C on ifer E c o s y s te m ....................................................................... 300 Z -2. Oak-Hickory E c o s y s te m ...............................................................301 Z -3 . Elm-Ash-Cottonwood Ecosystem ..................................................... 302 Z -4 . Maple-Beech-Birch Ecosystem 303 Z -5 . Aspen-Birch E c o s y s te m .............................................................. 304 AA-1. Age Class as a Proportion o f Stand Size Class by E c o s y s te m ................................................................................... 306 BB-1. C o n ifer Ecosystem, S o il Group 1 BB-2. C onifer Ecosystem, S o il Group2 .................................................. 309 BB-3. C onifer Ecosystem, S oil Group3 .................................................. 310 BB-4. Oak Ecosystem, S o il Group 1 ..................................................... 310 BB-5. Oak Ecosystem, S o il Group 2 .......................................................... 311 BB-6. ..................................................... 308 Elm-Ash-Cottonwood Ecosystem .................................................... 311 BB-7. Maple-Beech-Birch Ecosystem, S oil Group 1 312 BB-8. Maple-Beech-Birch Ecosystem, 312 BB-9. Aspen-Birch Ecosystem, S oil Group 1 S oil Group 2 313 X 1 11 TABLE Page BB-10. Aspen-Birch Ecosystem, S oil Group 2 313 CC-1. Q u an tities o f Outputs Produced on Forest Land Converted .................................................................................. 314 to Urban Use CC-2. Q uan tities o f Outputs Produced on Lands C u rren tly in In tensive Management and Environmental Emphasis . . 315 DD-1. Run A DD-2. Run B, Changes in Acreages A llocated to Management S tra teg ies as Compared to Run A ............................................ 319 DD-3. Run C, Changes in Acreages A llocated to Management S tra te g ie s as Compared to Run A ............................................ 320 DD-4. Run D, Changes in Acreages A llo cated to Management S tra teg ies as Compared to Run A ............................................ 321 DD-5. Run E, Changes in Acreages A llocated to Management S tra te g ie s as Compared to Run A ............................................ 322 EE-1. Surpluses and D e fic its in Receipts Derived from Linear Programming Solutions ............................................................ 323 River Basin Production ................................................................. 324 FF-1. ........................................................................................................ 316 LIST OF FIGURES FIGURE Page 1 -1 . Hap o f Regions in the Study A r e a ............................................. 1 -2 . Land Cover: A ctive A g ric u ltu ra l Land Use, 1972 1 -3 . Land Cover: Forested Land, 1972 ............................................. 26 1 -4 . Land Cover: Developed Land, 1972 27 1 -5 . Other Open Lands, 1972 .................................................................. 28 1 -6 . P la t Map o f Walton Township in Eaton County, T. 1 N .-R .5 W ...................................................................................... 29 Diagram o f an In te g rate d Land Inventory and E valuation S y s te m ............................................................................................... 40 Schematic Diagram o f the R ussell-Spofford ResidualsEnvironmental Q u a lity Planning Model .............................. 56 The Production Model w ith T ransportation and Environ­ mental D iffu s io n Components Incorporated ...................... 81 Steps from S to ring Land Inform ation to Constraining the Location Model, Given a Grid C ell Small Enough to C la s s ify Only One R e s o u r c e ........................................... 91 Steps in Constraining the Location Model from Land In fo rm atio n , Given a Grid C ell Small Enough to C la s s ify Only One R e s o u rc e .................................................... 92 Flow Chart o f an Algorithm to Generate Acreage Con­ s tr a in ts fo r the Location Model and the M u ltip le Land Use Assignment Model, Given a Grid Small Enough to C la s s ify Only One Resource C l a s s ............................... 99 Flow Chart o f an Algorithm to Generate Acreage Con­ s tr a in ts fo r the Location Model and the M u ltip le Land Use Assignment Model, Given a Grid C ell Long Enough to C la s s ify More Than One Resource Class . . 100 2 -1 . 2 -2 . 2 -3 . 2 -4 . 2 -5 . 2 -6 . 2 -7 . . . . 9 25 XV FIGURE Page 2 -8 . Flow Chart o f the C on strain t Generator, Assuming That Management S tra te g y , Resource Class, and Location are S p e c if i e d ................................................................. 103 2 -9 . Flow Chart o f the C on strain t Generator, Assuming a Small Grid Cell and Unspecified Resource Classes . . 104 2-1 0 . Flow Chart o f the C on strain t Generator, Assuming More Than One Management S trateg y Can be Assigned to a Grid C ell . . . .......................................................................... 105 2-11. Outputs from System Components ................................................ 3 -1 . Square DEFG is the R e g i o n .............................................................. 145 3 -2 . Acres o f Forest Land Converted to Urban Use Over T im e ........................................................................................................ 169 5 -1 . Diagram o f a L inear Program Tableau .................................... 232 5 -2 . Diagram o f a L inear Program ing Tableau Showing the E ffe c ts o f Adding the Time Dimension .............................. 235 110 CHAPTER I INTRODUCTION Statement o f the Problem The U.S. Forest Service is in te re s te d in developing an In te g ra te d land inven tory and ev a lu a tio n system useful f o r r i v e r basin planning. I t is c a lle d the M u ltip le Use Management Sim ulator (MUMS). The system should have the c a p a b ility to handle land uses and outputs o f land uses and be useful to o th e r agencies o f the U.S. Department o f A g ric u l­ tu re involved in r i v e r basin planning. Im portant aspects o f r iv e r basin planning are the lo c a tio n o f land management s tra te g ie s and the lo c a tio n o f outputs and impacts o f land management s tr a te g ie s . The o b je c tiv e o f th e U.S. Forest S ervice is to in v e s tig a te th e f e a s i b i l i t y o f b u ild in g a system th a t uses land resource in fo rm a tio n , a llo c a te s land management s tra te g ie s in space, and d isp lays the impacts o f these s tra te g ie s over space. There are a lte r n a tiv e models and system designs to in ven to ry land resource d a ta , a llo c a te management s tra te g ie s in space, and d is p la y impacts by lo c a tio n . General types o f models th a t could be used f o r the land ev alu atio n system include in p u t-o u tp u t models, lin e a r program­ ming models, sim ulatio n models, and hybrid models. There are o th er systems th a t can be used to s to re land data and in p u t i t to the land evalu atio n system. be handled. The output o f the land e v alu atio n system must also P art o f the problem is to id e n t if y the a lt e r n a tiv e s , since 1 2 th e re 1s some u n c e rta in ty as to which a lte rn a tiv e s e x is t and which are best. The problem e x is ts 1n a c o n tex t. MUMS may be used to s a tis fy th e inform ation needs o f r iv e r basin planning. The model could be used to te s t various land use plans and p ro je c t what is l i k e l y to occur. In the planning process, o b je c tiv e s f o r production o f goods and services and environmental conditions are d efin e d . They could be based on 1) national and regional economic conditions th a t are l i k e l y to impact on a region over tim e , and 2) th e p a r tic ip a tio n o f various le v e ls o f govern ment and the p u b lic . A lte r n a tiv e o b je c tiv e s fo r goods, s e rv ic e s , and environmental conditions could be used in d if f e r e n t runs o f th e model. Comparisons o f re s u lts could then be made. Current and fu tu re le v e ls o f achievement are to be p rojected in the planning process. The re ­ sources o f th e r iv e r basin are in v en to rie d and t h e i r c a p a b ilitie s appraised. The inven to ry d efines the a v a i l a b i l i t y o f resources to s a t­ is f y c u rre n t and fu tu re le v e ls o f o b je c tiv e s . Planning is concerned w ith how to use these resources to achieve o b je c tiv e s . The Water Resources Council has defined a se t o f goals f o r plan­ ning land and w ater resources in r iv e r basins. MUMS w ill be concerned w ith ev alu atin g land use plans to meet these o b je c tiv e s . The Water Resources Commission d efines fo u r basic sets o f o b je c tiv e s : a ) en­ hancement o f n atio n al economic development, b) enhancement o f environ­ mental q u a lit y , c) regional development, and d) social w e ll-b e in g (Water Resources C o u ncil, 19 72 ). A lte r n a tiv e plans can be developed, each o f which fa v o r one o b je c tiv e over the o th e rs. National economic development deals w ith th e value o f output o f goods and services and n atio n al economic e ffic ie n c y . B e n e fic ia l e ffe c ts 3 o f the plan Include: a) value to users o f Increased outputs o f goods and s e rv ic e s , and b) value o f output re s u ltin g from extern al economies. Adverse e ffe c ts inclu d e: a ) value o f resources required f o r or d is ­ placed by the plan and b) losses in output re s u ltin g from external d is ­ economies. Environmental q u a lity is evaluated in terms o f physical o r eco­ lo g ic a l c r i t e r i a o r dimensions, in clu d in g q u a lita tiv e aspects. This o b je c tiv e 1s concerned w ith the e ffe c ts on areas o f n atu ral beauty; w ater, la n d , and a i r q u a lity ; b io lo g ic a l resources and selected eco­ systems; g e o lo g ic a l, a rc h e o lo g ic a l, and h is to r ic a l resources; and i r ­ re v e rs ib le o r ir r e t r ie v a b le coiranitments o f resources to fu tu re use. The regional development aspect deals w ith the subnational e f ­ fe c ts and thus may deal w ith d is tr ib u tio n a l e ffe c ts over space and be­ tween so c ia l groups. B e n e fic ia l income e ffe c ts in clu d e: a ) value o f increased output o f goods and services w ith in re le v a n t regio ns, and b) value o f output re s u ltin g from e x t e r n a litie s occurring w ith in r e le ­ vant regions. Adverse income e ffe c ts inclu d e: a ) values o f resources w ith in re le v a n t regions requ ired fo r o r displaced by the p la n , and b) losses in output re s u ltin g from e x te r n a litie s w ith in re le v a n t regions. Other e ffe c ts include the number and types o f jo b s , e ffe c ts on popula­ tio n d is tr ib u tio n w ith in and among re g io n s , and e ffe c ts on th e re g io n 's environment. Social w e ll-b e in g seems to be a category in s e rte d to deal w ith th a t which was not covered 1n the above ca te g o rie s . I t includes re al income d is t r ib u tio n ; l i f e h e a lth , and s a fe ty e ffe c ts ; e d u c a tio n a l, c u lt u r a l, and re c re a tio n a l o p p o rtu n itie s ; and emergency preparedness. The U.S. Forest Service believes th a t 1 t 1s d e s ira b le f o r MUMS to have the c a p a b ility to be lin k e d to th e e x is tin g Economic Research Ser­ v ic e ’ s le a s t cost lin e a r program th a t w ill generate impacts o f a lte r n a ­ t iv e land management s tra te g ie s and a g ric u ltu r a l outputs. A land in ­ ventory system based on the S oil Conservation Service Conservation Needs Inventory already e x is ts . New sectors are being added to the model. These sectors are the fo re s t and pasture secto rs. urban land. The model excludes The h e a rt o f th e model is a set o f management s tr a te g ie s . These management s tra te g ie s produce a se t o f products c a lle d a productpackage which includes both p o s itiv e and negative aspects. uct has a row c o e ffic ie n t. t ic u la r demand. Each prod­ Each row can be constrained to meet a par­ Each management s tra te g y is assigned a cost fo r produc­ ing the product-package. The model then minimizes t o ta l production costs o f meeting c e rta in demands and shows various impacts o f the solu­ tio n . The model is not perm itted to change land use from crop to fo re s t to p astu re, e tc . Land use tra n s fe rs o f th is type can occur only when s p e c ifie d before the model is run. Management s tra te g ie s on crop­ land o r fo re s t land are allowed to change. Demands are incorporated in to the model in the form o f c o n s tra in ts . The i n i t i a l s e t o f demands are regional food and f ib e r p ro je ctio n s based on OBERS p ro je c tio n s . Requirements f o r o th e r products in each product-package can be developed w ith re p res en tative s o f th e p u b lic in a r iv e r basin. The model p ro je cts the acreages o f various management s tra te g ie s required to meet projected needs in th e years 2000 and 2020. The r iv e r basin lin e a r program is e s s e n tia lly spaceless. I t does not account f o r the costs o f b rin g in g consumers and products to g e th e r nor does i t account fo r th e s p a tia l d is tr ib u tio n o f resources. Study O bjectives The primary o b je c tiv e o f th is study is to examine the f e a s i­ b i l i t y o f b u ild in g an in te g rate d land inven tory and evalu atio n system fo r r iv e r basin planning s tu d ie s . Recommendations concerning the s tru c ­ tu re and development o f the model are to be made. This w il l involve conceptualizing the system, inclu d in g the types o f questions w ith which to d e a l, and analyzing the problems in and the f e a s i b i l i t y o f b u ild in g such a system. S p e c ific goals o f the study are lis t e d : 1. Survey the lit e r a t u r e to fin d e x is tin g models and concepts th a t can be incorporated in to the land inven tory and evalu­ a tio n system. 2. The emphasis is put on the lo c a tio n model. Study the f e a s i b i l i t y o f developing a lo c a tio n model th a t can be lin ke d to a production model, such as the Economic Research S e rv ic e 's le a s t cost lin e a r programming r iv e r basin model. Linkages to the production model must also be co nceptualized. The Forest Service is in te re s te d in several s p e c ific points in th is area o f emphasis: a. Id e n tific a tio n o f key v a ria b le s to form sub-regions o f r i v e r basins. These v a ria b le s should be im portant v a ria b le s fo r r iv e r basin planning. b. I f p o ssib le, an estim ate o f bias caused by fo rc in g subregions to conform to p o lit ic a l boundaries should be made. c. The d is tr ib u tio n o f key v a ria b le s should be displayed using a method th a t can be adapted to th e Economic Development A d m in is tra tio n 's two minute by two minute n atio n al g rid . 6 3. Conceptualize and study the f e a s i b i l i t y o f developing o ther parts o f the system. 4. Examine the s u i t a b il i t y o f the model fo r land use, s p e c ifi­ c a lly r iv e r b asin , planning by U.S.D.A. 5. Test the lo c a tio n model on the fo re s t sector o f the Kalamazoo River Basin and generate a lte r n a tiv e land useplans from i t . Research Approach The focus o f th is research p ro je c t is model b u ild in g . ect is d ivid ed in to a s e rie s o f steps: This p ro j­ 1) c o n ce p tu alizatio n o f the system and i t s components, 2) te s tin g o f some o f the components, speci­ f i c a l l y the lo c a tio n model, 3) an alysis o f the re s u lts o f te s tin g , and 4 ) discussion o f the s u i t a b i l i t y o f the system f o r land use planning and policy-m aking. discussed below. The a c t i v i t ie s undertaken in each step are b r i e f l y The d e ta ils o f these a c t i v i t ie s w ill be elaborated in l a t e r chapters. C onceptualization o f the System The questions to be approached by the system and the issues to be considered in answering them are d e fin e d . Once th is is done, a search fo r models and concepts to be used is undertaken. The system and i t s components are conceptualized by d e fin in g the components, the purpose o f each component, and the models th a t could be used in each component. The system and i t s components are then s p e c ifie d in mathematical form and flo w c h a rts . V a ria b le s , r e la tio n s h ip s , and assumptions are d efin ed . The lin kag es between the components are als o d efin ed . Testing During th is sta g e , the lo c a tio n model is tes ted to discover the exten t to which I t meets th e purpose fo r which 1 t was designed. A lte r n ­ a tiv e questions and assumptions concerning fu tu re land use in the Kalamazoo R iver Basin a re developed to be considered by the system. Data fo r the system are then c o lle c te d . ed. The computer model is co n stru ct­ Computer runs are made to te s t th e hypotheses and consider various land use questions. Analyses o f the Tests In th is stage re s u lts o f the computer runs are presented and analyzed. cussed. Impacts o f re s u lts on the hypotheses and questions are d is ­ Land use plans developed by the system are compared and the v a lid it y o f the s tru c tu re and data are analyzed. Changes th a t could be made in the system are recommended. Discussion o f System S u it a b i l it y The s u i t a b i l i t y o f the system f o r land use planning and p o lic y ­ making is analyzed. pointed o u t. Shortcomings, lim it a t io n s , and strengths are Recommendations as to th e f e a s i b i l i t y and s u i t a b i l i t y o f the system to land use planning and policy-m aking are discussed. D escriptio n o f the Study Area The model was te s te d on the fo re s t secto r o f the Kalamazoo R iver Basin 1n southwestern M ichigan. The Kalamazoo R iv e r Basin was chosen because the U.S. Forest Service is p a r tic ip a tin g in a planning study f o r th e r iv e r b asin . Data were made a v a ila b le by the Forest Service and o th e r U.S. Department o f A g ric u ltu re personnel. Most o f the work on the r iv e r basin study was undertaken in East Lansing, M ichigan, on the Michigan S ta te U n iv e rs ity campus making cooperation e a s ie r than i f the work was spread out a t various lo c a tio n s . M odelling the e n tire r iv e r basin system appears to be too larg e a task given the funds and time a llo c a te d to the research p ro je c t. The fo re s t sector was chosen ra th e r than the a g ric u ltu re o r pasture sectors since the p ro je c t was being funded by the U.S. Forest S ervice. The Kalamazoo R iver Basin study covers th e Kalamazoo, B lack, and Paw Paw r i v e r basins. These riv e rs d ra in in to Lake Michigan. hydrological basin covers portions o f eleven counties: The A lle g a n , B a rry, B e rrie n , Calhoun, Eaton, H ills d a le , Jackson, Kalamazoo, Kent, Ottawa, and Van Buren. Chicago. The r iv e r basin is west o f D e tr o it and northeast o f The Economic Research S e rv ic e , which is conducting the eco­ nomic a n a ly s is , elim in ated Kent county since only a small p o rtio n o f the county is in the r iv e r basin. The r iv e r basin was d ivid ed in to fo u r sub-basins by th e Economic Research S ervice. w ill be used in th is study. These sub-basins The r i v e r basin is o u tlin e d on the map in Figure 1-1 and includes regions one through fo u r. Region 1 includes portions o f Calhoun, Eaton, H ills d a le , and Jackson co u n ties. Region 2 includes portions o f A lle g a n , B a rry, and Kalamazoo co u n ties. 3 includes portions o f B errien and Van Buren co u n ties. Region Region 4 con­ ta in s portio ns o f A lle g a n , Ottawa, and Van Buren co u nties. Regions were defined fo r th is research p ro je c t outside o f the r iv e r basin. These regions (5 -1 2 ) serve as su p p liers o f goods and de- manders o f goods produced by th e fo re s t s e c to r. This p r o je c t, however, is not concerned w ith land use planning fo r those regio ns. contains Muskegon county and a p ortio n o f Ottawa county. Kent county. Region 5 Region 6 is Region 7 contains C lin to n and Io n ia counties and portions o f Berrien and Van Buren co u nties. Region 9 contains Branch and 9 STATE OF M I C H I G A N WAT ERS HEDS i i *. ?i rt , *Z±i+—.£ Figure 1 - 1 . --Map o f Regions in the Study Area. 10 S t. Joseph counties and portions o f Calhoun, H ills d a le , and Kalamazoo counties. county. Region 10 contains Ingham county and a p ortio n o f Jackson Region 11 contains Lake, Mecosta, Newaygo, and Osceola counties. Region 12 contains Montcalm and G ra tio t counties. Regions outside o f the r iv e r basin are defined along county lin e s whenever possible. Figure 1-1 illu s t r a t e s the regions. Population The population o f the ten county area in which th e Kalamazoo R iver Basin is located increased from 1960 to 1970. Table 1-1 contains the population fig u re s fo r 1960 and 1970 and the percentage changes in pop­ u la tio n fo r those ten counties. Population o f th e ten county region increased by 14.7 percent from 1960 to 1970. counties increased by more than 20 percent. B a rry, Eaton, and Ottawa A lle g a n , Kalamazoo, and Van Buren counties increased between ten percent and twenty p ercen t, w hile the re s t o f th e counties increased less than ten percent. Pop­ u la tio n d en sity o f th e ten county area in 1970 was 167 people per square m ile . The Economic Research Service compiled 1970 population fig u re s fo r the hydrological basin. These are shown in Table 1 -2 . The popula­ tio n o f the hydrological basin in 1970 was 187 people per square m ile . The counties in the ten county area vary in t h e ir u rb an -ru ral popr u la tio n d is t r ib u tio n . d is tr ib u tio n . Table 1-3 i ll u s t r a t e s the u rb an -ru ral population More than 50 percent o f th e population o f A lle g a n , B arry, Eaton, H ills d a le , and Van Buren counties l iv e o utsid e o f urban areas or places o f 1000-2500 pop ulatio n. The Economic Research Service also estim ated the urban population in the hydrological basin. This is shown in T able 1 -4 . Table 1-1 . — Population Figures fo r 1960 and 1970 and Percentage Change fo r Counties In the Kalamazoo R iver Basin. County Population 1970 Allegan Barry Berrien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Total Source: 66,575 38,166 168,875 141,963 68,892 37,171 143,274 201,550 128,181 56,173 1,045,820 1960 Percent Chanqe 57,729 31,738 149,865 138,858 49,684 34,742 131,994 169,712 98,719 48,395 911,436 15.3 20.3 9 .3 2 .2 38.7 7 .0 8 .5 18.8 29.8 16.1 14.7 Michigan S tate U n iv e rs ity , Cooperative Extension S e rvic e, County and Regional Facts, Regions I I , I I I , IV , V I, and V I I I . Table 1 - 2 .— 1970 Population fo r the Hydrological R iver Basin. Region 1 2 3 4 Total Population 158,959 234,218 74,575 88,626 556,378 12 Table 1 - 3 .— Urban-Rural Population D is tr ib u tio n , 1970. Percent o f Population County Urban Allegan Barry Berrien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Source: Places o f 1000-2500 Other 4 .6 8 .9 0 .8 3 .8 6.1 11.8 2 .8 2 .9 3 .4 12.0 22.6 17.0 4 6 .4 59.6 42.1 20.8 54.8 75.5 4 8 .3 21.6 72.8 73.9 45.6 36.6 51.8 67.4 42.4 21.6 48.3 66.4 Michigan S tate U n iv e rs ity , Cooperative Extension S e rv ic e , County and Regional Facts, Region I I , I I I , IV , V I, and V I I I . Table 1 -4 . — Urban Population in Sub-basins o f the Kalamazoo R iver Basin 1970. Region Urban Population 1 2 3 4 92,820 147,923 30,646 40,256 Percent Urban 58.4 63.2 41.1 45.4 These fig u re s in d ic a te th a t regions 1 and 2 are th e most populous regions in the basin and have predom inately urban populations w h ile regions 3 and 4 have predominately ru ra l populations. The urban popu­ la tio n o f region 2 is concentrated in Kalamazoo county w h ile i t is concentrated in Calhoun county in region 1. The incorporated c it ie s in the hydro lo g ical basin a re lis te d in Table 1 -5 . 13 Table 1 - 5 . — Population o f Incorporated C it ie s , 1970. Region C ity Population 1 Albion B a ttle Creek Marshall S p rin g fie ld C h a rlo tte Allegan Otsego Plainwel 1 Wayland Galesburg Kalamazoo Parchment Portage Benton Harbor Coloma W a te rv lie t H artfo rd Paw Paw Holland Bangor South Haven 12,112 38,931 7,253 3,994 8,244 4,516 3,957 3,195 2,054 1,355 85,555 2,027 35,590 16,481 1,814 2,059 2,508 3,053 26,337 2,050 6,471 2 3 4 Kalamazoo is the only c i t y in the r iv e r basin la r g e r than 50,000. are only s ix c it ie s la r g e r than 10,000. There The basin population liv e s la rg e ly in medium-sized and small towns, unincorporated exurban places, and in ru ra l areas. The population regions outside o f the r i v e r basin is presented in Table 1 -6 . Regions 5, 6 , and 10 are th e most populous and contain such c it ie s as Muskegon and Holland in region 5 , Grand Rapids in region 6 , and Lansing and Jackson in region 10. Regions 11 and 12 are the le a s t populated. Economy Table 1-7 l i s t s the t o ta l earnings o f each county in th e ten county area and the c o n trib u tio n o f each s e c to r. Total earnings are the sum o f 14 Table 1 - 6 .— Populations o f Regions Outside o f the R iver Basin, 1970. Reqion Population 5 6 7 8 9 10 11 12 Source: 230,737 411,044 173,503 165,585 162,422 391,894 76,483 78,906 Michigan S tate U n iv e rs ity , Cooperative Extension S ervice, County and Regional F acts, Regions I I , I I I , IV , V I, and V I I I . to ta l wage and s a la ry disbursements, o th e r la b o r Income and p ro p rie to r income. No fig u re s were a v a ila b le fo r Eaton and Ottawa co u nties. Manu fa c tu rin g accounts fo r less than 40 percent o f to ta l earnings only in Allegan and Van Buren counties and more than 50 percent o f t o ta l earn­ ings only in Berrien county. A g ric u ltu re makes i t s g re a te s t c o n tr i­ bution in Van Buren and Allegan counties and i t s le a s t c o n trib u tio n in Calhoun county. However, manufacturing is the most im portant secto r in terms o f earnings fo r a l l o f the counties. Table 1-8 w i l l help to g ive some p erspective in to the importance o f the tim ber economy in the area. This ta b le l i s t s the value added by manufacturing in each county and an estim ate o f value added by wood products manufacture in 1970. I t also gives an estim ate o f value o f roundwood produced in each county. The manufacture o f wood products appears to be q u ite im portant in A lleg an , B e rrie n , and Kalamazoo co u nties. The p o rtio n o f value added by manufacturing a ttr ib u te d to wood products is g re a te r than 30 percent fo r these th re e co u nties. B errien and Kalamazoo counties rank high in Table 1 - 7 . — Total Earnings and Percentage C ontributions from Each -S ec to r in 1969. Percent o f Total Earnings Total Earnings ($1000) County Allegan Barry Berrien Calhoun H ills d a le Jackson Kalamazoo Van Buren Sector 2 1 113842 8 .8 68101 6.1 521339 3 .7 477293 1 .4 75482 7 .6 466677 1.7 648994 0 .8 107620 12.5 17.0 18.9 7 .9 14.9 18.6 10.4 12.5 15.3 3 39.3 43.9 54.4 45.3 4 0 .2 45.7 4 7 .6 36.0 5 4 1 .2 * * 0.1 * 0.1 0.1 * 6 4 .9 3.1 3.7 3.1 4 .4 3.7 4 .0 5 .0 3.3 3 .2 5 .2 10.1 7 .5 3 .8 8 .3 2 .6 7 14.1 10.5 12.3 12.0 15.4 12.8 13.5 13.7 8 0 .9 * ★ 5 .6 * 2.4 2 .8 1 .6 9 10.1 10.5 10.6 11.3 7 .9 11.5 11.3 9 .3 10 0 .5 0 .4 0 .3 0 .3 0 .6 0.1 0.1 0 .8 Sector Code Sector Code 1 2 3 4 5 6 7 8 9 10 Source: Sector Farming Government Manufacturing Mining Construction T ra n s p o rta tio n , communications, and p u b lic u t i l i t i e s Wholesale andr e t a i l tra d e Finance, insurance, and re a l e s ta te Service Other Michigan S ta te U n iv e rs ity , Cooperative Extension S e rvic e, County and Regional F acts, Regions I I , I I I , IV , V I, and V I I I . value added by m anufacturing. ten counties is very sm all. The value o f roundwood produced by a l l In a l l c o u n tie s , th e value o f roundwood is less than one percent o f the to ta l earnings. The roundwood harvested in these counties is p rim a rily sawlogs and veneer lo g s. In 1970, Marquette county had the g re a te s t value o f roundwood production in Michigan w ith $ 3 ,1 8 3 ,0 0 0 . Only Barry county's roundwood production 16 Table 1 - 8 .— Value Added by Manufacturing and Wood Products Manufactur­ ing and Value o f Roundwood Production in 1970. County A1legan Barry Berrien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Value Added by Manufacture ($1000) 67,300 47,800 363,900 473,400 34,500 39,600 277,900 510,200 227,200 70,000 Value Added by Wood Products Manufacture ($1000) Percent Wood Products o f Total Value o f Roundwood Produced ($1000) 35.8 0 31.7 9 .4 14.9 8 .8 0 4 6 .2 14.5 7 .8 160 327 115 198 291 136 192 162 110 173 24.0602 0 115,337 44,322 5,128 3,503 D 235,5371 32,945 5,446 Excludes wood, fu r n it u r e , and fix tu re s due to d is clo su re possi b illtie s . ^Excludes pulp and paper due to d is clo su re p o s s ib ilit ie s . D— Excluded by the Census Bureau to avoid d is clo su re o f firm s ' operations. Sources: Bureau o f the Census, County and C ity Factbook, and Robert S. Manthy, Lee M. James, and Henry H. Huber, "Michigan Timber Production— Now and in 1985." exceeds ten percent o f th a t valu e. These ten c o u n ties , th en , are r e la t iv e ly small producers o f roundwood in M ichigan. However, the pro­ duction o f roundwood can be an im portant source o f income to landowners. Barry and Eaton counties had the la rg e s t value o f roundwood production 1n 1970. Table 1-9 l i s t s the number and type o f primary wood-using plants in each county 1n 1974. There 1s a to ta l o f 36 p la n ts , co n sistin g o f one p u lp m ill, fo u r veneer m ills , and 31 saw m ills. Only nine o f these sawmills have a c a p a c ity o f more than 500,000 board f e e t per y e a r. Only two m ills have a c a p ac ity g re a te r than 3 ,0 0 0 ,0 0 0 board f e e t per y e a r. 17 Table 1 - 9 .— Primary Hood-Using Plants in Each County in 1974. Sawmills (MBF) County Allegan Barry Berrien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Source: Pulpm ill Veneer <100 1 * * * * * * * * * * * 2 * * * * 1 * 1 * 1 * 2 + 1 * 1 * 1 100500 1 6 2 1 1 1 * 1 1 2 5001000 10003000 30005000 50007500 1 * 1 * * * 1 * * * 1 1 * * 1 1 * * * * * * * * 1 * * * * * * * * * * * * * * * 7500+ •k 1 * * * * * * * * 1974 D ire c to ry o f Primary Wood Using Plants in Michigan. There is a predominance o f small sawmills in these co u n ties . These m ills use p rim a rily hardwoods. 1970 per c a p ita income va rie s from $2149 in H ills d a le county to $3355 in Kalamazoo county. Per c a p ita incomes are higher in counties containing r e la t iv e ly la rg e c it ie s and having high values added by manufacturing. counties. county. Per c a p ita incomes are lower in ru ra l and a g ric u ltu r a l Table 1-10 illu s t r a t e s the per c a p ita incomes fo r each In Kalamazoo county, which ranked f i r s t in per c a p ita income, and B errien county, ranked fo u rth , wood products m anufacturing is an im portant p a rt o f the m anufacturing s e c to r. Allegan county which ranks ninth in per c a p ita income also has an im portant woods products s e c to r. The tim ber economy o f regions outside o f the r iv e r basin w il l be b r ie f ly discussed. The value added due to wood products manufacturing and the value o f roundwood produced in each county are presented in Table 1-1 1 . Kent, Muskegon, and S t. Joseph counties are r e la t iv e ly 18 Table 1 -1 0 .— Per Capita Income fo r Counties in the R iver Basin, 1970. County Per Capita Income ($ ) A11egan Barry B errien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Source: 2649 2849 3031 3309 3332 2149 3198 3355 3002 2680 Bureau o f the Census, County and C ity Factbook. Table 1 -1 1 .— Value o f Wood Production in Counties Outside o f the R iver Basin in 1970. County Branch Cass Cl inton G ra tio t Ingham Ion ia Kent Lake Mecosta Montcalm Muskegon Newaygo Osceola S t. Joseph Value Added From Wood Products Manufacturing ($1000) . 3,524 8,351 * * 2,499 * 288,266 * * ★ 27 ,349a * * 85,036 Value o f Roundwood Production ($1000) 195 281 207 372 374 399 327 1,493 393 405 341 838 617 79 a Excludes pulp and paper due to d is clo su re p o s s ib ilit ie s . Source: Robert S. Manthy, Lee M. James, and Henry H. Huber, "Michigan Timber Production— Now and in 1985." 19 larg e manufacturers o f wood products. The value added by wood products manufacturing in Kent county is la r g e r than any county in the ten county area o f the Kalamazoo R iver Basin. eig h t o f the ten counties. ten counties. S t. Joseph county is la r g e r than Muskegon county is la r g e r than s ix o f the However, th e larg e pulpm ill in Muskegon is excluded from the value added fig u re s because o f the disclo su re problems. Values o f roundwood production in G r a tio t, Ingham, Io n ia , Kent, Lake, Mecosta, Montcalm, Muskegon, Newaygo, and Osceola counties are a l l la r g e r than fo r any o f the counties in the ten county r iv e r basin area. Lake, Mecosta, Newaygo, and Osceola counties are im portant producers o f pulpwood fo r the Menasha Corporation o f Allegan county in region 2. Table 1-12 l i s t s the primary wood-using plants in counties in regions outside o f the r iv e r basin. Table 1 -1 2 .— Primary Wood-Using Plants in Counties Outside o f the River Basin, 1974. Sawmi11s (MBF) County Pulpm ill Branch Cass C li nton G ra tio t Ingham Ionia Kent Lake Mecosta Montcalm Muskegon Newaygo Osceola S t. Joseph Source: + * * * * * * * ★ k 1 * k * Veneer * * ★ * + * * * * * ★ * * * 100 * 3 * * 1 1 * ★ * * * * * ‘1 100500 * 1 * 2 2 1 ★ 1 * 1 1 2 2 * 5001000 10003000 30005000 50007500 7500+ * 1 * * 1 1 * 2 * * 1 2 2 * 1 * 1 * * 2 1 2 * 2 2 1 * * 1 * * * * * 1 * * * * 1 * * * * * * 1 * * ★ * ★ * * * * * * * * + * * * ★ * * * * * 1974 D ire c to ry o f Primary Wood-Using Plants in Michigan. 20 Land Use In terms o f to ta l acreage, a g ric u ltu re 1s the predominant land use in a l l ten counties as shown in Table 1 -1 3 . is less than 50 percent only in Ottawa county. A g ric u ltu ra l land use A g ric u ltu ra l land use exceeds 70 percent in Eaton and H ills d a le counties. Kalamazoo, Calhoun, and Berrien counties are the most urbanized counties w ith 1 6 .0 , 6 .7 , and 10.6 percent urban land re s p e c tiv e ly . three percent urban land. None o f the o th er counties exceed A lle g a n , B arry, Calhoun, Jackson, Kalamazoo, Ottawa, and Van Buren counties a ll have more than 20 percent fo re s t land. * A lleg an , B arry, and Van Buren counties exceed 25 percent fo re s t land. In a l l co u n ties, fo re s t land is the second la rg e s t land use in terms o f acreage. Recreation land use exceeds f iv e percent only in Allegan and Barry counties w ith 8 .4 percent and 7 .0 percent re s p e c tiv e ly . These two counties are also th e most fo res ted and among the le a s t urban. Table 1 -1 3 .— Percentages o f County Land in Each Land Use, 1970. County inlan d w ater Allegan Barry Berri en Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Source: 1 .3 2 .9 0 .7 1 .0 0 .2 0 .6 2 .6 3 .2 1 .5 2 .0 fo re s t 28.4 26.4 18.7 21.8 15.3 18.2 21.4 21.8 24.5 25.8 a g r i­ c u ltu re 52.2 55.9 58.2 63.7 71.1 72.6 57.8 51.5 49 .0 58.4 tran sp o r­ ta tio n 3 .6 4 .4 5 .2 4 .3 3 .8 3 .2 4 .2 4 .9 4 .8 3 .9 re c re ­ atio n 8 .4 7 .0 0 .5 0 .3 0.1 0 .7 3 .4 2.7 0 .6 0.1 urban o th er 2 .9 0 .8 1 0 .6 6 .7 2 .2 1 .8 2 .0 1 6 .0 2 .4 2 .4 4 .5 5 .5 6 .9 3 .2 7 .5 3 .6 11.2 3.1 18.7 9 .3 Michigan S tate U n iv e rs ity , Cooperative Extension S e rv ic e , County and Regional F acts. 21 The U.S. Forest Service has compiled acreages o f fo re s t ecosystems fo r the hydrological basin. basin: Five ecosystems are present in the r iv e r c o n ife r , o a k -h ic k o ry , m aple-beech-birch, elm-ash-cottonwood, and aspen-birch. Table 1-14 l i s t s these acreages. Table 1 -1 4 .— Acres o f Each Ecosystem in Each Region in the R iver Basin, 1966. Acres Ecosystem C on ifer Oak-Hickory Elm-AshCottonwood Maple-BeechBirch Aspen-Birch Total Source: Region 1 Region 2 Region 3 Region 4 T otal 4,376 30,828 9,812 66,385 2,529 23,681 8,901 38,965 25,618 159,860 25,062 39,650 19,022 25,120 108,859 14,619 10,942 85,827 30,038 21,927 167,813 12,647 8,905 66,784 19,964 12,060 105,010 77,269 53,834 425,434 Economic Research Service, Unpublished Data, 1974. Forest land is approxim ately 22 percent o f th e area o f the hydro­ lo g ic r iv e r basin area. Oak-hickory is the la rg e s t ecosystem in a l l regions follow ed by elm -ash-cottonwood, maple-beech, b ir c h , aspen-birch and c o n ife r. U rbanizatio n w i l l probably reduce the amount o f fo re s t land in the r iv e r basin in the fu tu r e . Table 1-15 l i s t s the net volumes o f growing stock and sawtimber in each o f the ten counties in 1966. Volume o f growing stock is the volume o f sound wood in th e bole o f sawtimber and poletim ber tre es from the stump to a minimum fo u r inch top diam eter o utside bark o r to the p o in t where the c e n tra l stem breaks in to lim bs. Volume o f sawtimber 1s the volume o f the sawlog p o rtio n o f liv e sawtimber tre e s in board f e e t , In te rn a tio n a l l/4 -1 n c h r u le , 22 from stump to a minimum seven inch top diam eter outside bark fo r s o f t ­ woods and nine inches fo r hardwoods (Chase, P f e i f f e r , and Spenser, 1970). Table 1 -1 5 .— Net Volume o f Growing Stock and Sawtimber, 1966. County Allegan Barry B errien Calhoun Eaton H ills d a le Kalamazoo Ottawa Van Buren Source: Growing Stock (MMCF) Sawtimber (MMBF) 8 5 .8 64.1 4 8 .2 66.6 36.0 4 8 .5 4 5 .4 4 6 .5 58.6 245.7 187.7 144.6 178.8 104.2 148.3 127.1 123.4 167.4 Clarence D. Chase, Ray E. P f e if e r , John S. Spenser, J r . , The Growing Timber Resource o f Michigan, 1966. Forest land in the r i v e r basin is la r g e ly unmanaged fo r tim ber purposes. stocked. Only 40 percent o f th e stands are considered medium to f u l l y Another 30 percent o f th e stand area is occupied by in h ib itin g vegetation th a t w il l preclude establishm ent o f a f u l l y stocked stand by natural means. Another 40 percent is considered e ith e r f a i r o r unfavor­ able 1n stocking. growing space. Rough and ro tte n tre es occupy much o f the a v a ila b le Poletim ber is th e dominant s iz e c la s s . Removals, mostly sawtimber, exceed allo w ab le cut by 80 p erc en t.(S h ro e d e r, 1974). Much o f th is removal may occur during the c le a rin g o f land fo r re s id e n tia l development. Due to the age d is tr ib u tio n o f tim ber stands, sawtimber removals may decrease in th e fu tu re . s iz e c la s s . Most stands are in the poletim ber Sawtimber removals may again increase when poletim ber tre es increase in s ize to sawtimber tre e s . 23 Ownership o f land in the ten county area is la r g e ly p riv a te . Table 1-16 l i s t s th e acreages o f land and percentages o f land in each county owned by the Michigan Department o f Natural Resources and the U.S. Forest S ervice. in the In no case is more than ten percent o f the land county p u b lic a lly owned. Only in Allegan and Barry counties is more than one percent o f the land p u b lic a lly owned w ith 8 .3 percent and 6.65 percent in public ownership re s p e c tiv e ly . The U.S. Forest Service owns only 11 acres in the ten county a re a , in Barry county. The re s t o f the p u b lic ownership 1s by the Michigan Department o f Natural Resources. Most fo re s t land 1n th e ten county area is p r iv a te ly owned. Maps drawn by the Michigan S tate U n iv e rs ity Remote Sensing P ro je c t f o r the Upper Kalamazoo Watershed, which corresponds c lo s e ly to region 1 show th a t fo re s t land occurs in small blocks sc atte re d over the w ate r­ shed area. Forest land appears to be interspersed among a g r ic u lt u r a l, marsh and brushy land. This p a tte rn suggests th a t ownership is h ig h ly fragmented w ith most woodlots being owned by farm ers. (See Figures 1 -2 , Table 1 -1 6 .— Public Ownership o f Land in the R iver B asin, 1974. County DNR (acres) Allegan Barry Berrien Calhoun Eaton H ills d a le Jackson Kalamazoo Ottawa Van Buren Source: 44 ,0 4 6 .3 2 23 ,35 7.50 880.56 132.19 7.70 2 ,4 2 4 .6 4 13,492.12 2 ,7 2 2 .8 0 1 ,2 0 7 .0 2 831.68 % o f county U .S .F .S . (ac re s) 8 .3 6.65 .24 .029 .002 .63 2.90 .75 .33 .21 0 11 0 0 0 0 0 0 0 0 % o f county 0 .003 0 0 0 0 0 0 0 0 Michigan S tate U n iv e rs ity , Graduate School o f Business, Michigan S t a t is t ic a l A b s tra c t, 1974. 24 1 -3 , 1 -4 , and 1 - 5 . ) A survey o f re c e n tly p rin te d platbooks in d ica te s th a t most ru ra l ownerships are less than 640 acres. are la rg e r than 160 acres. Very few o f these Figure 1-6 is a ty p ic a l township p la t map located in Eaton county in the Upper Kalamazoo Watershed. This township, Walton township, T1N~R5W, is located in an area w ith a r e la t iv e ly la rg e amount o f fo re s t land in the Upper Kalamazoo. fragmented. The ownership is h ig h ly The map l i s t s th e owner and the s ize o f the t r a c t . It appears th a t much o f the fo re s t land is located along streams in the area. Land C h a ra c te ris tic s The U.S. Forest Service has c la s s ifie d the fo re s t s o ils groups fo r the r iv e r basin study. Following is in to f iv e a d e s c rip tio n o f the s o il groups. Soil Group A. W ell-d rain ed and moderately w e ll-d ra in e d loamy and clayey s o ils w ith slopes from 0-18 percent. Hardwood production on these s o ils is high r e la t iv e to s o f t ­ wood production. Soil Group B. W ell-d rain ed and moderately w e ll-d ra in e d sandy and g ra v e lly s o ils w ith slopes from 0-18 percent. Conifers are favored on th is s o il. Soil Group C. Somewhat p o o rly-d rain ed to very p o o rly-d rain ed sandy, loamy, and clayey s o ils w ith slopes from 0-12 percent. N e ith e r hardwoods nor softwoods grow w ell on th is s o i l . Soil Group D. Very poorly drained organic and mineral s o ils . Growth o f both hardwoods and softwoods is lim ite d , although some species may grow w e ll. Soil Group E. W ell-d ra in e d and moderately w e ll-d ra in e d loamy, c la y e y , and sandy s o ils w ith slopes from 18 to 35 percent. Growth o f hardwoods and softwoods is probably b e tte r than on groups C and D. Table 1-17 gives the acreage o f each s o il group f o r each region in the r i v e r basin and the e n tir e r i v e r basin. Only fo re s t land is Figure 1 - 2 . --Land Cover: Source: Active A g ric u ltu ra l Land Use, 1972. Michigan S ta te U n iv e rs ity , P ro je c t fo r the Use o f Remote Sensing in Land Use P o lic y Form ulation, "Upper Kalamazoo Watershed Land Cover In v e n to ry ," 1973. 26 /- " X /' I * . Sv* «* ■ 'Vf i. «• ’ . r y**i . A _ ? '+ j L 2 ^ . *z *•.■*£ t *■ * 4 l i _ • ite* S s l # ’. >* *a ,*«** * A m ! W t »■ *— • ♦• ,t 7 ft •aV J jttA " • « .' i?>i--'*j' < . •’♦’- ' L .•*:■ ? • t , V * »1 Land Resource Data Mapped and Sub-area Inventory Exogenous Management Decision Display System Displays of Outputs Location Model I----------> Water Resources Council Directives Constraint Generator Goals for Outputs and Land Use Demands In stitu tio n al Restraints and Land Use Controls Figure 2-1.--Diagram of an Integrated Land Inventory and Evaluation System. 40 o r in te r-in d u s try model. This type o f model has a tran sactio n s m atrix representing transactio n s between d if f e r e n t sectors o f the econoruy. It solves fo r to ta l requirements in terms o f output from each u n it in the processing sector necessary to meet exogenously determined f in a l demands. There are several ways in which environmental linkages can be made. These linkages provide estim ates o f the amounts o f m a teria ls co ntributed to the ecosystem by processing sectors to meet fin a l demands. The s p a tia l aspect can be included by going to an in te rre g io n a l type o f model, each region having an in p u t-o u tp u t m a trix . In te ra c tio n s between regions would have to be accounted fo r w ith in the model. The second class is th e lin e a r programming model which optim izes an o b je c tiv e fu n c tio n . In th is approach, a c t iv it ie s can have in p u t, output, and resid ual c o e ffic ie n ts . must be e x p li c i t l y s p e c ifie d . An o b je c tiv e fu n c tio n and c o n stra in ts The ecological linkages are included by c o e ffic ie n ts in the a c t iv it y columns. The s p a tia l dimension is included by d iv id in g th e study area in to a s e t o f re g io n s , d e fin in g a c t i v i t ie s according to these regions. s p e c ifie d . In te ra c tio n s between these regions can be C losely re la te d to th is class o f models are tra n s p o rta tio n , land assignement, s p a tia l e q u ilib riu m , and q u ad ratic programming models. The th ir d class is the sim u latio n model. This type o f model is highly f l e x ib l e and can be t a ilo r e d to s p e c ific problems. models are n on-optim izing. a lte r n a tiv e outputs. over tim e. Sim ulation The user has to make value judgments about This approach is best fo r v a ria b le s th a t change This type o f model is u s u a lly re c u rs iv e . required to g e n e ra lize so lutio ns and make comparisons. M u ltip le runs are The s p a tia l aspects can be added to th is system by d e fin in g regions and generating values f o r each region. 41 Hybrid models are combinations o f the above approaches. Any o f the approaches can be best su ited to a c e rta in p a rt o f th e problem. This kind o f approach allows d iffe r e n t models to be lin ke d in order to b e tte r handle th e problem. approach. Sim ulation 1s o ften included 1n a lin e a r prograrmring Hybrid models are u su ally s p e c ia lly ta ilo r e d to f i t c e rta in types o f problems. The s p a tia l dimension can be added in the same way as i t was in the o th er approaches. Dynamic programning is a f i f t h 1972). p o s s ib ilit y (Agrawal and Heady, Dynamic programming optim izes over tim e. be a stage. Each stage has a number o f possible states th a t can be a llo c a te d to i t . o ptim ize. Each tim e period could Dynamic programming uses a recu rsive re la tio n s h ip to I t s ta rts a t the la s t time period and works backward to the present fin d in g the optimum s ta te fo r each stage. duced by d e fin in g regions. Space would be in t r o ­ E s s e n tia lly , a dynamic program would be de­ fin e d fo r each region and each class o f resource. Stages and states would be defined fo r each region and resource cla ss . A lt e r n a tiv e ly , dy­ namic programming could also o p tim ize over space and resource class given one time p erio d. Each region and resource class could be a stage with a number o f s ta te s , which would be management s tr a te g ie s , to be a llo c a te d to i t . A dynamic program would be required by each tim e p erio d. Accounting fo r the s p a tia l dimension req u ires more than d e fin in g regions. B a rrie rs to m o b ility caused by distance must be considered in the model. These b a rrie rs can be accounted fo r by in clu d in g tra n s p o rt costs or by inclu d in g a g ra v ity model. Inclu d in g tr a n s fe r costs is p a r tic u la r ly easy in a lin e a r programming model. A c t iv it ie s fo r tra n s ­ fe r r in g goods can be devised and the tr a n s fe r costs are then included in the o b je c tiv e fu n c tio n . With a g ra v ity model, the a ttr a c tio n between 42 two points is stressed. The a ttr a c tio n between two points (which could be the flow o f goods between two p o in ts ) is d ir e c t ly proportional to the product o f the magnitudes o f some dimension o f each o f two points and in v e rs e ly proportional to the distance between two p o in ts . Both approaches may g ive s im ila r re s u lts . However, the g ra v ity approach might be more e a s ily adaptable to some types o f problems. In p ut-o u tp u t does not seem to be a v ia b le a lte r n a tiv e fo r the problem defined fo r study in Chapter I . In p u t-o u tp u t deals more e x p lic it ly w ith trade between sectors ra th e r than land management. Much time and money would be spent on data not r e a lly c r i t i c a l to land use plan­ ning. To account fo r a subregion o f a r iv e r basin, th a t i s , to introduce the s p a tia l dimension, an in p u t-o u tp u t model would be required fo r each sub region thus ra is in g costs o f data c o lle c tio n . Flows between regions would also have to be included. Linear prograrming seems to be a good approach to the problem being d e a lt w ith in the land e v alu atio n system. Its o p tim iza tio n qual­ i t ie s can be useful to planners showing the best so lu tio n among a set o f a lte r n a tiv e s , provided th a t the proper o b je c tiv e fu nctio n and con­ s tra in ts have been s p e c ifie d . A p p licatio n s o f lin e a r programming have already been made to s im ila r types o f problems. Hence, th ere are ex­ amples to be follow ed which show th a t lin e a r programming might be w ell suited to the problem. The Economic Research S e rv ic e 's model to which the lo c a tio n model developed in th is study is to be lin k e d is a le a s t cost lin e a r program. Linkages o f the lo c a tio n model to the Economic Research Service model might be e a s ie r i f the lo c a tio n model is also a lin e a r programming model. 43 Sim ulation might be w ell su ited to c e rta in parts o f the problem th a t are non-optim izing and would not f i t w ell in to th e lin e a r program­ ming model. Dynamic programming might be d i f f i c u l t to use since each type o f problem requires a special alg orith m . An algorithm would probably have to be s p e c ia lly developed fo r th is problem. d i f f i c u l t y and expensive. This task could be very I t would also be d i f f i c u l t to keep tra c k o f m u ltip le outputs and constrain the s o lu tio n by the acreages o f the land resource. Past and Current Work The work discussed in th is section deals w ith the land evalu atio n system, emphasizing the lo c a tio n component, and the types o f problems to be encountered. Isard and O s tro ff discuss general in te rre g io n a l e q u ilib riu m (Is a rd and O s tro ff, 1970). They d efin e a system o f a number o f one- point regions and commodities. There are producers and consumers in a region. holdings o f commodities th a t can be Consumers have i n i t i a l consumed or traded. any two regions. There is a world tra d e r to ship commodities between Each producer in each region has a production fu n c tio n . Each consumer in each region has a u t i l i t y fu n c tio n which is a fu n ctio n o f f in a l demands. Prices are defined fo r each commodity in each regio n. Assets can flow between regions to provide a balance o f payments e q u ilib ­ rium. For the system o f regions to be in e q u ilib iru m , the fo llo w in g e q u ilib riu m conditions must hold: 1) Each producer uses inputs such th a t the marginal ra te o f tec h n ica l s u b s titu tio n between inputs 1s equal to the r a t io o f in p u t prices and produce output u n til marginal costs 44 equals p ric e . 2) Each consumer maximizes u t i l i t y subject to a budget co n stra in t by equating the marginal ra te o f s u b s titu tio n between two goods to r a tio o f prices o f the goods. 3) The d iffe re n c e between prices of a commodity 1n two regions equals the cost o f tra n s p o rtin g the com­ modity between the regions when th ere is tra d e between the two regions. This assumes th a t the world is a com petitive market. 4) Final demands in a region plus ex p o rts , including resources fo r tra n s p o rt, equals the i n i t i a l holdings plus production 1n the region plus Im ports. equals demand f o r each good 1n each re g io n .) must be in e q u ilib riu m fo r each region. {Supply 5) The balance o f tra d e The d iffe re n c e between the value o f exports and Imports is ju s t o ffs e t by the flow o f assets be­ tween regions. The number o f independant equations in th e system is equal to th e number o f unknowns. Once e q u ilib riu m prices are g iv en , an e q u ilib riu m se t o f shipments and asset tra n s fe rs can be determined by a computation s im ila r to a lin e a r program. The to ta l se t o f imports and exports are determined when e q u ilib riu m prices are s e t. Maximum gains from tra d e are defined by m inim izing to ta l tra n s p o rt costs. Once the p a tte rn o f exports and imports is s e t, the flow o f assets is determined to balance tra d e . Supplies and requirements o f tra n s p o rt services must be equal un­ der conditions o f in te rre g io n a l e q u ilib riu m , given a p o s itiv e tra n s p o rt cost. A fte r a l l consumers and producers have been furnished w ith i n t r a - regional requirements o f tra n s p o rt s e rv ic e s , the a v a ila b le world supply o f tra n s p o rt requirements must be e x a c tly equal to tra n s p o rt requirements to e ffe c t a minimum cost in te rre g io n a l shipment program which corresponds to a maximum gain from tra d e . 45 Isard and O s tro ff point to several problems l i k e l y to be encoun­ tered when dealing w ith a regional or In te rre g io n a l system. not closed systems. Regions are Flows o f goods, flows o f assets, and tra n s p o rta tio n costs must be d e a lt w ith . Demands and supplies are d is trib u te d in space. P rice d if f e r e n t ia ls can e x is t because o f the lack o f p e rfe c t m o b ility . Regions need not be s e l f - s u f f i c ie n t , they can export and import to e q u ilib r a te supply and demand. In a com petitive system, p ric e d i f f e r ­ e n tia ls in two regions w ill be no g re a te r than the tra n s p o rt costs be­ tween two regions in e q u ilib riu m . Location o f production can change in space as supply and demand parameters change in space, as can in te rre g io n a l flows. The system also in d icates th a t in p u ts , as w ell as outp uts, can move between regions. R. A. King and W. R. Henry claim th a t i t is a challenge to develop a model th a t is useful in ex p lain in g and p re d ic tin g p a r tic u la r lin e s o f production (King and Henry, 1959). The concept o f comparative advant­ age developed by the c la s s ic a l economists says th a t th e lo c a tio n o f pro­ duction is determined by r e l a t i v e , ra th e r than absolute, costs o f pro­ duction. The concept does not e x p li c i t l y incorpo rate costs o f tra n s ­ porting commodities among regions. Factor costs are p o in t values ra th e r than p ric e -q u a n tity re la tio n s h ip s . The tra n s p o rta tio n model 1s the sim plest form o f p o in t-tra d in g model. A surplus or d e f i c i t must be s p e c ifie d fo r each reg io n . Repre­ s e n ta tiv e shipping and re ce ivin g points and the u n it costs o f tr a n s fe r ­ rin g the commodity from each surplus region to each d e f i c i t region must be s p e c ifie d . tra n s fe r costs. market. The market is cleared w ith the minimum o u tla y fo r to ta l This s itu a tio n would tend to evolve in a com petitive 46 In the space model, In te rre g io n a l commodity tra n s fe r costs are composed only o f tra n s p o rta tio n co sts, th a t 1s, they deal only w ith the dimension o f space. Inform ation about the costs o f production, process­ in g , and In tra -m a rk e t d is tr ib u tio n can be added. Hult1-d1mens1onal tra n s­ p o rtatio n models consider o ther types o f tra n s fe r costs. In com petitive markets, tra n s p o rta tio n costs set upper lim it s to the separation o f commodity prices in the space dimension, storage costs s e t upper lim it s to the separation o f commodity prices 1n the time dimension, and other marketing charges se t upper lim its to the separation o f commodity prices by le v e l o f production and marketing (form dim ension). The space- form model allows production o f more than one good a t an o r ig in . receiving p oint has requirements fo r each product. Each T ran sfer costs in ­ clude costs o f processing (tr a n s fe r costs in the form dimension) and tra n s p o rt costs (tra n s fe r costs in the space dim ension). Processing capacity fo r each good in each supply region can be c a lc u la te d . The space-time model deals w ith tra n s fe rrin g commodities between time periods. The costs o f tra n s fe r are the costs o f storage and preserving the commodities (tra n s fe r costs in the time dim ension). age cap acity by lo c a tio n can be c a lc u la te d . Estimates o f s to r­ Hence the space-form -tim e model considers the costs o f tra n s fe rrin g goods in space, form , and tim e. J.C . Day has made an im portant a p p lic a tio n o f a lin e a r program­ ming model, in the form o f land assignment model, to flo o d p la in man­ agement (Day, 1972). I t appears to be h ig h ly a p p lic a b le f o r r iv e r basin p ro je cts w ith some m o d ific a tio n . The model employs a recu rsive lin e a r program fo r a llo c a tin g s p e c ific parts o f the flood p la in accord­ ing to a p ro d u c tiv ity index th a t takes in to account the hazard and sus­ c e p t i b il i t y o f the use to damage. The coircnunity is viewed as a s in g le 47 entrepreneur d e s irin g to use scarce land resources in an economically e f f ic ie n t way. The o b je c tiv e was to choose the most economically pro­ ductive s p a tia l d is tr ib u tio n o f land use a c t iv it ie s which includes em­ ployment o f s it e e le v a tio n and flo o d -p ro o fin g techniques given resources and expected economic growth and development. The o b je c tiv e fu nctio n maximized re la te s to the aggregate value o f goods and services produced by land uses. N o n -e ffic ie n c y o b je c tiv e s are expressed by c o n s tra in ts . Given a statement regarding land use requirem ents, n o n -stru ctu ral damage control a lte rn a tiv e s are evaluated 1n terms o f t h e i r economic f e a s i b il i t y and e ffe c ts on economic re n ts . An optimal s p a tia l ordering o f land use a c t iv it ie s is then selected fo r various planning periods. The model is designed to deal only w ith fu tu re development o f vacant land. Land uses considered are r e s id e n t ia l, commercial, and in d u s tr ia l. The s tru c tu re and approach o f the model are much more im portant than the actual land uses. The model uses re cu rs ive lin e a r programming, which is a sequence o f lin e a r program ing problems in which the o b je c tiv e fu n ctio n c o n s tra in t m atrix and/or rig h t-h an d side parameters depend upon the primal and/or dual s o lu tio n v a ria b le s o f the preceding lin e a r programming problems in the sequence. Each lin e a r program in the sequence solves f o r a planning period. The s ta te conditions are expected rents to land use a c t i v i t ie s a t the end o f the p erio d , stock o f land to accommodate growth, and urban planning c r i t e r i a regarding the in te n s ity o f land use. Endogenous tie s between sequences inclu d e 1) the c u rre n t rig ht-h an d side and previous land use elements and 2) the cu rren t value o f the o b je c tiv e fu n c tio n c o e ffic ie n ts and previous land use assignments. Exogenous data inclu d e: 48 1) preselected assignment o f a c t i v i t i e s , 2) determinants o f a c t i v i t y re n ts , 3) land use requirem ents, and 4) forecasted community growth. Rent determinants are re c a lc u la te d a t each step o f the recu rsive lin e a r program. Rents can be readjusted fo r Interdependencies between tim e periods. The a c t iv it ie s take the form o f X ^ p ( t ) . k k xi f p ^ ~ number acres devoted to each ( i f p ) combination in tim e period t 1 id e n t if ie s the s p e c ific type o f land use k re fe rs to the geographic lo c a tio n in the planning area f and p are special in d ld e s . A lte rn a tiv e lo catio n s fo r planning purposes may be defined by g rid zones or other bounded land u n its w ith in which net p ro d u c tiv ity is r e la t iv e ly homogeneous fo r each it h use. The to ta l number o f lo c a tio n s to be considered as a lte rn a tiv e s depends upon the p a r tic u la r economic and physical fa c to rs th a t in flu e n c e the p ro d u c tiv ity o f land in a lte r n a tiv e employment. onland to be developed C onstraints include 1) upper bounds in planning zones, 2) c o n s tra in ts (upper or low er) on the amount o f growth to be accommodated, 3) n o n -n e g a tiv ity requirements fo r each a c tiv ­ i t y , and 4 ) special c o n s tra in ts fo r flo o d control problems. The model is b a s ic a lly concerned w ith maximizing re n t but does not account f o r problems o f overcoming space, m ainly tra n s p o rta tio n co sts. R.L. Patterson has discussed constrained o p tim iza tio n models fo r land assignment (P a tte rs o n , 1972). He was concerned w ith lin e a r in te g e r programming, but many aspects he discussed are re le v a n t to land use lin e a r programming models. lim it in g land use. There is a v a rie ty o f ways and means o f Patterson fe e ls th a t i t is obvious th a t no s in g le 49 model is adequate to cover a l l combinations o f possible c o n s tra in ts . There can be o b je c tiv e and s u b je c tiv e c r i t e r i a to compare a lte r n a tiv e patterns o f land use. D iffe r e n t groups' c r i t e r i a can c o n f lic t . Develop­ ment always occurs over tim e in a sequential p a tte rn , so th a t no s in g le agency can id e n tify a t any p a r tic u la r time the s e t o f in te re s te d u sers, t h e ir set o f p refe rred a lte r n a tiv e s , or t h e ir c r i t e r i a fo r choice. Planning o r re g u la to ry agencies dannot "optim ize" land use decisions fo r other independant users. Patterson describes a s im p lifie d land use assignment problem. Parcels o f land are s p e c ifie d , each o f which is capable o f sustaining any one o f several a lt e r n a tiv e uses. The problem is to assign e x a c tly one use to each parcel in such a way th a t some measure o f user s a t is ­ fa c tio n is maximized given c o n s tra in ts on land use. s p e c ifie d . A lte r n a tiv e land uses are assigned. to each land use fo r each p a rc e l. Grid parcels are Values are assigned Following is the model which re q u ire s a lin e a r in te g e r programming alg orith m : maximize M £ N £ x ..v .. i= i j= i 1J i j (i) H = number o f fe a s ib le s ite s N = needs (lan d uses) x . . = parcel i in land use j *J v . . = value o f land use j a t s it e i IJ su b ject to : N E x .. = 1 j= l ( i - 1 , . . . ,M) This c o n s tra in t lim its one land use to a p a rc e l. (2 ) 50 M = (j ~1 , . . . ,M) (3 ) T j - number o f parcels o f land use j requ ired. J This equation requires th a t requirements fo r land use be met. x -j >_ 0 (4 ) This is the n on n eg ativity requirement f o r a c t i v i t ie s . Patterson also describes a m u ltip le land use assignment problem. One or more land usesare perm itted sim ultaneously in a amount o f usable land 1) the area in a parcel a v a ila b le fo r assignment parcel s u ita b le f o r a given land use. maximize in a parcel v a rie s . p a rc e l. The Upper lim it s are set f o r and 2) the area in a Following is the model: M N E E x -.v 4 . i= l j = l 1J (5 ) su b ject to : N E x . . = a. j= l 1 (i - 1 . . . - ,M) (6) This c o n s tra in t lim its th e area o f the parcel th a t can be assigned. M £ x .. i= l 1J = r . J (j = 1 , . . . ,N) (7 ) This c o n s tra in t requ ires th a t land use needs be met. O ^ x .j^ c .j ( i = 1 , . . . ,M) (8 ) ( j = 1 ..........M) This c o n s tra in t puts an upper l im it on land use j in parcel i and also requires n o n -n e g a tiv ity . Patterson c ite s fic several problems. I f values are placed on sp ed patterns o f land use the o b je c tiv e fu n c tio n becomes n o n -lin e a r. A lin e a r o b je c tiv e fu n c tio n assumes th a t the degree o f preference o f 51 one assignment o f uses to s ite s is the sum o f the In d iv id u a l "values" derived from assigning uses to each s it e se p a ra te ly . on p a r tic u la r patterns o f land use per se. cause s im ila r problems. No value 1s placed S u bjective c r i t e r i a can This type o f land assignment problem 1s inade­ quate to solve lo c a tio n -a llo c a tio n problems. In the lo c a tio n -a llo c a tio n problem, a decision is made concerning where to lo c a te a number o f land p arcels, each o f a s p e c ifie d s iz e f o r s p e c ific uses, 1n an optimal manner, subject to possible land use c o n s tra in ts . In the lo c a t io n - a llo ­ cation problem, the area required f o r each o f a fix e d number o f uses is sp e cifie d in advance. Possible s ite s are s p e c ifie d in advance. The problem is to lo c a te the uses in an optimal manner. There are also d i f f i c u l t i e s in sp ecifying c e ll s ize s . The sm aller the land u n it a re a , the more homogeneous i t s c h a ra c te ris tic s and the more uniform it s numerical d e s c rip tio n . However, increasing the number o f c e lls increases the to ta l number o f c o n s tra in t equations and computation­ al costs. Small c e lls also tend to "s p rin k le " land uses, th a t i s , th ere may be an u n r e a lis tic amount o f in te rm ix in g . These types o f models do not account fo r minimum requirements on s iz e o f lo c a l areas assigned to a given use. Takayama and Judge (1964) discuss s p a tia l p ric e e q u ilib riu m in a closed system o f n regions. W ithin a framework o f interconnected com­ p e t it iv e markets w ith ap p ro priate lin e a r dependencies between regional supply, demand, and p ric e , i t is possible to convert the SamuelsonEnke s p a tia l p ric e e q u ilib riu m problem in to a q uadratic programming problem. The com petitive optimal s o lu tio n fo r regional prices and q u a n titie s and in te rre g io n a l flows can be obtained from the program. Interdependencies between markets or regions in the production, p r ic in g , 52 and use o f commodities are considered. Interdependencies between com­ modities are disregarded. Each region is ch aracterized by a lin e a r demand function fo r each commodity (th e re can be more than one commodity) which is a function o f the prices o f a l l o th er commodities in the region. Prices o f each commodity in each region are a fu n ctio n o f in te rre g io n a l commodity flow s. Prices and in te rre g io n a l commodity flows are non-negative. Net so cial payoff is maximized. Net so cial p ayo ff 1s the sum o f consumers' and producers' surpluses fo r a ll commodities minus tra n s p o rt costs incurred in shipping costs between regions. The problem is formulated as fo llo w s : maximize f ( P ) = P'C - JgP'QP subject to : G'P <_ T P> 0 where: P = the vector o f each non-negative p ric e o f each conmodlty in each demand and each supply region C = the vecto r o f demand and supply equation in te rc e p t values Q = a symmetric, p o s itiv e , s e m i-d e fin ite m atrix com­ posed o f demand and supply behavior c o e ffic ie n ts T = the v e c to r o f tra n s p o rt costs fo r shipping each commodity between each region G - a vector o f V s , - V s , and 0 's th a t allows de­ mand and supply re la tio n s h ip s to be included in the program. The transverse guarantees th a t 53 th e prices 1n d if f e r e n t regions are not separ­ ated by more than the costs o f tra n s p o rtin g goods between them. The q uadratic problem can be reduced to a lin e a r programming problem including both primal and dual form ulations th a t can be solved by the simplex algorithm : maximize g fX .P .V H C -Q P j'P -T X ^ G X j'P -C G 'P + V P X ^ V 'X 0 subject to : G'P + V = T GX + QP - C P,V,X >_ 0 X = a vector o f non-negative in te rre g io n a l commodity flows V = a vector o f in te rre g io n a l tra n s p o rt costs minus in te rre g io n a l p rice d if f e r e n t ia ls The model solves fo r prices in each region and flows between each region. Inform ation is provided to solve fo r the q u a n titie s o f commodities supplied and demanded in each region. The program can be modified to handle th e case o f fix e d regional demands o r supplies. When both are f ix e d , the problem w il l degenerate to a c la s s ic a l tra n s ­ p o rtatio n problem. This fo rm u lation provides a basis f o r the analysis o f in t e r ­ regional a c t i v i t y models when the regional demands fo r f in a l commod­ it ie s are represented by well-behaved lin e a r functions and output is lim ite d by geographical d is tr ib u tio n o f resources, processing f a c i l i t i e s , e tc . sions. The model could be m odified to handle both time and space dimen­ Time p erio d s , carryin g costs or storage co sts, and flows between 54 time periods would have to be included. Other market form ulations be­ sides com petitive form ulations could be assumed. The preceding discussion deals w ith the s p a tia l aspect o f the land evalu atio n system. ecologic lin kag es. Now i t 1s ap p ro p riate to discuss the economic- Pompi and Chappelle discuss a model proposed by C liffo r d S. Russell and W alter 0. Spofford o f Resources fo r the Future (Pompi and Chappelle, 1974). I t is one o f the most complete hybrid approaches and must be considered an " id e a l" approach to the problem o f economic-ecologic lin ka g es. The components o f the model are 1) a lin e a r programming in te r -in d u s tr y model, 2) an environmental d iffu s io n model, and 3) a set o f receptor-damage fu n c tio n s . The lin e a r programming In te r -in d u s tr y model re la te s inputs and outputs o f various production processes and consumption a c t i v i t ie s a t s p e c ific location s in a region which includes the amounts o f various residuals generated by a u n it o f production, the costs o f transform ing residuals from one to another, the costs o f tra n s p o rtin g re s id u a ls , and the costs o f any f in a l discharge re la te d a c t iv it y . Environmental d iffu s io n models describe the f a t e o f various residuals a f t e r t h e ir discharge in to the environment. These models p red ict ambient concentrations in d if f e r e n t lo catio n s throughout the system. They deal w ith d iffu s io n , d ilu t io n , tra n s fo rm a tio n , and accumulation o f re s id u a ls . The se t o f recep to r damage functions r e la te concentration o f residuals in the environment to re s u ltin g damages. Damages may be sustained d ir e c t ly by humans or In d ir e c t ly through plants and animals in which man has a conm ercial, s c i e n t i f i c , or a e s th e tic in te r e s t. 55 Russell and Spofford viewed a l l re la tio n s h ip s as lin e a r . order to do th is they had to assume: In 1) The economic world is s t a t ic so th a t time does not e n te r as a decision v a ria b le in the production model; 2 ) R elationships in the model are d e te rm in is tic and steady s ta te ; 3) No in te ra c tio n takes place between re s id u a ls ; 4 ) The environment can­ not be modifed to change i t s waste a s s im ila tio n c a p a b ilit ie s . The model 1s run in an i t e r a t i v e fa s h io n , the lin e a r program is solved w ith no r e s tr ic tio n s o r prices on the discharge re s id u a ls . The residuals generated are entered as Inputs to the environmental d iffu s io n models and re s u ltin g ambient concentrations e n te r receptor-damage func­ tio n s . Ambient concentrations and damage values are used to c a lc u la te marginal damages a ttr ib u ta b le to each resid ual discharge. These marginal damages are then applied as in te rim e fflu e n t charges on discharge a c t iv it ie s in the in d u s try model which is then re -s o lv e d . Figure 2 -2 is a schematic diagram o f the R ussell-S pofford model. Earl 0. Heady has played an im portant r o le in developing lin e a r program ing models fo r a g ric u ltu r a l production problems and land use planning (Heady, 1976). Heady devoted much e f f o r t to developing the cu rren t Economic Research Service model. In recent e ffo r ts a t Iowa S tate U n iv e rs ity , he has incorporated a tra n s p o rta tio n model in to the produc­ tio n model developed fo r the e n tir e co n tin en tal United S ta te s . United States is d ivid ed in to 27 consumption regions. The Each consumption region is subdivided in to supply regions such th a t the United States is d ivided in to 223 supply regions. were developed in th e western U.S. A to ta l o f 51 w ater supply regions The o b je c tiv e fu n c tio n minimizes the to ta l costs o f production o f commodities, costs o f tra n s p o rtin g com­ m odities between re g io n s , and costs o f purchasing w ater to produce I 1 Marginal damages (Le., shadow prices) k u Residual discharge vectors Residuals treatment processes Primary residuals generated Imports (Production processes) Residuals generation Linear industry model Final consumption OBJECTIVE FUNCTION Residuals LINEAR INDUSTRY LP MODEL + < 5 ENVIRONMENTAL MODELS (Steady-stale, deterministic) RECEPTOR DAMAGE MODELS Figure 2*2.—Schematic Diagram o f the Russell-Spofford Residuals-Environmental Quality Planning Model. Source: Russell and Spofford, 1972. 57 crops. One set o f demand equations from the to ta l se t o f equations in the Heady model appears to be useful to s p a tia l a n a ly s is . This equa­ tio n determines surpluses, d e f i c i t s , and the flows o f goods between regions. v a ria b le s . tio n . Production re la tio n s h ip s are included through production P opulation, liv e s to c k , and national exports a ff e c t consump­ Goods are allowed to flo w between regions to s a tis fy requirem ents. Production and tra n s p o rt patterns are solved sim ultaneously given re ­ quirements and land c o n s tra in ts . The demand equation fo llo w s : 21 25 y i j Xi j " b1qN13 ‘ j f 22 Fkjq ' ekqEq ' f kpqGp + CTq k 'k ‘ Tq k k '] - 0 i = producing area = ( 1 , . . . , 2 2 3 ) j = type o f endogenous crop or liv e s to c k a c t i v i t y = ( 1 , . . . , 2 5 ) k = consuming region = ( 1 , . . . , 2 7 ) p = type o f endogenous liv e s to c k a c t i v i t y = ( 1 , . . . , 5 ) q = type o f commodity = b. *H 2) = per c a p ita consumption o f qth commodity in it h producing region ekq = Pr °P °rt10n ° f exports o f qth type commodity exported h is t o r ic a lly from kth consuming region E - national export a c t i v i t y fo r qth type comnodity H ^kpq = amount I***1 ^ P 6 c r°P commodity consumed by pth type exogenous liv e s to c k a c t i v i t y in Fkjq = amount 9th ^P ® kth consuming region commodity transformed in to feed fo r use by the j t h type o f liv e s to c k in th e kth consuming region 58 Gp = nation al a c t i v i t y f o r pth type o f liv e s to c k N.j = populat1on-1ndustry a c t iv it y in the 1th producing region Tqk«k = amount transported o f j t h commodity from kth consuming region to k 'th consuming region where k and k' must be contiguous except f o r long hauls X . . = le v e l o f the j t h product a c t iv it y in the it h producing *J region Y . . = y ie ld per acre o r per u n it o f a c t i v i t y o f j t h crop or *J liv e s to c k a c t i v i t y in th e it h producing area Choice o f General A lte rn a tiv e s fo r the Land Evaluation System The discussion o f the previous sections suggests th ree general a lte rn a tiv e s to provide answers fo r the issues to be considered in the land evalu atio n system. They are based on lin e a r programming and simu­ la tio n since in p u t-o u tp u t and dynamic programming do not seem to be w ell su ited to the problem. 1 .a . Following are the th re e a lte rn a tiv e s : A regional lin e a r program which is divided in to sub regions c a lc u la te s th e acreages on which management s tra te g ie s are a p p lie d . b. S p atial economic and environmental components can be in ­ cluded d ir e c t ly in to the production model d ir e c t ly i n f l u ­ encing the a llo c a tio n o f management s tr a te g ie s . c. Management s tra te g ie s can be a llo c a te d to g rid subdivisions o f sub regions by using a m u ltip le land use assignment model. 2 . a. A m u ltip le use o r s in g le land use assignment model calcu­ la te s the acreages o f management s tra te g ie s in in d iv id u a l g rid c e lls . 59 b. S p atial economic and environmental impacts are taken In to consideration but do not in flu en ce the a llo c a tio n o f man­ agement s tra te g ie s . 3 . a. The acreages o f management s tra te g ie s are ca lcu la ted out­ side o f the model. The re s u lts are put In to a sim ulation model to generate the production o f various products, b. S p a tia l economic and environmental Impacts are considered but do not a f f e c t the a llo c a tio n o f management s tra te g ie s . C r it e r ia are needed to evaluate these a lte r n a tiv e s . An o rd in al scale 1s used to ra te each a lte r n a tiv e according to each c r ite r io n . I t is f e l t th a t a q u a n tita tiv e answer cannot be c a lc u la te d . Louis Pompi suggested several c r i t e r i a to evaluate a lte r n a tiv e models (Pompi, 1975). The f i r s t c r ite r io n 1s inform ation output which asks i f the inform ation needs o f the user are met. Inform ation 1s needed in th is model fo r the issues to be considered. The second c r i t e r 1on is data input which includes q u a n tity and q u a lit y , th a t i s , le v e l o f d e t a i l , o f required d ata. p o licy g u id e lin e s . The th ir d c r ite r io n is the provision o f This is s im ila r to the f i r s t c r ite r io n except th a t i t considers how e a s ily p o licy g u id e lin es are developed from the out­ put o f the model. assumptions. The f i f t h temporal dimension. dimension. The fo u rth c r ite r io n is the relevance o f necessary c r ite r io n is the cap acity fo r d ealin g w ith the The s ix th is the cap acity to deal w ith the s p a tia l The seventh c r ite r io n 1s g e n e ra lity which concerns i t s e l f with th e exten t to which the model can be g eneralized to a v a rie ty o f problems. The e ig h t 1s s p e c if ic it y which concerns I t s e l f w ith how e a s ily the model can be adapted to s p e c ific problems. The f i r s t s ix and the eighth c r i t e r i a are a p p lic a b le fo r th is problem. A s p e c ific 60 problem fo r a p p lic a tio n has been defined. The question here 1s how well the a lte r n a tiv e 1s su ited fo r the defined problem. S p e c ific c r i t e r i a have been developed based on Pompi*s c r i t e r i a to evaluate these a lte r n a tiv e s . The c r i t e r i a are now discussed. The c r ite r io n o f inform ation output has been more s p e c ific a lly defined 1n th is problem. I t 1s a problem o f how w ell the model accounts f o r the s p a tia l economic and environmental aspects. is s p a tia l economic impact. The f i r s t c r it e r io n , th e n , I f the a llo c a tio n o f management s tra te g ie s is a ffe c te d by the s p a tia l economic Im pact, the a lte r n a tiv e receives the highest r a tin g , 1. The reason fo r th is ra tin g is th a t tra n s p o rt costs w ill a ffe c t the landowner's decision o f how to manage land. I f the s p a tia l economic impacts are generated but do not a f f e c t the a llo c a tio n o f management s tr a te g ie s , the a lte r n a tiv e receives a poorer r a tin g , 2. With th is s itu a tio n , i t is assumed th a t tra n s p o rt costs do not a ffe c t the landowner's d ecision o f how to manage land. A lte r n a tiv e 1 has a ra tin g o f 1 w h ile a lte rn a tiv e s 2 and 3 have ra tin g s o f 2. The second c r ite r io n is s p a tia l environmental impact. I f the a llo c a tio n o f management s tra te g ie s is influenced by the s p a tia l e n v ir­ onmental im pact, the a lte r n a tiv e receives the highest r a t in g , 1. I f the s p a tia l environmental impact is accounted f o r but does not in flu e n ce the a llo c a tio n o f management s tr a te g ie s , the a lte r n a tiv e receives a lower ra tin g o f 2. I t is f e l t th a t the generation o f environmental im­ pacts should a ffe c t land management decisions. A lte r n a tiv e 1 has a ra tin g o f 1 w h ile a lte rn a tiv e s 2 and 3 have ra tin g s o f 2. The c r ite r io n o f data in p u t, as stated p re v io u s ly , includes both q u a n tity and q u a lity aspects (Pompi, 1975). is q u a n tity o f data re q u ire d . The th ir d c r it e r io n , th en , In g e n e ra l, i t appears th a t sim ulation 61 models re q u ire more data than lin e a r programming models (Pompi, 1975). A lte rn a tiv e 3, then has the lowest r a t in g , 3. I t also appears th a t a lte r n a tiv e 1 requ ires more data than a lte r n a tiv e 2 , since management s tra te g ie s are a llo c a te d to grids in a second step in a lte r n a tiv e 1. A lte rn a tiv e 2 receives a ra tin g o f 1 and a lte r n a tiv e 1 receives a ra tin g o f 2. The fo u rth c r ite r io n is data q u a lity . Sim ulation models may be able to use data o f lower q u a lit y , in the sense o f measurement s c a le s , than lin e a r programming models (Pompi, 1975). a ra tin g o f 1. A lte r n a tiv e 3 receives A lte rn a tiv e s 1 and 2 receive ra tin g s o f 2. The f i f t h c r ite r io n is the p rovision o f p o lic y g u id e lin e s . L in ear programming models w ith t h e ir cap acity to provide optimal solutions requ ire less judgement to tra n s la te output in to p o lic y g uidelin es (Pompi, 1975). A lte rn a tiv e s 1 and 2 receive ra tin g s o f 1 w h ile a lt e r n ­ a tiv e 3 receives a ra tin g o f 2. The s ix th c r ite r io n is the relevance o f necessary assumptions. The assumptions o f lin e a r programming are g e n e ra lly more r e s t r ic t iv e than those o f sim u la tio n . In the case o f s im u la tio n , i t 1s impossible to say what the assumptions are except in the s p e c ific case (Pompi, 1975). A lte rn a tiv e 3 receives a ra tin g o f 1 w h ile a lte rn a tiv e s 1 and 2 receive ra tin g s o f 2. The seventh c r ite r io n is the cap acity to deal w ith tim e. While lin e a r programming is s t a t ic in n a tu re , time can be incorporated in a v a rie ty o f ways. These methods w ill be discussed l a t e r . S im u la tio n , however, is e a s ily adapted to the tim e dimension (Pompi, 1975). A lte rn ­ a tiv e 3 receives a ra tin g o f 1 w h ile a lte rn a tiv e s 1 and 2 receive ra tin g s o f 2. 62 C r it e r ia fo r th is s p e c ific problem have also been added. The eighth c r ite r io n is c o m p a tib ility o f the system w ith systems p res en tly used in U.S.D.A. r iv e r basin planning. A lte r n a tiv e 3 seems to be the most remote 1n r e la tio n to e x is tin g systems. A lte r n a tiv e 2 puts the production model on a sm aller g rid than cu rren t p ra c tic e . 1 uses the same s iz e su b divisio ns. A lte r n a tiv e In a l l cases, the economic and en­ vironmental dimensions, as w e ll as the tim e dimension, are added. A l­ te rn a tiv e 1 seems to be the most c lo s e ly re la te d to p res en tly used sys­ tems, so i t receives the highest ra tin g o f 1. a lower ra tin g o f 2. A lte rn a tiv e 2 receives A lte r n a tiv e 3 receives the lowest ra tin g o f 3. The n in th c r ite r io n is the cost o f operating the model. must include any manual work. This cost I t is f e l t th a t due to the larg e number o f ite r a tio n s in v o lv ed , operating a lin e a r programming model would be more c o s tly than o perating a sim ulation model. Due to the increased number o f steps involved in g e ttin g down to th e g rid le v e l and the f a c t th a t s p a tia l aspects a ff e c t s o lu tio n o f the production model, a lte rn a ­ tiv e 1 1s f e l t to be more expensive than a lte r n a tiv e 2. A lte r n a tiv e 3 requires su b sta n tial amounts o f work done outside o f the computer. It is f e l t th a t i f th is work is done in much d e t a i l , the cost could e a s ily be g re a te r than the cost o f making a lin e a r programming run. t iv e 2 receives a lower ra tin g o f 2. ra tin g o f 3. A lte rn a ­ A lte r n a tiv e 3 receives the lowest Table 2-1 contains a summary o f the ra tin g o f the a lte r n a ­ tiv e s . A lte r n a tiv e 1 receives th e highest ra tin g the most tim es. These ra tin g s occur in the c r i t e r i a f e l t to be most im portant to th e study, the s p a tia l impacts and the c o m p a tib ility w ith present systems. The assumptions o f lin e a r programming can be lim it in g , but in many cases can 63 Table 2 - 1 . — Rating o f A lte rn a tiv e s fo r th e Land Evaluation System. C rite rio n A lte rn a tiv e S p atial economic impact S p atial environmental Impact Q u a lity o f data Provision o f p o lic y g uidelin es Relevance o f necessary assumptions Capacity to deal w ith tim e C o m p a tib ility w ith present systems Operating cost 1 = highest be overcome. 1 2 2 1 1 2 1 2 2 1 2 2 2 1 1 2 2 2 1 2 2 3 2 1 1 3 3 3 - lowest 2 = lower I t is also f e l t th a t the o th er c r i t e r i a can be d e a lt w ith w ithout too much tro u b le . A lte r n a tiv e 1 1s the favored a lte r n a tiv e and the su b ject o f fu rth e r In v e s tig a tio n 1n th is p ro je c t. F u rth er in v e s t i­ gation o f o ther a lte rn a tiv e s could be pursued in o th e r s tu d ie s , however. Possible S tru c tu re o f the Land Evaluation System The land e v alu atio n system contains two components: duction component and 2) the lo c a tio n component. ponent w il l be a lin e a r programming model. in to regions. 1) the pro­ The production com­ The model is broken down An a c t i v i t y is defined fo r each management s tra te g y on each class o f land in each re g io n . Each a c t i v i t y w i l l produce a set o f products and w i l l be constrained by the acreage o f land a v a ila b le to i t . Demands f o r products are defined a t various lo c a tio n s . The lo c a tio n component can be broken down In to th ree subcompon­ ents: 1) the tra n s p o rta tio n component, 2) the environmental d iffu s io n component, and 3) th e land assignment component. The tra n s p o rta tio n component is a s e rie s o f lin e a r programming a c t i v i t ie s which r e la te 64 production 1n each region to demand fo r products a t various lo c a tio n s . The environmental d iffu s io n component is a se rie s o f equations which sim ulate the movement o f re sid u a ls produced by management s tra te g ie s through space. The land use assignment component takes acreages o f management s tra te g ie s and a llo c a te s them to subdivisions o f each region. The tra n s p o rta tio n component and the environmental d iffu s io n component could be incorporated d ir e c t ly in to the production component. These com ponents would then d ir e c tly a ffe c t th e s o lu tio n o f the production model. E ith er o r both o f these two components could also be separate compon­ ents, They would ju s t show the impacts o f so lutio ns o f th e production model. I f the tra n s p o rta tio n component was removed, production to meet regional consumption would be required in each region and would appear in the production model. The land use assignment component could not be included in to the production model. The land use assignment model would have no impact on the a llo c a tio n o f management s tra te g ie s among regions in the production model. It s purpose would be to lo c a te manage­ ment s tra te g ie s in space more p re c is e ly according to another se t o f c r ite r ia . Any or a l l o f these lo c a tio n components could be elim in ated from the land evalu atio n system. I f they are a ll e lim in a te d , the consider­ atio n o f lo c a tio n would be e lim in a te d from the land evalu atio n system. Following are a lte r n a tiv e combinations o f components: 1. A ll lo c a tio n components inclu d ed , the tra n s p o rta tio n and environmental d iffu s io n components are incorporated in to the production model. 2. Land use assignment model excluded, the tra n s p o rta tio n and environmental d iffu s io n components are incorporated in to th e production model. 3. Environmental d iffu s io n component excluded, the tra n s p o rta­ tio n component is incorporated in to th e production model. 4. Environmental d iffu s io n and land use assignment models exclud­ ed, the tra n s p o rta tio n component 1s incorporated in to the pro­ duction model. 5. Environmental d iffu s io n component excluded, the tra n s p o rta tio n component is separate. 6. Land use assignment and environmental d iffu s io n components ex­ cluded, tra n s p o rta tio n component 1s separate. 7. T ransportation component is excluded, the environmental d iffu s ' 1on component 1s incorporated in to the production model. 8. Tran spo rtatio n and land use assignment components excluded, the environmental d iffu s io n component is incorporated in to the production model. 9. T ransportation component excluded, the environmental d iffu s io n component is separate. 10. T ransportation and land use assignment components excluded, the environmental d iffu s io n component is separate. 11. A ll lo c a tio n components in clu d ed , the tra n s p o rta tio n and en­ vironmental d iffu s io n components are separate. 12. Land use assignment model excluded, the tra n s p o rta tio n and en­ vironmental d iffu s io n components are separate. 13. A ll lo c a tio n components excluded. Incorporating the Time Dimension in to L in ear Programming The time dimension presents special problems fo r lin e a r program­ ming which is s t a t ic by nature. The tim e dimension must be considered fo r the fo re s t resource due to the separation in time between p la n tin g , 66 th in n in g , or o ther c u ltu ra l a c t iv it ie s and production o f merchantable timber. Models w ith many a g ric u ltu r a l crops do not have th is problem since production occurs 1n a s in g le growing season. Timber growth, from establishment o f a stand to harvest o f tim b e r, occurs over a la rg e number o f years. Several a lte rn a tiv e s e x is t fo r in co rp o ratin g time In to lin e a r pro­ gramming: polyperiod lin e a r programming, re cu rs ive lin e a r programming, and pseudo-dynamic lin e a r programming. Recursive lin e a r programming solves fo r each time period sep ara tely (Day, 1972). period is optim ized. next time period. The f i r s t time This so lu tio n then constrains the so lu tio n o f the The so lu tio n fo r each tim e period is always constrained by the so lu tio n o f the previous tim e period. This process o f sequential optim ization was deemed undesirable fo r th is problem since i t does not optim ize over th e e n tir e time period. I t does not r e a lly seem w ell suited to the problem o f investment to meet a stream o f demands over tim e. This method could be d e s ira b le when considering what c u ltu ra l o p e ra tio n s , such as p la n tin g , th in n in g , or f e r t i l i z a t i o n to undertake given the p ractices undertaken in previous ye ars. in a y e a r, Timber growth and the impacts o f c u ltu ra l p ractices on growth would have to be considered when moving from one tim e period to the next by the use o f models outside o f the recursive lin e a r program. These models would have to account fo r timber growth and changes 1n w i l d l i f e h a b ita t. The impacts o f past and present c u ltu ra l and harvest operations on tim ber stand growth and d evel­ opment would have to be included. The amounts o f tim ber and hunterdays a v a ila b le fo r harvest a t d if f e r e n t location s would become inputs to the model fo r the next tim e period. Polyperiod lin e a r programming considers the tra n s fe r o f goods and the costs o f doing so (D uvick, 1970). The 67 tra n s fe r o f goods between time periods is not being considered 1n the model being developed. However, th is p o te n tia l could be Incorporated in to the approach to be used, pseudo-dynamic lin e a r programming. Pseudo­ dynamic lin e a r programming appears to be the best approach when consider­ ing investment problems (B u lle r , 1965). Costs and returns are discounted to the present fo r the o b je c tiv e fu n c tio n value. counting, time 1s im p lic it . period can be entered. Because o f th is d is ­ Products and c o n stra in ts fo r each tim e There would be a c o e ffic ie n t in the a c t iv it y fo r each product in each tim e period. A p a r tic u la r problem w ith th is method is th a t a l l a lte rn a tiv e s must be evaluated over the same time p erio d . The time period and the sequence o f c u ltu ra l a c t i v i t ie s must be e x p l i c i t ­ ly sta ted . This time problem makes in c lu s io n o f the fo re s t sector in to the current Economic Research S e rv ic e 's le a s t cost lin e a r programming model d iffic u lt. I f impacts o f c u ltu ra l p ractices on wood production are to be considered in the Economic Research S e rv ic e 's model, a l l o ther sectors must be changed to include the tim e dimension . This could become q u ite complicated fo r a g ric u ltu re since conversions between crops or crop ro tatio n s over the period o f an alysis would have to be considered. If the fo re s t sector is included in to the cu rren t Economic Research S e rv ic e 's model, only c u ltu ra l p ractices and the products th a t they a f fe c t in the same time period could be included. In d iv id u a l c u ltu ra l p rac tice s would be the a c t iv it ie s ra th e r than combinations o f p ractices over a period o f time as is the case in pseudo-dynamic lin e a r programming. The e ffe c ts o f c u ltu ra l p rac tice s on l a t e r y ie ld s o f merchantable tim ber and other products a t l a t e r times could not be e a s ily accounted f o r . E ffe c ts th a t could be included a re *th e immediate e ffe c ts on sedim entation, ero - 68 slon, animal populations, and amounts o f tim ber th a t could be harvested from stands ready to be cu t. The tim e dimension is not e a s ily handled in the cu rren t Economic Research Service model. Choosing Among A lte r n a tiv e Structures C r it e r ia are needed to choose among a lte r n a tiv e stru c tu res f o r the land evaluation system. These c r i t e r i a are based on those proposed by Pompi th a t were discussed e a r l i e r in th is chapter (Pompi, 1975). There are several c r i t e r i a fo r which a l l o f the a lte rn a tiv e s w il l have id e n t i­ cal re s u lts . They a l l have id e n tic a l c a p a c itie s to deal w ith time since a ll a lte rn a tiv e s use pseudo-dynamic lin e a r programming. The relevance of necessary assumptions w il l also be the same as w ill g e n e ra lity and and s p e c if ic it y since the same lin e a r programming format is being used. The q u a lity o f data needed w i l l also be the same due to the same basic lin e a r progranming framework. There are some d iffe re n c e s , however. w ill vary by a lte r n a tiv e . The q u a n tity o f data needed The inform ation output and the cap acity to provide p o lic y g u id elin es w il l also vary. V a ria tio n in these two c r i t e r i a is re la te d d ir e c t ly to the manner in which space is handled. The costs associated w ith a lte rn a tiv e s w il l also vary. Three c r i t e r i a w il l be defined th a t deal w ith space. is the a b i l i t y to deal w ith the s p a tia l economic aspects. The f i r s t I f the a l l o ­ cation o f management s tra te g ie s is a ffe c te d by the tra n s p o rta tio n c o s ts , th at i s , i f the tra n s p o rta tio n component is incorporated in to the produc­ tio n component, the a lte r n a tiv e receives th e highest ra tin g o f 1. If the s p a tia l economic impact is accounted fo r but does not a ffe c t the a llo c a tio n o f management s tr a te g ie s , th a t 1s, the tra n s p o rta tio n com­ ponent is sep arate, the a lte r n a tiv e receives a lower ra tin g o f 2. If 69 the s p a tia l economic aspect is not considered, th a t i s , the tra n s p o rta ­ tio n component is excluded, the a lte r n a tiv e receives the lowest ra tin g of 3. The second c r i t e r i a 1s the mental impacts. a b i l i t y to deal w ith s p a tia l environ­ I f the movement o f re sid u a ls a ffe c ts the a llo c a tio n o f management s tr a te g ie s , th a t i s , i f the environmental d iffu s io n model is included, the a lte r n a tiv e receives the highest ra tin g o f 1. I f the move­ ment o f re s id u a ls is accounted fo r but does not a ffe c t the a llo c a tio n of management s tr a te g ie s , th a t 1s, the environmental d iffu s io n model is separate, the a lte r n a tiv e receives a lower ra tin g o f 2. o f re sid u a ls is not accounted f o r , th a t I f the movement i s , the environmental d iffu s io n model is excluded, the a lte r n a tiv e receives the lowest ra tin g o f 3. The th ir d c r i t e r i a is the s p a tia l s p e c if ic it y o f a llo c a tin g manage­ ment s tra te g ie s . I f a m u ltip le land use assignment model is included which a llo c a te s the management s tra te g ie s in a region to a g rid network, the a lte r n a tiv e receives a ra tin g o f 1. I f th e land assignment model is excluded, the a lte r n a tiv e receives a lower ra tin g o f 2. The fo u rth c r i t e r i a is the cost o f constructing the model. The major component o f th is cost is o b tain in g the data to In p u t to the model. A ll a lte rn a tiv e s have the same production component which is the most expensive p a rt. added on. The ra tin g is based on the components th a t must be The most expensive component th a t can be added on 1s the m u lti­ ple land use assignment model. th is component. Large amounts o f data are necessary fo r The construction cost o f th is component is much g re a te r than the construction cost o f o th e r components. The construction costs o f components incorporated in to the production component are g re a te r than the costs o f those excluded. More data and m odelling e f f o r t is required 70 fo r components incorporated in to the production component since a l l tim e periods must be e x p li c i t l y considered. The construction cost o f the environmental d iffu s io n model w il l be assumed to be g re a te r than th a t o f the tra n s p o rta tio n component. The environmental d iffu s io n r e la t io n ­ ships could be much more complex than the tra n s p o rt re la tio n s h ip s . The tra n s p o rta tio n re la tio n s h ip s include tra n s p o rt ro u te s , m ileages, and cost per m ile fo r each comnadity. Environmental d iffu s io n r e la t io n ­ ships would include c h a ra c te ris tic s o f the tr a n s fe r media, fa c to rs a f f e c t ­ ing the tra n s fe r media, and fa c to rs a ffe c tin g the movement o f resid u als through the media. For a stream, speed o f the cu rren t and w ater temper­ ature might be very im portant. d i f f i c u l t to account fo r . In te ra c tio n s between re sid u a ls could be Much tim e might be required to sp ecify the environmental d iffu s io n re la tio n s h ip s . expensive. Data c o lle c tio n could also be The order o f construction cost o f each component from highest to lowest fo llo w s : a ) land use assignment model, b) incorporated environ­ mental d iffu s io n model, c ) incorporated tra n s p o rta tio n model, d) separate environmental d iffu s io n model, and e) separate tra n s p o rta tio n model. The a lte r n a tiv e w ith the lowest cost has the highest rank o f 1 in Table 2 -2 . The remaining a lte ra n tiv e s receive a ra tin g equal to t h e ir rank in construction cost. The f i f t h c r i t e r i a is o peration co st. The operatio n cost o f the production component, included 1n a l l a lte r n a tiv e s , is assumed to be the same f o r a l l a lte r n a tiv e s . The ranking o f operation cost w il l depend upon the operation cost o f components added. The land use assignment model has the la rg e s t cost due to I t s la rg e s iz e . I t probably requires a larg e number o f ite r a tio n s to c a lc u la te a s o lu tio n . It s cost w il l be assumed g re a te r than the sum o f the costs o f any combination o f tra n s - 71 Table 2 - 2 .— Rating o f A lte rn a tiv e Model S tru ctu res. A 1 tern a tiv e C rite rio n 1 2 3 4 5 6 7 8 9 10 11 12 13 tra n s p o rta­ tio n impact 1 1 1 1 2 2 3 3 3 3 2 2 3 environmen­ ta l d if f u ­ sion impact 1 1 3 3 3 3 1 1 2 2 2 2 3 s p a tia l spe­ c ific ity 1 2 1 2 1 2 1 2 1 2 1 2 2 construction cost 13 7 11 5 8 2 12 6 9 3 10 4 1 operation cost 13 7 12 6 9 3 11 5 8 2 10 4 1 1 = highest ra tin g p o rtatio n and environmental d iffu s io n components. The cost o f incorpor­ ated components w i l l be assumed much la rg e r than the cost o f separate components because tim e must be considered. The o peration cost o f the tra n s p o rta tio n component w il l be assumed la rg e r than th a t o f th e environ­ mental d iffu s io n component because o f the larg e number o f ite r a tio n s needed to solve a tra n s p o rta tio n model. The ranking o f operation cost o f each component from highest to lowest fo llo w s : a) land use assign­ ment model, b) incorporated tra n s p o rta tio n model, c) incorporated environ­ mental d iffu s io n model, d) separate tra n s p o rta tio n model, and e) separ­ ate environmental d iffu s io n model. The a lte r n a tiv e w ith the lowest cost has the highest ranking o f 1 and the a lte r n a tiv e w ith the highest cost has the lowest ranking o f 13. These rankings apply to Table 2 -2 . The fo llo w in g ta b le presents the re s u lts o f ra tin g each a lte r n a tiv e accord- 72 1ng to each c r it e r io n . A lte r n a tiv e 1 has the highest ra tin g fo r each o f the th ree p o lic y c r i t e r i a . o f the two cost c r i t e r i a . ignored. I t also has the lowest ra tin g fo r each For picking an ideal model, cost w il l be A lte rn a tiv e 1 w il l be considered to be the Id e a l. When de­ scribing the s tru c tu re l a t e r , the a lte r n a tiv e stru ctu res w il l also be discussed. Description o f the Ideal Land Evaluation System and Possible Changes O bjective Functions A lin e a r program requires an o b je c tiv e fu n c tio n . clude: A lte rn a tiv e s in ­ 1 ) lin e a r o b je c tiv e functions o f which th ere are two types: gain maxmizing and cost-m inim izing and 2 ) quadratic o b je c tiv e functions which require a special mathematical programming fo rm u latio n . With a cost-m inim izing lin e a r o b je c tiv e fu n c tio n , costs must be ca lc u la te d . A minimum le v e l o f demands must be s a tis fie d . minimizes the costs to meet these demands. proach fo r MUMS in clu d e: not have to be c a lc u la te d . however. The algorithm The advantages o f th is ap­ 1) Prices or p ric e -q u a n tity re la tio n s h ip s do Im p lic it assumptions about prices are made, 2) The Economic Research S e rvic e's model, a cost minim izing model, already has costs c a lc u la te d . The disadvantages in clu d e: 1) Only one set o f requirements is considered, and 2) The approach is e s s e n tia lly a requirements approach. With a gain-m axim izing lin e a r o b je c tiv e fu n c tio n , a fix e d net re ­ turn must be c a lc u la te d fo r each a c t i v i t y . be calcu la ted fo r each a c t i v i t y . c a p a c itie s are req u ired . resource c o n s tra in ts . Resource c o n stra in ts must Resource c o n stra in ts on productive The algorithm maximizes net gain subject to The Economic Research S e rv ic e 's model could be 73 converted to a gain-m axim izing model by c a lc u la tin g a p ric e fo r products and su b tracting costs to obtain a net revenue. and resource co n strain ts e x is t. Both demands fo r products The advantages o f th is approach are: 1) P rlc e -q u a n tity re la tio n s h ip s do not have to be c a lc u la te d , 2) Compu­ ta tio n costs are comparable to a cost-m inim izing approach, and 3) I t is not r e s tr ic te d to a s in g le set o f demands. The disadvantages include: 1) Prices must be fix e d , 2) I t may be d i f f i c u l t to c a lc u la te prices f o r many o f the commodities, and 3) Prices are not calcu la ted f o r the Eco­ nomic Research Service model. When the lo c a tio n component 1s separate from the production com­ ponent, the production component would be gain-m axim izing. The lo c a tio n model would minimize tra n s fe r costs subject to the so lu tio n o f the pro­ duction component. When the two models are incorporated in to one lin e a r program, p rice minus production and tra n s fe r costs would be maximized. Linder a q uadratic fo rm u la tio n , as put fo rth by Takayama and Judge, net so cial p ayo ff is maximized. A m odified simplex alg o rith m is req u ired . P ric e -q u a n tity re la tio n s h ip s and in te r-re g io n a l flows are considered. Supply or demand can be assumed fix e d . The advantage o f th is form ulation is th a t p rlc e -q u a n tity re la tio n s h ip s can be included and an economy can be simulated in g re a te r d e t a i l . The disadvantages are: 1) The Economic Research S e rv ic e 's model cannot be incorporated in to the Takayama and Judge form ulation since the u n its o f production a c t iv it ie s are expressed in acreages o f management s tra te g ie s ra th e r than in q u a n titie s o f com­ modities produced. 2) Higher computation costs w il l r e s u lt because o f the larg e lin e a r programming form at re q u ire d , and 3) There w il l be costs involved in estim atin g the p rlc e -q u a n tity re la tio n s h ip s . The Eco­ nomic Research S e rv ic e 's model cannot be incorporated In to the Takayama 74 and Judge fo rm u latio n . Before a q uadratic model can be considered, a primal problem must f i r s t be form ulated. The cost m inim ization approach is the favored a lte r n a tiv e , since th is approach would re q u ire the le a s t amount o f work in constructing the model. Nature o f the Linear Programming A c tiv ity As has been sta ted p re v io u s ly , a management s tra te g y is a combin­ atio n o f a c t iv it ie s th a t can be p racticed on a s in g le acre o f land. The management strate g y 1s a column, th a t i s , a lin e a r programming a c t i v i t y , in the production component o f the model. number o f products a t a given cost. a period o f tim e. These a c t iv it ie s produce a These a c t iv it ie s take place over The c u ltu ra l p ractices can occur a t d if f e r e n t points in tim e , which must be e x p li c i t l y s ta te d . C o e ffic ie n ts in the lin e a r programming a c t iv it y are s p e c ifie d fo r each product in each tim e period as w ell as fo r the amount o f land required f o r th e a c t i v i t i e s . Costs are also incurred a t d if f e r e n t points in time when the c u ltu r a l p ractices are undertaken. These costs are discounted to the present and are the o b jec tiv e function values o f the a c t i v i t ie s . Conversions o f management s tra te g ie s can also take place in the lin e a r program ing a c t i v i t y . The time o f the conversion, the c u ltu ra l p ractices in v o lv e d , and the costs incurred must also be e x p li c i t l y s ta te d . D e fin itio n o f V ariab les i = demand p o in t = ( 1 , 2 , 3 , . . . , ! ) 1 * = demand p o in t outside o f the r i v e r basin j = supply area = ( 1 , 2 , 3 , . . . ,J ) J' = supply area outside o f th e r iv e r basin a = management s tra te g y = ( 1 , 2 , 3 , . . . ,A) 75 when: a = ( b , . . . , h ) are management s tra te g ie s fo r fo re s t a = ( 1 , . , . , p ) are management s tra te g ie s fo r a g ric u ltu r a l land a = (q land z ) are management s tra te g ie s fo r pasture land k = component (product) o f a product-package = ( 1 , 2 , 3 * . . . ,K) k = ( a , . . . , p ) are market and non-market k “ ( q » . . . ( s) are s ta tio n a ry resid uals goods k = ( t , . . . , v ) are n o n -sta tio n a ry resid uals r = class o f fo r e s t resource = ( 1 , 2 , 3 , . . . ,R) r * = class o f n o n -fo re s t land Input v a ria b le s : Ka rj - production cost o f management s tra te g y a on resource class r in region j discounted to the present K * * = cost o f converting resource class r in region j to r e II J source class r * in region j nk i j t = tra n s ^e r c o e ffic ie n t o f residual k from s it e j to s it e i in tim e period t T k i j t - tra n s p o rt cost f o r good k from supply area j to demand point i in tim e period t Xk i t = demand f ° r component k a t demand p o in t i in time period t Xk j t = constra'*n t on production o f product k in region j 1n time period t Zflrj = l im it on management s tra te g y a on resource class r in region j 6a k r j t ” amount o f component k produced by one acre o f management i k r jt s tra te g y a o r resource class r in region j t in time period 76 output v a ria b le s : Ci t = tra n s p o rt cost o f meeting demands a t demand p o in t 1 1n time period t C jt = tra n s p o rt cost o f goods produced in supply area j 1n time period t Vr * r j = acreage o f resource class r 1n region j converted to resource class r * 1n region j Wr r * j = acrea9e resource class r * 1n region j converted to re ­ source class r in region Xa r j ~ acres j management s tra te g y a practiced on resource class r In supply area j Xk i j t = amount component k shipped from supply area j to de­ mand p o in t i in time period t * k j t = amount component k produced In tim e period t X • = acres o f resource class r in supply area j *J Y ^ t = amount o f product k a t supply p o in t j in excess o f the production requirem ent on th a t region 1n time period t Discussion o f the Production, T ra n s p o rta tio n , and Environmental D iffu s io n Components and Linkages This section w il l discuss the mathematical s p e c ific a tio n o f the production, tra n s p o rta tio n , and environmental d iffu s io n components and the linkages between components. The f i r s t a lte r n a tiv e combination o f components to be considered is the in c o rp o ra tio n o f the tra n s p o rta tio n and environmental d iffu s io n components in to the production model. te rn a tiv e s 1 and 2 ) . (A l­ The lin ka g e o f a land assignment model w il l be discussed in a l a t e r s e c tio n . 77 Equations o b je c tiv e fu n ctio n : Minimize to ta l production, tra n s p o rta tio n , and land conversion costs: a ZZ* K arjXarj + Z z j Z W k ljt + z K rr *jW rr*j + P*Kr* rjVr*rj <9> co n s tra in ts : A) Product k is the same fo r a l l product packages. Product k 1s summed across a l l management s tra te g ie s and shipped to any i a t which there is a demand fo r k. Both market and non-market goods are consider­ ed. I £ fo r 6a k r j t Xa r j " x Xk i j t “ 0 (10) k = ( a , . . . , p ) , a l l j , and a l l t B) Residual k is also the same fo r a l l product packages. This equation se t sums the re sid u a ls produced in each supply area. IJ W xarj ' Xk j t ' 0 fo r k = ( q , . . . , s ) , a l l j , <"> and a l l t Xk j t *ias an o b je c tiv e fu nctio n value o f 0 . C) Some o f the re sid u a ls might not be s ta tio n a ry . through the system. They might move The s e t o f equations sim ulates the movement o f resid uals through the system and allows q u a n titie s o f re sid u a ls a t various lo c a tio n s to be constrained: ^ nk i j t Xk j t - Xk i t J fo r k - ( t , . . . , v ) , a l l i , and a l l t 78 I f no l i m i t is placed on a re s id u a l, equation (12) is changed to (12a) to sum the q u a n tity received a t each s it e : j nk i j t Xk j t " Xk i t = 0 (12a^ Xk i t would have a value o f 0 the o b je c tiv e fu n c tio n . Equation set (12) or (12a) is the environmental d iffu s io n compon­ ent. D) This equation set requ ires th a t projected demands a t various points in th e r iv e r basin bemet. j Xk i j t + J, Xk i j 11 - Xk i t (13} fo r k = ( a , . . . , p ) , a l l i , and a l l t This equation set allows products to be imported to th e r iv e r basin to meet demands in the r iv e r basin. E) Demand points outside o f the r iv e r basin w ith a negative excess supply o f a good w i l l have a capacity to absorb excess production o f products in the r iv e r basin. They cannot buy i n f i n i t e amounts, however. T heir demands do not have to be s a tis fie d by r iv e r basin production, e ith e r . ^ Xk i j t — Xk i ' t (14} fo r k = ( a , . . . , p ) , a l l i ' w ith a negative excess supply, and a l l t F) There is also a l i m i t on the amount o f goods th a t a region o u t­ side o f the r iv e r basin w ith p o s itiv e excess supplies can export to meet r iv e r basin demands. * Xk i j ' t - Xk j ' t (15) fo r k = ( a , . . . , p ) , a l l j 1 w ith p o s itiv e excess s u p p lie s , and a l l t 79 G) Demands could also be made d ir e c t ly on the production o f a re ­ gion, th a t 1s a region could be required to produce a c e rta in q u a n tity o f a given good. The fo llo w in g equation se t w il l accomplish t h is : ? Xk i j t - Xk j t fo r a given k , fo r a ll j , and a l l t H) There are resource lim ita tio n s to production on each resource class 1n each region. I t is also possible fo r resource classes to be converted to another c la s s . land and v ic e -v e rs a . Forest land can be converted to n o n -fo rest The fo llo w in g equation s e t constrains production and allows conversions o f resource classes to occur. I a . - E W *. + z V * . < X . a rj r* rr*j r * r * r j - Ar j (17) V l/' fo r each r and j I f conversions between resource classes do not occur, the equation set changes to (1 7 a ). ia Xa r j i Xr j <17a> f o r a l l r and j I ) T ran sfer costs can be summed a t the lo c atio n s where they are captured to study d is tr ib u tio n a l e ffe c ts . This equation set sums the costs, a t each demand p o in t, o f tra n s p o rtin g products from supply areas to meet demands a t th a t p o in t. J I Tk i j t Xk i j t " Ci t = 0 (18} f o r a l l i and t C^t has an o b je c tiv e fu n ctio n value o f 0 . J ) This equation se t sums the c o s t, a t each supply re g io n , o f tran sp o rtin g goods to demand p o in ts. 80 \ £ Tk i j t Xk i j t " Cj t = 0 {19) fo r j and t Cjt has an o b je c tiv e fu nctio n value o f 0 . K) Other c o n stra in ts on land use by lo c a tio n can be put in the model by using th is general form: Xa r j — Za r j ^20^ Greater than or equal to co n s tra in ts o r equal to co n strain ts could also be put in . These equations allo w c o n stra in ts to be put on management s tra te g ie s by decisions exogenous to the model. Figure 2-3 illu s t r a t e s these equation se ts. The environmental d iffu s io n component can be removed. tiv e s 3 ,4 ,5 , and 6 ) . Equation set (12) or (A lte rn a ­ (12a) would be removed. Equation set (11) could be changed to : I a £ 5a r k j Xa r j r Xr j t (lla ) fo r k = ( q , . . . , v ) , a ll j , Removal o f the tra n s p o rta tio n component is more complex. atives 6 , 7 , 8 ,9 , and 1 0 ). are removed. and a l l t V ariab les C ^ , Ckj t , Requirements cease to be s p e c ific (A lte r n ­ Tk ij t , Xkij. t , andXk1t to demand p o in ts . Re­ quirements on production by the r iv e r basin or sub-basins are then made. With these a lte r n a tiv e s , the o b je c tiv e fu n ctio n is changed to : minimize r u n K, .X ,„ . + z ^ v.r ■? a rrJ a j rr*j rr*j + z K„* .V„* . r r * r j r wr j Demands are made fo r the products by eachsupply I £ 6a k r j t Xa r j - Xk j t fo r k = ( a , . . . , p ) , a l l j , and a l l t (21) region: (22) 81 9) Minimize z z z Ka r j Xa r j+ z J J s Tk 1 j t Xk i j t +* Kr r * j Wr r * j +S *lV * r j Vr * r j 10} I 11} H 12) J * a k r jt Xa r j “ 1 Xk i j t = 0 a r 6a k r j t Xa r j " Xk j t “ 0 ? nk1j t Xk j t - Xk1t J 13) j Xk i j t + j i Xk1j t - 14) ? xk1j t - xk1 ' t J 15) J Xk i j ' t - 16) ? Xk i j t - 17) 2 X_. - z a rj 18) 19) 20) * k it xk j * t Xk j t W * . + z V„* . 5 r r wj * r~ rj j I Tk i j t Xk 1 jt “ Ci t = 0 J I Tk i j t Xk i j t " Cj t = 0 rj Xa r j — Za r j Figure 2 - 3 .— The Production Model w ith T ran sp o rtatio n and Environmental D iffu s io n Components Incorporated. The environmental d iffu s io n model 1s Included In a lte rn a tiv e s 7 and 8 through equation sets (11) and (1 2 ). the acreage o f each resource c la s s . Equation s e t (19) co n traln s Equation s e t (20) allow s exogenous co n straints to be made on management s tra te g ie s . Equation sets ( 1 3 ) , (1 4 ), (1 5 ), (1 6 ), (1 8 ), and (19) are not included. The environmental d iffu s io n model could be elim in ated in a lt e r n ­ atives 5 and 6 . This is done by removing equation s e t (4 ) or (4 a ). Equation s e t (11) could be changed to (1 1 a ). With a lte rn a tiv e s 9 and 10, the environmental d iffu s io n model is separated but included. separation w ill be discussed in the next paragraph. This With a lte r n a tiv e 13, both the tra n s p o rta tio n and environmental d iffu s io n models are sep­ arated. The tra n s p o rta tio n and environmental d iffu s io n components could be included but made separate from the production component. To separ­ ate th e environmental d iffu s io n component, equation ( 12) or ( 12a ) is re ­ moved. (A lte rn a tiv e s 7 , 8 , 9 , and 1 0 ). the production model. Equation (11) would be l e f t in Equation set (25 ) would be solved s e p ara tely us­ ing inform ation from equation set ( 11); ? nk i j Xk j t = Xk i t J (25) fo r k = ( q , . . . , v ) , a l l i , and a l l t The production o f re s id u a ls could be constrained by s u b s titu tin g equa­ tio n set (24) fo r equation set (1 1 ): £ 6 t. -4.X ■ + Y. .* = a kat a a k r j t ara X, k jt fo r k = (q , . . . , v ) , a l l j , (24 ) ' ' and a l l t Equation (25a) would be s u b s titu te d fo r equation (2 5 ): 83 fo r k = ( q « ...» v ) a l l 1 , and a l l t The tra n s p o rta tio n component would be separated by changing equa­ tio n se t (1 0 ) to equation (2 3 ): J 3a k r j t Xa r j " Yk j t = Xk j t a fo r k = (q ^23* v ) , a l l j , and a l l t Equations (1 3 ), (1 4 ), (1 5 ), (1 6 ), (1 8 ), and (19) are then removed from the production model. The tra n s p o rta tio n model 1s then solved s e p ara tely using a lin e a r programming form at, o b je c tiv e fu n c tio n : Minimize to ta l tra n s p o rta tio n costs: minimize z z z e k 1 j t j j t ^2 6 ^ c o n stra in ts : The to ta l amount o f products produced in the production component must be shipped: J Xk1j t s Xk j t + Yk j t (27) Equation sets (1 3 ), ( 1 4 ) , (1 5 ), ( 1 8 ), and (1 9 ) are then Included in the tra n s p o rta tio n component to account f o r th e shipment o f products between regions. (A lte rn a tiv e s 5, 6 , 11, and 1 2 ). Linking a Land Assignment Model I t might be d e s ira b le to a llo c a te management s tra te g ie s to sub­ d iv is io n s w ith in a reg io n . Problems a re caused when more than one man­ agement s tra te g y is a llo c a te d to a resource class and more than one regional subdivision contains some acreage o f the resource c la s s . It is impossible to uniquely assign management s tra te g ie s to regional sub- 84 division s by d e fin in g the lo c atio n s o f the resource cla ss . A dditional c r it e r ia w ill be needed to choose the regional subdivision to which the management s tra te g ie s are a llo c a te d . The subdivisions would be s in g le grid c e lls 1n which land inform ation is stored. At th is p o in t in tim e, c r i t e r i a have assignment model would be used not been d efined. to a llo c a te the among the grids (P a tte rs o n , 1972). A land management s tra te g ie s A scale o f p r io r it y fo r a l l manage­ ment s tra te g ie s would have to be developed fo r each resource class and lo c a tio n . c e lls . A p r io r it y would have to be defined w ith in a c e ll and between Some o f the possible c r i t e r i a in clu d e: a c c e s s ib ility , desired p attern s, ownership, h is to r ic land use p a tte rn s , and re la tio n s h ip s to land forms and fe a tu re s . Each management s tra te g y a t each lo c a tio n could be assigned a value from 0 to 10 o r 0 to 100 depending upon the c r it e r ia and weights on the c r i t e r i a . This p r io r it y system would be used to d efin e o b je c tiv e function values. A value would be defined fo r each management s tra te g y fo r each resource class in each g rid . The value would show the r e la t iv e p r io r it y o f the s tra te g ie s in each g rid and between g rid s . assignment model would be used to maximize the A m u ltip le land use to ta l value o f the objec­ tiv e function fo r the r iv e r basin. Variables j * = subdivision o f j re g io n , th a t i s , a g rid c e ll Va r j * = value assigned to management s tra te g y a p rac tice d on re ­ source class r in region j * * a r j * = acrea9e (from p r i o r it y sc ale ) management s tra te g y a p rac tice d on class r in region j * * a r j = acrea9e management s tra te g y a p ra c tic e d on resource class r in region j which is c a lc u la te d in the lo c a tio n model Xr j * = acres resource class r 1n region j * Za r j * = )* = management s tra te g y a on resource class r 1n region j * Equations: o b jec tiv e fu n c tio n : Maximize the to ta l value o f the o b je c tiv e fu n c tio n . Maximize e e e a r j* V .*X . * a rj a rj (26) co n stra in ts : A) The acreage o f any management s tra te g y must be constrained by the acreage o f I t s resource class in any given re g io n . Management s tra te g ie s are a llo c a te d to every acre o f the resource class and th e follow ing equation accomplishes th is : I Xa r j f *= Xr j * <2 7 > fo r a l l r and j * . B) The to ta l acreage o f each management s tra te g y on each resource class in each j re g io n , which 1s determined in the production component, must be a llo c a te d . The management s tra te g ie s must be summed over each j * 1n each j region. * . Xa r j * " Xa r j <28> fo r a l l a , r , and j . C) The acreage o f a management s tra te g y in any j * region could be constrained by decisions made exogenous to th e model by use o f the fo llow ing types o f equations: 86 Greater than or equal to co n strain ts or equal to c o n s tra in ts could also be used. The lin kag e between th is m u ltip le land use assignment model and the lo c a tio n component occurs through Xa . fo r a l l a , r , and j . arj Each Xarj is c a lc u la te d in the lo c a tio n model arid then constrains the so lu tio n o f the land use assignment model. Land Management S trateg y Inform ation An im portant problem w ith th is system is th a t o f determ ining the product c o e ffic ie n ts , the R elationships must be determined to c a lc u la te these c o e ffic ie n ts . These re la tio n s h ip s must account fo r physical resource d a ta , the dimensions o f resource class r , the p ractices o f management s tra te g y a , and the p o in t in tim e: “a k r jt = f k f k = re la tio n s h ip to determine c o e ffic ie n t fo r product k These re la tio n s h ip s w ill not be prescribed in th is study. These r e la t io n ­ ships are best determined by p ra c titio n e rs in the f ie ld s s p e c ia liz in g in each o f the products. R elationships used in th is study w il l be des­ cribed in a l a t e r chapter. Goals fo r Land Use Management Requirements fo r products are im portant goals f o r land use manage­ ment. C a lc u la tin g these requirements is a problem. Requirements are normative statements concerning what ought to be produced. D efining re la tio n s h ip s to c a lc u la te the requirements on a m ic ro -s c a le , such as, subdivisions o f a r i v e r b as in , could be q u ite d i f f i c u l t . The le v e ls o f requirements which are projected a re a ffe c te d by the form o f the r e la t io n ­ ships, th e v a ria b le s Included in the r e a ltio n s h ip s , and the assumptions 87 behind the re la tio n s h ip s . R elationships used in th is study w il l be des­ cribed 1n the next chapter. Factors to be considered f o r c a lc u la tin g requirements fo r tim ber are c u rren t consumption, growth p o te n tia ls f o r In d u s tries using roundwood, lo c a tio n a l advantages, technology, and prices o f roundwood and i t s s u b s titu te s . V ariab les to be considered fo r calcu ­ la tin g re c re a tio n and hunterday requirements include population and population changes, cu rren t le v e ls o f economic a c t i v i t y , p ric e s , income, a v a ila b ilit y o f s u b s titu te s , and p o te n tia ls fo r change. Constraints on environmental impacts should consider desired uses to be made o f the resource needed f o r those uses. Linking the Land Evaluation System to the Land Inform ation S.ystlm Purpose o f the Linkage Between the Location Model and the Land Inform ation System Each management s tra te g y is la b e lle d according to i t s resource cla ss , r , and i t s re g io n , j . The purpose o f the land inform ation system is to provide th e inform ation fo r the c a lc u la tio n o f Xr j , the acreage o f resource class r in region j , and X the acreage o f resource class •J r 1n region j * . These acreages co n strain the acreage o f management s tra te g ie s a = ( 1 , 2 , 3 , . . . , A) on resource class r in any reg io n . Region j could be defined as a s e t o f g rid c e lls . would contain acreages o f various resource classes. Each g rid c e ll The acreages stored in these g rid s would be summed by the j region and resource class to c a lc u la te the acreage o f each resource class 1n each reg io n . The land inven tory system serves b a s ic a lly the same purposes fo r the land assignment model. The system provides inform ation to c a lc u la te the acreage o f resource class r in g rid c e ll j * , XrJ.* . 88 The purpose o f the lin kag e 1s to provide the resource co n stra in ts needed fo r the production component and the land assignment model. The land inform ation system must contain the data to c la s s ify the land resource classes and stored by g rid c e lls . The g rid c e lls must be r e ­ ferenced to allow r e t r ie v a l o f th is In fo rm atio n . system could also be used to generate maps o f The land inform ation the resource classes or s p e c ific items o f land in fo rm atio n . Resource C la s s ific a tio n The c la s s ific a tio n system is based on the concept o f a m u lt i- d imensional landtype (L acate, 1961). Dimensions to be used 1n c la s s ify in g the resource are those im portant to decision-m aking, 1n the case, those important to a llo c a tin g management s tra te g ie s in space. o f each dimension should be based on management needs. C la s s ific a tio n There must be a concern w ith the c u rre n t cover type or land use and c h a ra c te ris tic s o f the cover type or land use. As an example, the Forest Service is de­ fin in g management s tra te g ie s using fo re s t ecosystem, s o il a s s o c ia tio n , and stand s iz e class and c o n d itio n . Other data might also be im portant i f land use conversions are to be considered, such as, slo pe, topography, c lim a te , bedrock depth, th e presence o f m in e ra ls , and s o il s e rie s . For the purposes o f th is model, only c h a ra c te ris tic s o f the cu rren t cover type are necessary since the Economic Research S e rv ic e 's model does not consider land use conversions. Land could be c la s s ifie d fo r each po­ te n t ia l use i f conversion is to be considered. Each resource class r is defined as being a combination o f one class o f each o f n dimensions. There are R classes o f resources. Each class o f each dimension is defined such th a t th e cost or product-package o f a management s tra te g y does not change. For the fo re s t s e c to r, 89 there are fo u r dimensions each w ith a se t o f classes: b = 1 , . . . , 5 = fo re s t ecosystem c = 1 ,...,4 = stand s iz e class d = 1 ,...,5 = s o il association e = 1,2 = stand condition The maximum number o f fo re s t resource classes in th is study is 200. Some combinations may not e x is t. There are two ways to d e fin e these resource classes and t h e ir lo c atio n s . Each dimension and i t s classes could be surveyed and mapped se p ara tely. The resource class could then be defined by the use o f overlays or computer techniques. Each resource class would be defined by one class o f each dimension and would have i t s boundaries defined on a map. The o th e r method would be an in te g ra te d survey where a group goes out in to the f i e l d and d efines each m ult1-d 1mensional class and maps each. I f each dimension 1s mapped and c la s s ifie d in a desired manner, the f i r s t method w il l probably be used. The second method becomes more d es irab le i f the desired data does not e x is t . Grids A system o f grids is not th e only way to sto re and map land use inform ation. However, i t 1s th e most connion and perhaps the e a s ie s t method (Murray e t . a l . , 1971). A system o f g rid s is recommended be­ cause o f the more widespread use and th e p ro b a b ility th a t technology us­ ing th is system 1s b e tte r developed. The s iz e o f the g rid is an im portant problem. to two ca te g o rie s . The sizes f a l l in ­ The f i r s t s iz e is small enough to allow d e fin it io n o f only one resource c la s s , th a t i s , only one resource class is assigned 90 to a c e l l . The c e ll s iz e allows each resource dimension to be c la s s i­ fie d and mapped s e p a ra te ly . Each dimension can then be combined in to a resource c la s s ific a tio n o f each c e l l , perhaps by a computer program. The second s iz e 1s too la rg e to allo w the d e fin itio n o f only one resource class. The acreage o f each class must be assigned to each c e l l . The acreage o f resource classes must be determined outside o f the land in f o r ­ mation system and assigned to each c e l l . Whether or not a c e ll is too large depends upon the re s o lu tio n o r accuracy desired by the a n a ly s t. Computer cap acity and a v a ila b le budget can co n strain the number o f c e lls handled and thus may a f fe c t the s iz e o f th e g rid s . I f the g rid c e ll is small enough to a llo w the c la s s ific a tio n o f only one resource class to a g r id , the task o f the land Inform ation is defined as fo llo w s : 1) Land inform ation is stored by g rid c e ll fo r each dimension by class needed to d efin e a resource c la s s . 2) This Inform ation is processed by a computer alg orith m to c la s s ify each g rid c e l l . 3 ) The acreage o f each g rid c e ll constrains the land assignment model and 1s aggregated by j region to co n strain the lo c a tio n model. Figure 2-4 illu s t r a t e s the steps in th is process. I f the g rid c e ll is la rg e enough to allo w c la s s ific a tio n o f more than one resource class to a g r id , the task o f the land Inform ation sys­ tem changes: 1} Land info rm ation is c o lle c te d and mapped. 2) Land r e ­ source classes are defined and mapped from the land in fo rm atio n . 3) The g rid system is o v e rla id and acreages o f each class are assigned to each g rid c e l l . 4 ) The acreages o f each g rid c e ll co n strain the land assign­ ment model and are aggregated by j region to co n strain the lo c a tio n model. Figure 2-5 I ll u s t r a t e s the steps 1n th is process. I-----------------------------------1 Raw Land Data F ile Dimension 1 Constrain Location Model s' Aggregate by Region 7v Dimension Constrain M ultiple Land Use Assignment Model Resource C lassification F ile <- 2 Combination Program Dimension N i_____________________ J Figure 2 -4 .—Steps from Storing Land Information to Constraining the Location Model, Given a Grid Cell Small Enough to Classify Only One Resource. Maps of Land Data Dimension 1 Constrain Location Model Aggregate by Region Dimension 2 Constrain M ultiple Land Use Assignment Model Resource C lassification F ile Resource Class Map Dimension N L Figure 2 -5 .—Steps in Constraining the Location Model Enough to Classify Only One Resource. Land Information, Given a Grid Cell Small 4 93 Choosing a Grid C e ll Size The g rid c e ll s iz e 1s an Im portant fa c to r 1n developing a land Inventory system. discussed below. The advantages o f a la rg e or small g rid c e ll are A small g rid c e ll 1s a c e ll to which only one resource class can be assigned. A la rg e g rid c e ll is a c e ll to whichmore than one resource class can be assigned. These two terms are r e la t iv e to the accuracy o f the data c o lle c te d and th e desired accuracy o f mapping the data. Given a le v e l o f accuracy o f d a ta , th e re 1s a threshhold 1n area above which a g rid c e ll is la rg e and below which 1t is smallf o r a de­ sired le v e l o f accuracy o f mapping. As the desired lev el o f accuracy increases, given a le v e l o f data accuracy, the sm aller is the threshhold area. As data become more a c cu ra te, the desired le v e l o f accuracy o f mapping can increase thus decreasing the threshhold area between a la rg e and small g rid . C r it e r ia must be developed to choose a g rid c e ll s iz e . c o lle c tin g data is assumed Independant o f g rid c e ll s iz e . The cost o f The accuracy o f data and the q u a n tity w il l determine the cost o f c o lle c tio n . The s iz e o f a g rid c e ll is r e l a t i v e , given th e accuracy o f the data and the desired accuracy o f mapping th e d ata. The f i r s t c r i t e r i a is the cost o f c la s s ify in g resources. With the small g rid c e l l , th e process can be computerized. With the larg e g rid c e l l , the process might have to be done m anually. I f the process f o r a large g rid c e ll is com puterized, i t would be more complex than the c la s s i­ fic a tio n o f resources given a small g rid . I t would appear th a t the cost o f c la s s ify in g resources on a small g rid would be lower than the cost o f c la s s ify in g them on a la rg e g rid . A ra tin g o f 1 is assigned to the g rid c e ll s iz e w ith the lower cost o f c la s s ify in g resources, w h ile a ra tin g 94 o f 2 1s assigned to the g rid c e ll s iz e w ith the higher co st. A lower cost o f c la s s ific a tio n 1s p referred to a higher cost o f c la s s ific a t io n . The small g rid receives a higher ra tin g o f 1 and the la rg e g rid receives a lower ra tin g o f 2 . The second c r i t e r i a is th e ease o f d isp layin g maps o f resource classes or resource dimensions. With a small g rid c e l l , resource classes or a s in g le resource dimension can be mapped fo r a ll c e lls on a s in g le map. With a la rg e g rid c e l l , more than one map w i l l probably be required since more than one resource class could be assigned to a c e l l . The small g rid c e ll receives a higher ra tin g o f 1 w h ile the la rg e g rid c e ll receives a lower ra tin g o f 2 . The th ir d c r i t e r i a is th e ease o f mapping management s tra te g ie s allo cated to g rid c e lls by the land use assignment model. This mapping w ill be more d i f f i c u l t since more than one management s tra te g y can be assigned to a g rid c e l l . With a small g rid c e l l , resource c la s s ific a tio n w ill not be a com plicating fa c to r as i t w il l be in a la rg e g rid c e l l . The small g rid c e ll receives a higher ra tin g o f 1 w h ile the larg e g rid c e ll receives a lower ra tin g o f 2. Table 2-3 displays the re s u lts o f these th ree c r i t e r i a . Table 2 - 3 . — Rating Grid C e ll Size g rid c e ll s iz e c r ite r io n Cost o f c la s s ify in g land resources Ease o f mapping resources Ease o f mapping management s tra te g ie s 1 - high la rg e small 2 2 2 1 1 1 2 = low 95 Geographic Referencing Geographic referen cin g is also an im portant problem. possible systems in clu d e: Several 1) la titu d e -lo n g itu d e , 2 ) Universe Transverse M ercator, 3) s ta te plane co o rd in ates, and 4 ) the re cta n g u la r survey. The Universe Transverse Mercator system seems to be favored in the lit e r a t u r e (Murray e t , a l , 1971 and S ta te Planning D iv is io n , 1972). This system has several advantages: 1 ) each g rid u n it is square and uniform in s iz e , 2) the system is g lo b a l, 3 ) the system 1s m e tric , and 4) o ther referen cin g systems can be converted to i t by use o f computer programs. I t seems advantageous fo r u n its o f the fed eral government to use one system o f geographic re feren cin g so th a t data c o lle c te d by d i f ­ fe re n t agencies are com patible. Therefore, i t is d e s ira b le th a t data co lle c te d fo r r i v e r basin planning be based on a Universe Transverse Mercator g r id . Once la id o u t, grids can be la b e lle d by an X-Y coordin­ ate system to referen ce data c o lle c te d by the g r id . A v a ila b ilit y o f data, however, may fo rce use o f the rectan g u lar survey. The land e v a l­ uation system and the land inform ation system could be based on a v a r ie ty o f g rid systems, in c lu d in g the Economic Development Agency's two minute by two minute nation al g rid . F ile S tru ctu re There are several ways to organize data f i l e s . The f i r s t is se­ quential o rg an iza tio n where the records are stored 1n the s p e c ific order in which they are processed. This 1s the most common method o f sto rage. The second is random o rg a n iza tio n where data are stored and re trie v e d on the basis o f a p re d ic ta b le re la tio n s h ip and the d ir e c t address o f the lo c a tio n . between the key o f th e record This method has been used 1n the LUNR system and seems to o f fe r advantages in the speed o f r e t r ie v a l 96 when th ere are la rg e numbers o f c e lls . The th ir d method 1s 11st pro­ cessing where pointers are>used to d ivorce the lo g ic a l o rg an iza tio n from the physical o rg an iza tio n {Murray e t. a l . , 1971). Any o f these methods o f organizing and s to rin g data can be adapted to th e land In ­ ventory system. The c r i t i c a l problem is th e amount o f data to be stored and the cost involved in r e tr ie v in g d a ta . Media o f storage Inclu d e cards, tap es , and d is c s . advantages in to ta l volume o f storage. The d isc o ffe rs More records can be stored and more data items can be stored in each record. When combined w ith a method a random o rg a n iz a tio n , the disc o ffe rs one o f th e most advanced methods o f s to rin g land d ata. A prime example is the LUNR system d evel­ oped a t Cornell U n iv e rs ity (Shelton and Liang , 19 73 ). can also be useful in sm aller systems. tageous than Cards and tapes Tapes u s u a lly are more advan­ cards since they can be rewound to allo w the f i l e to be read several times fo r various operations in the same program. Sequen­ t i a l o rg an izatio n 1s the e a s ie s t method to implement. The data f i l e 1s a means o f s to rin g data records fo r each c e l l . The record f o r each c e ll should be s tru c tu red in such a way as to a llo w several operations to be performed using the f i l e as a data base. The record contains several types o f inform ation useful to various o peratio n s. Each piece o f in fo rm atio n is stored in a f i e l d . Blank f ie ld s may be l e f t in the record to a llo w new data items to be included In th e record a t la t e r times (Hardy and S h elton , 1970). When the g rid s are small enough to allo w c la s s ific a tio n o f only one resource, several types o f inform ation should be contained in the record: 1) lo c a tio n In fo rm a tio n , 2) basic resource d a ta , th a t i s , raw measurements o f the land resource, and 3) resource classes fo r d if f e r e n t 97 land uses. The lo c a tio n Info rm ation should contain the number o f the j region, the number o f the g rid c e ll grid c e l l. ( j * ) , and the coordinates o f the The f i r s t two lo c a tio n data Items are h elp fu l 1n developing acreage c o n s tra in ts . A ll lo c a tio n Items are In te g e r f ie ld s . The basic resource data could include such things as s o il a s s o c ia tio n , stand size class and c o n d itio n , ecosystem, c lim a te , topography, bedrock depth, geologic d a ta , land use, and o th e r data concerning cover ty p e . These data can be used to develop resource c la s s ific a tio n s fo r each use to be considered by the g rid . The MIADS combination program could be used for th is purpose (Amldon, 1964). When no land use conversions are con­ sidered, only one resource class 1s Included. The lo c a tio n data and basic resource data may be put In to th e record f i r s t . Operations may then be performed to d e fin e th e resource classes which are then put in ­ to the records. The resource classes are to be in te g e r f ie ld s . Blank fie ld s may be l e f t 1n the record fo r the In c lu s io n o f more resource data and c la s s ific a tio n s . J (12) J* (1 2 ) X (12) Y (12) Location Data An example o f such a record could be: A .................... N Real or In te g e r F ield s 1 .....................R (1 2 ) . . . . (1 2 ) Resource Data Resource Classes Blank F ield s The X-Y in te g e r f ie ld s are the coordinates o f the X-Y coordinate system. When the g rid s are la rg e enough to a llo w more than one resource to be c la s s if ie d , the record is d if f e r e n t . region, the g rid c e ll be Included. Again th e number o f the j ( j * ) , and the coordinates o f the g rid c e ll must Resource data could be In clu d ed . each dimension could be Included in a g r id . Each class o f each dimen­ sion would have a f i e l d in u n its such as acres. also Included. More than one class o f Resource classes are However, even 1 f no conversions are considered, th ere 98 could be more than one resource class f o r each g rid . Thus a f i e l d would be required f o r each resource c la s s , w ith the acreage o f each re ­ corded. The lo c a tio n data would remain in th e in te g e r f ie ld s . Both the resource data f ie ld s and th e resource class fie ld s would be re al fie ld s , since re a l numbers, which are non-1nteger numbers, would be stored 1n them. Constraining the Location Model and the M u ltip le Land Use Assignment Model A computer program could be developed to read resource class in ­ form ation, perform operations to c a lc u la te acreages o f resource classes and constrain th e lo c a tio n model and the land use assignment model. To constrain the lo c a tio n model, the acreage o f each resource class in each g rid would be summed to c a lc u la te and p r in t th e to ta l acreage o f each resource class in each j reg io n . To co n strain the land assignment model, the acreage o f each resource class 1n each g rid is found and printed o u t. The actual c o n s tra in ts o f the lo c a tio n model and the land assignment model are read from a computer p rin to u t and punched onto cards or o ther storage media. computer program. The cards could be punched as output from the See Figure 2-6 fo r a flo w ch art o f an alg orith m th a t calcu lates and p rin ts acreages o f resource classes by region and g rid c e l l. See Appendix A fo r the set o f flo w ch art symbols. Figure 2-6 assumes th a t the g rid s are small enough to c la s s ify only one resource. Since a small g rid c e ll is favored over a la rg e g rid c e l l , th is algorithm 1s favored over one th a t assumes a la rg e g rid c e l l . tra te s an alg o rith m th a t assumes a la rg e g rid c e l l . Figure 2 -7 i l l u s ­ 99 START > J * , R ) <-0 J *,R )« -0 J *» R ) + 0 2 0-1 ,M 1 READ S -l.P 0 ,0 * ,R X (0 .R )- X C 0 .R )+ 1 V (0 *,R )+ A C F R - l ,N 3 0 - 1 ,M R -l.N Y (J ,R )+ X (J ,R ) *ACF / 4 j ACF J J* R S » » Acreage o f G r id C e l l Region - ( 1 , . . . , H ) G rid - ( 1 P) Resource - ( 1 . . . . . N ) G r id b e in g processed PRINT J *,R ,V (J *.R ) j 4 J *-1 ,P R - 1 ,N A V (0*,R X (J ,R Y iO .R PRINT 0 ,R ,Y (J ,R ) 3 - Acreage o f re s o u rc e R I n g r i d J * ■ Number o f g r i d s I n re s o u rc e R 1n r e g i o n ' J - A c re a g e o f re s o u rc e R i n r e g io n 0 Figure 2 - 6 . — Flow Chart o f an Algorithm to Generate Acreage C onstraints fo r the Location Model and the M u ltip le Land Use Assignment Model, Given a Grid Small Enough to C la s s ify Only One Resource Class. 100 READ START R(l) S « 1 ,P V (J *.Q )*fl(Q ) R (Q )-0 7 Yes P RINT J .Q .X (J .Q ) P RINT END 0 J* Q S ■ * * R e g io n ■ ( 1 , . . . ,M ) G r id - ( 1 P) R e s o u rc e c l a s s ■ ( 1 , . . . , N ) G rid b e in g processed R (Q ) ■ V (J *,Q ) ■ X (0 ,Q ) » A creage o f A creage o f A creageo f R esource Q R e s o u r c e Q 1n g r i d J * R e s o u r c e Q 1n g r i d J Figure 2 - 7 . — Flow Chart o f an Algorithm to Generate Acreage C onstraints fo r the Location Model and the M u ltip le Land Use Assignment Model, Given a Grid Large Enough to C la s s ify More Than One Resource Class. 101 Linking a C o n strain t Generator to th e Land Evaluation System The purpose o f th is component 1s to co n strain the land evalu atio n system by land management decisions made exogenously to th e model. These exogenous land management s tra te g ie s d efin e a s p a tia l p a tte rn o f land management s tra te g ie s which could be mapped. This mapped Inform ation could be used to determine Za rj» the l i m i t on management s tra te g y a on resource class r 1n region j , fo r th e production component or Zapj * , the lim it on management s tra te g y a on resource class r in g rid c e ll j * , fo r the land assignment model. In some Instances* the decision to manage land 1n a given manner would be based on the resource or dimension c la s s ific a tio n . A map o f resource classes or desired resource classes could be generated from the land inform ation system to a s s is t 1n making such decisions. The exo­ genous decision would then sim ultaneously determine the resource class and the management s tra te g y . to g rid c e lls . The management s tra te g ie s could be assigned I f more than one management s tra te g y could be assigned to a g rid c e l l , the acreage o f each s tra te g y 1n the c e ll would have to be determined. The acreages o f the c e ll could be obtained by using a planimeter or a d i g i t i z e r . In th is case, the acreage o f a g rid c e ll would have to be broken up among management s tra te g ie s when suiranlng over grid c e lls . I f more than one resource can be c la s s ifie d In a g rid c e ll which 1s not a favored a lt e r n a t iv e , the acreage o f each management s t r a t ­ egy on each resource class would have to be assigned to a g rid c e ll and then summed to constrain the lo c a tio n model. I f a small number o f grids were involved the summations could be done manually. However, 1 f a la rg e number o f grids are involved o r th e task 1s to be done many tim es, th e acreage o f each management s tra te g y on each resource class 1n each g rid 102 c e ll could become Input to a computer alg o rith m . This algorithm would then sum th e acreages to co n strain the producton model. A lis tin g o f each Za r j and could be obtained which then could be used to con­ s tra in the models. Cards could be produced to be used as c o n s tra in t cards 1n the lin e a r programming alg orith m . Figure 2-8 Illu s t r a t e s a flow ­ chart to do th is ta s k . Land management decisions also could be made exogenously to the land evalu atio n system w ith ou t consulting the resource c la s s ific a t io n . In such a case, management s tra te g ie s would have to be compared to the c la s s ifie d land use to determine th e Z „ . ' s a rj and the Z „ . * ' s . a r jw I f the grid is small enough to allo w only one resource class which is the favored a lt e r n a t iv e , th e task 1s r e la t iv e ly sim ple. The resource class must be determined and the acreages d ivided among the a lte r n a tiv e man­ agement s tr a te g ie s . Figure 2-9 is a flo w ch art to accomplish t h is . I f more than one resource class Is assigned to a g rid which 1s not the favored a lt e r n a t iv e , the process changes. Assumptions have to be made concerning how to d is tr ib u te management s tra te g ie s among resource classes. I f the number o f g rid s is small enough, the process could be carried out m anually. With a la rg e number o f g rid s , a computer program would be h e lp fu l in completing th is ta s k . flow chart o f such an a lg o rith m . Figure 2-10 I llu s t r a t e s a I t assumes th a t management s tra te g ie s w ill be evenly d is trib u te d among resource classes. Mapping Three mapping ro u tin es were in v e s tig a te d . The in v e s tig a tio n was re s tric te d to p rin tin g ro u tin es operable on the MSU computer. P rin tin g routines contain as much Info rm ation as p lo t te r ro u tin es and are cheaper to use. A ls o , handling grldded data on small g rid s w il l become very 103 Y {B ,R ,.J *)*0 START ^ ^ Z (B ,R ,J )+ 0 2 B -1 ,A R -l.H S«1,P 1 V. Z (B ,R .J K V Z (B ,R ,J )+ A C (A ,R ) < . ” No ^ / J-1.H P R IN T B ,R ,J , X (B ,R ,J *) READ J .J * . b .r , ac(b , r ) Y (B .R .J )A C (B ,R ) PRINT B ,R ,J , Z (B ,R .J ) ,P c 0 ■ R e g io n ** ( 1 , . . . , H ) J* ■ Grid - (1 P) B ■ Management S t r a t e g y ■ ( I , . . . , A ) R ■ R esource C la s s » ( 1 , . . . , N ) S - G r id b e in g p ro ce ss ed ■ Z (B ,R ,J ) ■ A c r e a g e o f M a n a g em e n t S t r a t e g y re s o u rc e c la s s R In re g io n J AC ( B , R ) - A c re a g e o f Management S t r a t e g y reso u rce c la s s R X ( B . R . J ) ■ A c r e a g e o f M a n ag e m e n t S t r a t e g y r e s o u r c e c l a s s R 1n r e g i o n J Y ( B , R , J * ) ** A c r e a g e o f M a n a g e m e n t S t r a t e g y r e s o u r c e c l a s s R 1n g r i d J * Figure 2 - 8 . — Flow Chart o f the C o n stra in t G enerator, Assuming th a t Management S tra te g y , Resource C lass, and Location are S p e c ifie d . B on B on B on B on 104 ( start T (B ,K ,L )*0 U (B ,R .J )*0 V (B ,R ,J J + O )—\ READ 51 READ 2 J ,J *,K ,L .R S -1 .P 5 -1 , P K ,L ,B ,A C 1 T (B ,K ,L )*A C 3 — > < ^ T (B .K .L )« 0 r^ > ii^ B -1 .A V fB .R .J K T (B ,K ,L ) V (B ,R ,0 K V (B ,R ,J )+ U (B ,R ,0 *) -------- => lYes 5 2 4 B-1 ,A R-1 ,N —■ V. J - 1 ,M No / -^ 7 3 V PRINT B .R .J , V (B .R .J ) 1 6 5 -------5> J *-1 ,P PRINT B .R .J *. V (B ,R .J *) K ,l B R J J* S » > C o o r d in a t e s Management S t r a t e g y ■ { 1 . . . . . A ) R esource C la s s » ( 1 . . . . . R ) R egion - { 1 . , M) G r id * G r id b e in g pro ce s s ed AC ■ A c re a g e T { B , K , L ) - A c re a g e o f Management S t r a t e g y B a t c o o r d i n a t e s K,L U ( B , R , J * ) - A c re a g e o f Management S t r a t e g y B on r e s o u r c e R 1n g r i d J * V ( B , R , J ) ■ A c re a g e o f Management S t r a t e g y B on resou rce R In g r id J Figure 2 - 9 . — Flow Chart o f the C o n strain t G enerator, Assuming a Small Grid C ell and Unspecified Resource Classes. 105 / - ---------------------N. f START 1 N ____ _ _ S / \ T B .K .L ) * 0 U fB .Q .J *) V ( B ,Q , 0 ) * READ R (l) S-1 ,P 2 / 1 TlB.IC.Lj+ACtB) S -1 .P R (H )j K ',l,B ,A C (B } 3 4 Q-1.N B-1 ,A R (Q )/A C (B )X T yt J - l ,M C oordin ates Management S t r a t e g y - ( I , . . . , A ) Region G rid G rid bein g processed q b Resource C l a s s . - ( 1 . . . . . N ) R(q) - Acreage o f re s o u rc e c la s s Q BtQtJ* V tB .Q .J) PRINT B .Q . J * ll(B ,Q ,J *) AC(B) - Acreage o f Management T ( B , K , L ) ■ Acreage o f Management c o o r d i n a t e s K,L U ( 8 , R , 0 * ) - Acreage o f Management re s o u rc e R I n g r i d J * V ( B , R , J ) - Acreage o f Management re s o u rc e R i n g r i d J J *-l,P S tra te g y B S tra te g y B a t S t r a t e g y B on S t r a t e g y B on. Figure 2 -1 0 .— Flow Chart o f the C o n strain t G enerator, Assuming More Than One Management S trateg y Can be Assigned to a Grid C e ll. 106 expensive w ith p lo t t e r ro u tin e s . The routines are 1) GRIDS (Murray e t . a l . , 1971), 2) SYMAP (Young, 19 72 ), and MIADS (Amldon, 1964). SYMAP can be used to map la rg e areas but Is not w ell su ited to g rid d ata. must be s p e c ifie d fo r each su b d ivisio n . d iv is io n . An o u tlin e Data 1s assigned to th e sub­ This would be a d i f f i c u l t process f o r a la rg e number o f g rid s . A maximum o f ten classes o f data can be mapped. The program p rin ts out a symbol fo r a p a r tic u la r class o f data 1n the g r id . combinations o f ch aracters which allo w shading. The symbols are A region 1s mapped en­ t i r e l y w ith the symbol o f the data value assigned to 1 t. GRIDS 1s a routine developed a t Harvard to s p e c if ic a lly handle data stored 1n a g rid network. The form at o f in p u t data can be s p e c ifie d by th e user allow ing the program to be adjusted to any type o f storage media and record f o r ­ mate. GRIDS could be e a s ily adapted to th e f i l e s tru c tu re discussed e a r lie r . grids. A maximum, o f ten classes o f data can be a llo c a te d to the map GRIDS uses symbols s im ila r to SYMAP. o f data classes to be mapped. I I can map many more. SYMAP and GRIDS do. MIADS allows a la rg e number MIADS I can map 98 classes, w h ile MIADS MIADS, however, does not shade 1n the way th a t An alphanumeric 1s assigned to each class o f d ata. The alphanumeric symbol 1s p rin te d on the map. MIADS can handle a la rg e number o f g rid s . Resource Data Maps showing classes o f d if f e r e n t resource c h a ra c te r is tic s , th a t 1s, the dimensions o f resource c la ss es , could be p rin te d . For each r e ­ source dimension, a map could be p rin te d showing classes o f the dimen­ sions. These maps draw on th e raw resource data f ie ld s o f the data f i l e . GRIDS appears to be a good choice since th e In p u t form at can be w r itte n to read th e proper data from the resource f i l e . I f resource data 1s 107 stored on tape or d is c , maps o f several resource dimensions could be printed in succession. However, a maximum o f ten classes o f each * dimension can be p rin te d . I f more classes are d e s ire d , MIADS would have to be used. The shading provided by GRIDS has a b e tte r visu al e f f e c t than MIADS. SYMAP 1s not w ell su ited to th is task since an o u tlin e would have to be described fo r each g rid c e l l . GRIDS 1s the favored a lte rn a tiv e when the number o f resource classes is less than o r equal to te n . MIADS 1s the only a lte r n a tiv e when the number o f classes 1s greater than te n . Maps o f resource classes could also be p rin te d . I f only one r e ­ source class 1s assigned to a c e l l , a l l classes could be put on one map. Only MIADS could do the job since th ere are more than ten r e ­ source classes. The In p u t problems o f MIADS are not a l l th a t serious since only one map is re q u ire d . could be produced. A p rin to u t o f resource classes by g rid Once the g rid 1s coded and the cards are punched, many maps could be p rin te d . I f conversions are to be considered, a map could be p rin te d fo r each land use c la s s , th a t 1s , a g r ic u ltu r e , f o r e s t , or pasture. MIADS 1s the only a lte r n a tiv e In v e s tig a te d th a t 1s capable of doing the desired ta s k . I f more than one resource class could be assigned to a g rid c e l l , some problems 1n mapping resource classes would occur. One map could not d is p la y resource classes unless th e g rid c e ll s iz e Is small enough to c la s s ify only one resource. Both the classes o f resources and the acreages would have to be mapped. This would be d i f f i c u l t . I t might be possible to set up an alg orith m to rank the resource classes and then p rin t a map fo r each rank. However, acreages would not be l is t e d . only MIADS could do th is jo b . Again, A ta b u la r p rin to u t o f th e acreage o f each resource class 1n a g rid c e ll might provide as adequate a d es crip tio n as a map. However, th e re would be no visual Impact. L is tin g s o f resource data and classes could be useful to guide exogenous management s tra te g y decisions as w ell as being useful 1n de­ termining c o n s tra in ts to be generated. Output Tables and maps can be p rin te d fo r the lo c a tio n and the m u ltip le land use assignment components. can be mapped. Each management s tra te g y , a = ( 1 , . . . , A ) , A map would be p rin te d f o r each management s tra te g y . symbol could be assigned to a range o f acreages. A For the m u ltip le land use assignment model, GRIDS and MIADS are the only v ia b le a lte r n a tiv e s . With less than ten management s tr a te g ie s , GRIDS is the favored a lte r n a ­ t iv e . GRIDS. MIADS can do the same jo b , but the visual e ff e c t is b e tte r w ith I f GRIDS is used, a special program could be used to put output on a tape th a t could be read by GRIDS. This would be d e s ira b le o n ly I f a larg e number o f maps were to be p rin te d . I f output from the production model is to be mapped, SYMAP becomes the favored a lte r n a tiv e . The output o f the lo c a tio n model would be mapped 1f the m u ltip le land use assignment model could not be developed as was the case o f the Kalamazoo R iver Basin. would be o u tlin e d . With SYMAP, each subdivision A se t o f symbols could be developed fo r the percent­ age o f fo re s t land 1n each general management s tra te g y which could then be mapped by re g io n . GRIDS and MIADS could be adapted to the same jo b , but SYMAP 1s p a r t ic u la r ly w e ll su ited to th is jo b . In summary, 1) th e GRIDS program 1s p a r t ic u la r ly w ell suited to mapping data from the resource data f i l e and output from the land use assignment model. 2 ) MIADS 1s w ell su ited to mapping resource classes 109 and output from the land use assignment model. to mapping re s u lts from th e production model. fo r the regions. 3 ) SYMAP 1s w ell su ited Tables could be p rin te d I t 1s not necessary to produce maps fo r th e regions 1 f re s u lts from the land use assignment model a re mapped. Figure 2-11 shows the output produced by components o f the system and the algorithm s used. Tabular output could be developed fo r Inform ation besides the lo ­ cation o f management s tr a te g ie s . The q u a n titie s o f products produced 1n each re g io n , the shipments o f products between re g io n s , and the excess o f products received over demands could a l l be presented 1nta b u la r form to In d ic a te the Impacts o f a lte r n a tiv e land use plans. Summary This chapter discusses the Issues to be considered by the MUMS system and the components o f the system. ents o f the system were discussed. and choices were made among them. were made. A lte rn a tiv e s fo r the compon­ These a lte rn a tiv e s were evaluated Recomnendations fo r th e Ideal model The recommendations fo r each component fo llo w . Land Evaluation System The recommended system 1s a regio nal lin e a r programming model w ith the tra n s p o rta tio n and environmental d iffu s io n components Incorporated into the production component. The s o lu tio n o f th e model 1s d ir e c t ly affected by In c lu d in g the tra n s p o rta tio n and environmental d iffu s io n Into the environmental d iffu s io n component. was e x p li c i t l y discussed. The s tru c tu re o f th is model A m u ltip le land use assignment model 1s lin k e d to a llo c a te management s tra te g ie s among c e lls In a g rid network when regions are subdivided In to a g rid network. SYMAP Location Model Tabular Output M ultiple Land Use Assignment Model OLL Tabular Output MIADS Figure 2-11.--Outputs from System Components. Resource Class F ile MIADS <— Resource Data File Start < m Forms o f re la tio n s h ip s to c a lc u la te product c o e ffic ie n ts and re ­ quirements are not being recommended 1n th is study. Land Inventory System The c la s s ific a t io n o f resources should be based on th e landtype concept. A g rid c e ll should be small enough to allo w c la s s ific a t io n o f only one resource class 1n th e c e l l . Geographic referen cin g should be based on the Universe Mercator (UTM) system. able and could e a s ily be used. Other systems are a v a il­ E x is tin g storage technology and storage media should be adapted to the data needs o f the problem. Recommendations fo r the s tru c tu re o f the record were made. Constraint Generator Flow charts o f recommended algorithm s were presented. The favored a lte rn a tiv e s a re based on the assumption th a t a g rid c e ll is small enough to allow only one resource c la s s . One flo w c h a rt assumes th a t the lo ca­ tio n o f resource classes is determined p r io r to determ ining the lo c a tio n o f the management s tra te g y . Another assumes th a t th e lo c a tio n o f resource classes are not determined p r io r to determ ining the lo c a tio n o f the management s tra te g y . Displays Mapping ro u tin es are als o recommended. able on the MSU system were discussed. resource data by g rid c e l l . Only p r in te r routines oper­ GRIDS is recommended fo r mapping MIADS is recommended f o r mapping resource classes and the output produced by the m u ltip le land use assignment model. SYMAP is recommended fo r any mapping based on regions o r the r iv e r b a s in ,th a t 1s , la rg e areas w ith ir r e g u la r boundaries. CHAPTER I I I MODEL TO BE TESTED AND DATA USED The purpose o f th is chapter is to discuss the model to be tested and data to be used in te s tin g the model. As p reviou sly s ta te d , the model is to have economic, e c o lo g lc , and spatial lin k a g e s . However, when d ealing w ith fo re s t resources tim e is also an im portant dimension. A number o f years o fte n pass between the ap p licatio n o f c u ltu r a l p ra c tic e s such as th in n in g , p la n tin g , or f e r t i l ­ iz a tio n , and the production o f merchantable tim b e r. an Investement process extending over many y e a rs . Growing tim ber 1s Time must be considered when planning fo re s t resources. The lin e a r programming form at w i l l be re ta in e d in th is study. Time w ill be incorporated through pseudo-dynamic lin e a r programming since 1t is well su ited to investment problems. With pseudo-dynamic lin e a r pro­ gramming, a l l costs Incurred over tim e by each a c t i v i t y are discounted to the present. A planning period 1s s p e c ifie d f o r the a n a ly s is . Prod­ ucts and c o n s tra in ts a t various points 1n time can be accounted fo r 1n d iffe re n t rows. o f an a ly s is . A s in g le tableau 1s constructed fo r the e n tir e period Time 1s an im p lic it v a ria b le because a l l costs are discounted to the present. The o b je c tiv e fu n c tio n w il l be to minim ize the present value o f the sum o f production costs (costs o f management s tr a te g ie s ) and tra n s ­ portation costs. Only fo r e s t land is being considered. 112 Four products 113 w ill be produced by the management s tra te g ie s : merchantable tim b e r, big game hunter days, small game hunter days, and erosion. Six tim e periods w ill be considered: 1966-1975, 1976-1985, 1986-1995, 1996-2005, 2006- 2015, and 2016-2025. The management s tra te g ie s produce q u a n titie s o f each product in each time period. averages f o r each tim e period. gions. C o e ffic ie n ts fo r each product are The r iv e r basin 1s divided In to fo u r re ­ There are also e ig h t regions outside o f the basin which can sup­ ply or demand products. and hunter days. The outside regions can supply or demand tim ber Production o f erosion can be constrained 1n the fo u r regions contained 1n the r i v e r basin. tween regions. Products can be transported be­ Transport routes have been defined between each o f the four regions in the r iv e r basin and from each o f those to each o f the eight outside regions. The management s tra te g y is a combination o f land p rac tice s on an acre o f land which generates a s e t o f outputs. The combination o f o u t­ puts, the tim ing o f outputs, and the costs are a ffe c te d by the land practices and the c h a ra c te ris tic s o f the land resource. source is d ivid ed in to classes. The fo re s t r e ­ Each resource class is defined by one sub-d1v is 1on o f each o f th e dimensions o f fo re s t ecosystem, s o il group, stand s iz e c la s s , and stand c o n d itio n . ecosystem dimension a re : c o n ife r, o a k -h ic k o ry , m aple-beech-blrch, elm- ash-cottomwood, and asp en -birch. and E. The subdivisions o f the fo re s t There are f i v e s o il groups: There are fo u r stand s iz e classes: poletim ber, and sawtimber. A ,B ,C ,D , non-stocked, seedl1ng-sapl1ng, There are two stand co n d itio n classes: 1) adequate co n dition fo r the p ra c tic e o f In te n s iv e management and 2 ) tim ber stand improvement needed to p ra c tic e In te n s iv e management. In te n s iv e management Involves Investment 1n fo re s t stands through the a p p lic a tio n 114 of c u ltu ra l p rac tice s to Increase wood y ie ld s and economic re tu rn s . For example, one resource class may co n sist o f the fo llo w in g classes o f each dimension; ecosystem: poletlmber; stand c o n d itio n : oak-h1ckory; s o il group: B; s ta n d -s lze c la s s : adequate. The a v a i l a b i l i t y o f data fo r the Kalamazoo R iver Basin 1s an im­ portant co n sideratio n . S oil associations are defined and mapped by the Soil Conservation S ervice. However, maps o f s o il se rie s do not e x is t fo r the e n tir e r iv e r basin. Acreages o f fo re s t ecosystems and stand size classes are estimated fo r fo u r regions 1n the r iv e r basin by the Forest Service using Forest Survey d a ta . a v a ila b le from fo re s t Inven tory d ata. Conditions o f stands are also Forest Survey data are c o lle c te d using areal samples and maps have not been produced. Remote sensing data have been obtained from th e Michigan S ta te U n iv e rs ity remote sensing p ro je c t. Forest land maps have been drawn. However, these data do not provide enough inform ation to a llo c a te management s tra te g ie s to lo c a tio n s . The classes o f fo re s t land Include: brush. deciduous, c o n ife ro u s , mixed, and This 1s not enough d e ta il fo r Forest Service management purposes. At the present tim e , the data base fo r fo re s t land 1n the Kalamazoo River Basin cannot support a land Info rm ation system based on grids smaller than a reg io n . formation. Other r iv e r basins may contain th is type o f in ­ In some National Forests 1n the Western U .S ., even stand s iz e classes are mapped. More p recise s p a tia l data w il l have to be c o lle c te d 1f mapping 1s to take place on the Kalamazoo R ive r Basin. Because o f th is s c a rc ity o f d a ta , 1t 1s not possible to estim ate the bias caused by fo rcin g regions to conform to p o lit ic a l boundaries. able e ith e r on a region or county basis. Data are a v a il­ 115 S tru ctu re o f the Model to be Tested Variables Some v a ria b le s are redefined from Chapter I I and new v a ria b le s are added. k = 1= tim ber k - 2= deer hunter k =3= small gamehunter days k =4 = days erosion Input V ariab les: h^t “ amount o f product k produced on land to be converted to urban use in region j and time period t . = cost o f producing product k on land to be converted to urban use in region j and tim e t . 1k j = supply o f good k a v a ila b le to meet requirements 1n region j when a l l production o f good k 1n the the r iv e r basin and the e ig h t outside regions is consumed. Nkj t = cost o f meeting requirements fo r good k In region j 1n time t when a l l production in the r iv e r basin and th e e ig h t outside regions 1s consumed. Output V a ria b le s : Hk j t = aniount product k produced on lands to be converted to urban use in region j 1n tim e t . = e x tra supplies o f product k brought in to meet requirements in region j and tim e t when a l l production 1n the r iv e r basin and e ig h t outside regions 1s consumed. Equations O bjective Function: 116 Minimize sum o f to ta l production c o s ts , tra n s p o rta tio n co sts, costs o f bringing products produced on fo re s t land to be converted to urban use In to the r i v e r basin system, and costs o f b ring ing in any extra supplies to meet f in a l demands. M1n a r j Kar^XarJ + Mk j t Hk j t + I j l k 1 j t Tk1^ t Xk1j t + I j t ^ Nk j t Lk j t C onstraints: A) Each product 1s summed across a l l management s tra te g ie s and resource classes in region 1 through 4 and can be shipped to any demand point where th ere 1s a demand fo r the product. Production o f products on any land to be converted to urban use are accumulated during each time period fo r each regio n. I I r a 5a k r j t Xa r j + Hk j t “ 1 Xk i j t =0 (31} fo r k = ( 1 , 2 , 3 ) , j = ( 1 , . . . , 4 ) , and a l l t . B) Erosion Is summed across a l l management s tra te g ie s and resource classes in region 1 through 4 . Production o f erosion on lands to be converted to urban use are accumulated during each time period f o r each region. I t * £ & , . + H, ,. - X, .. = 0 a k r jt a rj k jt k jt (32) ' ' f o r k - 1 , j = ( 1 , . . . , 4 ) , and a l l t Environmental d iffu s io n w il l not be considered 1n te s tin g the model. C) Projected demands a t various points in the r iv e r basin must be met. A special v a ria b le 1s included to guarantee th a t demands are met by providing e x tra supplies once a l l production o f a good 1n the riv e r basin and a l l outside regions is consumed. These supplies are provided a t a cost much higher than th e cost o f Im porting goods from the 117 outside regions. When such a v a ria b le enters the s o lu tio n 1 t shows th a t the r iv e r basin production 1s not meeting demands. j Xk1j t + j , Xk1j ' t + Lk j t - Xk1t fo r k = ( 1 , 2 , 3 ) , a l l 1 , and a l l t Products can be Imported to the r iv e r basin from outside the r iv e r basin to meet demands 1n the r iv e r basin. D) Demand points outside o f th e r iv e r basin w ith a negative ex­ cess supply fo r a product w il l have a cap acity to absorb excess produc­ tion in the r iv e r basin. They cannot buy I n f i n i t e amounts, however. Their demands do not have to be s a tis fie d by r iv e r basin production. | Xk1j t — Xk1 11 <14) f o r k - ( 1 , 2 , 3 ) , a l l 1* w ith a negative excess supply, and over a ll t E) There 1s also a l i m i t on th e amount o f goods th a t regions o u t­ side o f the r iv e r basin can export to meet r iv e r basin demands. These regions w il l have p o s itiv e excess supplies f o r a given product. ^ Xk i j ' t - Xk J *t (15) fo r k = ( 1 , 2 . 3 ) , a l l j ' w ith a p o s itiv e excess supply, and a l l t F) Requirements f o r the production o f tim ber in the r iv e r basin regions w il l be made 1n some runs o f the model. be OBERS demands. These requirements w i l l These requirements a re not assigned to a s p e c ific demand p o in t. J Xk1j t - Xk j t fo r k - 1 , j => ( 1 , . . . , 4 ) , and t = ( 1 ,3 ,6 ) 118 G) There a re resource lim ita tio n s to production on each resource class 1n each regio n. I Xa r j < Xr j (3 4 ) a fo r a l l r and j H) The fo llo w in g equation s e t req u ires th a t a l l goods produced on fo re s t lands which w il l be converted to urban use o r on fo re s t lands which are managed In te n s iv e ly a t the present be brought in to th e system to s a tis fy requirements. Hk j t = hk j t (35) f o r a l l k, j = ( l a. . . , 4 ) , and a l l t I ) The amounts o f products th a t can be purchased to meet re q u ire ­ ments 1n the r iv e r basin 1f production cannot meet these products 1s lim ite d in the fo llo w in g equation. | Lk j t — 1kj (36) f o r k - ( 1 , 2 , 3 ) , and j = ( 1 , . . . , 4 ) J ) Costs o f tra n s fe r rin g products from supply areas to meet de­ mands are summed a t demand p o in ts . ? I Tk i j t Xk i j t “ c 1t = 0 (18 ) f o r a l l 1 and t C.jt has an o b je c tiv e fu n c tio n value o f 0 . K) Costs o f tra n s fe r rin g products to demand points are summed a t each supply p o in t. * I Tk i j t Xk i j t “ Cj t = 0 fo r a l l j and t Cjt has an o b je c tiv e fu n c tio n value o f 0 . (19 ) 119 L) Other co n strain ts on land use by lo c a tio n can be put 1n the model by using th is general form: Xarj ± Zarj (20> Greater than o r equal to c o n s tra in ts or equal to co n stra in ts could also be In s erted . A ll a c t iv it ie s are su b ject to n o n -n e g a tiv ity c o n stra in ts since no a c t iv it y can have a negative value. C a lc u la tin g Requirements fo r Roundwood Pulpwood There appear to be two demand points fo r pulpwood produced 1n the Kalamazoo R iver Basin: 1) The Warren Company 1n Muskegon, M ichigan, and 2) The Menasha Corporation in Otsego, Michigan. 1s 1n region 2 o f the Kalamazoo R iver Basin. The Menasha Corporation The y e a rly consumption o f pulpwood by each p la n t 1s not published or made a v a ila b le by the p la n ts . However, Lockwood's D ire c to ry o f the Paper and A llie d Trades has published an average d a ily consumption o f pulpwood fo r some plants 1n Michigan. The fig u re s published f o r the Warren Company are 430 cords per day and fo r the Menasha Corporation are 150 cords per day (Lockwood's D ire c to ry o f the Paper and A llie d Trades, 1970). These d a lly consumption fig u re s are not published fo r a l l plants in Michigan, but they are published fo r a l l plants 1n th e Lower Peninsula of Michigan. Pulpwood production 1n the Lower Peninsula was a llo c a te d among p u lp m llls in the Lower Peninsula. The decision to do th is based on two assumptions; 1) The proportion o f to ta l Lower Peninsula production purchased by each p la n t each y e a r 1s co n stant, and 2) The Lower Peninsula 1s s e lf - s u f f ic ie n t 1n pulpwood production, th a t 1s , th ere are no Imports 120 or exports. fig u re s . The second assumption 1s supported by U.S. Forest Service Host exports have gone to Wisconsin and most Imports have come from Canada 1n the past 24 years (B ly th e , B o e lte r, and Danielson, 1975). I t 1s being assumed th a t most o f the exports and Imports are occurring in the Upper Peninsula. A ls o , l i t t l e pulpwood 1s hauled between th e Upper and Lower Peninsulas due to t o l l s on the Mackinac Bridge (Leushner, 1972). The average d a lly pulpwood purchase fig u re s fo r each p la n t 1n the Lower Peninsula were found 1n Lockwood's d ire c to ry and summed to 1730 cords per day (Lockwood's D ire c to ry o f Paper and the A llie d Trades, 1970). A ra tio was ca lcu la ted fo r each p la n t by d iv id in g I t s d a lly consumption by 1730. The fra c tio n o f to ta l Lower Peninsula pulpwood consumption 1s 0.249 f o r the Warren Company and 0.087 fo r the Menasha C orporation. The ye arly production o f pulpwood 1n the Lower Peninsula was obtained from Michigan Pulpwood Production p rin te d each year by the Michigan Department o f Natural Resources (DNR). A tim e se rie s o f purchases by the two plants was generated by m u ltip ly in g annual pulpwood production 1n the Lower Peninsula by the fr a c tio n o f to ta l Lower Peninsula pulpwood production fo r each p la n t. requirements. period. A seven y e a r average was c a lc u la te d to estim ate present Each o f these seven years 1s Included 1n the f i r s t tim e The estim ates were converted from cords to cubic f e e t. Table 3-1 presents the seven-year time s e rie s and the average f o r the Lower Peninsula, the Warren Company, and the Menasha Corporation. Sawlogs and Veneer Logs Requirements f o r roundwood f o r the fo u r regions 1n the r i v e r basin were based on 1972 consumption le v e ls . 1972 estim ates were chosen ra th e r Table 3 - 1 . — Estimated Pulpwood Consumption by the Menasha Corporation and the Warren Company 1n Time Period 1. Year Lower Peninsula (C cf) 1966 1967 1969 1970 1971 1972 1973 519,771 400,303 461,334 488,493 476,703 499,502 506,915 seven ye ar average Source: Warren Co. (C cf) Menasha Corp. (C c f) 129,423 99,676 114,872 121,635 118,699 124,376 126,222 45,220 34,826 40,136 42,499 41,473 43,457 44,102 119,271 41,673 F orestry D iv is io n , Michigan DNR, Michigan Pulpwood Production. than averages to e lim in a te the e ffe c ts o f new plants en tering business and other plants going out o f business. I t seems th a t the most recent consumption ra te s would be the best in d ic a to r o f requirements since few plants are l i k e l y to leave o r e n te r in a sh o rt period o f tim e. Figures to c a lc u la te consumption in 1972 have been recorded by the U.S. Forest Service. Production o f lumber o r purchases o f sawlogs were not recorded at the county or region le v e l. However, re s id u a ls produced were recorded in Table 27 o f Primary Forest Products Ind ustry and Timber Use, M ichigan, 1972 (B ly th , B o e lte r, and Danielson, 1975). A constant was c a lc u la te d to estim ate roundwood purchased from re s id u a ls produced. Total Michigan receip ts o f hardwood and softwood roundwood are found in Table 4 o f the same re p o rt. Total wood and bark residues produced 1n M ichigan, exclud­ ing residues from pulpwood, came from Table 27. Roundwood re c e ip ts , ex­ cluding pulpwood, were d ivided by to ta l wood and bark resid u es, exclud­ ing pulpwood residues. fo r softwoods. residues. The constants a re 1.65 f o r hardwoods and 2 .1 0 The u n its are cubic f e e t o f purchases per cubic fe e t o f These constants were asumed to hold f o r a l l acreas o f the s ta te , 122 a ll processes, and a l l species. Roundwood purchases f o r each county, excluding pulpwood, were c a lc u la te d by m u ltip ly in g hardwood and softwood residues produced in each county by th e ap p ro p riate constant. County production data are found 1n Appendix B. The fig u re s fo r each region were then c a lc u la te d from the county fig u re s . This was done by estim atin g the lumber producing c a p a c itie s of each reg io n . The F orestry D iv is io n o f the Michigan DNR In v en to rie s m ills by county and l i s t s t h e i r m a ilin g addresses (F o restry D iv is io n , Michigan DNR, 1974). The m ailin g addresses were used 1n conjunction with county maps to place the m ills In to regions. Sawmills are c la s s fle d into s iz e classes in terms o f annual lumber production (thousand board fe e t). Other primary wood-using p lan ts a re not c la s s ifie d th is way. The high production fig u re o f the range f o r each p la n t was used to sum the maximum lumber production fo r each county. The same was done fo r each portion o f th e county a llo c a te d to each re g io n . A fr a c tio n o f lumber production a llo c a te d to each region from each county was c a lc u la te d by d iv id in g the lumber production a llo c a te d to each region from the county by the to ta l county production. C. These fra c tio n s are recorded in Appendix Roundwood purchases were a llo c a te d to regions by m u ltip ly in g t o ta l county roundwood purchases by the fr a c tio n o f county lumber production occurring in each region. This assumes th a t roundwood purchases are d i ­ re c tly re la te d to lumber production. Purchases o f roundwood a llo c a te d to each region were summed by region to estim ate regional roundwood pur­ chases. Weaknesses o f th is method in c lu d e: 1) The ranges o f lumber pro­ duction in a given class are wide which means the estim ates o f lumber production a llo c a te d to a given region a re not very p re c is e , and 2 ) Round­ wood using p lan ts o th e r than sawmills do not have s ize classes so they 123 are not Included in the c a lc u la tio n s o f the fra c tio n s thereby causing biased estim ates. Requirements fo r sawlogs and veneer logs 1n regions outside o f the r iv e r basin were c a lc u la te d by averaging estim ated purchases 1n 1972, 1969, and 1965. The average was chosen because these demands were to be used 1n c a lc u la tin g the d iffe re n c e between production o f roundwood and purchases by m ills 1n the re g io n , th a t i s , an excess supply o f round­ wood by re g io n . I t was f e l t th a t lo c a l production would respond to lo c al demand, so th a t the e ffe c ts o f plants leaving and en terin g business would not hurt the estim ates o f excess supply. The 1972 fig u re s were c a lc u la t­ ed using the same method as th a t used fo r fig u re s f o r regions in the r iv e r basin. The fig u re s on re s id u a ls were not a v a ila b le fo r 1965 and 1969. However, 1n 1965 and 1969, the Michigan DNR c o lle c te d fig u re s on lumber production by county 1n thousand board f e e t (F o restry D iv is io n , Michigan DNR, 1969, and F orestry D iv is io n , Michigan DNR, 1965). This was con­ verted to an estim ate o f hundred cubic f e e t o f roundwood purchased by m u ltip lyin g lumber production by 1 .6 6 7 . Appendix B. These county estim ates a re in These county estim ates were aggregated In to regions in the same way 1n which the 1972 fig u re s were. The 1965 and 1969 estim ates are biased 1n th a t they leave out veneer production. The estim ates o f consumption 1n 1965, 1969, and 1972 were averaged to estim ate present requirements and veneer lo g s . Table 3 -2 contains requirements f o r saw­ logs and veneer logs by region fo r tim e period 1 . Projecting Roundwood Requirements In to the Future Making fu tu re p ro je c tio n s is always a d i f f i c u l t ta s k . Assumptions must be made. In th is study, several a lte r n a tiv e sets o f assumptions w ill be made. Future p ro je ctio n s are based on p ro je ctio n s made in the 124 Table 3 - 2 .--Requirem ents fo r Sawlogs and Veneer Logs by Region 1n Time Period 1. Region 1 2 3 4 5 6 7 8 9 10 11 12 Q uantity (Mcf) 872 828 201 227 913 1455 3198 542 1125 859 2103 671 Outlook f o r Timber in the United States (F orest S e rv ic e , USDA, 1973). The Forest Service p ro je ctio n s were based on assumptions concerning how r e la tiv e p rices behave in the fu tu re . The Forest Service assumed th ree levels o f population growth and growth o f economic a c t i v i t y w ith th ree sets o f p ric e assumptions fo r each. A ll p ro je c tio n s 1n th is study w i l l be based on medium le v e l p ro je c tio n s o f population growth and economic a c tiv ity .^ The two sets o f p ric e assumptions to be used 1n th is study are 1970 r e la t iv e prices and r is in g r e la t iv e wood p ric e s . makes p ro je ctio n s only fo r 1980, 1990, and 2000. The study The la s t two tim e The medium le v e l assumes th a t population 1n the U.S. ris e s to 281 m illio n in the year 2000. GNP ris e s a t a r a te o f 4.0% per y e a r. Labor p ro d u c tiv ity Increases a t a r a te o f 3.4% per y e a r. Technological changes th a t appear l i k e l y in the various tim ber using sectors have been accounted f o r . 2W1th r is in g r e la t iv e p ric e s , th e p rices o f wood products increase fa s te r than the 1970 r a t e . Lumber Increases a t a ra te o f 1.5% per y e a r fa s te r than 1970 p ric e s ; plywood, miscellaneous products, and fuelwood Increase a t a ra te o f 1% per y e a r , and paper and board increase a t a ra te o f 0.5% per y e a r. 125 periods must also be accounted f o r . I t 1s assumed th a t th e ra te s o f population and economic growth w i l l continue through tim e periods 5 and 6 . The le v e ls o f demand fo r sawlogs, veneer lo g s , and pulpwood were calcu lated . F ir s t , r e la t iv e le v e ls o f demand were ca lcu la ted by d iv id ­ ing projected q u a n titie s demanded fo r 1980, 1990, and 2000 by the quan­ t i t i e s demanded 1n 1970. 2020. These trends were then projected to 2010 and Not a l l the p ro je ctio n s by the Forest Service are s tr a ig h t lin e projections from 1970 to 2000. To account f o r the c u r v ilin e a r nature o f the tre n d s, the f i r s t order ra te o f change o f demand per ye ar was calculated from 1970 to 1980, 1980 to 1990, and 1990 to 2000 A tim e ). (a demand/ A s tr a ig h t l in e was then f i t t e d to these points using le a s t squares regression. The ra te o f change fo r each tim e period was then estimated from th e trend l in e . This f i r s t d e r iv a tiv e trend lin e was then in te g rate d to estim ate the r e la t iv e le v e ls o f demand fo r each time period. These r e la t iv e le v e ls were then m u ltip lie d by the 1970 le v e ls o f consumption o f each commodity 1n each region to get estimated absolute levels o f consumption. same as th e n a tio n . into account. Under these assumptions, each region behaves th e Regional advantages and disadvantages are not taken Appendix D shows the r e la t iv e le v e ls o f demand and Appendix E shows the absolute le v e ls o f demand f o r each product. Require­ ments f o r each product 1n each region were then summed to g et to ta l round­ wood requirem ents. Appendix F shows these requirem ents. ments are in cubic f e e t per y e a r. The re q u ire ­ I t is assumed th a t these are average figu res fo r each te n -y e a r tim e p erio d. 126 Roundwood Production Outside o f th e R iver Basin A v a ila b le fo r Use 1n the R ive r Basin Pulpwood County fig u re s on pulpwood production were obtained from annual data put out by the Michigan DNR (F o restry D iv is io n , Michigan DNR). Some years are skipped, however. Only oak, b irc h , aspen, and o ther hardwoods were summed since these are species used by the Menasha Corp­ o ratio n , the only p u lp m lll 1n th e r iv e r basin. The harvest o f these species was sunmed to g et county production o f pulpwood. Data on pulp­ wood production was obtained from 1966 to 1973. County production was a llo c a te d to re g io n s . I t was assumed th a t the timber resource 1s d is trib u te d uniform ly over the co u n ties. centage o f a county in a region was found. The per­ For the most p a r t, regions outside o f the r iv e r basin fo llo w county lin e s . However, some counties are divided in to areas In s id e and outside o f the r iv e r basin . The pro­ portion o f each county \ s acreage in the r iv e r basin was obtained from the Soil Conservation S e rvic e. This acreage was subtracted from to ta l county acreage to o btain the acreage o f the county outside o f the r iv e r basin (Michigan S ta te U n iv e rs ity , Cooperative Extension S e rv ic e , 1973). The acreage o f a county 1n a p a r tic u la r region was divided by to ta l county acreage to g et th e p ortio n o f the county in the re g io n . proportions are 1n Appendix G. These County pulpwood production was m u ltip lie d by th is r a t io to estim ate pulpwood production o f th a t p o rtio n o f the county In a p a r tic u la r re g io n . Estimates o f county pulpwood production a llo c a te d to regions were summed over the region to c a lc u la te the regional pulpwood production. 127 These estim ates were made f o r each region f o r each y e a r. A seven year average f o r those years 1n time period 1 was computed fo r each r e ­ gion. Table 3-3 contains the estim ates o f pulpwood production fo r each region outside o f the r iv e r basin in tim e period 1 . Table 3 - 3 . — Estimates o f Pulpwood Production Region Average pulpwood production (C cf) 5 6 7 8 9 10 11 Source: in Outside Regions. 2461 210 295 117 181 0 50,195 F orestry D iv is io n , Michigan DNR, Michigan Pulpwood Production. Sawlogs Sawlog production 1s not recorded a n n u a lly . The years 1972, 1969, and 1965 were chosen because these were years 1n which purchases of sawlogs by m ills 1n a county could be estim ated. The 1972 data by county were found 1n Table 15 o f Primary Forest Products Ind ustry and Timber Use, M ichigan, 1972 (B ly th e , B o e lte r, and Danielson, 1975). The 1969 data were found 1n Michigan Commercial Sawlog, Veneer Log, and Lumber Production, 1965 (F o re s try D iv is io n , Michigan DNR, 1969). The 1965 data were found 1n Michigan Sawlog and Lumber Production, 1965 (F o restry D iv is io n , Michigan DNR, 1965). These fig u re s were tab u lated f o r each county o f in te r e s t and each y e a r. The co u nties' sawlog production was a llo c ate d to regions by the same method used to a llo c a te pulpwood pro­ duction to regio ns. An average o f the th re e years was c a lc u la te d fo r each region to be used as an estim ate o f sawlog production. Table 3-4 128 contains the sawlog production by reg io n . Table 3 - 4 . — Estimated Sawlog Production in Outside Regions. Sources: Region Production (Mcf) 5 6 7 8 9 10 11 12 726 1051 2400 799 1105 1291 2822 1534 B ly th , B o e lte r, and Danielson, Primary Forest Products Ind ustry and Timber Use, 1972, F orestry D iv is io n , Michigan DNR, Michigan £onwercia1 Sawlog, Veneer Log, and Lumber Production, 1965, and F o restry D iv is io n , Michigan DNR, Michigan Sawlog and Lumber Production, 1965. Veneer Logs Data on veneer log production by county 1s a v a ila b le only f o r 1972 and 1969. The data fo r 1972 were obtained from Table 21 o f Primary Forest Products Ind ustry and Timber Use, Michigan, 1972 (B ly th , B o e lte r, and Danielson, 1975). The 1969 data were obtained from Michigan Commercial Sawlog, Veneer Log and Lumber Production (F o re s try D iv is io n , Michigan DNR, 1969). These data were tab u lated by county and a llo c a te d to regions 1n the same way as sawlogs and pulpwood. production. Appendix I contains veneer log U nits were converted from board f e e t to cubic f e e t . An average o f the production f o r two years was c a lc u la te d fo r each region and used to estim ate the veneer log production fo r the present. 3-5 contains the estim ates o f yeneer log production. Table 129 Table 3 - 5 .— Estimated Veneer Log Production in Outside Regions. Region Veneer Log Production (Mcf) 5 6 7 8 9 10 11 12 Source: 15 18 67 86 24 32 45 12 B lyth e, B o e lte r, and Danielson, Primary Forest Products Industry and Timber Use, 1972, and F o restry D iv is io n , Michigan DNR, Michigan Conriercial Sawlog, Veneer Log, and Lumber Production. Excess Supply Estimated requirements fo r roundwood purchased by m ills 1n regions outside o f the r iv e r basin were subtracted from the estim ated production of roundwood to c a lc u la te an excess supply o f roundwood a v a ila b le fo r use in the r iv e r basin. When excess supply 1s n e g a tiv e , the region can accept roundwood produced in the basin . When excess supply is p o s itiv e , the region makes roundwood a v a ila b le to the r i v e r basin. Sawlogs and veneer logs were suimed since requirements fo r the two could not be sep­ arated. For pulpwood, a l l th e excess supplies are in terms o f roundwood a v a ila b le to the Menasha Corporation. Excess supplies fo r a l l regions outside o f the r iv e r basin f o r d iffe r e n t p ric e assumptions are found 1n Appendix J. C a lc u la tin g Requirements fo r Hunterdays Deer Requirements fo r hunter days by region were c a lc u la te d by using the fo llo w in g form ula: 130 regional population hunters - hunter days = hunter days fo r th e region person hunter I t 1s assumed th a t hunter days per hunter equals fo u r (Jordan and Baker, 1973). The number o f hunters per person was c a lc u la te d by fin d in g the average number o f hunters from 1963 to 1972 In a Michigan DNR zone and d ivid in g th is average by the population o f the zone (R y e !, 1974). A ll Michigan DNR zones fo llo w county lin e s so th a t population fig u re s based on the 1970 census are r e a d ily a v a ila b le (Michigan S tate U n iv e rs ity , Cooperative Extension S e rvic e, 1973). I t 1s assumed th a t hunters in these regions are lo c a l, th a t 1s, they l iv e in the reg io n . Any long distance t r a v e llin g 1s assumed to be going to the northern h a lf o f the Lower Peninsula. Table 3-6 contains th e number o f hunters per person and hunter days per person f o r each o f the Michigan DNR zones th a t a f f e c t the r iv e r basin a rea . Table 3 - 6 . — Hunters per Person, Hunterdays per Hunter, and Hunterdays per Person f o r Each DNR Zone. Zone Hunters/Person 13 14 17 18 .028 .035 .031 .039 Source: Hunterdays/Hunter 4 4 4 4 Hunterdays/Person .112 .140 .124 .156 R ye!, The 1973 Deer Seasons. The population o f regions In s id e the r iv e r basin were c a lc u la te d by the Economic Research S ervice. Table 1-2 on page 10 1n Chapter I . These fig u re s a re Illu s t r a t e d in Figures f o r population 1n regions outside o f the r i v e r basin were c a lc u la te d and are Illu s t r a t e d 1n Table 1-5 on page 12 1n Chapter I . The requirements fo r hunterdays were ob- 131 talned by m u ltip ly in g population times hunter days per person fo r each portion o f each county In each reg io n . These requirements were then summed to o btain requirements fo r regions. Appendix K contains th e re ­ quirements fo r hunterdays by county and region. Table 3-7 gives the requirements fo r deer hunterdays by region In tim e period 1. These re ­ quirements are an average f o r each ye ar 1n the ten year p erio d . Table 3 - 7 .— Requirements fo r Deer Hunterdays in Each Region 1n Time Period 1. Region Hunterdays 1 2 3 4 5 6 7 8 9 10 19,958 36,537 11,634 11,524 25,842 46,037 23,418 25,832 22,587 52,771 Small Game The same formula fo r c a lc u la tin g deer hunterdays was used to c a lc u la te small game hunterdays. c o tto n ta ils . Small game includes s q u irre ls and The number o f hunters per person was c a lc u la te d by aver­ aging the number o f hunters fo r c o tto n ta ils and s q u irre ls from 1963 to 1973 in DNR Region I I I and d iv id in g by the population o f DNR Region I I I (Hawn, 1974). The number o f hunterdays per hunter was recorded by the Michigan DNR fo r th e s ta te (Hawn, 19 74 ). I t is assumed th a t these figu res would hold f o r hunters 1n Michigan DNR Region I I I . Hunters per person was m u ltip lie d by hunterdays per hunter to get hunterdays per person as shown 1n the fo llo w in g form ula: hunters per person hunterdays „ hunterdays per person hunter Table 3-8 shows these fig u re s . Table 3 - 8 .— Hunters per Person, Hunterdays per Hunter, and Hunterdays per Person by Species. Species hunters/person Squirrel C o tton tail 0.021 0.030 hunterdays/hunter hunterdays/person 6 .8 10.1 0.143 0.303 Hawn, Michigan Small Game K ill Estim ates, 1973. Source: Requirements fo r s q u irre l and c o tto n ta il hunterdays were calcu­ lated in th e same way as deer hunter days. fo r each region as stated p re v io u s ly . Population was c a lcu la ted Requirements fo r hunterdays fo r both species were found fo r each p a rt o f each county 1n each region by m u ltip lyin g population times hunterdays per person. The requirements were then summed by region to get requirements by re g io n . Table 3-9 con­ tains the requirements fo r hunterdays by regio n. P rojecting Future Requirements fo r Hunterdays Requirements fo r hunterdays must be pro jected fo r fu tu re tim e periods. Hunterdays per person and hunterdays per hunter were assumed to remain constant over a l l tim e periods. Requirements f o r hunterdays, then, Increase a t the same r a te as p o p ulatio n. The Economic Research Service pro jected population f o r the riv e r, basin. I t 1s assumed th a t the population o f the regions Increases a t th e same r a te . p rojections were made f o r 1990 and 2020. Population Population was assumed to in - Table 3 - 9 . — Requirements f o r Small Game Hunterdays by Region 1n Time Period 1. Region Small Game Hunterdays 1 2 3 4 5 6 7 8 9 10 70,735 104,227 33,186 39,439 102,678 182,915 77,209 73,685 72,278 174,393 crease lin e a r ly between the present and 1990 and between 1990 and 2020. M u ltip lie rs were c a lc u la te d fo r each time p erio d. The hunterdays re ­ quired fo r each region 1n time period 1 were m u ltip lie d by the m u lt ip lie r in each tim e period to get the requirements fo r th a t time period. Appen­ dix L Includes the requirements fo r deer and small game hunterdays f o r each region and tim e p erio d. Table 3-10 contains the m u ltip lie r s fo r each time period. Table 3 -1 0 .— Population M u ltip lie r s fo r Each Time Period. Source: Time Period M u lt ip lie r 1 2 3 4 5 6 1.00 1.10 1.20 1.27 1.34 1.41 Economic Research S e rv ic e , Unpublished Data, 1974. 134 Supplies o f Hunterdays in Regions Outside o f th e R iver Basfn The supplies o f hunterdays were estim ated fo r c o tto n ta ils , s q u ir­ re ls , and deer by using the fo llo w in g form ula: reqional game k i l l „ hunter .. hunterdays _ hunterdays x k 'lll x hunter " Deer The average buck k i l l per square m ile fig u re s fo r 1963 to 1972 for Michigan DNR Region I I I zones 13, 14, 17, and 18 were taken from Michigan DNR fig u re s (R ye!* 1974). There were 0 .5 bucks k ille d per square mile f o r zones 14, 17, and 18 and 0 .7 bucks k ille d per square m ile fo r zone 13. These fig u re s were assumed to be v a lid fo r estim atin g deer k i l l s fo r each region outside o f the r iv e r basin. counties. tie s . The DNR zones are groups o f The k i l l per square m ile fig u re s were not a v a ila b le fo r coun­ Deer h a b ita t 1s assumed to be homogeneously d is trib u te d over the DNR zones. per acre. These k i l l fig u re s per square m ile were converted to k i l l s For does, the k i l l from 1968to 1973 fo r Michigan I I I was averaged and d ivid ed by acreage per acre. DNR region o f Region I I I to g e t the doe k i l l The doe k i l l estim ates are probably less r e lia b le than th e buck k i l l fig u re s fo r two reasons: 1) The doe fig u re s are c a lc u la te d fo r a la rg e r area than the buck fig u re s , and 2) The doe season 1s h ig h ly con­ tro v e rs ia l and 1 t 1s d i f f i c u l t to know how many doe permits w il l be Issued in any given y e a r. Table 3-11 illu s t r a t e s the k i l l per acre fo r bucks and does. These k i l l per acre fig u re s were m u ltip lie d by th e acreage o f a county 1n a region to estim ate the k i l l s 1n th a t p ortio n o f the county 1n the re g io n . The ap p ro p ria te zone was chosen f o r each county. dix M contains th e k i l l per county 1n each reg io n . Appen­ 135 Table 3 -1 1 .— Deer K ills per Acre. Sex and Region K ill per Acre Does in 1 3 ,1 4 ,1 7 ,1 8 Bucks 1n 1 4 ,1 7 ,1 8 Bucks in 13 Source: 0.000234 0.000781 0.001093 R ye!, The 1973 Deer Seasons. The number o f hunters per k i l l was the re cip ro ca l o f th e average k i l l per hunter. The average k i l l per hunter was found by averaging the success ra tes o f deer hunters from 1968 to 1973 1n Michigan DNR Re­ gion I I I . The number o f hunters per k i l l 1s 9.34 (1 /0 .1 0 7 ) (R y e !, 1974). I t is assumed th a t hunters are s a tis fie d w ith th is ra te o f success and w ill continue to hunt. The number o f hunterdays per hunter 1s assumed to be fo u r (Jordan and Baker, 1973). is 4 /0 .1 0 7 o r 3 7 .4 . The number o f hunterdays per k i l l The number o f hunterdays supplied by each county 1n each region was computed using the fo llo w in g formula: hunterdays _ k i l l county “ county „ . These county fig u re s were then summed by region to estim ate the supply of hunter days by region outside o f the r iv e r basin. the hunterdays supplied by each county in each basin. Appendix N shows Table 3-12 shows the supply o f hunterdays in regions outside o f the r i v e r basin. Small Game Small game k i l l s by each county in each region were c a lc u la te d . The k i l l s fo r c o tto n ta ils and s q u irre ls from 1969 to 1973 1n Michigan DNR Region I I I were averaged (Hawn, 1974). The average k i l l was divided by th e acreage o f Michigan DNR Region I I I to estim ate k i l l per ac re . 136 Table 3-12.--S u p p l1es o f Hunterdays 1n Regions Outside o f the R iver Basin. Region Supply o f Deer Hunterdays 5 6 7 8 9 10 30,257 25,095 51,732 25,282 48,845 26,430 Table 3-13 shows these estim ates. Table 3 -1 3 .— Small Game K ills per Acre in DNR Region I I I . Source: Species K ill per Acre C o tto n ta il S q u irre l 0.068 0.043 Hawn, Michigan Small Game K111 Estim ates, 1973. The k i l l per acre was m u ltip lie d by the acreage o f the region to get k i l l per reg io n . 1s assumed. An even d is tr ib u tio n o f game h a b ita t 1n DNR Region I I I Appendix N contains the game k i l l s fo r each re g io n . The number o f hunters per k i l l was th e re c ip ro c a l o f k i l l per hunter. The number o f hunterdays per hunter was also found fo r each species (Hawn, 1974). Both o f these fig u re s were found f o r 1973 and were assumed to be re p re s e n ta tiv e fo r p ro je c tio n purposes. The number o f hunterdays per k i l l was estim ated by m u ltip ly in g hunters per k i l l by hunterdays per hunter. Table 3-14 contains hunters per k i l l , hunterdays per hunter, and hunterdays per k i l l fo r each species. 137 Table 3 -1 4 .--E stim ates o f Hunters per K i l l , Hunterdays per Hunter, and Hunterdays per K ill fo r Each Small Game Species. Species H u n te rs /K ill 1 /5 .6 1 /4 .4 C ottontail Squirrel Source: Hunterdays/Hunter 10.1 6.82 Hunterdays/K1ll 1.8 1.55 Hawn, Michigan Small Game K ill Estimates. The number o f hunterdays supplied by each region was computed by m ultiplying k i l l per region by hunterdays per k i l l to get hunterdays per region. Table 3-15 shows estimates o f hunterdays supplied by each region outside o f the region. Table 3-15. — Estimates o f Small Game Hunterdays Supplied by Regions Outside o f the River Basin. Region 5 6 7 8 9 10 S quirrel Hunterdays 40,714 37,025 83,295 44,403 85,819 47,261 C o tto n tail Hunterdays 74,771 67,995 152,970 81,543 157,600 86,793 Total 115,485 105,020 236,265 125,946 243,419 134,054 Excess Supplies o f Hunterdays Excess supplies were calcu lated fo r hunterdays to estim ate the amount th a t might be a v a ila b le to the r iv e r basin from regions outside of the r iv e r basin. Excess supply was calcu lated fo r big and small game hunterdays fo r each time period by subtracting each reg io n 's re ­ quirements from i t s supply 1n each time period. Small game hunterday requirements were calcu lated by summing the requirements fo r sq u irre l 138 and c o tto n ta il hunterday requirem ents. The supply o f hunterdays was assumed constant fo r each tim e period. Requirements f o r small game hunterdays were projected by using the population m u ltip lie rs th a t were used to p ro je c t big game hunterdays. fo r each time period and region. Appendix L contains th e requirements When excess supply 1s n e g a tiv e , the region can consume surpluses o f hunterdays produced by th e r iv e r basin. When excess supply is p o s itiv e , the q u a n tity 1s a v a ila b le to th e r iv e r basin. Appendix 0 contains the excess supplies o f big and small game hunterdays a v a ila b le in each regio n. D efin ing Regions Regions have been defined to account fo r s p a tia l d if f e r e n t ia t io n o f the economy and o f land resources. outlin es the regio ns. Figure 1-1 on page 7 1n Chapter I Regions 1 through 4 are Id e n tic a l to regions de­ fined by the Economic Research Service and make up th e r i v e r basin. gions 5 through 12 a re outside o f the r iv e r basin . Re­ These regions can supply goods to the r i v e r basin and can purchase goods produced 1n the riv e r basin. An attem pt was made to approximate a square when d e fin in g a region w h ile fo llo w in g county lin e s and r i v e r basin boundaries. r iv e r basin was surrounded w ith regio ns. The These regions include what appear to be Im portant supply and demand areas fo r goods produced 1n the region. Regions 5 through 10 can supply and demand tim b e r, deer hunter days, and small game hunter days. Regions 11 and 12 were defined s p e c ific a lly to supply roundwood to the Menasha C orporation. regions supply only tim b er. The Menasha Corporation purchases la rg e quan­ t i t i e s o f tim ber 1n region 11. Region 12 was added because 1 t was almost surrounded by regions 6 , 7 , and 11, defined 1n these regions. These two Representative demand points were In regions 1 through 4 , demand points were de- 139 fined near the c e n te r o f the region close to the ju n c tio n o f two major highways. The regions and th e re p re s e n ta tiv e demand points are lis t e d 1n Table 3-1 6 . Table 3 -1 6 .— Representative Demand Points 1n the R iver Basin. Region Demand Point Junction 1 2 3 4 Marshall P lain w ell Paw Paw Holland 169,194 US131,M89 M 40.I94 US31,M43 The Ir r e g u la r shape o f region 4 presents problems. Most o f the population and demanders o f wood products are s itu a te d near Holland a t the north end o f the reg io n . However, when goods are supplied to r e ­ gions outside o f the region outside o f region 4 , they w i l l fo llo w a route from a supply p o in t located a t South Haven, s itu a te d near the geo­ graphic cen ter o f the southern p o rtio n o f region 4. Representative demand points are also defined f o r regions outside of the r iv e r basin. These demand points are located a t c it ie s which are r e la t iv e ly larg e demanders o f roundwood f o r the regio ns. These demand points fo r roundwood are assumed to be re p re s e n ta tiv e demand points fo r hunterdays. These demand points a re located as close to the ju n c tio n of two major highways where p o ssible. lis te d 1n Table 3 -1 7 . These re p re s e n ta tiv e points are Regions 11 and 12 are net exporters o f tim ber so th a t a demand p o in t was not defined fo r e ith e r re g io n . C a lc u la tin g T ran s fe r Costs General Concepts T ra n s fe r costs are the costs o f overcoming the b a r r ie r o f d1s- 140 Table 3 -1 7 .— Representative Demand Points fo r Regions Outside o f the R iver Basin. * * * * " ■ ■— n rn , • Region 5 6 7 8 9 10 — — — — — ■ ■ - ■ Demand Point Junction Muskegon Sparta Portland Cassopolls Union C ity Mason I69,US131 on M37 on 196 M60,M62 on M60 US127.M36 lance between th e lo c a tio n o f production and the lo c a tio n o f th e con­ sumer. Um ber 1s tra n s fe rre d from a fo re s t resource assumed to be d is ­ trib u te d evenly over the region to demand points th a t process roundwood which may be 1n the region o r o th er regio ns. at the s it e o f production. Hunterdays are consumed Hunters tr a v e l from points o f population con­ cen tratio n to th e fo re s t resource, again assumed to be evenly over th e region. Umber 1s hauled by tru c k w h ile hunters tra v e l 1n automobiles. A ll tra v e l 1s over highways. Conversations w ith the U.S. Forest Service personnel a t C a d illa c , Michigan, In d ic a te th a t most roundwood 1s hauled to the m ill by tru c k . Defining Transport Routes Transportation Between Regions: Routes o f tra v e l are chosen to lin k supply areas to demand p o in ts . Each route extends from the demand p o in t to the edge o f th e supply a re a , where 1t lin k s In to the tra n s p o rta tio n network o f the supply area. The roads chosen were fa s te s t o r the sh o rtest routes between two p o in ts . There were several classes o f roads defined fo r tra v e l between regions: 1) In t e r s ta te , 2 ) U.S. highway, 3) s ta te highway, fo u r la n e , and 4 ) s ta te highway, two lan e. Wherever p o s s ib le , In te r s ta t e o r o th e r fo ur lane 141 highways were chosen. The area 1s w ell k n it w ith such roads. Transportation routes were p lo tte d between each supply area and demand p o in t in the r iv e r basin and between each demand p o in t and supply area in the r iv e r basin and demand points and supply areas outside o f the riv e r basin. Each route was numbered and coded. of the tra n s p o rta tio n routes. Appendix P contains a ll Two routes are required whenever goods are required to be moved two ways between regions. transportation routes were d efined. In t o t a l , 68 such The mileage was c a lc u la te d by measur­ ing the distance o f each road on a route on county maps w ith a map-measur­ ing wheel. The length in inches was then converted to m ileage. Transportation Between Regions: The tra n s p o rta tio n system in each region was d ivided in to classes. Report No. 162 o f the Michigan Highway Department o f S tate Highways and Transportation contains in Table 2-3 the mileage o f various classes o f highways by county (Michigan Department o f S tate Highways and Transporta­ tio n , 1975). These classes do not correspond to classes o f highways de­ fined by the U.S. Forest S ervice. are based on tra v e l speeds. U.S. Forest Service classes o f roads The S tate o f Michigan c la s s ifie s roads on the basis o f surface m a te ria ls and co n dition o f su rface. surface m a te ria ls include: Classes o f 1) mixed bituminous surface on concrete o r b ric k , 2) concrete o r b ric k , 3) mixed bituminous surface on g ra v e l, 4) bituminous surface tre a te d g ra v e l, 5) gravel and s im ila r m a te ria ls , 6 ) graded and drained e a rth , 7) graded and drained e a rth , and 8) unim­ proved e a rth . Conditions o f the road surface include: 1) adequate fo r use by expected t r a f f i c , and 2) inadequate fo r use by expected t r a f f i c . T r a ffic speeds are assumed to be higher on hard surface roads, which are concrete, b ric k , and bituminous su rfaces, than on gravel roads. The tra v e l 142 speeds on gravel roads a re , 1n tu rn , assumed to be g re a te r than those on unimproved earth roads. Travel speeds are assumed to be g re a te r on ade­ quate condition roads than on inadequate co n dition roads fo r any type o f road surface. Classes o f S tate highways which are based on road surface material and surface conditions were a llo c a te d among U.S. Forest Service classes o f highways which are based on tra v e l speeds as fo llo w s: * Forest Service Classes High-Speed: S tate Highway Classes concrete o r b ric k — adequate, mixed bituminous surface on concrete or b ric k — adequate, mixed bituminous surface on g ra v e l— adequate, b itu m i­ nous surface tre a te d g ra v e l— adequate. 1: concrete o r b ric k — inadequate, mixed bituminous surface on concrete o r b ric k — inadequate, mixed bituminous surface on g ra v e l--in a d e q u a te , b it u ­ minous surface tre a te d g ra v e l— in ­ adequate. 2: g ra v e l— adequate, graded and drained e a rth — adequate. 3: g ra v e l— inadequate, graded and drained e a rth — inadequate. 4: unimproved e a rth . 5: p riv a te logging road. No mileage is recorded fo r th is c la s s . The high-speed class was fu rth e r broken down in to three sub-classes: Transportation Network: T ru nklin e Roads: Each region is criss-cro ssed w ith a n o rth south road and an east-w est road th a t in t e r ­ cept roads between regions. This mileage is found in Report No. 162, Table 2 -1 , the mileage o f the tra n s p o rta tio n network was sub­ tra c te d since the tra n s p o rta tio n network 1s made up o f tru n k lin e highways. Non-Trunk Highways: Residual o f High-Speed Class. 143 Mileages o f each class were then a llo c a te d to regio ns. The tra n s ­ portation system was assumed to be evenly d is trib u te d over the county. The proprotion o f the area o f a county In a region was m u ltip lie d by the mileage 1n each class to compute the mileage o f each class a llo c a te d to a region. The mileage from each county a llo c a te d to each region was summed to get the mileage o f each class in each region. The mileage fig u re s by each class were tab u lated 1n order to com­ pute an average o f the number o f m iles tr a v e lle d on each class o f road to reach the tra n s p o rta tio n network. The fo llo w in g formula developed by Hamilton was used to compute the average mileage tra v e lle d on each class o f highway (Wynd and Manthy, 1971): n -i-1 X., - 1 M“ 7 e j=0 X_ n‘J i= n , n -1 . n -2 ..........1 X^ = m iles tr a v e lle d on class i i = class o f highway = l t . . . , n n = to ta l number o f classes = 8 Xn_ j = m iles tr a v e lle d on class n - j ; XR_ j = 0 , when 1=n-8 M-j.-] “ accumulated m iles o f road per square m ile fo r a l l roads in classes higher than th a t under co n sid e ra tio n . To c a lc u la te M^ -j, the m iles o f each class o f highway in a region was divided by the re g io n 's area in square m iles to compute m iles in each class per square m ile . The accumulated m iles per square m ile fo r class is the sum o f the m iles o f each class from 1 to i where class 1 is the transpo rtatio n net work and class n is p riv a te logging roads, th a t 1s: 1 M. = u r n . 1 k=l K m^ - m iles per square m ile o f class k 144 cannot be c a lc u la te d fo r class 1 , th a t 1s, the tra n s p o rta tio n network, since no 1s a v a ila b le . However, an average mileage tr a v e lle d 1s com­ puted fo r each class In clu d in g p riv a te logging roads. Appendix Q l i s t s the mileage tr a v e lle d on each class o f road. Estim ating the distances tra v e lle d on the tra n s p o rta tio n network presents a b i t o f a problem. The region is assumed to be a square w ith the fo re s t resource d is trib u te d evenly over the regio n. There 1s a north-south, east-w est tra n s p o rta tio n network which in te rs e c ts the demand node a t the cen ter o f the regio n. See Figure 3 -1 . Ham ilton's formula c a lc u la te s the average distance tra v e lle d to reach the tra n s p o rta tio n network. Given the uniform d is tr ib u tio n o f the fo re s t resource, once tim ber reaches the route to the demand p o in t, 1 t w ill be uniform ly d is trib u te d along th a t ro u te . The average distance tra v e lle d to leave the re g io n , th a t i s , to lin k up to a route going to an outside demand p o in t, w il l be distance a 1n Figure 3-1 which is onefourth o f the to ta l mileage o f the tra n s p o rta tio n network. To compute the average distance tr a v e lle d to leave the reg io n , the to ta l mileage o f the tra n s p o rta tio n network 1s d ivided by fo u r. Appendix Q contains th is inform ation fo r each reg io n . The average distance to the demand node in the region is found by finding a square containing o n e -h a lf o f the fo r e s t resource w ith the de­ mand node as a c e n te r. This 1s square HIJK in Figure 3 -1 . Distance d is the average distance tr a v e lle d to reach the demand node in the region. One-half o f th e fo re s t resource 1s In s id e square HIJK w h ile o n e -h a lf 1s outside. The distance 1s now derived . By d e fin itio n : d = 1 /2 e The area o f HIJK 1s: A^ = e2 A1 = area o f HIJK 145 E M F Figure 3 - 1 .— Square DEFG 1s the regio n. Point C is the demand p o in t. Lines NS and LM are the roads 1n the tra n s p o rta tio n network, b is the length o f one side o f square DEFG. a = l/2 b . e is the length o f one side o f square HIJK. d = l/2 e . The area o f HIJK is o n e -h a lf the area o f DEFG. 146 The area o f the DEFG 1s: Aq = b Aq = area o f DEFG By d e f in it io n : Thus: Aj = l/2A g e2 = l / 2 b 2 As a re s u lt: e = b S2~~ Since d = l /2 e and a = l /2 b , d = a / / T . To compute the average distance tra v e lle d on the tra n s p o rta tio n network to reach the demand node 1n the re g io n , the mileage o f the tra n s p o rta tio n network Is d ivided by 4 / T . Appendix Q contains th is in fo rm atio n . There are several problems w ith using th is method to estim ate d is ­ tances tra v e lle d on the tra n s p o rta tio n network: (1 ) The regions defined In th is study are not square, but th is problem 1s unavoidable; (2 ) The demand node o fte n 1s not 1n the c e n te r; (3 ) The tra n s p o rta tio n network defined 1n the study may not be the major roads fo r hauling tim ber o r fo r hunters t r a v e llin g to hunting spots; (4 ) Travel might not occur over the sh o rtest distance from the fo re s t resource to the tra n s p o rta tio n network; and (5 ) The fo re s t resource 1s probably not evenly d is trib u te d over the region. C alculating Timber T ran spo rtatio n Costs Transportation costs per m ile per cubic fo o t were obtained from the U.S. Forest S ervice o f fic e a t C a d illa c , M ichigan. d iffe re n tia te d by tru ck class and highway c la s s . The costs are The class o f tru ck chosen was the same as th a t used by Wynd and Manthy (Wynd and Manthy, 1971). The truck chosen was a s ix fo o t by fo u r fo o t fla tb e d w ith tandem a x le and s e lf unloader th a t weighs 37,000 pounds, combined gross w eig h t. fo r each class are ro u n d trlp and are lis t e d 1n Table 3 -1 8 . The costs 1 47 Table 3 -1 8 .— Hauling Costs fo r Timber in M ichigan, 1975. Road Class Highspeed I II III IV V Standby, d elay , load, unload Source: Speed (mph) Cost per M ile per Ccf 45 35 25 16 8 4 $0.12 $0.17 $0.25 $0.35 $0.63 $1.15 $2.09 U.S. Forest S e rvic e, personal correspondence, 1975. F ir s t , the cost o f reaching the tra n s p o rta tio n network was calcu ­ lated fo r each regio n. The mileage o f each class o f highway was m u lti­ plied by the cost per m ile per hundred cubic fe e t o f th a t class to calcu ­ la te the cost per hundred cub'ic f e e t fo r each road class in the region. The cost per hundred cubic fe e t was summed fo r each road class and summed to standby costs to compute to c a lc u la te the cost per hundred cubic fe e t to reach the tra n s p o rta tio n network. The tra n s p o rta tio n network was assumed to be in the highspeed c la s s . The mileage to leave the region was m u ltip lie d by cost per m ile per hundred cubic fe e t fo r the highspeed c la s s . The cost per hundred cubic fe e t on the tra n s p o rta tio n network to reach the demand p o in t in the region was added to the cost per hundred cubic fe e t to reach the tra n s p o rta tio n network to compute the cost per hundred cubic fe e t to haul tim ber from the fo rest resource to the market in the region. The route connecting each supply region to demand points outside the region were assumed to be in the high-speed c la s s . The to ta l mileage o f each route was m u ltip lie d by the cost per m ile per hundred cubic fe e t fo r the high speed class to compute the cost per hundred cuhic fe e t on 148 the route. The cost per hundred cubic fe e t to reach the tra n s p o rta tio n network, the cost per hundred cubic f e e t on the tra n s p o rta tio n network to leave the reg io n , and the cost per hundred cubic fe e t on the route to the demand p o in t were summed to get the cost per hundred cubic fe e t to haul timber from the fo re s t resource in the supply region to a demand point outside o f the region. The cost per hundred cubic fe e t was calcu ­ lated fo r a l l routes between supply areas and demand p o in ts . These costs are contained in Appendix R. Calculating T ransportation Costs f o r Hunterdays The cost per m ile per hunterday was estim ated fo r both big and small game hunting. I t is assumed th a t a l l hunters tra v e l 1n automobiles. F ir s t, a cost per m ile o f o perating an automobile was c a lc u la te d . The U.S. Department o f Tran spo rtatio n has developed cost per m ile fig u re s fo r operating automobiles. The fig u re s were derived fo r stand ard -sized cars, compacts, and sub-compacts. Not a l l costs included by the Depart­ ment o f T ransportation are used in th is study. were included. Only o perating costs These costs Include d e p re c ia tio n , re p a irs and maintenance, replacement t i r e s , gas, o i l , and taxes on gas, o i l , and t i r e s . Assumptions were used to c a lc u la te the cost per m ile o f operating an automobile. F ir s t are the d escrip tio n s o f the cars: 1. Standard-sized car: 1972 4-door sedan, Equipment: V-8 engine, automatic transm ission, power s te e rin g and brakes, a i r c o n d itio n ­ in g , tin te d g lass, ra d io , c lo c k , w h ite -w a ll t i r e s , body molding. 2. Compact: 1972 2-door sedan. Equipment: 6 -c y c lin d e r engine, autom atic transm ission, power s te e rin g , ra d io , body molding. 3. Sub-compact: 1972 2-door sedan. Equipment: ment plus radio and body molding. Repairs and maintenance are required and inclu d e: standard equip­ lu b r ic a tio n , repacking wheel bearings, flu s h in g cooling system, aiming headlamps, replacement o f 149 sparkplugs, fa n b e lts , ra d ia to r hoses, d is tr ib u to r caps, fu e l f i l t e r , p o llution control f i l t e r , brake jo b s , w ater pumps, c a rb u reto r overhaul, universal jo in t s , and valve jo b s. assumed th a t seven new re g u la r during the l i f e o f the c a r. T ire s must be replaced, so 1 t is t ir e s and fo u r new snow t ir e s are purchased Accessories include f lo o r mats purchased during the f i r s t y e a r, seat covers purchased in the s ix th y e a r, and some miscellaneous item s. Gasoline consumption is assumed to be 13.6 m iles per gallon fo r a stand ard -sized c a r, 15.97 m iles per gallon fo r a compact car, and 21.43 m iles per gallon fo r a sub-compact c a r. 1s assumed to be 1 gallon o f o il fo r 186 gallons o f O il consumption gas fo r a compact car, and 1 g allo n o f o il fo r 135 m iles o f gas fo r a sub-compact. A car is assumed to operate fo r ten years and 100,000 m iles and then be scrapped (U.S. Department o f T ran s p o rta tio n , 1972). The Department o f T ran spo rtatio n re p o rt gave a l l prices 1n 1972 prices. In fla tio n and increases in gasoline prices have changed these prices. I t is assumed th a t gasoline $0.52 per gallon and o il cost $0.90 per q uart. Federal taxes were held constant. The 1972 cost per m ile figures fo r d e p re c ia tio n , re p a irs and maintenance, replacement t i r e s , and accessories were summed and in f la te d to 1975 p ric e s . based on U.S. Bureau o f Labor S t a t is tic s re p o rts . The i n f l a t o r was The consumer p ric e index rose by 3.3% in 1972, 6.2% in 1973, and 10.6% in 1974. Bureau o f Labor S t a t is t ic s , 1974 and Dennis, 1974). in fla te d to 1973, the 1973 fig u re was in fla te d to 1975. Table (U.S. The 1972 cost was in f la t e d to 1974, and the 1974 fig u re 3-19 shows the 1972 fig u re s to be In f la t e d , the 1975 fig u re s a f t e r i n f l a t i o n , and the 1975 cost per m ile fo r each car cla ss . fig u re s . The cost per m ile fig u re s are doubled to get round t r i p 150 Table 3-19- — Cost per M ile Figures fo r O perating an Automobile. car class 1972 costs (excludes gas and o i l ) (cen ts) standard compact sub-compact 1975 costs (excludes gas and o i l ) (ce n ts ) 6 .9 7 4 .8 8 4.21 8.46 5.92 5.11 1975 costs (inclu d es gas and o i l ) (cen ts) 12.75 9.59 7.86 The next step was to get an average cost per m ile by aggregating over a ll classes o f cars on the road. Figures on c a r production were obtained from the Motor V ehicle Manufacturers Association o f the U .S ., Inc. Production fig u re s were kept from 1968 to 1974 (Motor V ehicle Manu­ facturers A sso ciatio n, 1974). These fig u re s were not aggregated accord­ ing to standard compact, and sub-compact c la s s e s , however. The Motor Vehicle Manufacturers Association fig u re s were a llo c a te d to classes in the fo llow ing manner: 1. standard: h ig h , re g u la r, in te rm e d ia te , passenger van 2. compact: 3. sub-compact: compact, sport sub-compact, import The proportion o f each o f these classes was c a lc u la te d from 1968 to 1974. portions. tio n . A se t o f weights was developed to be m u ltip lie d by these pro­ F ir s t , the ra te o f removal o f cars was taken in to considera­ The Department o f T ran sp o rtatio n s ta ted th a t 50% o f th e cars pro­ duced in a given y e a r are s t i l l on the road a f t e r ten y e a rs . years, they are assumed scrapped. A fte r ten I t Is assumed th a t 100% o f the cars b u ilt in 1974 are s t i l l on the road, w h ile 50% o f the cars b u i l t 1n 1965 are s t i l l on the road. I t is assumed th a t the ra te o f removal 1s constant over the ten ye ar p erio d . The percentage o f a given y e a r's cars on the 151 road was decreased by a constant amount from the fo llo w in g y e a r's pro­ portion. A s e t o f automobile production weights was also c a lc u la te d to ac­ count fo r d iffe re n c e s in y e a r ly production. o f 1 .0 . 1974 was assigned a weight The production o f each years was d ivid ed by 1974 production to get a r e la tiv e w eigh t. to be id e n tic a l to 1968. Production in 1965, 1966, and 1967 was assumed The removal w eight and the production w eight were m u ltip lie d to g eth er to g et a to ta l w eight. in Appendix S. These weights are lis t e d The proportion o f each class o f car produced in each ye ar was m u ltip lie d by th is w eight. summed over the ten y e a r p erio d . The weighted percentage o f each class was The percentage o f each c a r class pro­ duced in each year is lis t e d in Appendix T. The to ta l weighted percent­ age fo r each class was d ivid ed by the to ta l o f a l l classes to get a per­ centage o f each class o f car on the road a t the present tim e. portion o f each class o f car was found to be: The pro­ sub-compact— 18%, compact— 17%, and standard— 65%. The next step was to fin d the number o f hunters in a p a rty fo r small game and b ig game. The number o f passengers per car was found in a pub­ lic a tio n p rin te d by the U.S. Department o f In t e r i o r . There were 2.46 passengers per c a r fo r b ig game. This fig u re is assumed to hold f o r deer hunters in the r i v e r basin a re a . There were 2.17 passengers per c a r fo r small game. This fig u re was assumed to hold fo r s q u irre l and ra b b it hunters in the r iv e r basin a re a . The same p u b lic a tio n provided inform a­ tion to c a lc u la te the number o f days per t r i p . days was. d ivided by the number o f days per t r i p . The number o f hunting The number o f hunting days was d ivid ed by the number o f hunting t r ip s to c a lc u la te the number o f hunterdays per t r i p . There is 1 .3 7 days per t r i p f o r big game and 152 1.09 days per t r i p fo r small game. These n atio n al fig u re s were assumed to hold fo r hunters in the r iv e r basin area (U .S . Department o f In t e r io r , 1971). Cost per m ile per hunterday fo r small and big game were c a lc u la te d fo r each class o f automobile according to the fo llo w in g formula: cost per m ile * passengers per car * days per t r i p Table 3-2 0 shows the re s u lts in terms o f round t r i p costs. Table 3 -2 0 .— Cost per M ile per Hunterday fo r Each Class o f Car. Class o f Car Small Game (cen ts) Standard Compact Sub-compact 10.78 8.11 6.64 Big Game (cen ts) 7.56 5.69 4 .6 6 Each class o f car was m u ltip lie d by the p roportion o f each class on the road and summed to get an average round t r i p cost per m ile fo r big game and small game. For big game, the cost per m ile per hunterday was estimated to be 6.72 cents. For small game, the cost per m ile per hunterday was estim ated to be 9 .5 8 cents. The cost per m ile per hunterday fig u re s were assumed to hold fo r a ll classes o f road. The to ta l mileage tr a v e lle d from any demand p o in t to any supply areas was summed and m u ltip lie d by the cost per m ile per hunterday to get the costs per hunterday fo r both big game and small game. The same mileage fig u re s were used as those c a lc u la te d fo r tim b er. Appendix R contains these costs. Transport Costs fo r the Lin ear Program Transportation costs were c a lc u la te d f o r each good fo r each tra n s - 153 port route and each time p erio d . The fu tu re value a t the end o f a te n - year period was c a lc u la te d fo r the tra n s p o rt cost per u n it o f commodity incurred in each ye ar o f the te n -y e a r period. The fu tu re values fo r each year in the te n -y e a r period then were summed to compute the fu tu re value o f a ll tra n s p o rt costs per u n it o f commodity incurred in the te n -y e a r period. This fu tu re value was discounted to the present which in th is model is assumed to be 1965. The fu tu re value was discounted over ten years fo r time period 1 , 20 years fo r tim e period 2 , 30 years fo r tim e period 3, 40 years fo r tim e period 4 , 50 years fo r time period 5, and 60 years fo r time period 6. A discount ra te o f 5.88% was used. These costs are the present value o f tra n s p o rta tio n costs in each tim e p erio d . These costs are o b je c tiv e fu n ctio n values fo r tra n s p o rta tio n a c t i v i ­ ties 1n the lin e a r programming model. A c t iv itie s th a t tr a n s fe r tim ber from regions outside o f the r iv e r basin to regions in s id e the r iv e r basin have an added c o s t, the cost o f h arvesting tim ber. This cost is added since the cost o f harvesting tim ber in the region is accounted fo r in the o b je c tiv e fu n ctio n values o f the production a c t i v i t i e s . I f these added harvesting cost were not accounted f o r , the model would choose to Import tim ber to meet r iv e r basin requirements ra th e r than produce tim ber 1n the regio n. The tru e cost o f im porting tim ber would not be c a lc u la te d I f the h arvesting cost was not f u l l y considered. Generating Forest Production A c tiv itie s Aggregating Management S tra te g ie s and Resource Classes Large amounts o f data are used 1n th is model. I t 1s time-consuming and co s tly to c a lc u la te product c o e ffic ie n ts fo r each management s tra te g y on each resource c la s s . Costs o f d e riv in g a s o lu tio n to a lin e a r program­ 154 ming model increases as the number o f c o e ffic ie n ts in the model increases. I f the problem becomes too la rg e , i t is possible to exceed the core lim its o f the computer. To reduce co s ts , time involved in c a lc u la tio n s , and computer core requirem ents, management s tra te g ie s and resource classes were aggregated. I f was found th a t the c o e ffic ie n ts c a lcu la ted by the U.S. Forest Service fo r the in te n s iv e f ib e r and m u ltip le use management s tra te g ie s were very s im ila r . To conserve on computer tim e , i t was decided to ag­ gregate these two management s tr a te g ie s . ents were id e n tic a l. U s u a lly , the hunterday c o e f f i c i ­ The g re a te s t inform ation loss occurred in f ib e r production and erosion. The c o e ffic ie n ts were aggregated by averaging. The aggregated management S trateg y is renamed in te n s iv e management. The current use and environmental emphasis management s tra te g ie s remain. I t was decided th a t, in some cases, resource classes could be aggregated. As a r e s u lt, the to ta l number o f a c t iv it ie s is reduced. Re­ source classes were aggregated by s o il group and, in some cases, condi­ tion classes. However, stand s iz e classes were not aggregated. Table 3-21 shows the aggregated s o il groups, the o rig in a l s o il groups contained In the aggregation, and the co n dition classes included in each resource class. Each o f these 13 groups has fo u r stand s ize classes associated w ith it. Appendix V shows the range o f values fo r each o f the f ib e r production coefflcents in each o f these groupings. The management s tra te g ie s were aggregated by averaging the c o e ffic ie n ts from each resource class which was aggregated. Time Time presents a special problem in d e fin in g a c t i v i t i e s . A ro ta tio n 155 Table 3-21 . —Aggregation o f S oil Groups and Condition Classes. Ecosystem Conifer 0ak-H1ckory Elm-Ash-Cottonwood Maple-BeechBirch Aspen-Birch Aggregated S o il Group S oil Groups Condition 1 1 2 3 1 1 2 A,B,E A,B,E C D A,B,D,E A,B,C,E 0 Adequate TSI Both Both Adequate TSI Both 1 A,B,C,D,E Both 1 1 2 1 2 A,B,C,E A,B,C,E D A,B,E C,D Adequate TSI Both Both Both time must be defined f o r each management s tra te g y on each resource c la s s . Time periods must also be defined fo r each stand s iz e c la s s . R otation lengths were defined fo r in te n s iv e management by co nsulting The Growing Timber Resource o f M ichigan, 1966 and the s t a f f o f th e Manistee National Forest (Chase. P f e i f f e r , and Spenser, 1969). The recommended ro ta tio n length fo r the cu rren t use management s tra te g ie s fo r each resource group was defined by tak in g a period somewhere between the c u rre n t ro ta tio n length and the o ld e s t age class o f the resource group found in M ichigan's Lower Peninsula. When the ro ta tio n age fo r the in te n s iv e management strategy and the o ld e s t age class are the same, the ro ta tio n age fo r the current use management s tra te g y is the same. When the recommended ro ta ­ tion age fo r the in te n s iv e management s tra te g y is in the second o ld e s t age class o f the resource group found in the Southern Lower Peninsula, the ro ta tio n age fo r the c u rre n t use management is the highest age o f the oldest age c la s s . 156 Defining the re la tio n s h ip between age class and stand s ize class was more d i f f i c u l t . The acreage o f each class was found f o r the southern h a lf o f the Lower Peninsula in The Grow­ ing Timber Resource o f Michigan, 1966. ecosystem 1n each stand s iz e The acreage o f each ecosystem in various age classes was determined fo r the whole s ta te . The same in f o r ­ mation was found fo r subdivisions o f the s ta te in Michigan DNR p u b lic atio n s for each regio n. However, th e re was no inform ation fo r the southern h a lf of the Lower Peninsula. The acreage o f the ecosystem in each age class was found by su b tractin g the acreage o f the re s t o f the s ta te from the acreage fo r the e n tir e s ta te . The resid ual was a llo c a te d to the southern h alf o f the Lower Peninsual. The acreage o f each ecosystem in each stand size class is shown in Appendix W. The acreage o f each ecosystem in each age class was shown in Appendix X. I t was assumed th a t the age d is tr ib u tio n w ith in an age class was even. Non-stocked areas were a llo c a te d evenly among the stand s iz e classes. Age classes were summed, s ta r tin g w ith the youngest, u n til the acreage o f the s e e d lin g -s a p lin g class was approximated. poletimber and sawtimber. The same was done fo r When i t was necessary to subdivide on age class, which occurred only w ith the seed-sapling age c la s s , the acreage of the stand s iz e class was d ivided by the acreage o f age class 0 -2 0 . This r a t io was m u ltip lie d by 20. The product o f the la s t y e a r in the age d is trib u tio n o f the stand s iz e c la s s . m ultiple o f f iv e . This was rounded to the nearest This process y ie ld e d a c ro s s-s ec tio n al re la tio n s h ip of age-classes in the stand s iz e classes. The re la tio n s h ip was assumed to hold over time thus g iv in g the time p erio d , in y e a rs , a stand spends in a stand s ize c la s s . Table 3-22 shows the ro ta tio n age and stand s ize class time periods for each management strategy in each ecosystem. These times were assumed to hold fo r every resource class. Table 3 -2 2 .— Rotation Age and Time Periods in Each Stand Size Class. Ecosystem Management Strategy Time Period in Eachi Stand Size Class Rotation Age SeedSapl ing Conifer Oak-Hickory Elm-AshCottonwood Maple-BeechBirch Aspen-Birch Poletimber Sawtimber CU IM CU IM 120 120 120 140 15 15 15 15 25 25 35 35 80 80 70 90 CU 140 15 35 90* CU IM CU IM 140 140 50 60 20 20 15 15 40 40 25 25 80 80 10 20 CU = Current Use Management Strategy IM = Intensive Use Management Strategy in t e n s iv e management is not considered because Dutch Elm Disease makes th is ecosystem non-commercial. The fo re s t resource is conceptualized as a s e t o f age cohorts mov­ ing through time. There w ill be a se t o f ten -ye ar age cohorts from zero through ro ta tio n age. Each cohort w ill age by ten years a f t e r the pass­ ing of a ten-year time period. 1966. For example, th ere is a 0-10 cohort in In 1975, th a t cohort w ill be 10-20 in 1985, 20-30 in 1995, 30-40 in 2005, e tc . The age cohorts w ill move smoothly through time so th a t in 1970, the age class a c tu a lly is 5-1 5. At the end o f r o ta tio n , the cohorts w ill move back to 0-10 a f t e r timber removals. This technique w ill be used to c a lc u la te how much tim ber becomes a v a ila b le 1n d if f e r e n t time periods. Each age class can be traced through time in th is manner. Linear Programming Production A c t iv itie s The production a c t iv it ie s are a statem ent o f the outputs produced * over time by th e combinations o f land management p ra c tic e s . The c o e f f i c i ­ ents o f the time period r e f le c t the management s tra te g y ap p lied to a given class o f land during the production p erio d. A given parcel o f land can remain in one management s tra te g y fo r the e n tir e period o f a n a ly s is . However, conversion o f a management s tra te g y on a parcel o f land can also occur. An a c t iv it y has to be formulated fo r each combination o f manage­ ment s tra te g ie s over tim e. S im p lify in g assumptions are made concerning when conversion decisions can be made and what conversion decisions can be made in order to l i m i t the number o f a c t i v i t i e s . The s im p lify in g assumptions are: 1. Once a t r a c t o f land is devoted to the in te n s iv e management o r environmental emphasis management s tr a te g ie s , no conversions can be made. Conversions can only be made from the cu rren t use management s tra te g y to in te n s iv e management o r environmental emphasis. Land devoted to environmental emphasis w il l be se t aside in parkland. production. Most parklands are removed from tim ber Land is assumed to be devoted to in te n s iv e manage­ ment a f t e r a d e lib e ra te decision-m aking process by the land­ owner 1n which he weighs the costs and b e n e fits o f in te n s iv e management in terms o f h is own goals over tim e. I t is being assumed th a t the landowner w il l not change his goals during the period o f a n a ly s is . A conversion decision can be made only once fo r astand s iz e class and w il l take place a t the ju n c tu re w ith the fo llo w in g stand s iz e class or a t the present. Conversion can take place a t: a. present b. se ed H n g -s ap lin g — poletim ber ju n ctu re c. poletim ber— sawtimber ju n ctu re d. ju s t before the stand 1s cut e. a f t e r the stand 1s cut Once a cut has been made, no conversions can take p lace. No conversions are made a f t e r a cut since i t 1s assumed th a t the landowner w il l decide a f t e r tim ber 1s harvested whether to devote land to in te n s iv e management o r to leave the land un­ managed. Land devoted to in te n s iv e management before harvest remains in In te n s iv e management. I t is then assumed th a t the landowner w il l not change his goals during the period o f a n a l­ y s is . Conversion o f non-stocked land to seed!1ng-sapling can occur only a t the present o r the ye ar 2000. Conversion from c u rre n t use to the in te n s iv e management s t r a t ­ egy on land needing tim ber stand improvement can occur only w ith an investment and conversion to the adequate co n d itio n cla s s . When the needs-timber-stand-1mprovement and adequate co n dition classes are aggregated the conversion from c u rre n t use to in ­ ten sive management w il l re q u ire an investm ent. For non-stocked fo re s t la n d , only conversion to in te n s iv e man- agement w ill be considered. In most cases, the q u a n titie s o f tim ber and hunterdays produced over time on non-stocked land o r non-stocked land converted to in te n s iv e management are g re a te r than or equal to the amounts o f these commodities pro­ duced on non-stocked land converted to cu rren t use. 8. Conversions o f fo re s t land to urban land w ill be handled o u t­ side o f the model. Products produced on lands to be converted during each time period w il l be added In to the model. Products produced on lands c u rre n tly in the in te n s iv e management s t r a t ­ egy w il l be handled 1n the same way. Appendix Y contains a 11st o f the a c t i v i t ie s fo r the resource classes. Calculating Timber C o e ffic ie n ts Data were provided by the U.S. Forest Service concerning the outputs of products by management s tra te g ie s on each resource c la s s . C o e ffic i­ ents were provided fo r the annual growth o f wood f ib e r fo r each fo re s t ecosystem, stand s iz e c la s s , stand co n dition c la s s , s o il group and manage­ ment s tra te g y . These f ib e r c o e ffic ie n ts cannot be used d ir e c t ly in th is model since the product 1n th is model 1s tim ber th a t can be sold to the m ill. A model is proposed th a t w il l c a lc u la te tim ber production. It assumes th a t a l l tim ber to be sold is cut a t the end o f the ro ta tio n . I t also assumes th a t tim ber growth per year fig u re s provided by the U.S. Forest Service are accu rate. hold constant over tim e. I t also assumes th a t the re la tio n s h ip s w il l The model is : 161 MVHa r “ merchantable volume o f tim ber harvested per acre by manages tra te g y a on resource class r a t the end o f the ro ta tio n , s = s ta te s ize class 5a i when s = 1, the stand s iz e class is seed-sapUng when s - 2 , the stand s iz e class 1s poletim ber when s « 3 , the stand s iz e class 1s sawtimber = net growth o f to ta l f ib e r per acre per year in stand s iz e class s w ith management strate g y a on resource class r . So" = number o f years th a t the stand 1s in stand size class s w ith management s tra te g y a on resource class r . Ca r = amoun't merchantable tim ber produced per u n it o f to ta l volume o f f ib e r w ith management s tra te g y a on resource class r a t the ro ta tio n age. Cgr is ca lcu la ted from the fo llo w in g product: Growing stock volume 4 to ta l f ib e r volume x Growing stock harvest 4 growing stock volume x Merchantable volume 4 growing stock harvest Growing stock harvest/grow ing stock volume fo r the c u rre n t use man­ agement s tra te g y is c a lc u la te d by d iv id in g growing stock removals per year by growing stock a v a ila b le fo r h arv es t. data. This was approximated by 1966 Growing stock removals were divided by the allow able cut o f grow­ ing stock (Chase, P f e i f f e r , and Spenser, 1969). growing stock a v a ila b le are Allow able cu t is the f o r commercial use in a given y e a r. These fig u re s shown fo r softwoods and hardwoods in Table 3 -2 3 . For the in te n s iv e management s tra te g y , growing stock harvest/grow ing stock volume is assumed to be one. 162 Table 3 -2 3 .— C a lc u la tin g Growing Stock Harvest/ Growing Stock Volume. Growing stock removals (MCF) Growing stock allow able cut (MCF) rem ovals/allowable cut softwood hardwood 50,002 127,612 .392 156,461 252,339 .620 Merchantable volume/growing stock harvest was c a lc u la te d by d iv id ­ ing In d u s tria l roundwood production by tim ber removals from growing stock. These fig u re s were calcu la ted f o r 1966 and 1972. The fig u re s fo r 1966 are shown 1n Table 3-24 (Chase, P f e i f f e r , and Spenser, 1969). The fig u re s Table 3 -2 4 .— Merchantable Volume/Growing Stock Harvest, 1966. Output o f roundwood products (MCF) Timber removals from growing stock (MCF) Output/removals hardwood softwood 149,051 156,463 .953 47,622 50,002 .952 for 1972 are shown in Table 3-25 (B ly th e , B o e lte r, and Danielson, 1975). Table 3 -2 5 .— Merchantable Volume/Growing Stock Harvest, 1972. Volume o f in d u s tria l roundwood (MCF) Growing stock removals fo r indus­ t r i a l roundwood Roundwood/removals hardwood softwood 43,601 140,305 46,041 .947 148,300 .946 The average fo r both years is .95 fo r both hardwoods and softwoods. figure w il l be used. This 163 C a lcu latin g the volume o f growing s to c k /to ta l volume o f f ib e r was more d i f f i c u l t since th is type o f Inform ation is not re a d ily a v a ila b le . The volume o f growing stock is the volume o f tim ber up to a fo u r-in c h top. Gardner and Hahn studied 176-y ea r-o ld lodgepole pine (N ational M a te ria ls Policy Comnission, 1974). They found th a t th ere were 6174 cubic fe e t per acre o f f ib e r up to a s ix -in c h top w h ile th e re were 4333 cubic fe e t per acre o f residue. The residue was 41% o f to ta l volume. 82% o f the residue was between s ix inches and three inches in diam eter, w h ile 97% was between six inches and 0 .0 6 inches in diam eter. To c a lc u la te the p ortio n o f a tree up to a fo u r-in ch to p , th e tre e was assumed to be a cone. I t was calculated th a t the volume p o rtio n o f a cone w ith a 6 inch base between a diameter o f s ix inches and fo u r inches was 70% according to the fo llo w ­ ing c a lc u la tio n s : Volume o f a cone w ith a s ix -in c h base: y 32h = 3nh Volume between s ix inch diam eter and fo u r inch diam eter o f the cone: j 32h - y 22 | h = 2 .1 1 nh The r a tio o f the two volumes is 2.11 h /3 h = 0 .7 0 . The portion o f the whole lodgepole pine in a volume w ith a s ix -in c h bottom and a fo u r-in c h top is .41 x .7 = .2 9 . The volume o f the tre e up to a fo u r-in ch top is .59 + .29 = .88 which is growing stock volum e/total fib e r volume. Samuel F. Gingrich did s im ila r work w ith s h o rtle a f pine (G in g ric h , 1972). He presented an equation to c a lc u la te the p ortio n o f a s h o rtle a f pine up to a fo u r-in c h top. The values approach 98%. A pine w ith a height o f 50 fe e t and a dbh o f nine inches would have 93% o f the to ta l volume in th a t p ortio n up to a fo u r-in c h top. A tre e 54 fe e t high w ith 164 a dbh o f 12 Inches would have 96% o f the volume 1n th a t p ortio n up to a four-inch top. Bryce Schlagel did s im ila r work w ith quaking aspen. Merchantable volume up to a th re e -In c h top and fiv e -in c h top both approach 98.6% o f to ta l volume (S c la g e l, 19 71 ). I t was decided to s e t growing stock volum e/total f ib e r volume a t 92% f o r th is study. The values o f were c a lc u la te d and are presented in Table 3-2 6 . Table 3 -2 6 .— Merchantable Volume/Total F ib e r Volume. Ca r Hardwood Management S trategy In ten sive Management Current Use 0.87 0.54 Softwood 0 .8 7 0 .3 4 Once the merchantable volume o f tim ber per acre produced a t the end o f the ro ta tio n fo r each management s tra te g y is c a lc u la te d , special weights must be devised to show what r e la t iv e amounts w i l l be a v a ila b le at d iffe r e n t time periods. Acreage c o n s tra in ts are developed fo r stand size classes, not age cohorts. The d is tr ib u tio n o f age cohorts w ith in a resource class must be accounted fo r when c a lc u la tin g the amount o f timber th a t is a v a ila b le in a given time p erio d . The p o rtio n o f the age class in a resource class is c a lc u la te d by using the age class in a r e ­ source class is c a lc u la te d by using the age d is tr ib u tio n ta b le in Appen­ dix AA. The ra tio s between age cohorts and resource class acreages w il l be the same as those shown in th a t ta b le . When a p a r tic u la r age cohort reaches ro ta tio n age, i t s p ortio n o f the to ta l acreage o f th e resource class is m u ltip lie d by merchantable volume o f tim ber per acre. The tim ­ ber production fig u re also is an annual average fo r a te n -y e a r p erio d. The volume o f tim ber is produced by an age class over a te n -y e a r p erio d. 165 The timber produced per acre must be m u ltip lie d by 1/1 0 . This 1s sum­ marized by the follow ing equation: TPCact. - 1/10 x pc(. x MVHa r ur = portion o f resource class r a t ro ta tio n age a t time period c TPCa„ w - Timber harvest per ye ar by management strateg y a on re aC r source class r in time period c. Appendix AA contains the proportion o f each stand s ize class reaching ro ­ tation age in each time period. Calculating C o e ffic ie n ts fo r Other Products The c o e ffic ie n ts fo r other products w ill also be averages fo r te n year periods. The ten -year age cohort w il l move completely in to the next ten-year age class a t the end o f the period. The c o e ffic ie n t fo r the ten-year period is an average o f the c o e ffic ie n ts o f the age classes existing a t the beginning and end o f the time period. When an age class extends over 20 ye ars, the ten -year d iv is io n s have a frequency equal to 1/2 o f the to ta l o f the 20 year age cla ss . These c o e ffic ie n ts must be averaged fo r each cohort in the stand size cla ss . Each cohort is m u lti­ plied by the acreage proportion o f th a t cohort in the stand s ize class. The resu ltin g product fo r each cohort in the stand s ize class is then sum­ med together. When a conversion between management s tra te g ie s occurs in an a c t iv it y , the c o e ffic ie n t o f the appropriate stand size class and management strateg y is used fo r each time period. For example, when cur­ rent use is converted to in te n s iv e management a t the jun ctu re between the seedling-sapling and poletim ber stand size classes, the c o e ffic ie n ts fo r current use is used fo r the seed lin g -sap lin g class and the c o e ffic ie n ts for intensive management are used fo r the poletim ber cla ss . The fo llo w ­ ing equation expresses the c a lc u la tio n o f c o e ffic ie n ts fo r hunterdays and 166 erosion. COb r - ip c r O /2 C 0ac + l/2 C 0 a c + ]) C CO^r = c o e ffic ie n t fo r a c t i v i t y b on resource class r C0,_ = c o e ffic ie n t o f cohort c in management s tra te g y a aC c = cohort f = la s t cohort in resource class r Pc r = proportion o f acreage o f resource class r in cohort c The c o e ffic ie n ts fo r each cohort are taken from the data provided by the U.S. Forest S ervice. The c o e ff ic ie n t fo r cohort c is the co ef­ fic ie n t fo r the stand s iz e class tic u la r time p erio d . o f which cohort c is a member in Some o f the stand s iz e classes extend over of 15years ra th e r than m u ltip le s o f te n . The c o e ffic ie n ts ten-year period are se e d lin g -s a p lin g c o e ffic ie n ts . a par­ a period o f the fir s t The c o e ffic ie n ts o f the second te n -y e a r period are the averages o f the se e d lin g -s a p lin g co­ e ffic ie n ts and the poletim ber c o e ffic ie n ts . Appendix Z l i s t s the coef­ fic ie n ts in terms o f m u ltip le s o f stand s ize class c o e ffic ie n ts fo r each resource class a t each period in tim e. Calculating Costs fo r Production A c t iv itie s Two types o f costs were developed by the U.S. Forest S ervice: production costs and 2) development co sts. of harvesting tim b er. 1) Production costs are the costs Development costs are the costs o f managing a stand. The production cost per ye ar was c a lc u la te d by m u ltip ly in g th e cubic fe e t per year o f merchantable tim ber harvested per acre by the production cost in d o lla rs per cubic fo o t. A ll production costs fo r a management strategy were discounted to the presen t. The planning horizon extends from 1965 to 2025, a period o f 60 y e a rs . No costs beyond th a t tim e were 167 considered. The discount ra te is 5.88% as determined by the Water Re­ sources Council in August 1974. The fu tu re value o f production costs a t the end o f a te n -y e a r period incurred in each year o f the ten year period was c a lc u la te d . Annual fu tu re values were then summed to compute the future value a t the end o f the te n -y e a r period fo r a l l costs incurred in the ten -ye ar p erio d . The fu tu re value a t the end o f the ten ye ar period was discounted to the p resen t, which is 1965 in th is study. The present values o f costs f o r each te n -y e a r period were sunned to compute the pres­ ent value o f production cost fo r each a c t i v i t y . The development costs are the costs o f managing a stand. costs must also be spread over tim e, These since these costs are incurred only when a stand is converted to the adequate condition c la s s , they are Incurred a t jun ctu res between stand s iz e classes. Since the junctures are spread over tim e , the costs must also be spread over tim e. The por­ tion o f a stand s iz e class in an age cohort is m u ltip lie d by the develop­ ment cost and d ivided by the number o f years in the cohort to compute a development cost per y e a r. A present value o f development costs incurred in a management s tra te g y incurred in a management s tra te g y is c a lc u la te d fo r each age cohort and discounted back to 1965 a t 5.88%. The present value fo r each age cohort in a stand s ize class to c a lc u la te a discounted development cost fo r each management s tra te g y . 1965 and 2025 are considered. Only costs incurred between The to ta l cost fo r each production a c t i v i t y is the sum o f production and development costs in c u rre d . Appendix BB con­ tains these costs f o r each production a c t i v i t y . Land Conversion Conversion o f fo re s t land to urban use is handled exogenous to the model. The acres converted during the time period o f an a ly sis were removed 168 from each resource c la s s . The amount o f each product produced on each class o f land were ca lcu la ted and summed fo r each region and each time period. In order to c a lc u la te these products, a conversion ra te was re ­ quired. The Economic Research Service p ro jected the conversion o f fo re s t land to urban use from the present to 1990 and 2020. Table 3-27 contains the acreage o f fo re s t land converted in each region during each time period and the proportion o f to ta l 1966 fo re s t land converted. Table 3 -2 7 .— Conversion o f Forest Land to Urban Use by Region. Region 1967-1990 (acres) 1 2 3 4 % o f 1967 f o r ­ e s t land 1967-2020 (ac re s) .21 1.78 2.90 2.62 1401 5116 2997 4758 181 2982 1934 2753 % o f 1967 fo r e s t land 1.63 3.05 4.49 4 .5 3 Proportions o f to ta l 1967 fo re s t land converted by the end o f each time period were c a lc u la te d . A s tr a ig h t lin e re la tio n s h ip was assumed from 1966 to 1990 and from 1990 to 2020 fo r each re g io n . in Figure 3 -2 . This is shown The proportion fo r the la s t ye ar in each time period was calcu lated by taking the ap p ro priate p o in t from these re la tio n s h ip s . Table 3-28 contains these p ro po rtion s. I t is assumed th a t a l l resource classes in a region are converted a t the same r a te . ed during The acreage convert­ each time period was c a lc u la te d by m u ltip ly in g the acreage o f each resource class in a region and tim e period by the re g io n 's conver­ sion proportion in th a t time period. This acreage was subtracted from the to ta l acreage converted from 1966 to 2025 to compute the acreage not yet converted in th a t time p erio d . The acreage not y e t converted f o r one Region H Acres 5000 r Region TL Region H I Region I Year 1965 1975 1985 1995 2005 Figure 3-2.—Acres of Forest Land Converted to Urban Use Over Time. 2015 2025 170 Table 3 -2 8 .--P ro je c te d Percentage o f 1967 F o res t Land Converted through Each Time Period. Time Period jion 1 1 2 3 4 .088 .742 1.208 1.092 2 3 4 5 6 .176 1.484 2.416 2.184 .447 3.262 4.755 4.849 .920 3.685 5.285 5.486 1.393 4.108 5.815 6.123 1.866 4.531 6.345 6.760 time period was averaged w ith the acreage a t the end o f the next time period to get the average number o f acres in production during th a t time period. This average was m u ltip lie d by the c o e ffic ie n ts o f the c u rre n t use management s tra te g y to get the products produced during each time period on each resource c la s s . A ll products produced in a region were summed.Appendix CC contains th is in fo rm atio n . Lands c u rre n tly in in te n s iv e management and environmental emphasis are handled exogenously, a ls o . Acreages c u rre n tly in in te n s iv e management i were ca lcu la ted fo r each resource c la s s . These acreages were m u ltip lie d by c o e ffic ie n ts fo r each product in each time period to c a lc u la te q u a n ti­ tie s o f products produced in each time period. These products were then summed w ith those produced on land converted to urban use and added in to the model through a special a c t i v i t y . the harvest cost per cubic fo o t. The cost o f adding in tim ber was A ll o th er products have no cost o f adding the products in to the model. These products can be shipped to demand points lik e goods produced in the production component. Extra Supplies In order to prevent in fe a s ib le so lutio ns in meeting requirem ents, supplies o f goods th a t can be purchased from outside the 12 region area 171 o f analysis by each region in the r iv e r basin are made a v a ila b le a t a cost much higher than any im porting cost from o th e r regions. this high co st, th is supply o f goods is a la s t re s o rt. Due to A pool o f these goods is made a v a ila b le fo r each region in the r iv e r basin th a t can be drawn upon in each time period. Table 3-29 l i s t these pools o f su p plies. Table 3 -2 9 .— Extra Supplies o f Goods A v a ila b le to Each Region from Outside the 12 Region Area o f A n alysis. Good Region 1 1 1 2 2 2 3 3 3 4 4 4 ' Timber (MCF) Deer Hunter Days Small Game Hunter Timber (MCF) Deer Hunter Days Small Game Hunter Timber (MCF) Deer Hunter Days Small Game Hunter Timber (MCF) Deer Hunter Days Small Game Hunter Amount Days Days Days Days 6,391,000 145,893 517,073 83,164,100 267,086 761,900 1,472,000 85,044 242,591 1,664,000 84,240 288,298 Summary This chapter has discussed th e model to be tested and the data to be used in the model. and discussed. were discussed. V ariab les were defined and equations were presented Data requirements and the methods o f o b ta in in g these data Requirements fo r tim ber and hunterdays fo r regions in the r iv e r basin were c a lc u la te d over a l l time periods. Excess supplies of timber and hunterdays fo r regions outside o f the r iv e r basin were calculated f o r a l l time p erio ds. discussed. The procedure fo r d e fin in g regions was T ran s fe r costs fo r tim ber and hunterdays were c a lc u la te d . D e fin itio n o f re p re s e n ta tiv e tra n s fe r routes was discussed. Costs per 172 mile were c a lc u la te d fo r tim ber and hunterdays. C a lc u la tin g c o e ffic ie n ts for lin e a r program ing production a c t iv it ie s were also discussed. tions were presented. aggregated. Assump­ Management s tra te g ie s and resource classes were Methods fo r c a lc u la tin g each product c o e ffic ie n t fo r each timber period were presented. a c tiv itie s were discussed. Methods o f c a lc u la tin g costs fo r production Problems associated w ith land conversion and supplying e x tra q u a n titie s o f products were also discussed. CHAPTER IV ANALYSIS AND RESULTS The purpose o f th is chapter is to present and analyze the re s u lts of tes tin g the model. out. P a r tic u la r problems w ith the model w il l be pointed Recommendations f o r land management w ill be discussed. Types o f Computer Runs Hade Five runs were made on the Michigan S ta te U n iv e rs ity Control Data Corporation 6500 computer using APEX I , a lin e a r programming alg orith m developed by Control Data C orporation. These runs represent d if f e r e n t levels o f requirements fo r tim ber and hunterdays over tim e. The methods of p ro jectin g these requirements over time were discussed in Chapter I I I . Short descrip tio n s o f these f iv e runs fo llo w . A. This b aselin e run assumes th a t tim ber and hunterday requirements remain constant over tim e. Is assumed. No growth in economic a c t i v i t y o r population However, conversion o f fo re s t land to urban use is assumed to continue. B. Requirements fo r tim ber grow only in regions w ith p u lp m ills , that i s , regions 2 and 5. Requirements fo r tim ber 1n the o th e r regions and requirements fo r hunterdays in a l l regions remain co n stant. Require­ ments fo r tim ber in regions 2 and 5 grow a t ra tes assumed w ith ris in g r e l ­ ative tim ber p ric e s , as discussed 1n Chapter I I I . The purpose o f th is run 1s to show the e ffe c ts o f uneven growth ra te s o f tim ber requirements over space on land management. 173 174 C. In th is run, tim ber requirements 1n a l l regions grow a t rates associated w ith ris in g r e la t iv e tim ber p ric e s . Requirements fo r hunter­ days grow a t the same ra te as p rojected population growth. The purpose o f th is run 1s to show the Impact o f growth o f both tim ber and hunterday requirements on land management. D. Timber requirements grow a t rates associated w ith 1970 p ric e s . Hunterday requirements grow a t the same ra te as the population. The purpose o f the run 1s to show the Impact o f an even higher ra te o f growth of timber requirements on land management. E. Timber requirements remain constant over tim e. fo r hunterdays grow a t the same ra te as population. Requirements The purpose o f th is run is to show the impact o f no growth in wood products in d u stry w h ile population continues to grow. Discussion and Analysis o f Land Management Results The purpose o f th is model is to provide recommendations fo r land management planning and provide info rm ation concerning the impacts o f a lte rn a tiv e plans. This section w ill Include discussion o f the land man­ agement re s u lts o f these f iv e runs. The land management a c t i v i t ie s can be d ivid ed In to two groups: timber-producing and 2) non-t1mber-producing. 1) Timber producing a c t iv it ie s produce merchantable tim ber during the period o f a n a ly s is . These a c t iv it ie s Include the c u rre n t use management s tra te g y and the conversion from c u r­ rent use to the In te n s iv e management s tra te g y on the fo llo w in g resource classes: 1) c o n ife r , oak, and maple sawtimber s iz e classes 1n adequate stand condition classes, 2) c o n ife r , oak and maple sawtimber s iz e classes 1n stands re q u irin g tim ber stand Improvement to convert from c u rre n t use to in te n s iv e management, 3) c o n ife r sawtimber s iz e classes in which con- 175 ditlon classes are not d iffe r e n tia te d but produce merchantable tim b er, and 4) aspen-birch s e e d lin g -s a p lin g , poletim ber, and sawtimber size classes. Groups 2 through 4 w il l be re fe rre d to as non-adequate condi­ tion classes since the condition o f these classes is not c u rre n tly ade­ quate to convert from c u rre n t use to in te n s iv e management. Non-adequate condition classes include those classes where tim ber stand improvement is needed to convert from c u rre n t use to in te n s iv e management and where condition classes are not d if fe r e n tia te d . Non-timber producing a c t i v i t ie s do not produce tim ber during the time period o f a n a ly s is . Some stand s iz e classes w il l not reach harvest age during the tim e period o f a n a ly s is . Some resource classes w il l not produce merchantable tim ber a t any age. Environmental emphasis manage­ ment s tra te g ie s w il l not allow removal o f any tim b er, so they are non­ timber producing s tra te g ie s . Current use and the conversion from c u rren t use to in te n s iv e management s tra te g ie s on the fo llo w in g resource classes are non-timber producing: 1) c o n ife r, oak, elm, and maple se ed lin g -sap lin g and poletim ber s iz e classes and 2) c o n ife r, oak, elm, and maple saw­ timber size classes which produce no merchantable tim ber. Timber-producing lands are classes o f land capable o f producing timber during the time period o f a n a ly s is . The environmental emphasis management s tra te g y , a non-tim ber producing management s tra te g y , can be applied to tim ber producing lan d. Non-timber producing lands are classes o f land which are not capable o f producing tim ber during the time period of an alysis. Both tim ber-producing and non-tim ber producing lands can be in adequate o r non-adequate stand co n dition classes. Timber-Producing A c t iv itie s Timber-producing a c t i v i t ie s w il l be discussed f i r s t . There are two 176 levels o f tim ber production among these f iv e d iff e r e n t runs. Runs A and E have Id e n tic a l land management patterns in the lower le v e l o f production. Runs B, C, and D have id e n tic a l land management patterns in the higher level o f production. More tim ber is produced in time periods 4 and 5 a t the higher le v e l o f production than a t the lower le v e l o f production. Timber production is equal a t both le v e ls o f production in time periods 1, 2, 3, and 6. The re s u lts o f runs A and E w il l now be discussed. A ll tim b er-p ro ­ ducing stands in adequate co n dition classes are converted to in te n s iv e management before they are c u t, a t the e a r lie s t possible tim e. The same is tru e o f tim ber-producing stands re q u irin g tim ber stand improve­ ment. Classes in which co n dition classes are not d iffe r e n tia te d are more complex. A ll sawtimber classes, both c o n ife r and asp en -birch, are con­ verted to in te n s iv e management before the harvest. Aspen-birch p o le­ timber s ize classes are a ll converted to in te n s iv e management a t the e a rlie s t possible tim e. However, aspen-birch s e ed lin g -sap lin g s iz e classes are a ll converted to environmental emphasis in which there is no tim ber production. Production o f tim ber in the aspen-birch se ed lin g -sap lin g size classes is concentrated in time periods ments fo r tim ber in time periods 4 and 4 5 and 5 . A ll re q u ire ­ in runs A and E are s a t is ­ fied by management s tra te g ie s on o th e r classes o f fo re s t land- These management s tra te g ie s also produce tim ber in o th e r time periods. Aspen- birch se ed lin g -sap lin g s ize classes are kept out o f tim ber production to reduce costs w ithout decreasing production in time periods 1, 2 , 3 and 6. I f other classes o f tim ber producing land were kept out o f production, requirements in time periods 1, 2 , 3 and 6 could not be s a t is f ie d . There is no s p a tia l v a ria tio n in th is p a tte rn fo r runs A and E. The only s p a tia l v a ria tio n in acreages is due to v a ria tio n s in the land resource. The re s u lts o f runs B, C, and D are id e n tic a l except fo r the seedling-sapling s iz e classes o f aspen-birch. With these runs, aspen- birch seed lin g -sap lin g s iz e classes are converted from c u rre n t use to intensive management a t the present, the e a r lie s t conversion possible. The only d iffe re n c e between the runs a t the higher le v e l o f tim ber production and the runs a t th e lower le v e l o f tim ber production is the status of se ed lin g -sap lin g classes o f aspen-birch. In runs a t the lower level o f tim ber production a l l classes o f tim ber-producing lands, except aspen-birch s e ed lin g -sap lin g classes are converted from c u rre n t use to intensive management a t the e a r lie s t possible tim e. In runs a t the higher level o f tim ber production, a l l classes o f tim ber-producing land are con­ verted from c u rre n t use to in te n s iv e management a t the e a r lie s t possible time. At the higher le v e l o f tim ber production, requirements fo r tim ber are not s a tis fie d in time periods 4 and 5 even though aspen-birch seedling sapling s iz e classes are converted to in te n s iv e management a t the e a r lie s t possible tim e. Timber requirements appear to be the most d i f f i c u l t requirements to meet. A ll tim ber requirements are met only when th ere is no growth in timber requirem ents. As soon as th ere is growth in tim ber requirements in regions w ith p u lp m ills , any unused tim ber-producing p o te n tia l is forced in to the most in te n s iv e form o f management. Two fa c to rs emerge which appear to s e rio u s ly a f f e c t the p a tte rn o f land management. The f i r s t fa c to r is the time d is tr ib u tio n o f production, that i s , how much tim ber is produced in each time period by a management 178 strategy on a resource c la s s . of timber. The second fa c to r is the cost per u n it Included are harvesting and development costs. costs are the only d if f e r e n t ia t in g fa c to r . Development Harvesting cost per u n it o f timber are equal fo r a l l management s tra te g ie s . The time d is trib u tio n o f production seems to be the most im portant factor in determining the p a tte rn o f management o f tim ber producing land. The production o f tim ber in the aspen-birch s e ed lin g -sap lin g classes is concentrated in time periods 4 and 5. When there is no growth in tim ber requirements, tim ber production can exceed requirements in time periods 4 ized. and 5 . As a r e s u lt, tim ber producing capacity is not f u l l y u t i l ­ Timber-producing a c t iv it ie s o th er than the aspen-birch s e ed lin g - sapling classes spread tim ber production over more time periods. As a re s u lt, i t is d i f f i c u l t to remove these o th er a c t i v i t ie s from production since tim ber requirements in o th e r time periods can no longer be met. With growth in tim ber requirem ents, requirements in the r iv e r basin can no longer be met, even when tim ber-producing cap acity is f u l l y u t iliz e d . All timber producing classes are converted to in te n s iv e management in an attempt to s a tis fy these tim ber requirem ents. Costs also seem to be im p ortan t. With adequate co n dition classes, the cost per u n it o f tim ber which may include harvesting and development costs is the same regardless o f the management s tra te g y since development costs are not necessary, according to Forest Service personnel. The most e f fic ie n t form o f management on the adequate classes is conversion to intensive management a t the e a r lie s t possible tim e. Development costs are incurred by a l l classes re q u irin g tim ber stand improvement to convert to in ten sive management and by classes in which stand co n d itio n classes are not d if f e r e n t ia t e d . Under c e rta in circumstances, these development 779 costs could keep acreages out o f in te n s iv e production. Poletim ber and sawtimber classes o f the aspen-birch ecosystem have no development co s ts , so Intensive management would be the most e f f i c i e n t use o f these classes. The combination o f development costs and time d is tr ib u tio n o f pro­ duction appears to keep the s e ed lin g -sap lin g classes o f the aspen-birch ecosystem out o f production when th ere is no growth in tim ber requirem ents. When there is growth in tim ber requirements over time in runs B, C, and D, timber requirements are not s a t if ie d in time periods 2 through 6. As a re s u lt, the model w ill in c u r any cost in an attem pt to increase tim ber production. The time d is tr ib u tio n o f production w il l not cause the model to keep lands capable o f producing tim ber out o f tim ber production. Acreages o f land in each management s tra te g y are presented in Appen­ dix DD. Non-Timber Producing A c t iv itie s The p attern o f land management s tra te g ie s is more d i f f i c u l t to d is ­ cuss because each run is d if f e r e n t . However, production p o te n tia l o f hunterdays c u rre n tly is not being used to it s l i m i t . Im porting p o te n tia ls from regions outside o f the r iv e r basin are not being f u l l y u t il i z e d , e ith e r. Other fa c to r s , besides those a ffe c tin g tim ber production, w ill have an e f f e c t on land management. The re s u lts o f the runs on non-tim ber producing lands w il l be r e ­ viewed and analyzed. Refer to Appendix DD f o r the acreages o f each management s tra te g y on each resource class 1n each re g io n . results o f run A w il l be discussed. low. F i r s t , the Changes in the o th e r runs w il l f o l ­ A ll ecosystems w ith adequate stand conditions are converted to in ­ tensive management. A ll are converted to in te n s iv e management a t the present except f o r the s e e d lin g -s a p lin g s iz e class o f oak which is con- 180 verted to in te n s iv e management a t the ju n ctu re between seedling-sapl1ng and poletimber size classes. The remaining classes are in c u rre n t use, except fo r some classes in regions 2 and 3. In region 2, the elm pole­ timber s iz e class is converted to in te n s iv e management and the elm seedlin g -sap lin g s iz e class is converted to in te n s iv e management a t the juncture between poletim ber and sawtimber. In region 3, the c o n ife r pole­ timber size classes in a ll non-adequate classes are converted to in te n ­ sive management. The oak poletim ber s iz e class when stand condition classes are combined and no merchantable tim ber is produced is also con­ verted to in te n s iv e management. The elm s e ed lin g -sap lin g s iz e class is converted to in te n s iv e management a t the ju n c tu re between poletim ber and sawtimber. With run B, th ere is a movement toward less in te n s iv e management. On adequate condition classes, there is a trend toward conversion to in ­ tensive management a t l a t e r time periods. In region 1 , the maple-beech- blrch seed lin g -sap lin g s iz e class converts to in te n s iv e management a t the juncture between poletim ber and sawtimber ra th e r than a t the present. The same is tru e fo r the oak se e d lin g -s a p lin g s iz e class in regions 2 and 4. ment. There are no changes in classes re q u irin g tim ber stand improve­ In classes where stand co n dition classes are combined and which can also produce merchantable tim b er, th ere is also a trend toward less intensive management. Some o f the acreage o f the c o n ife r poletim ber s iz e class in region 3 remains in cu rren t use w hile some converts to in te n s iv e management. In run A, a l l the acreage o f the c o n ife r poletim ber class converts to in te n s iv e management. There is also a change toward less intensive management when both co n d itio n classes are combined and no mer­ chantable tim ber can be produced. A ll o f the elm s e e d lin g -s a p lin g s iz e 181 class acreage remains In cu rren t use. In run A, a l l o f th is acreage 1s converted to In te n s iv e management a t the ju n ctu re between poletim ber and sawtimber size classes. In run C, there 1s a movement toward less In te n s iv e management o f some classes and toward more In te n s iv e management 1n o th er classes r e la ­ tive to A. as B. In the adequate co n dition classes, the changes are the same In the stands re q u irin g tim ber stand Improvement th ere 1s a move­ ment toward more In te n s iv e management. The oak poletim ber s iz e class converts from c u rre n t use to In te n s iv e management, w h ile 1n run A i t re ­ mains 1n cu rren t use. When both co n dition classes are combined and mer­ chantable tim ber can be produced, th ere is no change from run A. When no merchantable tim ber can be produced, there are changes 1n both d ire c ­ tions. In region 2 , the elm seed lln g -sap H n g class remains 1n c u rre n t use w hile remaining from c u rre n t use to in te n s iv e management in run A. The c o n ife r poletim ber s iz e class converts from c u rre n t use to In te n s iv e management, w h ile remaining in c u rre n t use in run A. Run D has only one change as compared w ith C. In region 2, only a portion o f the acreage o f the oak poletim ber s iz e class in the condition class re q u irin g tim ber stand Improvement is converted from cu rren t use to in tensive management. The remaining acreage is in c u rre n t use. In run C, a l l the acreage o f th is class is converted from c u rre n t use to in ­ tensive use. Run E moves toward more in te n s iv e management o f non-timber-produc1ng lands than run A. A ll changes are made in classes where both co n d itio n classes are combined and no merchantable tim ber can be produced. In re ­ gion 2 , the oak poletim ber s iz e class converts from c u rre n t use to in te n ­ sive management. In run A, th is class remains in cu rren t use. In region 3, the oak s e e d lin g -s a p lin g s ize class converts from c u rre n t use to in te n - 182 slve management a t the ju n ctu re between poletim ber and sawtimber. A, th is class remains in c u rre n t use. In run In region 4 , the oak poletim ber size class converts from cu rren t use to in te n s iv e management. In run A, this class remains in c u rre n t use. Timber-producing management s tra te g ie s also produce big and small game hunterdays. In g en eral, more hunterdays are produced w ith in te n s iv e management than w ith cu rren t use. Non-timber-producing management s t r a t e ­ gies w ill re ac t to changes in in te n s ity o f management on tim ber-produc­ ing lands and s p e c if ic a lly to changes in production and time d is tr ib u tio n o f production o f hunterdays from tim ber-producing management s tr a te g ie s . Timber-producing management s tra te g ie s do not produce enough hunterdays to meet requirements. Non-timber-producing management s tra te g ie s produce the remaining q u a n titie s o f hunterdays needed to s a tis fy hunterday re q u ire ­ ments. Given fix e d demands fo r hunterdays, in te n s ity o f managing non­ timber-producing lands should decrease as in te n s ity o f tim ber management increases. This re s u lt should occur because the production o f hunterdays increase on tim ber-producing lands as management becomes more in te n s iv e . With fix e d requirem ents, fewer hunterdays must be produced on non-tim ber producing lands to meet hunterday requirem ents. As a r e s u lt , the non- timber-producing lands can be managed less in te n s iv e ly . in run B. This r e s u lt occurs Management o f nontimber-producing lands w ill a ls o re a c t to changes in time d is tr ib u tio n o f tim ber-producing lands to meet the r e ­ quirements f o r hunterdays. Total import p o te n tia l is not u t il i z e d . hunterdays in the r iv e r basin does not occur. Maximum production o f As a r e s u lt , th ere is an important t r a d e -o ff between costs o f im porting and development costs. Development costs are costs o f converting lands from c u rre n t use to in - 183 tensive management 1n order to Increase production o f goods to meet re ­ quirements. In some cases. I t may be cheaper to Import than to In te n s ify management o f non-tim ber-producing lands. In o th er cases, 1 t may be cheaper to In te n s ify management than to Im port. Problems associated w ith the time d is trib u tio n o f production may complicate the t r a d e - o f f , however. A ll adequate condition class stands are converted to In te n s iv e man­ agement in run A. This occurs because development costs are zero. It costs no more to convert lands to in te n s iv e management than to leave them in current use. According to Forest Service personnel developing these c o e ffic ie n ts , the basic d iffe re n c e is landowner in te n t concerning how to use these lands. I t is d i f f i c u l t to see, however, how landowner In te n t changes land p ro d u c tiv ity unless some p o s itiv e , c o s tly a c tio n is taken. The problem o f time d is tr ib u tio n seems to ex p la in why the oak seed lin g sapling class converts a t a l a t e r time in region 1 than the o th er regions in run A. D iffe r e n t time d is trib u tio n s o f production are possible in these adequate co n dition class stands a t the same co sts. T h e re fo re , more than one optimal so lu tio n is possible fo r a given s e t 'o f requirem ents. Surpluses could be produced in e a r l i e r time periods a t the same cost i f a ll conversions o f s e ed lin g -sap lin g classes took place a t the present. The problem o f im porting versus conversion to in te n s iv e mangement becomes more im portant on non-adequate stand co n dition classes in run A. Region 4 exports hunterdays; th ere is no need to in cu r development costs to increase production to meet requirements in th a t regio n. Region 1 im­ ports hunterdays, but no conversion o f these lands to in te n s iv e manage­ ment occurs. I t would seem th a t the costs o f im porting hunterdays is too cheap to j u s t i f y in c u rrin g development costs to in te n s ify production to meet requirements in region 1. 184 The model forces some o f the non-adequate stand condition classes Into Intensive management. and outside the basin. section. basin. Big-game hunterdays are Imported from In s id e Flows o f a l l goods w il l be discussed in a l a t e r Small game hunterdays are Imported only from in s id e the r iv e r I t would seem th a t some Im porting costs are high enough to cause conversions to In te n s iv e management to occur. Costs o f im porting small game hunterdays are g re a te r than costs o f im porting big game hunterdays. Also, small game hunterdays are not imported from outside the r iv e r basin. I t would seem th a t the costs o f im porting small game hunterdays cause development costs to be incurred to in te n s ify management. I t is cheaper •to incur development costs to In te n s ify management than to import small game hunterdays from outside the region. i. The model also forces non-adequate stand co n dition classes in to intensive management in region 3. This region imports big game hunter­ days in some time periods from region 4 but exports them in time period 6. Small game hunterdays are imported from in s id e and o utside the r iv e r basin. This region is fa r th e r from big game hunterday exporting regions outside o f the r iv e r basin than small game hunterday exporting regions outside o f the r iv e r basin. I t would appear th a t the conversion o f non- adequate stand condition classes in to in te n s iv e management is needed to meet requirements fo r big game hunterdays a t lower co st. I t appears th a t land p ro d u c tiv ity , development co s ts , im porting costs, and the time d is trib u tio n o f production a l l seem to be im portant factors in converting non-adequate stand condition classes to in te n s iv e management. The re s u ltin g p a tte rn is d i f f i c u l t to e x p la in . The problem of j o i n t production associated w ith lin e a r programming may com plicate the pattern o f land management. I t is im p ortan t, however, to p o in t out th a t 185 that there is a s p a tia l d if f e r e n t ia tio n o f land management p atterns o f non-timber-producing lands in the non-adequate stand co n d itio n classes. Costs o f im porting, an im portant fa c to r in bring ing space in to th is model, appear to have an impact on "optim al" land management patterns because they tr a d e -o ff w ith development costs. In run B, th e re is more in te n s iv e tim ber management a c t i v i t y re ­ sulting from growth in tim ber requirements in region 2. growth in hunterday requirem ents. There Is no Non-timber-producing lands move in to a less in te n s iv e s ta te o f management. Changes in time d is tr ib u tio n o f hunterday production by tim ber-producing management s tra te g ie s r e s u lt in la t e r conversions to in te n s iv e management thereby reducing surpluses o f hunterdays in e a r l i e r time periods. As s ta ted e a r l i e r , more hunter­ days could be produced a t the same cost on adequate co n d itio n classes. Non-adequate stand co n dition class stands changed to c u rre n t use in r e ­ gions 2 and 3 in order to decrease development costs w h ile meeting r e ­ quirements f o r hunterdays. In run C, the only d iffe re n c e as compared w ith run A occurs in the non-adequate co n d itio n classes. Some changes are toward more in te n s iv e management w h ile others are toward less in te n s iv e management. This re ­ s u lt r e fle c ts a change in the time d is tr ib u tio n o f hunterday requirem ents. Requirements are higher in l a t e r time periods. A lso , region 4 begins to import small game hunterdays thus decreasing i t s export p o te n tia l. As a re s u lt, more production a t l a t e r time periods is required in both regions 2 and 3. The cost o f in te n s iv e production seems to be less than the cost o f Im porting. In run D, th ere is a s lig h t change in the management p a tte rn as com­ pared w ith run C. A small p o rtio n o f the acreage o f oak poletim ber s iz e 186 class 1n the non-adequate stand co n dition classes remains 1n c u rre n t use, while the remainder 1s converted to In te n s iv e management. This change Is not e a s ily explained. In run E, the management o f non-tim ber-producing lands 1s more In ­ tensive than in the case o f run A. A ll Increases in management in te n s ity beyond the s itu a tio n in run A occur in classes where both co n dition classes are combined. More in te n s iv e production is needed to meet growth in hunterday requirements. The model forces some o f the acreage o f non- adequate stand co n dition classes in to in te n s iv e management f o r the f i r s t time in region 4 . Regions 2 and 3 also increase in te n s ity o f management. Both regions 2 and 3 import from region 4. I t appears to be cheaper to in te n s ify management in regions 2 , 3, and 4 than to import from outside the r iv e r basin. Region 1 continues to im port from outside the r iv e r basin w ithout in te n s ify in g management. I t appears to be cheaper to Import hunterdays than to in te n s ify management to Increase production o f hunter­ days. Run E shows th a t i t 1s cheaper to in te n s ify management o f n on-tim ber-producing classes o f land than on tim ber-producing classes o f land 1n order to meet increases in hunterday requirements when tim ber re q u ire ­ ments remain constant. curred. In th is way tim ber harvesting costs are not in ­ In order to minimize co s ts , the model converts land in co n d itio n classes re q u irin g tim ber stand improvement w ith r e la t iv e ly low develop­ ment costs from cu rren t use to In te n s iv e management. Factors A ffe c tin g Location o f A c t iv itie s Patterns o f managing tim ber-producing classes o f land do not vary between regions. Timber requirements are-h igh r e la t iv e to the productive capacity o f the land. I f tim ber requirements are to be met, a l l classes 187 of timber-producing land must be managed in te n s iv e ly . In runs A and E, surpluses o f tim ber are produced 1n time periods 4 and 5. As a r e s u lt , the aspen-birch s e e d lin g -s a p lin g s iz e classes are removed from tim ber production. runs B, C, and D which produce no surpluses o f tim b er, In the aspen-birch seedl1ng-saplIng s iz e classes are converted to in te n s iv e management. meet these high le v e ls o f tim ber requirem ents, regions To must import tim b e r, i f p o s s ib le , and tim ber-producing lands must be managed in te n s iv e ly . The only fa c to r which d iffe r e n tia te s the s p a tia l d is trib u tio n o f management s tra te g ie s is the s p a tia l d is tr ib u tio n o f land resources. Im portant fa c to rs th a t determine the p a tte rn o f manage­ ment are development co s ts , harvesting co sts, the time d is tr ib u tio n o f production, and the le v e l o f tim ber requirements over tim e. The patterns o f managing non-tim ber-producing lands are more com­ plex. There is d if f e r e n t ia t io n o f p atterns o f management between regio ns. Non-timber-producing management s tra te g ie s produce the resid ual o f hunter­ days not produced by tim ber producing management s tra te g ie s to meet hun­ terday requirements. S p a tia l fa c to rs besides the d is tr ib u tio n o f land resources seem to be im portant. ant fa c to r. T ran spo rtatio n costs become an im port­ There is a tr a d e - o f f between in c u rrin g costs o f im porting goods and in c u rrin g development costs to increase production o f goods in the r iv e r basin. to be made. Increasing le v e ls o f requirements cause these tra d e -o ffs When a region cannot support i t s requirements f o r hunterdays, 1t must in te n s ify management o r im port hunterdays, th a t i s , hunters must go outside o f the region to hunt. The alg o rith m used in th is model w ill choose the cheapest way to meet requirem ents. A region may import a l l hunterdays a v a ila b le from another region w ith o u t in te n s ify in g management and w ithout s a tis fy in g requirem ents. A t r a d e - o f f between im porting and 188 intensifying must again be evalu ated. This t r a d e - o f f 'Is complicated by the time d is trib u tio n o f production and the problem o f j o i n t production o f big and small game hunterdays. The le v e l o f requirements 1s the fa c to r th a t u ltim a te ly determines whether there w ill be s p a tia l d if fe r e n tia tio n 1n patterns o f land manage­ ment. I t seems th a t land management patterns w il l become more s e n s itiv e to transport costs as le v e ls o f requirements decrease. Timber requirements are high r e la t iv e to the productive capacity o f the regio n. Transport costs have no Impact on the s p a tia l d is trib u tio n o f land management on tim ber-producting classes o f land. The only v a ria tio n s in the p a tte rn o f management are caused by the time d is tr ib u tio n o f production and the spa­ t ia l p attern o f land resources. Import p o te n tia ls are depleted in some time periods even a t the lowest le v e ls o f requirements th e re fo re re q u ir­ ing in te n s ific a tio n o f management to meet requirements regardless o f cost. At lower le v e ls o f tim ber requirem ents, production p o te n tia l is greater than requirements in some time periods. As a r e s u lt, aspen- birch seedl1ng-sapling classes are removed from production to avoid har­ vesting costs. However, as soon as th ere is growth in requirem ents, the most in te n s iv e form o f management is re q u ire d . Importing p o te n tia ls are depleted so th a t management becomes more in te n s iv e to meet tim ber re q u ire ­ ments. In f a c t , even the most in te n s iv e form o f management cannot meet these requirements. Requirements fo r hunterdays, however, are low r e la t iv e to the pro­ ductive cap acity o f the land. As a r e s u lt , costs o f in te n s iv e management must be compared to costs o f im porting. In te n s iv e management w il l be located in areas w ith r e l a t i v e ly high requirements in order to lower transpo rtatio n co sts. The tr a d e -o ff between costs o f im porting and costs 189 of Intensive management 1s Im portant only when the capacity to Import has not been depleted. However, given a le v e l o f development co sts, intensive management becomes more a ttr a c t iv e as the costs o f importing increase. Receipts o f Goods The amount o f goods received a t each region in the basin w ill be discussed in th is s e c tio n . Surpluses above and d e fic its below re q u ire ­ ments w ill be pointed out. Appendix EE contains the d e f ic it s and su r- pluses. In runs A and E, a l l requirements were met in a l l time periods and regions. 5. There was a surplus o f tim ber in regions 1 and 4 in time period In run B, there were d e f ic it s o f tim ber in region 2 through 6. 2 in time periods A ll o th er tim ber requirements were met. The d e fic it o f timber in region 2 brings about the change in management o f aspen-birch seedling-sapl ing s iz e classes from environmental emphasis to in te n s iv e management. 1. There was a surplus o f hunterdays in region 4 in time period In run C, there is a d e f i c i t o f tim ber in region 1 in time period 3 and region 2 in tim ber periods 2 through 6. ments are met. A ll o th er tim ber re q u ire ­ A ll requirements fo r hunterdays are met. There is a sur­ plus o f small game hunterdays in region 4 in time period 1. In run D, there are tim ber d e f ic it s in region 1 in time periods 3, 4 , and 6 and region 2 during time periods 2 through 6. are met. A ll o th e r tim ber requirements A ll requirements fo r hunterdays are met. There 1s a surplus o f small game hunterdays in region 4 in time period 1. Timber d e f ic its in runs B, C, and D in d ic a te th a t i f p rojected tim ­ ber requirements are to be met, tim ber purchases w ill have to be made from areas outside o f the regions included in th is analysis during c e rta in time periods. Region 2 w i l l have to make these purchases 1n time periods 2 through 6 1n runs B, C, and D. These d e f ic it s In d ic a te th a t the pulp- m ill 1n region 2 might have d i f f i c u l t y 1n o b tain in g tim ber supplies to expand pulp-making cap ac ity . Region 1 would have to make these purchases 1n time period 3 in run C and time periods 3 , 4 , and 6 in run D. Um ber surpluses in runs A and E are o f short d u ratio n . These surpluses rep re­ sent an export p o te n tia l fo r th a t time period ra th e r than an o pportunity for growth o f tim ber-using In d u s trie s . These surpluses occur in regions 1 and 4 in time period 5 in runs A and E. Hunterday surpluses in d ic a te p o s s ib ilitie s fo r increased consumption by people in the region o r an export p o te n tia l. These surpluses are o f sh o rt d u ratio n . The surpluses are in region 4 in time period 1 in runs B, C, and D. A ll these surpluses remain in the region in which alg o rith m minimizes they were produced. The costs by not In c u rrin g tra n s p o rta tio n co sts. Production The actual q u a n titie s o f goods produced w i l l not be presented in this s e c tio n , but ra th e r are shown in Appendix FF. Tables w i l l be used to show the orders o f runs in the production o f various goods. duction 1n the r iv e r basin w il l be discussed. F ir s t , pro­ Next, production in the regions w ill be discussed. River Basin Production Table 4-1 ranks each plan according to th e amount o f each commodity produced in each time period. In order to make comparisons o f the runs e a s ie r, a ra tin g system was used to evaluate these patterns over tim e. o f 1 through 5 in each time p erio d . Each run receives a rank A rank o f 1 goes to the run w ith the highest production o f the commodity in the time p erio d . A rank o f 5 goes 191 Table 4 - 1 . — Ranking o f Runs f o r Production o f Commodities 1n the Kalamazoo R ive r Basin Time 1 2 3 4 5 6 Timber a =b =c=d =e A=B=C=D=E A=B=C=D=E B=C=D>A=E b=c= d >a =e A=B=C=D=E Big Game Hunterdays Small Game Hunterdays E>A>C>D>B D>C>B>A>E C>D>E>B>A C>D>E>B>A D>C>E>A>B E>C>D>A>B D>C>B>A>E D>B>C>E>A D>C>B>E>A C>D>B>E>A C>B>D>A>E B>C>D>E>A Erosion B>C>A>E>D A>C>D>E>B A>E>C>D>B E>A>C>D>B A>E>C>D>B A>E>C>D>B to the run w ith the lowest production in the time period. The rank o f the run in time periods 1 through 6 is summed to get a to ta l score and the run w ith the lowest to ta l score gets a rank o f one. higher score gets the next highest rank up to 5. weighted eq u ally in th is ra tin g system. fo r each commodity. Each successively Each time period is These rankings are c a lc u la te d Table 4 -2 contains these ra tin g s . Table 4 - 2 . — Ranking o f Total R iver Basin Production fo r Each Commodity. Commodity Ranking Timber Big Game Hunterdays Small Game Hunterdays Erosion B=C=D>A=E B>D>E>A>B C=D>B>A=E A>E=C>D>B Regional Production The r e la tiv e le v e ls o f production o f a l l commodities in a l l time periods in a l l regions w il l now be discussed. Timber. Runs A and E are id e n tic a l in a l l time periods. C, and D are id e n tic a l in a l l time periods. Runs B, The only d iffe re n c e between the two groups is th a t production is g re a te r in the fo u rth and f i f t h time 192 periods fo r runs Bt C, and D than runs A and E. Big Game Hunterdays. This p a tte rn is more d i f f i c u l t to describe. There is much more d if f e r e n t ia t io n in time and space than w ith tim ber production. Table 4 -3 gives these rankings f o r the fo u r regions in each time period. Because o f the la rg e volume o f in fo rm atio n , these re s u lts are not contained in an appendix. The same ranking used to rank r iv e r Table 4 - 3 . --Ranking o f Big Game Hunterday Production by Run in Each Time Period. 1 Time 2 B=C=D>A=E B=C=D>A=E B=C=D>A=E d =c=d >a =e B=C=D>A=E B=C=D>A=E 1 2 3 4 5 6 3 E>A>C>D>B E>A>C>D>B C>D>B>E>A OD>E>B>A C>D>E>A>B C>D>E>A>B A=B=C=D=E A=E>C=D=B C=D>D>E>A C=D>B>E>A C=D>E>B>A C=D>B>E>A 4 E>A>C>D>B e >c>d >b >a C>D>B>A>E d >c >e >b>a d >e >c >b >a E>C>D>B>A basin production over time was used to rank regional production. The results o f th is ranking are presented in Table 4 -4 . Table 4 - 4 . — Ranking o f O verall Big Game Hunterday Production by Run fo r Each Region. I — Region Ranking 1 2 3 4 B=C=D>A=E C>U=E>A>B C=D>B>E>A C=E>D>B>A 1 Small Game Hunterdays. to e x p la in . ' ■ 1■ ■ This p a tte rn o f production is also d i f f i c u l t There is much d if f e r e n t ia t io n o f production in time and space. The p attern o f small game hunterday production is d if f e r e n t th a t the p a t- 193 tern o f big game hunterday production. Table 4 -5 Illu s t r a t e s the rank­ ing fo r each region in each time period. Because o f the la rg e amount o f data, these re s u lts are not contained in an appendix. Each run was ranked Table 4 - 5 .— Ranking o f Small Game Hunterday Production by Region fo r Each Time Period. Region Time 1 2 3 4 1 2 3 4 5 6 B=C=D>A=E B=C=D>A=E B=C=D>A=E B=C=D>A=E B=C=D>A=E B=C=D>A=E C>D>B>E>A E>A>C>D>B C>D>B>E>A C>D>E>A>B C>B>D>E>A D>C>B>E>A B=C=D>A=E b=o d >a =e D>B>C>A>E C=D>B>E>A b=c >a >d>e B>C=D>E>A A>D>C>B>E D>B>E>C>A C>D>B>E>A C>D>B>E>A B>C>D>E>A C>D>B>E>A fo r each region by using the same method used in the previous two sec tions. These re s u lts are shown in Table 4 -6 . Table 4 - 6 . — Ranking o f Small Game Hunterday Production Over A ll Time Periods fo r Each Region. Erosion. Region Ranking 1 2 3 4 B=C=D>A=E C>D>B>E>A B=C>D>A>E C=D>B>E>A Regions one and th ree have id e n tic a l p a tte rn s . two and four are more d i f f i c u l t to describe. Regions Table 4 -7 ranks the pro­ duction o f erosion in each time period fo r each run. Because o f the large amount o f in fo rm a tio n , these re s u lts are not contained in an appen­ dix. The o v e ra ll production o f erosion was also ranked. The ranking is 194 presented in Table 4 -8 . Table 4 - 7 .--Ranking o f Production o f Erosion by Run in Each Time Period. Region Time 1 ,3 2 4 1 2 3 4 5 6 A=E>B=C=D A=E>B=C=D A=E>B=C=D A=E>B=C=D A=E>B=C=D A=E>B=C=D B=C=D>A=E C>D>B>A>E A=E>C>D>B C>D>E>A>B C>D>E>B>A C>D>B>E>A B=C=D>A=E A>E>B=C=D A>E>B=C=D A>E>C>D=B A>C>B=D>E A>C>B=D>E Table 4 - 8 . — Ranking o f Production o f Erosion Over A ll 1 Time Periods fo r Each Run in Each Region. Region Ranking 1 .3 2 4 A=E>B=C=D D>C>B>E>A A>C>B=D>E OBERS Demands The r iv e r basin cannot meet Series C OBERS demands fo r sawtimber removals as c a lc u la te d by the Economic Research Service (Economic Research Service, personal correspondence, 19 75 ). Series C p ro je c tio n s are r e la ­ t iv e ly low p ro je ctio n s compared to o th e r s e rie s . The only run made which included OBERS demands as c o n stra in ts was found to be in fe a s ib le . Table 4-9 l i s t s OBERS demands by time period and the production in those time periods in the in fe a s ib le run. 6. OBERS demands are met only in time period I n f e a s ib i li t i e s occur 1n time period 1 in regions 2 , 3, and 4 and time period 3 in regions 3 and 4 . 195 Table 4 - 9 . — OBERS Demands and R iver Basin Production 1n the In fe a s ib le Run. OBERS Time 1 3 6 Source: Demand ( c f ) Basin Production ( c f ) 4,9 56 ,1 00 5,718,506 5,439,500 4,899,604 5,334,562 6,145,187 Economic Research S ervice; personal correspondence, 1975. Runs in which OBERS demands are not a c tiv e cannot meet these re ­ quirements e ith e r . ods 1, 3, and 6 . Runs A through E have id e n tic a l re s u lts in time p e r i­ These re s u lts are lis t e d in Table 4 -1 0 . Runs A through Table 4 - 1 0 .— R iver Basin Timber Production in Time Periods 1 , 3 , and 6 f o r Runs A Through E. Time 1 3 6 Basin Production 4 ,5 45 ,6 04 3,366,448 6,145,187 E f a l l short o f OBERS demands in time periods 1 and 3. These re s u lts show, however, th a t the time d is tr ib u tio n o f production o f tim ber can be changed. Flows o f Goods Between Regions The tra n s p o rta tio n component is the mechanism through which produc­ tion requirements are a llo c a te d over space. The flows o f goods between regions w il l be a fu n ctio n o f the production and the time d is tr ib u tio n o f production 1n regio ns, costs o f production, requirements and growth o f regional requirem ents, tra n s p o rt co sts, and surpluses and d e f ic it s o f commodities in regions outside o f the r i v e r basin. The actual volumes o f 196 the flows are not contained 1n an appendix because o f the la rg e amount of inform ation. Timber Run A is the baseline run to which a l l o th er runs are compared. Regions from which goods are imported and to which goods are exported were id e n tifie d by time p erio d. to conserve space. However, actual q u a n titie s are not shown Table 4-11 in d ica te s o rig in regions from which a re ­ gion imports tim ber and d e s tin a tio n regions which export tim b er, by time period. Table 4 -1 1 .— Exports and Imports o f Timber fo r Run A. Region 1 2 3,4 Region 1 2 3 4 Region 2 imports only. Imports From Region During Time Periods 1 2-4 2 , 3 , 4 ,6 1-6 1-6 1 -4 ,6 1-3 1-4 9 10 1 3 4 8 11 12 — Exports to Region During Time Periods 2 - 2 2 2 -4 ,6 - 1-6 1-6 Regions 3 and 4 export o n ly. ports and exports sim ultaneously in time 2 through 4 . Region 1 im­ This p attern 197 must be caused by a s lig h t cost advantage such th a t 1t 1s cheaper to move goods to region 2 through region 1. regions in the r iv e r basin. Region 2 imports from a l l o th er Imports to region 2 decrease in time period 5 due to r e la t iv e ly high production. Region one does not import in time period 5. Regions 3 and 4 appear to be p re fe rre d im porting regions over region 1. Region 1 exports to region 2 only in poorer production years. High production in regions 3 and 4 in time periods 5 and 6 r e s u lt in im­ ports from regions 11 and 12 stopping w h ile imports from region 8 continue. I t appears th a t region 8 is p refe rred to regions 11 and 12 f o r im porting by region 2 , because the costs o f im porting from region 8 are lower than the costs o f im porting from regions 11 and 12. Changes in the im porting and exporting fa c to rs brought about in run B are shown in Table 4 -1 2 . Table 4 -1 2 .— Changes in Imports and Exports o f Timber in Run B. Region 1 2 Imports From Region 10 1 9 n 4 Region 1 12 8 Exports To Region 2 During Time Periods 2-6 3-6 1 1-6 1-6 5 During Time Periods 3-6 These re s u lts show the importance o f changes in requirement growth and production p a tte rn s . Region 5 is no longer a surplus region because 198 of growth 1n pulpwood requirem ents. Region 4 Imports from region 8 while exporting I t s to ta l product to region 2. Total requirements in region 4 in time period 5 are imported from region 8 . Total q u a n titie s of timber moving to region 2 increase because o f increased requirements in th a t region over tim e. Import p o te n tia ls are exhausted. Changes in the im port and export p o te n tia l brought about 1n run C are shown in Table 4 -1 3 . Requirement growth in a l l regions and reduction in import p o te n tia ls change the p a tte rn o f imports and ex p o rts . potentials are exhausted e a r l i e r . Import Region 1 imports from region 11 in time period 2 . Table 4 - 1 3 .— Changes in Imports and Exports o f Timber in Run C. Region Change in Imports From Region During Time Period 10 11 1 9 11 12 8 2-6 2 3-6 1 1-6 1-6 5 1 2 4 Region Change in Exports To Region 1 2 During Time Period 3-6 The changes in the im port and export p a tte rn brought about by run D are shown in Table 4 -1 4 . Requirements increase in run D and reduce surpluses a v a ila b le fo r importing even fu r th e r . a re s u lt. Less tim ber is imported from o utsid e regions as Region 10 can export only in time periods 1 and 2. Region 8 199 Table 4 -1 4 .— Changes 1n Exports and Imports o f Timber in Run D. During Time Period Change in Imports From Region Region 1 10 11 1 8 11 12 2 2 5 1-3 1-6 1-6 Region Change in Exports To Region During Time Period 1 2 2 5 can export only in time period 1 through 3. These increases in re q u ire ­ ments re s u lt in regions in the the r iv e r basin exporting less in order to meet t h e ir own requirem ents. Run E is id e n tic a l to run A. Requirements and tim ber production are Id e n tic a l, so the flow patterns should be id e n tic a l. Big Game Hunterdays Run A is again the b aselin e run. The p a tte rn o f imports and ex­ ports o f big game hunterdays is presented in Table 4 -1 5 . Regions 1, 2, and 3 im port, w h ile region 4 exports to regions 2 and 3. exports to region 2 in time period 6 . Region 3 Regions 5, 7 , and 9 are the only regions outside o f the r iv e r basin w ith surpluses. Regions 5 and 9 seem to be p refe rred by region 1 which does not im port from regions in s id e the r iv e r basin. Region 2 p refers to im port from regions 2 , 3, and 9. Region 3 imports only from region 4 . to region 2 in time period 6 . Region 3 has a surplus to export 200 Table 4 -1 5 .— Big Game Hunterday Importsand Exports in Run A. Region 1 2 3 4 Imports From Region 5 7 9 3 4 9 4 — Time Periods 1-6 5 1 -4 ,6 6 1-6 1-6 2-5 — Region Exports To Region Time Periods 3 4 2 2 3 6 1-6 2-5 The changes brought about by run B are illu s t r a t e d in Table 4 -1 6 . Table 4 - 1 6 .--Changes in Imports and Exports o f Big Game Hunterdays Brought About by Run B. Region Change in Imports From Region 2 3 3 4 Region Change in Exports To Region 3 4 2 3 During Time Period 2-4 During Time Period 2-4 This p attern r e fle c ts a surplus o f production in region 3 in time period 5 w ith o u t an increase in requirem ents. more in te n s iv e tim ber production. The surplus re s u lts from The changes 1n the im port and export p a tte rn brought about by run C are illu s t r a te d in Table 4 -1 7 . Table 4 -1 7 .--Changes in Imports and Exports o f Hunterdays Brought About by Run C. Changes in Imports From Region Region 1 5 7 9 1 3 4 9 4 5 2 3 4 Changes in Exports To Region Region 1 3 4 2 2 2 3 During Time Period 1 ,2 4 -6 1-3 2-6 * 1,6 1-6 2-6 6 During Time Period 2-6 - 1-6 2-6 Region 5 exports only 1n time periods 1 and 2 because o f increases in requirements fo r hunterdays. begins to export to region 2. in a ll time periods. Region 7 picks up the s la c k . Region 1 Region 3 ceases to export and must import Region 4 begins to import in time period 6 . In ­ creases in requirements fo r hunterdays cause the r iv e r basin regions to import more. Changes brought about by run D on the p a tte rn o f imports and exports are shown in Table 4 -1 8 . These changes are ra th e r su rp ris in g since the pattern o f production is s im ila r to run C w h ile requirements a t a l l lo c a­ tions remain the same. Table 4 -1 8 .— Changes in Imports and Exports o f B1g Game Hunterdays Caused by Run D. Changes in Imports From Region Region 1 During Time Period 5 7 9 1 3 4 9 4 5 2 3 1.2 3 ,5 ,6 1-3 3-6 - 1 ,5 ,6 1-6 2-6 6 Changes in Exports to Region Region 4 During Time Period 2 1 ,5 ,6 Changes in the imports and exports o f b ig game hunterdays caused by run E from run A are shown in Table 4 -1 9 . in time period 6 . Region 4 begins to import Region 3 imports fo r a longer period o f tim e. These changes r e f le c t increases in requirements fo r big game hunterdays w ith ­ out increasing demands fo r tim ber. A d iff e r e n t p a tte rn o f production develops as a r e s u lt. Small Game Hunterdays Run A is again the b aseline run. tern o f imports and exp orts. Table 4-20 illu s t r a t e s the p a t­ Region 1 imports and exports sim ultaneously. Region 1 imports only from outside regions. Region 2 imports from regions 1, 3, and 4 in s id e o f the r iv e r basin and from region 8 o utside o f the riv e r basin. Region 3 imports and exports sim ultaneously. Imports from in s id e and outside the r iv e r b asin . Region 3 Region 4 exports to Table 4 -1 9 .— Changes 1h Imports and Exports o f Big Game Hunterdays Caused by Run E. Region 1 Changes in Imports From Region During Time Period 3 4 5 7 8 9 1 4 4 5 Region Changes in Exports To Region During Time Period 2 2 3 2-6 1,6 2-6 2 1 4 1 ,2 3 € 1 ,2 ,5 2-6 1,6 2-6 6 Table 4 - 2 0 .--Im p o rts and Exports o f Small Game Hunterdays in Run A. k. Region Imports From Region During Time Period 1 2 9 1 3 4 8 4 8 1-6 1 2-6 1-5 1 1 1-6 3 4 — Region Exports To Region During Time Period 1 3 4 2 2 2 3 1 2-6 1-6 1 204 regions 2 and 3. 8 and 9. The only imports in to the r iv e r basin come from regions Regions 1 and 2 export small game hunterdays to each o th er simultaneously. This re s u lt Is d i f f i c u l t to e x p la in . A problem in model s p e c ific a tio n o r in the s o lu tio n algorithm could be possible causes o f th is r e s u lt. The changes in the import and export p attern brought about by run B are illu s t r a t e d in Table 4 -2 1 . The r iv e r basin imports fewer small Table 4 -2 1 .--Changes in the P attern o f Imports and Exports o f Small Game Hunterdays Caused by Run B. Region Changes in Imports From Region 2 3 8 8 game hunterdays. During Time Period 2-6 Requirements fo r hunterdays have not increased. In ­ creased tim ber production increases production o f small game hunterdays. The changes in patterns o f imports and exports th a t occur in run C are illu s t r a t e d in Table 4 -2 2 . Region 4 ceases to export a f t e r time period 1 and begins to im port. Region 1 and 2 again import from each other in time period 1. 8. Regions 1 and 4 increased im porting from region Region 1 exports to region 2 w h ile im porting from regions 8 and 9. This change in the p a tte rn o f imports and exports r e fle c ts the increase in requirements fo r hunterdays. Import p o te n tia ls are decreased. Regions must keep more o f the production in the region to s a t is fy requirem ents. As a re s u lt im porting is increased. The changes in import and export patterns brought about in Run D are shown in Table 4 -2 3 . Region 1 increases im porting from region 2 in 205 Table 4 -2 2 .— Changes In the P attern o f Imports and Exports Caused by Run C. Changes in Imports From Region During Time Period 4 2 8 1 4 8 1 2-6 1-6 1 2-6 Region Changes in Exports To Region During Time Period Region 1 2 2 4 1 2 1 1 Table 4 -2 3 .— Changes in the P attern o f Imports and Exports o f Small Game Hunterdays Caused by Run D. Changes in Imports From Region During Time Period 1 ,5 2-6 3 4 2 1 4 8 4 8 8 Region Changes in Exports To Region During Time Period 1 2 2 4 2 2-6 1,5 3 Region 1 2 3 1 - 1 2-6 3-6 206 time period 5. Region 4 exports to region 2 1n time period 3 w h ile Im­ porting from region 8 . 2 through 6 . Region 2 Imports from region 1 1n time periods This change in p attern is ra th e r s u rp ris in g . The le v e l o f requirements is the same as run C and the p a tte rn o f production is sim­ i la r . The changes in the patterns o f imports o f hunterdays are caused by run E are shown 1n Table 4 -2 4 . Region 2 imports from region 1 during i more time periods than run A. 4 over fewer time periods. Region 2 also imports from regions 3 and Region 3 ceases to import from region 4. Table 4 - 2 4 .— Changes in the Patterns o f Imports and Exports o f Small Game Hunterdays Caused by Run E. Region 2 3 Changes 1n Imports From Region During Time Period 1 3 4 4 1-6 1-4 2 Flows An im portant observation is th a t the r iv e r basin does not export to regions outside o f the r iv e r b asin . basin. A ll surpluses stay in the r iv e r I t appears th a t the only way to cause surpluses to be exported is to re q u ire th a t exports occur when d e fin in g the in e q u a litie s . There appear to be some im portant fa c to rs a ffe c tin g the p a tte rn o f * flows. The most obvious fa c to r 1s tra n s p o rta tio n co sts, one aspect o f the o b je c tiv e fu nctio n to be minimized. The growth o f requirements and the a v a i l a b i l i t y o f imports over time are also very im portant. These two facto rs determine how much o f a commodity can be imported in to 207 the r iv e r basin and how much o f a commodity is required a t any lo c a tio n . The time p attern o f production is also an im portant fa c to r . The time pattern o f production determines how much o f a commodity 1s a v a ila b le in the region to tra n s fe r to o th er regions. Production, however, is a function o f the requirements a t the various lo c a tio n s , the a v a i l a b i l i t y o f im ports, the le v e ls o f tra n s p o rta tio n co s ts , and the le v e ls o f pro­ duction costs. As stated p re v io u s ly , the a llo c a tio n o f management strateg ies appears to be s e n s itiv e to the r e la t iv e le v e ls o f tra n s p o rta ­ tion costs and development costs. Costs The o b je c tiv e function was adjusted by su b tractin g the costs o f meeting d e f ic it s in requirements from the pools o f e x tra su p p lies . The costs o f im porting goods in to the r iv e r b as in , the costs o f tra n s p o rtin g goods w ith in the r iv e r basin , and the costs o f producing goods were calcu lated . These costs are presented in Table 4 -2 5 . I t is im portant Table 4 - 2 5 .— Costs Incurred in the R iver Basin fo r Each Run. Run Costs o f Importing A B C D E 15,535,952.18 2 2 ,5 3 4 ,4 8 7 .6 3 21,207,846.19 17 ,95 9,46 6.68 16 ,86 2,90 7.50 Production Costs in the Basin Transport Costs in the Basin 13,677,593 14,606,691 14,925,737 14,827,427 14,224,689 . 23 7,284,833.54 23 8,667,515.30 23 9,105,766.80 23 8,697,590.30 2 3 7,551,699.50 to r e a liz e th a t the costs o f im porting in runs B, C, and D are underesti mated because the requirements fo r tim ber are not being com pletely met a t these costs. The impacts o f run E on costs r e la t iv e to A are discussed f i r s t . 208 Hunterday requirements Increase w hile tim ber requirements remain con­ stant over time 1n run E. run A. Importing costs are g re a te r 1n run E than 1n More costs are incurred by people liv in g in the r iv e r basin to leave the r iv e r basin to hunt. However, i t is d i f f i c u l t to estim ate the amount spent in the r iv e r basin and the amount spent outside o f the r iv e r basin. Item izin g o f costs would be required to become more s p e c ific . However, even then i t would s t i l l be d i f f i c u l t to s ta te how much o f the to tal import b i l l was spent in s id e and outside o f the r iv e r basin. Item ­ izing would increase the s iz e o f the lin e a r programming m atrix which would ev en tu ally cause problems w ith the amount o f computer core a v a il­ able and th is could increase costs. N o n -tran sp o rtatio n costs spent o u t­ side o f the r iv e r basin are not taken in to account. Improved an alysis of leakages o f money due to im porting would probably be b e tte r c a rrie d out as a side study ra th e r the lin e a r program. than attem pting to handle a l l aspects w ith in In th a t way actual patterns o f spending could be studied w ith the re s u lts being applied to costs generated by the model. The costs incurred in the r iv e r basin are g re a te r fo r run E than run A. This r e fle c ts more in te n s iv e management o f land and increased flows o f hunters between regions in the r iv e r basin. ‘ Both tra n s p o rt and production costs are g re a te r in run E than in run A. A major problem is that the means by which landowner costs are to be covered is not speci­ fie d . Landowners might not in v e s t in land s t r i c t l y fo r w i l d l i f e purposes unless they can charge fo r hunting, receive fin a n c ia l a s sis tan ce , o r receive a tax break. The costs o f runs B, C, and 0 r e la t iv e to A are now discussed. these runs, tim ber requirements are increased over run A. In However, im­ porting costs in these runs do not account fo r costs o f im porting from 209 regions outside o f the area o f an alysis to meet tim ber requirem ents. D e fic its are g re a te s t 1n run D, run C 1s 1n the m iddle, and run B In ­ volves the sm allest d e f ic it s . More costs w ill have to be incurred to meet d e fic its such th a t run D w il l have g re a te r im porting costs than run C which in turn w il l have g re a te r costs than run B. In these runs, i t is also d i f f i c u l t to determine who is re ce ivin g the im porting costs and where they are lo cated . timber is combined. specified. F ir s t , both costs o f im porting hunterdays and Second, the lo c a tio n o f haulers and c u tte rs is not T h ird , the cost o f harvesting tim ber in outside regions are combined w ith the costs o f tra n s p o rtin g the tim ber in to the r iv e r basin. These problems probably would be handled best outside o f the model. Run C has g re a te r costs w ith in the region than run D which in tu rn 1s g reater than run B. Both tra n s p o rt and production costs in the r iv e r basin fo llo w th is trend . I t would seem th a t runs C and D should have very s im ila r costs since production patterns are s im ila r . of d e fic its may have an impact. regions as requirements increase. The handling There are,a s a re s u lt,fe w e r flows between Flows decrease because more o f the pro­ duction 1s needed to s a tis fy the producing re g io n 's requirem ents. timber must be imported. More Much o f th is im portation is handled by the pool o f e x tra su p plies. The im p lic a tio n is th a t the order o f im porting costs fo r these fiv e runs i s , from h ig hestto lowest: occur w hile im porting. D, C, B, E, and A. Leakages undoubtedly I t would seem th a t leakages would increase as importing increases such th a t the order o f leakages from h ighestto lowest is also D, C, B, E, and A. 210 Recommendations fo r Land Management U ltim a te ly the purpose o f th is type o f model is to provide recom­ mendations fo r land management. the re su lts o f th is study. w ill increase over tim e. These recommendations w il l be based on I t appears l i k e l y th a t tim ber requirements In order to s a tis fy these requirements in an economically e f f i c i e n t manner as defined in the model, a l l tim b er-p ro ­ ducing lands in c u rre n t use management should be converted to a more in ­ tensive form o f management as soon as p o ssib le. A ll lands in environ­ mental emphasis or in te n s iv e management a t the beginning o f the study remain in those uses as assumed in Chapter I I I . Lands converted to urban use remain in c u rre n t use as assumed in Chapter I I I . Recommendations fo r non-tim ber producing lands are more com plicated. Growth in requirements fo r hunterdays w ill probably increase. P r io r it ie s are set on non-tim ber-producing lands to s a tis fy requirements fo r hunter­ days in an economically e f f i c i e n t manner. The f i r s t p r i o r it y on non­ timber-producing lands is to convert a l l adequate condition class lands in current use to in te n s iv e management as soon as possible. Lands to be converted to urban use are excluded. E ffo rts on non-adequate class lands, the second p r i o r it y , should be concentrated in regions 2 , 3, and 4 on c e rta in key land classes. When there is no growth in tim ber and hunterday requirem ents, the elm p o le timber class in region 2 and the elm s e e d lin g -s a p lin g class should be converted to in te n s iv e management w h ile they are in the poletim ber s iz e class. In region 3, a l l c o n ife r poletim ber classes in non-adequate con­ d itio n classes and the elm se e d lin g -s a p lin g class should be converted to Intensive management w h ile they are in the poletim ber s iz e c la s s . lands to be converted to urban use are excluded. A ll 211 Changes in management g u id elin es must be made when tim ber re q u ire ­ ments Increase. When tim ber requirements Increase 1n region 2 and a l l others remain constant over tim e , the elm seedling-sapH ng class remains in current use ra th e r than being converted to In te n s iv e management as occurs when th ere is no growth 1n tim ber requirem ents. When there is growth in both tim ber and hunterday requirem ents, o th e r changes are made from when there 1s no growth. The oak poletim ber class re q u irin g tim ber stand improvement to be converted to in te n s iv e management converts to Intensive management in region 2. In region 4 , the c o n ife r poletim ber class which produced no merchantable tim ber is converted to in te n s iv e management. Changes in the p a tte rn o f land management caused by Increasing w ild lif e requirements over time w h ile keeping tim ber requirements con­ stant are contrasted w ith the land management p a tte rn associated w ith no growth in requirem ents. In region 2 , the oak poletim ber class produc­ ing no merchantable tim ber is converted to In te n s iv e management w h ile i t is in the poletim ber c la s s . In region 3, the oak s e e d lin g -s a p lin g class producing no merchantable tim ber should be converted to in te n s iv e manage­ ment when the stand is in the s e e d lin g -s a p lin g c la s s . In region 4 , the elm s e ed lin g -sap lin g class should be converted to In te n s iv e management when the stand 1s in the poletim ber c la s s . The oak poletim ber class which can produce no merchantable tim ber should be converted to in te n s iv e management w h ile i t is s t i l l in the poletim ber c la s s . I t is im portant to p o in t out th a t the conversion to In te n s iv e man­ agement o f non-tim ber producing lands in the adequate co n d itio n classes takes place e a r l i e r than conversions to in te n s iv e management on non-ade­ quate class lands. Conversion o f adequate co n dition class lands should 212 take place a t the e a r lie s t possible tim es, according to the re s u lts o f the model. S eed lin g -sap lin g classes on non-adequate co n dition class lands th a t are converted to in te n s iv e management are converted a f t e r they grow in to the poletim ber s iz e c la s s . These recommendations are based on the period o f an alysis and the selected discount ra te . Increasing the time period o f an alysis w ill in ­ crease the number o f resource classes which are capable o f producing timber. Forestland in the non-tim ber-producing classes in one time period o f analysis can become tim ber-producing in a longer time period o f analysis. The impact o f lengthening the time period could be to increase the number o f classes o f land in cu rren t use which should be converted to intensive management as soon as p o s sib le , assuming the same trends o f requirements used in th is study. However, a sm aller percentage o f re ­ maining non-tim ber-producing lands might be converted to in te n s iv e manage­ ment. Hunterday requirements might be supplied more com pletely on tim ­ ber-producing lands. Lands which are not capable o f producing merchant­ able tim ber, than, might not receive any in te n s iv e management i f the time period o f an alysis is lengthened. Increasing discount ra te s , given a time period o f a n a ly s is , w il l encourage postponement o f investments in land. Impacts o f Land Management on Regional Growth Some growth in tim ber-using in d u s trie s 1n the region can be accom­ modated by in te n s ify in g management, given the technologies assumed in th is analysis. The r e la t iv e ly small amount o f commercial fo re s t lan d , the conversion o f fo re s t land to urban use, and the status o f land tenure lim its p o s s ib ilitie s fo r growth in the tim ber-using in d u s trie s . Much growth in wood consumption in the r iv e r basin is supplied by im porting 213 from outside o f the r iv e r basin and from outside o f the 12 region area of an alysis. Increasing output from the pul pirn'll 1n the r iv e r b as in , the Henasha Corporation, would seem to be severely lim ite d . Growth o f th is firm would have to be supplied in c re a s in g ly by tim ber in the northern lower peninsula of Michigan outside o f the 12 region area o f a n a ly s is . This would appear to put the Menasha Corporation a t a com petitive disadvantage r e la t iv e to other m ills located c lo s e r to the tim ber resource. This fir m 's p r o f it margin would decrease r e la tiv e to the o ther firm s due to the longer h a u l­ ing distances. Given the w eight losin g c h a ra c te ris tic s o f tim b er-u sin g in d u stries, growth in these in d u s trie s would probably be encouraged c lo s e r to the larg e tim ber esource in the northern low er peninsula o f Michigan. I t would seem th a t output o f the Menasha Corporation would increase a t a rate lower than the outputs o f o th e r firm s in the lower peninsula. Fac­ tors th a t might combat th is trend could be the a v a i l a b i l i t y o f lab o r and capital and economies o f s c a le . S h o rt-ro ta tio n popular c u ltu re might rapidly increase supplies o f pulpwood in the region by taking advantage of sub-marginal farm land. The p o te n tia ls fo r growth o f p u lp m ills could be encouraged as a r e s u lt. Growth o f sm aller operations could probably be accommodated. These smaller m ills produce s p e c ia lty products and use hardwoods fo r the most part. W hile the supply o f tim ber is lim it e d , high q u a lity hardwood timber can be produced because o f the clim a te and the f e r t i l i t y o f the s o il. Increased s ilv ic u lt u r a l p rac tice s could improve the q u a lity o f the tim ber produced and concentrate growth in higher q u a lity tre e s . There appears to be much p o te n tia l to increase the supplies o f hunterdays, given the inform ation and assumed technologies in the model. 214 Supplies, 1 t appears, could be Increased fa s te r than projected population growth, both through In te n s iv e management and im p o rtatio n . could be e a s ily created in e a r l i e r time periods. Surpluses The basic problem is providing in cen tives to th e landowner to manage his woodlot and to provide access to the p u b lic . Ap p lic a b ility o f Results to Other R iver Basins I t appears d i f f i c u l t to apply the re s u lts o f th is study to other riv e r basins. The most productive lan ds, i t would s e e m ,s till ought to be converted to in te n s iv e management as e a rly as possible ( t h a t i s , the adequate co n d itio n class la n d s ). The marginal classes o f non-adequate forest land to be converted from c u rre n t use to in te n s iv e management which were defined in th is study cannot be ap p lied to o th e r r iv e r basins. The marginal class o f fo re s t land w il l vary from r iv e r basin to r iv e r basin. Each r iv e r basin w il l have i t s unique s e t o f lo c a tio n fa c to rs . The lev el o f requirements o f d if f e r e n t commodities r e la t iv e to the pro­ ductive cap acity o f the land probably w ill not be the same from r iv e r basin to r iv e r basin. Given p rojected high le v e ls o f demand fo r tim ber products by the U.S. Forest S e rvic e, tim ber producing land ought to be converted to in te n s iv e management as soon as p o ssib le. The p ro d u c tiv ity and s p a tia l d is tr ib u tio n o f land resources w il l not be the same fo r every riv e r basin. The costs o f tra n s p o rta tio n and the tra n s p o rta tio n network w ill be d if f e r e n t fo r each r iv e r basin . by ecosystem and land type. also vary. Development costs might vary The lo c a tio n and le v e ls o f requirements w il l There are a la rg e number o f s p a tia l featu res unique to every region th a t can a f f e c t the s p a tia l d is tr ib u tio n o f land management s tra te g ie s . The presence o f these fa c to rs which are unique to every re ­ gion makes i t d i f f i c u l t to apply these re s u lts to o th e r r iv e r basins. 215 Discussion o f Problems Encountered During Testing Problems in Using the Model S ilv ic u ltu r a l p ra c tic ie s to change the age o r s iz e d is tr ib u tio n o f stands and fo re s ts were not considered in the model. Impacts o f prices and costs on desired ro ta tio n len g th s, desired stocking le v e ls , and merchantable tre e diameters and forms were not considered. I t may be desirable to include such fac to rs to meet various demands over time and to meet fo re s t management goals fo r area and age d is tr ib u tio n s . In c lu d ­ ing such fa c to rs , however, would increase the s ize o f the lin e a r program­ ming m atrix and could, perhaps, cause problems by exceeding computer core lim it s . Sustained y ie ld o f the e n tire r iv e r basin was not an ex­ p lic it goal because o f the nature o f land tenure. With a la rg e number of small tra c ts owned by a v a rie ty o f people, the concept o f sustained yield management o f the e n tir e r iv e r basin might mean l i t t l e given his time preferences and scale o f production. to the owner, The conversion o f forest land to urban use also discourages th is p o in t o f view. I t is d i f f i c u l t to in te r p r e t costs from the cost equations defined in the model. The costs o f Im porting in d iv id u a l goods could not be ob­ tained since a l l costs were summed. the lo c atio n o f spending. I t was also d i f f i c u l t to sp ecify More s p e c ific d e f in it io n o f costs could in ­ crease the s iz e o f the lin e a r programming problem g r e a tly , re s u ltin g in computer core lim it s being exceeded. Erosion was not constrained fo r the r iv e r basin o r fo r in d iv id u a l regions. As shown in Chapter I I , erosion could e a s ily be constrained. However, c o n stra in ts were d i f f i c u l t to d e fin e . The Economic Research Service did not have erosion c o n stra in ts defined fo r fo re s t land in i t s 216 analysis. Economic Research Service personnel In d icated th a t fo re s t land 1s not an im portant c o n trib u to r to erosion in th is study. Erosion, thus, was summed, not constrained. Production surpluses 1n the r iv e r basin were not exported. I t ap­ pears th a t the only way to force exporting to occur is to re q u ire th a t a certain amount o f a cormiodity be sent to a region. In th is a p p lic a tio n , regions with negative excess supplies could have been elim in ated from the analysis thus reducing the s ize o f the problem. Changing patterns o f production in regions outside o f the r iv e r basin were not considered. every time p erio d. Production was assumed to remain constant 1n I t was d i f f i c u l t to p ro je c t production patterns over time in these outside basins due to lack o f d ata, tim e, and money. Environmental d iffu s io n re la tio n s h ip s were not considered as stated in Chapter I I I . This component was excluded because o f a lack o f d ata, expertise, and tim e. This could be included as shown in Chapter I I . Inclusion, however, could re q u ire computer core beyond what is a v a ila b le . More than one optimal so lu tio n is possible in runs B, C, and D. This occurs because development costs on adequate co n dition c la s s , non­ timber producing lands are zero regardless o f the time o f conversion to intensive management. Surpluses o f hunterdays could be produced in some time periods w ith no changes in to ta l co st. I t is d i f f i c u l t to under­ stand, however, why changes in output o f hunterdays on these lands would occur w ith no investment in the land. Forest Service personnel did not provide an explanation fo r th is when the data were obtained. This prob­ lem with the optimal s o lu tio n could be overcome by allow ing conversion to in ten sive management a t only one p o in t in time on these adequate con­ dition c la s s , non-tim ber producing lands. 217 I t was d i f f i c u l t to te s t a lte r n a tiv e s tru c tu re s fo r the tra n s p o rta­ tion component. When designing these p o s s ib ilit ie s , i t was decided that the OBERS demands would be the requirements fo r the production com­ ponent when the tra n s p o rta tio n component was separate. demands could not be met. However, the OBERS I t makes no sense to use e x is tin g le v e ls o f production because the re s u lts would be id e n tic a l to re s u lts already calculated. The e ff e c t o f d if f e r e n t ia l access to supplies o f hunterdays on p riv a te ly owned lands was not included. I t was assumed th a t a l l supplies of hunterdays were accessible by consumers. However, no trespassing signs are commonplace on p riv a te lands in Michigan. As a r e s u lt , sup­ plies a v a ila b le fo r consumption might be overestim ated in th is study. Problems w ith the Algorithm APEX I was the lin e a r programming alg o rith m used on the Control Data Corporation 6500 computer a t Michigan S tate U n iv e rs ity . A v a ila b le computer core lim its the s iz e o f problems th a t can be solved. The maxi­ mum f ie ld length on the CDC 6500 a t Michigan S ta te is 170,000g. The recommended f i e l d length c a lc u la te d fo r th is model is 161,000g. As a re s u lt, there is not much room to expand th is model w h ile using APEX I . I t i s , then, d i f f i c u l t to include more regions, time perio ds, goods, man­ agement s tr a te g ie s , environmental re la tio n s h ip s , cost equations, or land use sectors. The only way to overcome th is problem on the CDC 6500 is to use APEX I I . This alg orith m was designed to handle much la r g e r problems. This alg o rith m is more expensive to run and more d i f f i c u l t to use. A lso, few runs have been made a t Michigan S ta te using th is a lg o rith m , th e re fo re i t is reasonable to expect th a t problems might s t i l l e x is t in APEX I I . 218 There was also a problem w ith an APEX I option which e x is ts to change the s tru c tu re o f the lin e a r programming I n i t i a l tab lea u . The option allows techn ical c o e ffic ie n ts , row c o n s tra in ts , and o b je c tiv e function values in the tableau to be changed. Equations and v a ria b le s can be added to and deleted from the ta b le a u . The changes are made by requesting the option on the APEX I control card and inclu d in g the changes a t the end o f the in p u t deck. There was a bug 1n the option which required special programming to overcome. became more expensive and time consuming. Changing the tableau As a r e s u lt, APEX I became less f le x ib le . Costs o f M odelling Costs o f Developing the Model One y e a r was spent in c o lle c tin g data and preparing the model fo r the runs. For approxim ately s ix months, twenty hours per week were spent. For the remaining s ix months, f o r t y hours per week were spent. So, approx Imately th re e -q u a rte rs o f one man-year was spent to implement th is model once i t was conceptualized. $300. Keypunching was contracted out a t a cost o f The fo llo w in g tasks were undertaken during th is ye ar: 1) c o lle c ­ tion o f d a ta , 2 ) c a lc u la tio n o f c o e ffic ie n ts , co sts, requirem ents, and acreage c o n s tra in ts , 3) coding, 4) checking o f punched cards, 5) c o rre c ­ tion o f punched cards, 6 ) c re a tio n o f card f i l e on tap e, 7) rechecking o f card f i l e using APEX I , and 8 ) re c o rre c tio n o f card f i l e and remaking o f tape. Costs o f Running the Model Following are the costs o f o b tain in g the i n i t i a l which served as a s ta r tin g basis fo r runs A through E. in fe a s ib le s o lu tio n Computation costs were a t the lowest p r io r it y ra te group a t Michigan S tate to economize resources: Computation costs: $49.11 P rin tin g costs: $10.17 T o ta l: $59.28 The computation costs o f runs A through E varied from $3.71 to $12.66, The p rin tin g cost fo r each run was $3.60. runs A through E is $54.05. The to ta l costs o f making However, costs o f using permanent f i l e s , purchasing a tape, crea tin g a card f i l e on tap e, and unsuccessful runs are not Included 1n these fig u re s . Changes Recommended fo r the Model A fte r Testing Testing th is model In d icated th a t some changes could be made 1n the model to improve I t o r s im p lify i t . For example, the number o f con­ versions from cu rren t use to In te n s iv e management on timber producing lands could be reduced. A ll conversions on tim ber producing lands took place a t the e a r lie s t possible tim e. could have been elim in ated . Conversions 1n la t e r time periods I t is possible th a t 1n o ther r iv e r basins conversions a t la t e r time periods might occur. However, given growth rates 1n demands fo r tim ber as projected 1n the Timber Outlook Study (U.S. Forest S ervice, 1973), conversion to In te n s iv e management as soon as possible appears to be the favored a lte r n a tiv e In an optim izing model such as th is one. Conversions on adequate condition class lands 1n the seedling-sapling s ize class could also be reduced. Conversions from current use to In te n s iv e management a t the present produces the most hunterdays in every time period a t the same costs as o ther conversions. Reducing the number o f conversions would reduce the number o f a c t iv it ie s and would reduce the amount o f computer core required. 220 Changes could also be made 1n the area o f cost a n a ly s is . The equations could be made more s p e c ific in reference to product and lo ca­ tion o f spending 1 f more s p e c ific an alysis o f costs was d es ired . Outside studies would probably s t i l l be requ ired to estim ate impacts on regional growth. More complete s p e c ific a tio n o f costs would re q u ire a d d itio n a l equations which could g re a tly increase computer core requirem ents. If less s p e c ific cost an a ly sis was d e s ire d , cost equations could be e lim in ­ ated com pletely. In some lin e a r programming alg o rith m s , such as APEX I , summation of a c t iv it ie s fo r erosion and costs could be e lim in a te d . Rows fo r eros­ ion and costs could be defined so th a t they are s e t g re a te r than o r equal to zero. The alg orith m w i l l sum a l l row a c tlv it e s so th a t production o f erosion o r costs could be summed w ith o u t using special a c t i v i t i e s . Summary Results o f te s tin g the model were presented 1n th is ch apter. Trends 1n land management, production, consumption, flows o f goods, and costs were discussed and analyzed. made. Recommendations fo r land management were The costs o f co n stru ctin g and running the model were discussed. Several conclusions fo llo w from th is ch apter. A lin e a r program­ ming model which f u l l y accounts fo r time and space in fo re s t land plan­ ning 1s fe a s ib le to co n stru c t and run. costly to use. I t is d i f f i c u l t to construct and The model developed in th is study does a llo c a te production requirements fo r tim ber among regions given requirements a t demand points and the productive ca p a c ity o f various regions. Several Im portant fa c ­ tors are id e n t if ie d which a f f e c t land management p a tte rn s : costs o f management, costs o f tra n s p o rta tio n , lo c atio n s o f requirem ents, time d is ­ trib u tio n o f production, j o i n t production, and s p a tia l d is tr ib u tio n o f 221 land resources. An Im portant t r a d e -o ff between costs o f In te n s iv e man­ agement and costs o f Im porting Is discussed. The time period o f analysis and the ra te o f In te r e s t also could have Im portant impacts on land man­ agement p attern s. CHAPTER V CRITICAL ANALYSIS OF THE MODEL FOR POLICY ANALYSIS AND ITS USEFULNESS TO LAND USE PLANNING The purpose o f the model is to lo c ate land management s tra te g ie s in space given requirements fo r products and resource inform ation 1n USDA r iv e r basin planning s tu d ie s . R iver basin planning must concern i t s e lf w ith n ation al economic development» environmental q u a lity , regional development, and so cial w e ll-b e in g . R iver basin planning studies recommend land use plans to meet fu tu re demands fo r products. The study area to which th is approach is being ap p lied is a ru ra l area in which a g ric u ltu re and fo re s ts are the la rg e s t land uses. A griculture is an im portant income producing s e c to r. Land in the study area is la r g e ly p r iv a te ly owned and h ig h ly p a rc e liz e d . There 1s l i t t l e public ownership o f land in the r iv e r basin. The model being proposed can be applied to several types o f problems. 1) I t can be used by fe d e ra l or o th e r government agencies to help develop land management plans on pub lic lands managed by the agency. 2) I t can be used by fe d e ra l o r o ther government agencies to help develop land use plans on which to base recommendations con­ cerning land management to p riv a te landowners given the agency's ob­ je c tiv e s . 3) I t can be used to p re d ic t how land w il l be managed given demands fo r products and c o n s tra in ts on land use such as q u a litie s and q u a n titie s o f land resources and land use re g u la tio n s . 222 The th ir d 223 use o f the model assumes th a t the model w il l sim ulate how landowners w ill behave under c e rta in co n d itio n s. In the Kalamazoo R iver b as in , the fe d e ra l government owns no lan d. The only problems to which th is system can be applied 1n the basin are . types 2 and 3. Since the fe d e ra l government does not have ownership, the police power, condemnation powers, o r property ta x a tio n powers, 1t cannot req u ire th a t land management plans be Implemented. The only powers th a t the fe d e ra l government has to guide land use is the spend­ ing power and the power to make Inform ation a v a ila b le and to educate. These land management plans could become useful to extension e ffo r ts and federal assistance programs to landowners. A Review o f the Problems o f the Current USDA Approach Throughout th is re p o rt, problems w ith the cu rren t USDA approach have been discussed. These problems w il l be reviewed. Space 1s brought In only by considering the s p a tia l d if f e r e n t ia t io n o f land resources. The lo c atio n o f demands f o r products produced on the land and what Im­ pacts th is might have on land management decisions are not considered. As a r e s u lt, tra n s p o rta tio n co s ts , the costs o f overcoming the b a rrie rs of space, are not considered in the o b je c tiv e fu n c tio n . These costs can p o te n tia lly in flu e n c e the decisions o f landowners and ought to be considered in the model when the lo c a tio n o f land management s tra te g ie s is being evalu ated. C losely re la te d to th is p o in t is the fa c t th a t the current USDA approach does not consider the openness o f the r iv e r basin economy. The r iv e r basin undoubtedly exports some products and imports o th e rs . The region 1s not s e l f - s u f f i c ie n t and goods flo w in and out o f the re g io n . The lo c a tio n o f su p p liers and demanders o utside 224 of the r iv e r basin can also In flu e n ce th e decisions o f landowners. The cu rren t approach assumes th a t land 1s the only lim itin g factor. Other resources, such as lab o r and c a p it a l, are neglected. I t appears th a t the model assumes th a t these resources are not f u l l y employed and th e re fo re do not 11m lt production. The cu rren t USDA approach 1s not w ell su ited to problems in which time 1s an Im portant component. when dealing w ith fo re s t resources. Time 1s Im portant to consider A la rg e number o f years can pass between an investment in a fo re s t stand such as p la n tin g , th in n in g , or f e r t i l i z a t i o n and a y ie ld o f merchantable tim b er. stand occurs over a larg e number o f ye ars. Growth o f a The cu rren t Economic Re­ search Service approach deals only w ith c e rta in In d iv id u a l y e a rs . This approach seems p e rfe c tly acceptable fo r most a g ric u ltu r a l problems where p lan tin g and harvesting occur 1n a s in g le y e a r. The approach 1s not so w ell su ited to problems which consider a la rg e number o f years. The o b je c tiv e fu n ctio n used in the cu rren t approach 1s a cost minimizing approach to meet c e rta in demands. terms o f maximizing returns given c o n s tra in ts . People probably th in k 1n However, th ere are problems w ith estim atin g prices fo r c e rta in In ta n g ib le s such as recreation o r scenery. N either approach w il l account f o r any degree of in d iffe re n c e to co sts. People may not always be maximizers or mlnimizers b u t, r a th e r , may be s a tis fie d w ith "adequate" le v e ls o f per­ formance in some cases. This s a tis fic in g approach could r e s u lt 1n a d iffe re n t a llo c a tio n o f resources than an o ptim izing approach. Both optimizing approaches must beware o f d is tr ib u tio n a l e ffe c ts in specifying th e o b je c tiv e fu n c tio n . The determ ination o f requirements fo r a cost m inim izing so lu tio n also has d is tr ib u tio n a l im p lic a tio n s . 225 Both determining the products to be considered and the q u a n titie s re ­ quired can favo r some groups over others 1n planning. D is trib u tio n a l effects such as these must always be considered 1n model co n s tru c tio n . Closely re la te d to the problem o f d is tr ib u tio n a l e ffe c ts 1s the problem o f what management options to consider. The optimal so lu tio n Is affected by the management s tr a te g ie s , which represent land manage­ ment options, Included 1n the lin e a r programming problem. The manage­ ment options considered w i l l have d is tr ib u tio n a l e ffe c ts since each option can fav o r d if f e r e n t in te r e s ts . management options fo r fo re s t lands. The Forest Service has proposed They Include In te n s iv e tim ber management, environmental emphasis, m u ltip le use, and cu rren t use. Other possible options seem to be n eg lected. Management s tra te g ie s could be developed to emphasize the production o f d if f e r e n t species o f w ild lif e , hunterdays, or o th e r re c re a tio n a c t i v i t i e s . management s tra te g ie s could also be considered. Other tim ber In p a r t ic u la r , short rotation fo re s try management fo r various species should be developed. Once new management options a re developed, new products flow ing from these options would re q u ire co n sideratio n by the model. Problems discussed above in d ic a te conceptual d e fic ie n c ie s o f the current approach. There are o th er data problems encountered in r iv e r basin planning studies th a t w il l make any approach d i f f i c u l t . There 1s a lack o f data a t the sub-county le v e l in the Kalamazoo R ive r Basin. Most data used in th is study was obtained from the U.S. Forest S ervice. Many o f these data are published by county or substate re g io n . Remote sensing data were obtained from the Michigan S ta te U n iv e rs ity remote sensing p ro je c t concerning land cover. Info rm ation f o r sub-county u n its could be obtained from maps based on remote sensing d a ta . However, 226 data were not s p e c ific enough fo r Forest Service land management pur­ poses. The data base lim it s the d e fin itio n o f s p a tia l d if f e r e n t ia t io n of the resource. A g rid framework can be no f in e r than the data base w ill allow i t to be. In th is study, useful fo r e s t resource data could be defined 1n no area sm aller than a r iv e r sub-basin. I t 1s the data base, ra th e r than computer technology, which lim its the s p a tia l s p e c ific ­ it y o f th is r iv e r basin study. Problems were also encountered w ith data obtained from the Forest Service f o r use 1n th is study. For example, data prepared fo r the Kalamazoo R iver Basin planning study were not documented. Sources o f data, operations performed on d a ta , and assumptions behind c a lc u la te d c o e ffic ie n ts and acreages were not provided, thereby making 1t d i f ­ f ic u lt to know what the data meant and how they could be used. I t is d i f f i c u l t fo r Independent researchers and c itiz e n s to use data 1n t h e ir present form. C ritic is m o f the Id eal Model Assumptions o f the Model There are a v a r ie ty o f assumptions behind the id e a l model which w ill a f f e c t the usefulness o f the model fo r r iv e r basin planning. F irs t o f a l l , th ere are the assumptions o f lin e a r programming. The f i r s t assumption o f lin e a r programming is l i n e a r i t y which means a l l proportions remain constant 1n an a c t i v i t y , regardless o f the le v e l of the a c t i v i t y . Dim inishing returns could be handled by In c lu d in g several a c t i v i t ie s w ith c o n s tra in ts on the le v e ls o f the a c t i v i t i e s . However, dim inishing retu rn s are not included 1n th is model. The second assumption is complete d i v i s i b i l i t y o f In p u t and output u n its . 227 Fractional p arts o f any a c t i v i t y are p o s sib le . In tegers could be r e ­ quired through the use o f mixed In te g e r lin e a r programming, however. The th ird assumption is a d d it iv it y and Independence which means th a t there are no In te ra c tio n s between a c t i v i t i e s . When th ere are in t e r ­ actions, they must be combined In to a s in g le a c t i v i t y . The fo u rth assumption 1s th a t Inputs and outputs are homogeneous. There 1s no variatio n o f the c h a ra c te ris tic s o f each In p u t o r output. number o f a c t i v i t ie s th a t can be considered must be f i n i t e . lim itin g fa c to rs a re re q u ire d . and prices a re constant. F if t h , the S ix th , The seventh assumption 1s th a t costs This r e s t r ic t io n can be overcome through the use o f q uadratic programming. E igh th, the model must e ith e r maximize or minimize an o b je c tiv e fu n c tio n . This model minimizes co sts. The ninth assumption is th a t a l l a c t i v i t y le v e ls must be non-negative. Since pseudodynamic lin e a r programming is recommended in the ideal model and used in the a p p lic a tio n , a d d itio n a l assumptions must be l is t e d . Pseudodynamic lin e a r programming minimizes an expected stream o f d o lla r s , or other u n its o f va lu e , over a given tim e p erio d , The tim e period o f consideration must be the same fo r a l l a c t i v i t ie s included 1n the model. Time 1s an im p lic it v a ria b le in th is model because the o b je c tiv e func­ tion values are discounted d o lla r values. of an In te r e s t r a te . Time enters through the use A time period o f an a ly sis must also be d efin ed . There are also some sp ecial assumptions f o r the id e al model. F ir s t, the r iv e r basin 1s viewed as a s in g le entrepreneur who desires to use scarce land resources 1n an economically e f f i c i e n t way. region's economy 1s assumed to be an open system. and out o f the system. The Goods can flo w 1n Goods can also flo w between r iv e r sub-bas1ns. Transfer costs and the lo c a tio n o f markets are assumed to a f f e c t the 228 allocation o f land management s tra te g ie s . The model also assumes th a t requirements fo r various goods produced by management s tra te g ie s can be projected. I t 1s also assumed th a t tra n s p o rt routes and supply and demand areas can be d efin e d . Implications o f the Assumptions These assumptions have im p lic atio n s fo r the economic system, technological p o s s ib ilit ie s , and behavior o f th e environment. The assumptions o f l i n e a r i t y , a d d it iv it y , and independence have very Impor­ tant ra m ific a tio n s . Economies o f scale 1n th e management and h arvest­ ing o f timber are neglected. The Impact o f the s iz e o f a contiguous area o f a given management s tra te g y 1s not considered. Management and harvesting costs o f a s in g le t r a c t o f 1000 acres o f land in the in te n ­ sive tim ber management s tra te g y are the same as those on 1000 Is o la te d , single-acre tr a c ts . Minimum s iz e tr a c ts fo r a given management s tra te g y cannot be included in the lin e a r program. In te ra c tio n s between two d iffe re n t classes o f land such as a g ric u ltu r a l o r fo re s t land a re not included. For example, edge e ffe c ts on w i l d l i f e populations are not considered. The only way these kinds o f e ffe c ts can be Included 1s by developing an a c t i v i t y which w il l Include these In te ra c tio n s . Also, effects o f d if f e r e n t p attern s o f land use cannot be considered. Not inclu d in g dim inishing returns a ffe c ts the realism o f the model since varying proportions o f inputs are not considered. This problem is compounded since only the fa c to r o f land is lim it in g . Other possible u n its are not Included and thus must be considered n o n -lim itin g . The assumption th a t land owners a c t as a s in g le entrepreneur desiring to use resources 1n an economically e f f i c i e n t way lim it s the re s u lts . This assumption could be v a lid only under the fo llo w in g 229 conditions: 1) There 1s only one land owner, or 2 ) There 1s ce n tra l planning o f In d iv id u a l e ffo r ts and th e power to enforpe the p la n , or 3) Land owners have the same goals and work 1n such a way as to e ffic ie n tly use resources w ith ou t c o n f lic t . In the d es crip tio n o f the study area 1n the f i r s t ch apter, 1t was shown th a t land ownership Is la rg e ly p riv a te and h ig h ly p a rc e llz e d , so th a t the f i r s t p o s s ib ility 1s elim in ated . The second p o s s ib ility c o n flic ts w ith the American p o lit ic a l system. Planning 1n th is country g e n e ra lly t r ie s to avoid serious co n flicts ra th e r than plan f o r the optimum use o f lan d. N e ith e r the states nor the fed eral government have the power, a t th is tim e, to compel la rg e numbers o f p riv a te land owners to manage land in a c e rta in way. The p o lic e power 1s used to avoid c o n f lic t s . In special cases, eminent domain 1s used to fo rc e a c e rta in parcel o f land in to a given use. Central planning and Implementation l i k e l y would take place during a nation al emergency. But fo r the time being, land owners are free to make a larg e number o f decisions w ithout government In te rv e n ­ tion. The th ir d p o s s ib ility seems u n r e a lis t ic . P riv a te land owners appear to have a v a rie ty o f goals 1n managing the land th a t they own. Economic e ffic ie n c y may not be the most Im portant m o tiv a tio n . The U.S. Forest Service has discussed the problem o f p riv a te , n o n -in d u s tria l ownership o f fo r e s t lands. These fo re s t lands were c la s s ifie d accord­ ing to the goal o f ownership as fo llow s (U .S. Forest S ervice, 1973): a) Perhaps 5% o f th is land 1s in te n s iv e ly managed on a continuing basis. b) About a th ir d o f the owners have some In te re s t 1n fo re s try and manage t h e ir lands under extensive fo re s try p rac tice s 230 th a t are u su ally unplanned or accomplished a t random. c) N early h a lf o f the landowners d is p la y no in te r e s t in in ­ te n s ifie d fo re s try p ra c tic e . Timber on these lands may be sold from time to tim e. d) Perhaps 15% o f th is land is held fo r non-timber purposes. Most o f these fo re s t land owners appear to be more in te re s te d in ob­ taining p erio d ic income from s e llin g tim ber than in v es tin g in fo re s t management to increase fu tu re growth and re tu rn s . The re tu rn to In ­ vestment might be too small to m e rit much co n sid eratio n . Perhaps the most im portant problem is the long planning period In volved . Private land owners may be th in k in g in terms o f 5 years w h ile fo re s t Investments may take place over 50 or more ye ars. This sh o rt planning period is a good reason fo r the Forest Service to in v e s tig a te the p o s s ib ility o f encouraging sh o rt ro ta tio n fo re s try on p r iv a te ly -h e ld , n o n -in d u s tria l, sub-marg1nal a g ric u ltu r a l lands. I t would appear, th en , th a t the model probably would not be a good p re d ic to r o f what would happen given various land use plans and constraints on th e system. Although, th e s tru c tu re o f the economic system, p a r tic u la r ly the d is tr ib u tio n o f land ownership r ig h ts , is not approximated very w ell by the assumptions o f the system, the model might be used to generate g u id e lin es to a fo re s try extension program. I t might also be h elp fu l 1n showing which management options should receive p u b lic assistan ce. Some o f the model's assumptions are intended to o ffe r improve­ ments over the c u rre n t Economic Research Service approach. nomic system is assumed to be an open system. out o f the system. The eco­ Goods can flo w in and Goods can also flo w between sub-basins o f the r i v e r 231 basin. The reason fo r these assumptions 1s to overcome th e concept of s e lf-s u ffic ie n c y . In r e a l i t y , 1 t seems u n lik e ly th a t r iv e r basins would be s e lf - s u f f ic ie n t 1n the production o f many products. ing and exporting is the ru le ra th e r than the exception. Import­ Accounting for the tra n s fe r o f goods requires th a t the lin e a r programming m atrix be increased 1n s iz e . Problems a ris e 1n d e fin in g where goods are demanded and the q u a n tity demanded a t each lo c a tio n . I t becomes more d if f i c u l t to p ro je c t demands or requirements fo r a region as the area decreases since the amount o f data a v a ila b le decreases. Specifying demand models would become more d i f f i c u l t since v a ria b le s which vary over space would have to be Included. specifying tra n s p o rt ro u tes. A problem also a ris e s 1n Not a l l routes can be Included because the number o f tra n s fe r a c t iv it ie s would become too g re a t. I t is d i f ­ f ic u lt to pick re p re s e n ta tiv e tra n s p o rt routes between demand points and supply areas. i Time is also Included to overcome a shortcoming o f the c u rren t approach. As discussed e a r l i e r , choosing among tim ber management * options requires th a t time be considered. I t 1s ra th e r d i f f i c u l t to Include time In to a lin e a r programming framework, but an attem pt has been made to include 1t in th is model. Problems Encountered by Inclu d in g Space Including space in to a lin e a r programming m atrix has g re a t im­ pact on the s iz e o f the m a trix . A set o f rows and columnsmust defined f o r each region to m aintain s p a tia l d if f e r e n t ia t io n . s e n tia lly , each region has I t s own m a trix . the form such a m a trix might ta k e . be Es­ Figure 5-1 Illu s t r a t e s Each region has approxim ately the same number o f non-zero c o e ffic ie n ts . There 1s some v a ria tio n 1n the Figure 5 -1 .--D iagram o f L inear Program Tableau. Shaded areas are non zero c o e ffic ie n ts . White areas are a l l zeros. The num­ bers 1, 2 , 3, and 4 id e n tify the regions. 233 number o f non-zero c o e ffic ie n ts 1n each reg io n . For purposes o f th is discussion, however, they can be assumed constant. The to ta l number of non-zero c o e ffic ie n ts Is a lin e a r fu n c tio n o f the number o f regions as shown in the fo llo w in g equation: non-zero c o e ffic ie n ts = c o e ffic ie n ts /re g io n x number o f regions. The number o f rows is a lin e a r fu n c tio n o f the number o f regions as shown in the fo llo w in g equation: rows = rows/region x number o f regions. The number o f columns can vary s lig h t ly between regions. for purposes o f However, th is discussion, i t 1s assumed th a t the number o f columns is the same fo r each region. The number o f columns is a lin e a r fu n c tio n o f the number o f regions as shown in the fo llo w in g equation: columns - columns/region x number o f regions. To d e riv e the to ta l number o f elements in the m a trix , the number of rows is m u ltip lie d by the number o f columns as shown in the fo llo w ­ ing equation: to ta l elements = row s/region x columns/region o x (re g io n s ) . As a re s u lt the to ta l number o f elements increase by the square o f the number o f regions. The to ta l number o f zero c o e ffic ie n ts in ­ creases a t a ra te much fa s te r than the number o f non-zero c o e ffic ie n ts . When space 1s Included by su b -d ivid in g an area in to reg io n s, the density o f the region decreases by adding la rg e numbers o f zeroes. 234 Problems Encountered by Including Time Including time also increases the s iz e o f the m a trix . coefficients must be Included fo r each time period. Transportation a c tiv itie s must also be included f o r each time p erio d. constraints are included only once. Product Resource Figure 5-2 illu s t r a t e s the e ffe c ts of time fo r th a t p ortio n o f the m atrix a llo c a te d to one reg io n . The number o f non-zero c o e ffic ie n ts increase lin e a r ly w ith time as shown by the fo llow ing equation: Non-zero c o e ffic ie n ts * resource c o n s tra in t c o e ffic ie n ts + [{p ro d uct and tra n s fe r c o e ff1c ie n ts )/tim e p erio d ] x number o f time periods. The number o f rows increases lin e a r ly w ith the number o f time periods as shown in the fo llo w in g equation: rows = resource c o n tra in t rows + [(p ro d u ct and tra n s fe r row s)/ time p erio d ] x number o f time periods. The number o f columns also increases lin e a r ly w ith the number o f time periods: columns = management s tra te g ie s + [tra n s p o rt a c t iv it ie s /t im e period x number o f time p e rio d s .] The to ta l number o f elements increases w ith the square o f the time periods. way. However, dnly the tra n s p o rta tio n component increases th is The number o f elements in the production component Increases lin e a rly w ith the number o f tim e perio ds. to ta l number o f elements = resource c o n s tra in t c o e ffic ie n ts + [product c o e ff1c t e n t s /t 1me period + tra n s p o rt c o e ffic ie n ts /tim e p erio d ] 235 Management S tra te g ie s Transport A c tiv itie s Figure 5 - 2 .— Diagram o f L inear Programming Tableau Showing the E ffe c ts o f Adding Time Dimension. The shaded areas contain non­ zero c o e ffic ie n ts . The numbers 1, 2, 3 , and 4 in d ic a te the region in which the non-zero c o e ffic ie n ts belong. 236 X (tim e p e rio d s )2 . The number o f zero c o e ffic ie n ts Increases much more p ra ld ly as the number o f regions Increases than as the number o f time periods in ­ creases. Including both time and space w il l increase th e costs o f a lin e a r program. The Increased number o f c o e ffic ie n ts w il l increase the costs o f reaching a s o lu tio n . I t 1s possible th a t the s iz e o f the m atrix could grow so la rg e as to fo rce a more expensive alg orith m to be used or to make s o lu tio n Im possible. C ritic is m o f the S p e c ific A p p lic a tio n There are also special problems and assumptions associated w ith the s p e c ific a p p lic a tio n o f the model. These assumptions were made to make the problem e a s ie r to handle. There are assumptions d ealin g with both conceptual and data problems. These assumtlons w i l l a f f e c t how w ell the model 1s su ited to the problem. Conceptual Problems There are a v a r ie ty o f assumptions concerning the conceptual basis o f the a p p lic a tio n . Conversions between major classes o f land use are not p ossible in the model. Forest land cannot be converted to a g ric u ltu r a l land and v ic e -v e rs a . This assumption is b u i l t in to the Economic Research Service model. Impacts o f converting fo re s t land to urban land are handled outside o f the model. sions are assumed not to occur. Other conver­ Management s tra te g ie s and resource classes were aggregated to reduce the number o f a c t i v i t ie s In the lin e a r programming model. Maximum wood production and m u ltip le use management s tra te g y c o e ffic ie n ts were aggregated re s u ltin g in an 237 Information lo s s . S oil groups and stand co n d itio n classes were aggregated fo r th e fo re s t ecosystems. The number o f columns was r e ­ duced by aggregation since conversions between management s tra te g ie s were being considered. There are o th er assumptions which were made concerning fo re s t management s tra te g ie s . Once a t r a c t o f land is managed In te n s iv e ly or under the environmental emphasis management s tra te g y , no conver­ sions can take place. converted. Only land 1n the c u rre n t use management can be This assumes th a t once a decision 1s made to manage land for timber or to remove land from tim ber production, the decision w il l not be reversed. Decisions to convert land from one management strategy to another can occur only once during the time th a t a stand 1s in a c e rta in stand s iz e c la s s . This assumption was made to l i m i t the number o f a c t iv it ie s re s u ltin g from converting management s tra te g ie s . A separate a c t iv it y 1s required fo r each conversion a t a d iffe r e n t p o in t in tim e. The d ecision to convert land from one management s tra te g y to another can occur only before the f i r s t harvest a fte r 1965. Once the f i r s t harvest a f t e r 1965 occurs, the land w il l remain in a given management s tra te g y . Whenever fo re s t land re ­ quiring tim ber stand improvement is 1n the c u rre n t use s tra te g y , an investment in management w il l be required to convert the land to Intensive management. The land w il l then be 1n the adequate co n dition class. There were also some Im portant assumptions concerning tim e. Assumptions were made concerning the growth o f the fo re s t resource. A ro ta tio n length was estab lished f o r each fo re s t ecosystem and management s tra te g y . A period o f tim e was defined fo r each ecosystem 238 during which a growing stand remains in a s p e c ific stand s iz e c la s s . Also growth ra tes were assigned to each stand s iz e class o f each eco­ system. These assumptions were needed to c a lc u la te merchantable tim ber c o e ffic ie n ts and o th er product c o e ffic ie n ts fo r each time p erio d. A planning period o f 60 years was defined and a discount r a te o f 5.88% was used. The planning period coincides w ith the period o f an alysis •used by the Economic Research Service in the Kalamazoo R iver Basin (Economic Research S e rvic e, personal correspondence, 1974). The d is ­ count ra te was determined by th e Water Resources Council fo r land use planning studies (Water Resources C ouncil, 1974), These assumptions have several ra m ific a tio n s . Management options are s im p lifie d . Forest management conversions th a t might take place are e lim in a te d . A bias might be b u i l t in to the system by not allow ing conversions from environmental emphasis to In te n s iv e management o r current use and by not allo w in g conversions from in te n s iv e manage­ ment to environmental emphasis or c u rre n t use. Management options become more gross through aggregation o f management s tr a te g ie s . formation is lo s t . In ­ C o e ffic ie n ts which are ca lcu la ted may become less accurate. The model also s im p lifie d landowner behavior. The bias in management options biases landowner behavior by r e s t r ic t in g the courses of actio n a landowner may ta k e . Landowner behavior Is also s im p lifie d by r e s t r ic t in g the points in tim e when a conversion can take p la ce . The planning period chosen might not be re p re s e n ta tiv e o f the planning period held by people liv in g 1n the r i v e r basin . The discount ra te may not r e f le c t people's time preferences o r opp ortun ity costs o f c a p ita l. These s im p lific a tio n s may reduce the s u i t a b i l i t y o f the model 239 fo r p re d ic tin g producer behavior. The n atu ral system 1s also s im p lifie d . Resource classes are aggregated thus co n so lid atin g management s tra te g ie s and causing losses 1n Info rm ation 1n the c a lc u la tio n o f product c o e ffic ie n ts . V ariations 1n the land resource are averaged out to s im p lify the problem. V a ria tio n s 1n the land resource a re not expressed 1n the production o f products. 1n the model. Also environmental d iffu s io n was not Included The growth o f tim ber stands and changes 1n fo r e s t eco­ systems are als o s im p lifie d . The tim e o f tim ber harvest and m a tu rity is g re a tly s im p lifie d by d e fin in g a uniform ro ta tio n age fo r each fo res t ecosystem and management s tra te g y . The tim e period during which a growing stand remains 1n a stand s iz e class 1s als o uniform fo r each ecosystem and management s tra te g y . V a ria tio n s In growth o f stands over space are g re a tly s im p lifie d 1n th is manner. The p r e d ic t a b ilit y o f th e model would seem to decrease as as­ sumptions s im p lify human behavior and n atu ral fu n c tio n s . Bias may also re s u lt from lim ita tio n s on th e management options considered. Therefore, i t 1s d i f f i c u l t to estim ate the accuracy o f th e model. Data Problems There were a v a r ie ty o f assumptions made because data problems were encountered. There were a number o f assumptions concerning demands and supplies o f roundwood. P u lp m llls In the lower peninsula of Michigan were assumed to demand a constant proportion o f the lower peninsula pulpwood production each y e a r. The lower peninsula was assumed to be s e l f - s u f f i c ie n t 1n pulpwood production. was made because o f a c o n f id e n t ia lit y problem. This assumption The Michigan Depart­ ment o f Natural Resources would not re lea se volume data f o r pulpwood 240 purchased by p u lp m llls each y e a r. Requirements fo r sawlogs and veneer logs f o r regions 1n the r iv e r basin were based on the data o f a given year. Purchase data fo r sawlogs and veneer logs by county a re extrem ely scarce. Purchase estim ates were based on residual production by as­ suming th a t re s id u a ls were a constant p roportion o f roundwood purchases. Requirements f o r sawlogs and veneer logs were taken as an average o f purchases fo r th ree d if f e r e n t y e a rs . much 1s consumed. I t 1s d i f f i c u l t to fin d out how Other fa c to rs th a t might a f f e c t demand a re d i f f i c u l t to d efin e and include 1n data c o lle c tio n e f f o r t s . Roundwood demands are assumed to increase according to Forest Service assumptions 1n the Timber Outlook Study. as the n a tio n . Each region 1s assumed to grow a t the same ra te This assumption does not a llo w fo r regional d if f e r e n ­ tia tio n from the n a tio n . However, lack o f data makes 1t d i f f i c u l t to specify models and p re d ic t supply and demand fo r each re g io n . Production o f roundwood or regions outside o f the study regions was based on s ta te fig u re s . Roundwood production was assumed to be constant during each time period f o r each re g io n . Supplies o f each type o f roundwood were based on an average o f only th ree data p o in ts . Not enough data are a v a ila b le to s p e cify a supply fu n c tio n fo r tim b er. Factors which determine c a lc u la tio n . tim ber supply were not considered 1n the Hence, v a ria tio n s 1n supply re s u ltin g from changes 1n factors which determine supply a re not considered. Assumptions were also made concerning hunterdays. fo r hunterdays are d ir e c t ly re la te d to p o p u latio n . hunterdays per person 1s assumed constant. o f I n f l e x i b i l i t y in to the system. Requirements The number o f This Introduces a degree There are not s u f f ic ie n t data to specify a demand model f o r each region f o r hunterdays. Increases 1n 241 requirements, th en , are assumed to increase d ir e c t ly w ith Increases in population. Population growth, based on Economic Research Service p ro jectio n s, 1s assumed to increase a t the same ra te as the population of the s ta te . considered. Regional d if f e r e n t ia t io n caused by m igration 1s not Hunter behavior in terms o f tra v e l was determined from national d ata. average. Hunters are assumed to behave according to th e n ation al There is a lack o f data fo r lo cal hunter behavior. There could be a bias 1n the number o f hunters 1n a p a rty and the number o f days per t r i p . Assumptions were made concerning tra n s p o rta tio n co sts. Regions were assumed to be square w ith a s in g le demand p o in t in the c e n te r. north-south, east-w est tra n s p o rta tio n network 1s d efin ed . are evenly d is trib u te d over the area. Other roads These assumptions were made to calcu late distances tra v e lle d 1n a re g io n . r e a lis t ic , A They a re , however, un­ Some regions do not even approach a square shape. points o fte n are not in the center o f the reg io n . R e a lis t ic a lly , there is o fte n more than one demand node fo r a commodity. commodities may have d if f e r e n t demand nodes. d is trib u te d over the area o f the reg io n . Demand D iffe r e n t Roads are not evenly Transport routes chosen were assumed to be re p re s e n ta tiv e o f routes across which people and goods move. Representative routes were chosen to l i m i t the number o f tra n s fe r a c t iv it ie s 1n the m a trix . This approach assumes th a t the most Im portant tra ve l routes were always chosen. These assumptions s im p lify the tra n s p o rta tio n network o f the re g io n . However, i t should be recognized th a t milages based on these assumptions could r e s u lt In Inaccurate tra n s p o rta tio n co sts. D if f i c u lt i e s were encountered in c la s s ify in g roads in to classes fo r purposes o f c a lc u la tin g tra n s p o rta tio n costs. 242 This may be another source o f Inaccuracy 1n c a lc u la tin g tra n s p o rta tio n costs. In c a lc u la tin g tra n s p o rt co sts, I t was also assumed th a t the proportion o f each class o f c a r ownership was the same in the region as i t was in the n a tio n . There was some d i f f i c u l t y in c la s s ify in g automobiles and c a lc u la tin g the number o f each class o f automobile on the road. This may also be a source o f inaccuracy. This discussion points out th a t th ere are many problems involved in a study o f th is s o rt. Few data are a v a ila b le to help c a lc u la te supplies, demands, excess su p p lies , and tra n s p o rt co sts. I t 1s d i f f i c u l t to devise good p ro je c tio n models from the a v a ila b le d a ta . Undoubtedly, there is g re a t d is p e rs io n , and possibly b ia s , in the estim ates made. C o n fid e n tia lity might also be a problem in o btain ing consumption data from larg e firm s , as i t was in th is study. I t would be d i f f i c u l t to obtain these data fo r a study which is to be made a v a ila b le to the general p u b lic . Assumptions made to overcome these data problems have ra m ific a ­ tions fo r the economic and n atu ral systems. Behavior o f the pulpwood market o f the lower peninsula o f Michigan is assumed to be h ig h ly in ­ f le x ib le . The lower peninsula o f Michigan is assumed to be a closed market w ith p u lp m ills purchasing a fix e d share. r e a lis tic . This is h ig h ly un­ The impacts o f p ric e on regional demands fo r and supplies o f timber are not recognized. No reco g n itio n o f regional advantages and disadvantages in the wood markets is Included. of demand fo r hunterdays 1s very in e la s t ic , The p ric e e l a s t i c i t y per ca p ita consumption o f hunderdays 1s assumed constant regardless o f the cost o f hunting. Regional v a ria tio n s 1n population growth are not considered. The natural system is also s im p lifie d . V a ria tio n s in the q u a lity 243 and q u a n tity o f w i l d l i f e h a b ita t over space in regions outside o f the riv e r basin are not Included. Factors a ffe c tin g growth and d ec lin e o f w ild lif e populations are omitted 1n the p ro jectio n s o f supply, Natural factors a ffe c tin g the growth and supply o f tim ber 1n regions outside of the r iv e r basin are also neglected. In summary*assumptions behind the conceptual basis o f the model introduce u n r e a litie s In to the d e s c rip tio n o f the r iv e r basin system. Host o f these assumptions were required to overcome data d e fic ie n c ie s . Usefulness o f the Model to P o licy Analysis The purpose o f the model is to a llo c a te land management strate g ies among resource classes and regio ns, given goals and con­ s tr a in ts . The model, then, can be used to a s s is t policy-m akers by generating g u id elin es fo r land management. Impacts o f a lte r n a tiv e guidelines f o r land management can be generated w ith th is model. Im­ pacts o f v a ria tio n s o f product requirements over time and space can be studied. Growth rates o f reqquirements and s p a tia l v a ria tio n s in growth ra tes can be studied by varying product requirem ents. By the same token, the Impacts o f favoring c e rta in product users can be in ­ vestigated by varying the le v e ls and growth ra tes o f product re q u ire ­ ments r e la t iv e to each o th e r. A lso, impacts o f varying c o n s tra in ts on environmental impacts over space and time can be studied 1n a s im ila r way. Impacts on g u id e lin es to land management from a llo c a tin g land to various uses according to d if f e r e n t c r i t e r i a can also be stu d ied. Land uses in c e rta in areas can be determined based on c r i t e r i a not in the model. These s tra te g ie s can be used to co n strain the model by use 244 o f a c o n s tra in t generator. The model can then be run to o ptim ize the objective fu nctio n given these c o n stra in ts on land use. Impacts o f changes in the tra n s p o rta tio n system, tra n s p o rta tio n technology, and fu el costs can also be stu d ied . u ltim a te ly change the tra n s p o rt co sts. Such changes w il l The costs o f the tra n s p o rt a c t iv it ie s can be varied 1n the model to study impacts on land manage­ ment. There are a v a r ie ty o f questions th a t are not e a s ily handled by the model. For example, In d iv id u a l s it e problems, such as planning a park or o ther small scale problems, cannot be e a s ily handled by th is model. The model w ill not choose the best s it e o f a given area from a set o f a lte r n a tiv e s ite s . Since the model 1s a land management model, I t does not seem w ell su ited to such problems as m ining, m anufacturing, w holesaling, and r e t a i l in g . However, impacts on land use could be con­ sidered through a c t i v i t ie s in the model although they might be handled more e a s ily outside o f the model. The model does not deal w ell w ith problems o f d is tr ib u tio n a l e ffe c ts on social groups w ith in a given region. Also, the model does not seem w ell suited to problems o f urban growth because o f interdependencies involved 1n urban growth. There 1s one p o lic y question th a t can be handled by the model which might be more e a s ily handled w ith a d if f e r e n t type o f model. A ll lands may be a llo c a te d to management s tra te g ie s outside o f the model. The model could then be used to produce s p a tia l economic and en viron ­ mental Impacts. This problem might be handled more e a s ily by using a sim ulation model to generate the goods produced by each o f these manage ment s tra te g ie s . The s p a tia l e ffe c ts could then be generated by use o f separate environmental d iffu s io n and s p a tia l economic models. No 245 examples o f sim ulatio n models lin ke d to s p a tia l economic and environ­ mental d iffu s io n models were found. The Honey H111 re p o rt describes a sim ulation model which generates the Impacts o f land uses fo r in ­ dividual g rid c e lls (Murray e t . a ! . , 1971). The movement o f impacts through space are not considered in th is model, however. Final Assessment o f the S u it a b ilit y o f the Model The approach used in th is study appears to be w ell su ited to pro­ viding p o lic y g uidelin es f o r managing p u b lic ly owned lands. The model could be employed by fe d e ra l o r s ta te land management agencies. This Is a s itu a tio n where a normative model 1s d e s ira b le since 1t says what ought to be done to meet o b jec tiv es given c o n s tra in ts . The model could also be used by s ta te agencies to develop g u id elin es fo r the ap­ p lic a tio n o f p o lic e powers, ta x a tio n powers, and spending powers to guide land use toward s ta te land use goals. also be used as a g u id e lin e F in a lly , the model could fo r extension e ffo r ts o f fe d e ra l land * agencies. The model could help to in d ic a te what management options should be encouraged by education and pub lic assistance programs, given the agency's land use goals and resource c o n s tra in ts . However, the model does not in d ic a te how to implement such a program. There are some im portant lim ita tio n s o f th is approach. The neglect o f economies o f scale and in te ra c tio n s between land management s tra te g ie s e lim in a te Im portant aspects o f land management options. Economies o f scale can be Included through separable programming, how­ ever. In te ra c tio n s can be included only by developing special a c t i v i t ie s fo r the model. However, th e minimum contiguous area f o r a land manage­ ment s tra te g y to be p racticed cannot be s p e c ifie d . I t is expensive to 246 Include the dimensions o f time and space 1n the model. This model also has large data requirements which may be the most serious lim it a t io n . Both the s p a tia l s p e c if ic it y and accuracy o f re s u lts are dependant upon the q u a n tity and q u a lity o f data a v a ila b le fo r s p a tia l d iv is io n s o f the resource base. Many o f the assumptions brought about by data problems 1n the ap p lication could be overcome by b e tte r d a ta . Because o f the data problems, th ere are serious doubts about the accuracy o f the re s u lts o f the model. In order fo r th is approach to be •‘mplemented, b e tte r data sources need to be developed. Overcoming these data problems w il l probably be the most expensive b a r r ie r to Implementing th is approach. No m atter what 1s done, however, assumptions w i l l be re q u ire d . Models are ab stractio n s o f r e a l i t y , not s u b s titu te s f o r r e a l i t y . The purpose o f models such as th is one 1s to help policy-m akers to under­ stand the ra m ific a tio n s o f t h e ir proposed actions or d e s ire s . cannot become a s u b s titu te fo r decisionmaking. bear f u l l re s p o n s ib ility f o r t h e ir decisio n s. Models Decision-makers must However, the assumptions behind any model used should be made e x p li c i t so th a t the shortcomings of the model can be b e tte r understood. There are some problems w ith lin k in g th is model o f the fo re s t sector to the cu rren t USDA model. This problem is based on tim e . model solves f o r s ix time periods sim ultaneously. fo r each time period in d iv id u a lly . This The USDA model solves E ith e r the c u rre n t USDA model must be changed to a pseudodynamic lin e a r programming fo rm a t, o r some o th er approach which considers tim e , or the fo re s t sector must be handled sep arately w ith the re s u lts entered in to the USDA model. Inclu d in g many time periods would c rea te problems f o r the a g ric u ltu r a l sector since 247 large numbers o f conversions in crops could e a s ily make the problem unmanageable. The tra n s p o rta tio n and environmental d iffu s io n components could be e a s ily added onto th e c u rre n t model used in r iv e r basin plan­ ning. This study has made several improvements over the c u rre n t USDA approach. Time has been included. More aspects o f space have been included. The tra n s p o rta tio n network, tra n s p o rt co s ts , and s p a tia l aspects o f demand have been included in the a p p lic a tio n . D iffu s io n o f environmental impacts through space were discussed in the id eal model but not included in the a p p lic a tio n . The r i v e r basin econorny was modeled as an open system. The model seems to be poorly su ited to the problem o f p re d ic tin g what production " w ill" occur given a set o f requirem ents, c o n s tra in ts , and re s tr ic tio n s on land use. The basic problem is the assumption th a t the comnunity acts as a s in g le en trepren eu r. This assumption does not agree w ith the s tru c tu re o f the American p o lit ic a l and economic system. People may be s a tis fic e r s ra th e r than o p tim ize rs . A lso, th ere may be a degree o f in d iffe re n c e to d iffe re n c e s in costs or b e n e fits in decisionmaking. People may not change land management i f changes in costs and b e n e fits are not la rg e enough. For purposes o f p re d ic tin g landowner behavior in the r iv e r basin s tu d ie s , i t is h ig h ly recommended th a t the Forest S ervice o r some o th e r branch o f th e USDA study the p o s s ib ility o f developing a sim ulation model. The model should be de­ signed to p re d ic t what behavior Is l i k e l y to be, ra th e r than what i t ought to be. That is to say, 1 t should be a non-optim izing model. In connection w ith such a study, more tim e should be spent analyzing the determinants o f land owner behavior. CHAPTER VI SUMMARY AND CONCLUSIONS Summary The primary o b je c tiv e o f th is study 1s to examine the f e a s i b i l i t y of b uilding an in te g ra te d land inventory and ev a lu a tio n system fo r r iv e r basin planning s tu d ie s . This study is concerned w ith the lo c a tio n a l aspects o f planning fo re s t resources. Planning by USDA must concern i t ­ s e lf w ith national economic development, environmental q u a lity , regional development, and social w e ll-b e in g . The purpose o f the model developed in th is study is to lo c a te land management s tra te g ie s in space given requirements fo r products and resource s tra te g ie s . Four stages were involved in developing th is model: 1) l i t ­ erature search, 2) co n ce p tu alizatio n o f the model, 3) te s tin g the model, and 4) c r itic is m o f the model. The emphasis o f the study was on lo c a tio n ­ al aspects and lin k in g new concepts to e x is tin g Economic Research Service models. The summary w il l concentrate on the la s t three stages o f the study. Conceptualizing the Model P relim in ary work included determ ining what ought to be included in the model. Several issues were id e n t if ie d to be considered by the model: 1) space and time aspects o f demand, production, and environmental impact, 2) tra n s fe r o f goods through the economy, 3) openness o f the econorny, 4) r e g io n a liz a tio n , and 5) d is trib u tio n a l e ffe c ts . 248 A s e t o f components 249 were id e n tifie d fo r the system: 1) the land evalu atio n system which in ­ cludes production and lo c a tio n a l aspects, 2) land inventory system, 3) constraint generator, 4) land management s tra te g y d a ta , 5) goals, and 6) displays. A s e t o f a lte r n a tiv e model categories were put fo rth which could be used in the land evalu atio n system: 1) in p u t-o u tp u t models, 2 ) lin e a r programming models, 3) sim ulation models, 4) dynamic programming models, and 5) hybrid models. S p e c ific a p p lic a tio n s and th eo ries were discussed a fte r a survey o f the l it e r a t u r e . Three general a lte r n a tiv e s , th en , were developed fo r the land evalu atio n system. I. A regional lin e a r programming model w ith s p a tia l economic and environmental components which a llo c a te s tra te g ie s among re ­ gions. A m u ltip le land use assignment is used to a llo c a te management s tra te g ie s among g rid c e ll subdivisions o f the regions. II. A m u ltip le land use assignment model a llo c a te s management s tra te g ie s among g rid c e lls . S p a tia l economic and en viron ­ mental aspects are included through separate re la tio n s h ip s but do not in flu e n c e the a llo c a tio n o f management s tr a te g ie s . III. A sim ulatio n model generates production o f commodities fo r a lte r n a tiv e land use plans developed outside o f the model. These re s u lts become in p u t to re la tio n s h ip s which c a lc u la te s p a tia l economic and environmental impacts. A se t o f c r i t e r i a were used to evalu ate these th ree a lte r n a tiv e s : 1) spa­ t i a l economic im pact, 2) s p a tia l environmental impact, 3} q u a lity o f data needed, 4) p rovision o f p o lic y g u id e lin e s , 5) relevance o f necessary assumptions, 6 ) c a p ac ity to deal w ith tim e, 7) c o m p a tib ility w ith the 250 present Economic Research Service model, and 8 ) o perating co st. The f i r s t a lte rn a tiv e was chosen as the a lte r n a tiv e favored fo r fu rth e r In v e s tig a ­ tion . The s tru c tu re o f the f i r s t a lte r n a tiv e was more s p e c ific a lly d e te r­ mined. C r ite r ia were used to choose among a lte r n a tiv e s tru c tu re s : 1) transpo rtatio n im pact, 2) environmental d iffu s io n impact, 3) s p a tia l s p e c ific ity , 4 ) construction c o s t, and 5) operating co st. The tra n s p o rta ­ tion and environmental d iffu s io n components are incorporated d ir e c t ly In to the production model in order to have Impact on the a llo c a tio n o f manage­ ment s tra te g ie s among regions. Time 1s Incorporated through the use o f pseudo-dynamic programming and costs are discounted to the p resen t. A cost-m inim izing approach, the c u rre n t approach o f the Economic Research Service, 1s used. A m u ltip le land use assignment model a llo c a te s manage­ ment s tra te g ie s among g rid c e lls . V ariab les and equations were d efin ed . Land management s tra te g y Info rm ation consists o f product c o e f f i c i ­ ents fo r management s tra te g ie s a t d if f e r e n t points in tim e. must be defined to c a lc u la te these c o e ffic ie n ts . R elationships V ariab les 1n these re ­ latio n sh ip s should be based on physical resource d a ta , tim e , and land p ractices. Goals f o r land management and output are a lte r n a tiv e c o n stra in ts and requirements fo r land use and land products. These must be determined fo r every r iv e r basin study. The purpose o f the land Info rm ation system 1s to s to re Inform ation needed fo r c a lc u la tin g acreage c o n s tra in ts fo r management by resource class and lo c a tio n . Acreages o f each resource class must be d efin ed . Resource classes should be based on the m ulti-dim ensional land type con­ cept. Each dimension 1s a class o f data Im portant to d ed sio n -m akln g . 251 There are two methods to d efin e the acreages o f these resource classes. F ir s t, each dimension could be mapped sep arately and th e acreages o f each resource class determined by overlays o f the maps o r through use o f com­ puter techniques based on a g rid system. Second, each resource class could be mapped In d iv id u a lly through an In te g ra te d in v en to ry. Grid c e lls sto re land inform ation by lo c a tio n . The g rid c e ll 1s chosen to store inform ation in th is system because o f i t s widespread use and the a v a i l a b i li t y o f computer technology based on the g rid c e l l . There are two general sizes o f g rid c e lls . One s ize is small enough to allow only one resource class o r dimension to be assigned to i t . The sec­ ond s iz e is larg e enough to allo w more than one resource class o r dimen­ sion to be assigned to i t . C r it e r ia selected to determine the s iz e th a t should be used in the system include: 1 ) cost o f c la s s ify in g the resource 2) ease o f mapping resource data and classes, and 3) ease o f mapping man­ agement s tra te g ie s . The s iz e chosen is a c e ll small enough fo r only one resource class o r dimension to be assigned to i t . The desired accuracy o f land use inform ation determines the threshhold a t which a small c e ll be comes a large c e l l . Geographic referen cin g is needed to determine the lo c a tio n o f each grid c e l l . A lte rn a tiv e systems include la titu d e -lo n g itu d e , Universe Transverse M ercator, s ta te plane co o rd in ates, and the re cta n g u la r survey. The Universe Transverse Mercator system was selected as the id e al because o f many d es irab le c h a ra c te r is tic s . However, many e x is tin g secondary data sources w il l be referenced by o th er systems. The means o f data storage w ill vary according to the needs o f the s p e c ific s itu a tio n . There are a lte r n a tiv e means o f o rganizing data f i l e s : sequential o rg a n iza tio n , random o rg a n iz a tio n , and l i s t processing. A l­ te rn a tiv e storage media also e x is t , th a t i s , cards, d is c s , and tapes. 252 The combination o f f i l e o rg an iza tio n and storage media chosen depends on the amount o f data stored and the frequency o f access. The combination o f random o rg an iza tio n and disc storage seems to be w ell su ited to a larg e amount o f data th a t 1s accessed fre q u e n tly . sive, however. This combination 1s expen­ Records, which make up f i l e s , should contain lo c a tio n inform ation, resource data fo r the g rid c e l l , th a t i s , each dimension, and the resource class o f the g rid c e l l . Blank fie ld s could be in the record to allo w new data to be added to each g rid c e l l . A lte rn a tiv e flow charts to generate resource c o n s tra in ts fo r the production model and the land use assignment model were i llu s t r a t e d . algorithms are r e la t iv e ly sim ple. The Use o f a computer program would be p a r tic u la r ly useful when th ere is a larg e number o f g rid c e lls . The c o n s tra in t generator develops c o n s tra in ts f o r the production model and the land use assignment model according to decisions on land management made outside o f the system. tra te d . A lte r n a tiv e flow charts were i l l u s ­ A computer program would be p a r t ic u la r ly useful w ith a la rg e number o f g rid c e lls o r w ith a la rg e number o f a lte r n a tiv e sets o f land management decisions made outside o f the system. P rin te r routines f o r mapping th a t can be used on the CDC 6500 were surveyed. The routines were GRIDS, SYMAP, and MIADS. favored fo r mapping resource d ata. GRIDS and MIADS are MIADS is favored fo r mapping resource classes and the output o f the land assignment model. SYMAP is favored fo r any maps made o f the sub-regions. Testing o f the Model The model tes ted was a co s t-m in im izin g , pseudo-dynamic lin e a r programning model. Total production and tra n s p o rta tio n costs are minimized. 253 The tra n s p o rta tio n component is incorporated in to the production model while the environmental d iffu s io n model was not included in th is t e s t . The products Included in th is an alysis were tim b e r, big-game hunterdays, small-game hunterdays, and erosion . Resource classes were based on fo res t ecosystem, s o il group, stand s iz e c la s s , and stand co n d itio n c la s s . Six ten -year time periods from 1965 to 2025 were included. There are four sub-areas in the basin and e ig h t demand regions outside o f the basin. The land use assignment model which would a llo c a te management s t r a t ­ egies among g rid c e lls was not included. The reason fo r th is is th a t the land resource data base fo r the Kalamazoo R ive r Basin 1s not lo c a tio n sp e c ific enough to support a g rid system. not mapped. S oil management groups are A ll fo re s t inven tory data was on a county b a s is . Remote sensing d ata, though s p e c ific enough in s p a tia l term s, was not s p e c ific enough fo r management d ecisio n s. The r e s u lt , th en , is th a t management s tra te g ie s can only be a llo c a te d among regions and not among g rid c e lls . Data were c o lle c te d fo r the s p a tia l and temporal economic aspects o f the fo re s t se cto r. Requirements fo r roundwood were c a lc u la te d . sources include the U.S. Forest S e rvic e, theM ichigan Data Department o f Natu­ ral Resources, and Lockwood^ D ire c to ry o f the Paper and A llie d Trades. Requirements were c a lc u la te d f o r each county in the studyarea and a l l o ­ cated to regions on the basis o f tim b er-u sin g c a p a c ity . P ro jectio n s i n ­ to the fu tu re were based on medium-level p ro je c tio n s o f tim ber consumption in the Outlook fo r Timber in the United S ta te s . regions outside o f the r iv e r basin was estim ated . aged fo r each county. the basis o f a rea . used. Roundwood production in Production was aver­ This production was a llo c a te d among regions on Michigan Department o f N atural Resources data were The production o f tim b er was assumed constant over each 10 -ye ar 254 period. Excess supplies o f tim ber fo r regions outside o f the r iv e r basin were calcu la ted by su b trac tin g requirements from production. Consumption requirements fo r hunterdays fo r each region were calcu­ lated by m u ltip ly in g the consumption o f the region by hunterdays per per­ son. Requirements were projected over time by using population p ro je c ­ tions c a lc u la te d by the Economic Research S ervice. Supplies o f hunter­ days fo r regions outside o f the r iv e r basin were also c a lc u la te d by mul­ tip ly in g acres times k i l l per acre fo r each county times hunterdays per k ill. Supplies were a llo c a te d to regions on the basis o f area. Excess supplies over lo c a l consumption were c a lc u la te d fo r regions outside o f the r iv e r basin by su b tractin g requirements from su p p lies . Transport costs were c a lc u la te d . Transport routes were defined from the supply area to the demand p o in t. Classes o f roads were defined and the average number o f m iles tra v e lle d on each class o f road to get to the fin a l d e s tin a tio n was c a lc u la te d . Timber tra n s p o rt costs per m ile were based on U.S. Forest Service fig u re s . Hunterday tra n s p o rt costs per mile were based on U.S. Department o f T ra n s p o rta tio n , U.S. Department o f In te r io r and Motor V ehicle Manufacturers Association fig u re s . Transport costs per cubic fo o t o f tim ber o r per hunterday were c a lc u la te d f o r each year in a 10 y e a r period and discounted to the present a t 5.88%. The d is ­ counted annual cost per u n it each y e a r in the 10 y e a r period was then summed. Production costs and c o e ffic ie n ts fo r production a c t i v i t ie s were c a lc u la te d . Management s tra te g ie s and resource classes were aggregated when fe a s ib le to reduce c a lc u la tio n s and computer core requirem ents. ro ta tio n was defined fo r each management s tra te g y . stand s iz e class and time was assumed. A r e la tio n between An age d is tr ib u tio n based on A 255 fo re s try Inven tory data fo r th e southern h a lf o f the lower peninsula was also assumed. The fo re s t system was then conceptualized as a sys­ tem o f age cohorts moving through tim e. Harvesting and management were assumed to be even-aged 1n ch a rac ter w ith no merchantable cuts made ex­ cept a t r o ta tio n . Conversions between management s tra te g ie s were lim ite d to s im p lify the problem. Average annual tim ber costs per acre fo r each 10 year period were c a lc u la te d given growth, r o ta tio n , and waste. In fo r ­ mation was obtained from the U.S. Forest Service and the Michigan Depart­ ment o f Natural Resources. Average annual c o e ffic ie n ts fo r hunterdays and erosion were averaged fo r each 10 year period and were based on the movement o f age cohorts through tim e. expenditures were in c u rre d . Points in time were determined when These expenditures were then discounted to the present a t 5.88%. A number o f computer runs were made: Run A: A b aselin e run w ith tim ber and hunterday requirements assum­ ed constant over tim e. Run B: Timber requirements in pulpwood-uslng regions grow a t a ra te assuming r is in g r e la t iv e prices w h ile a l l o th er re ­ quirements remain constant over tim e. Run C: Timber requirements grow a t a ra te assuming ris in g r e la t iv e p rices w h ile hunterday requirements grow a t the same ra te as population. Run D: Timber requirements grow a t a ra te assuming 1970 r e la t iv e p rices w hile hunterday requirements grow a t the same ra te as populatio n. Run E: Timber requirements remain constant over tim e w h ile hunter­ day requirements grow a t the same ra te as p o p u latio n . 256 There 1s no s p a tia l v a ria tio n 1n the p a tte rn o f managing tim ber producing lands. Two le v e ls o f production e x is t . In runs A and E, a l l timber producing lands are converted to in te n s iv e production as soon as possible, except fo r s e e d lin g -s a p lln g classes o f aspen-blrch which are converted to environmental emphasis. In runs B, C, and D, a l l tim ber pro­ ducing lands are converted to In te n s iv e management as soon as possible. The timber producing p o te n tia l 1s f u l l y u t iliz e d w ith these th ree runs. On non-tim ber producing lan ds, a ll adequate class lands are convert­ ed to in te n s iv e management as soon as p o ssib le. Most classes not in ade­ quate condition remain in c u rre n t use w ith some exceptions. In run A, intensive management o f some o f these classes occurs in regions 2 and 3. In run B, fewer acres o f these lands are converted to in te n s iv e manage­ ment in regions 2 and 3 because o f increased hunterday production on tim ­ ber producing lands. In runs C and D, the number o f acres converted to Intensive management decreases in some ecosystems and increases in others re la tiv e to run A.Some acres are converted to in te n s iv e management in region 4 . In run E, more o f these acres are converted to in te n s iv e man­ agement in regions 2 , 3, and 4 than in run A. This occurs because th ere were no increases in hunterday production on tim ber producing lands w h ile requirements fo r hunterdays increased. The hunterday production p o te n tia l o f the r iv e r basin is not f u l l y u t iliz e d in any o f these runs. There were a v a rie ty o f fa c to rs a ffe c tin g the lo c a tio n o f manage­ ment s tra te g ie s and marginal lands. The le v e ls o f requirements and t h e ir d is trib u tio n over time and space are the most Im portant. Development costs, harvesting co sts, tra n s p o rt co s ts , and Im porting costs are a ll Important fa c to rs . There is an im portant t r a d e - o f f between development costs and im porting costs in determ ining whether lands are to be managed 257 In te n s iv e ly . The time d is trib u tio n o f production 1s another im portant fa c to r. Surpluses in goods received over q u a n titie s required seldom occur. There are tim ber surpluses in time period 5 In regions 1 and 4 o f run A. Small surpluses o f small game hunterdays e x is t in time period 1 o f runs B, C, and D in region 4 . There were d e f ic it s o f tim ber in time periods 2 through 6 in runs B, C» and D. Production was ranked fo r each product, reg io n , and time p erio d . OBERS demands could not be met 1n time periods 1 and 3. between regions were discussed. were discussed. follow s: Flows o f goods Production, tra n s p o rt, and im porting costs Importing costs are ranked from lowest to h ig hest as A, E, B, C, and D. These re s u lts have im p lic atio n s fo r growth 1n the tim ber in d u s try . Small amounts o f fo re s t lan d , conversion o f fo re s t land to urban use, and the s ta te o f land tenure l i m i t growth p o s s ib ilitie s fo r tim ber-using In d u s trie s . The Menasha Corporation appears to be a t a com petitive d is ­ advantage compared to o th e r Michigan p u lp m ills due to i t s distance from the pulpwood resource o f the northern h a lf o f the lower peninsula. It might be ab le to overcome these disadvantages through the a v a i l a b i l i t y o f labor and c a p it a l, economies o f s c a le , and sh o rt ro ta tio n on sub-marg1nal farmlands 1n the r iv e r basin. a lt y m ills could probably be accommodated. poplar c u ltu re The growth o f s m a ll, speci­ In te n s iv e tim ber management could improve wood q u a lity and Improve the growth p o te n tia l o f these firm s . I t is d i f f i c u l t to apply these re s u lts o f th is te s tin g to o th e r r iv e r basins. Each r iv e r basin w il l have i t s unique set o f lo c a tio n fa c to rs , i t own natural resources, and i t s own economic s tru c tu re . A lin e a r programming model accounting fo r time and space in fo re s t 258 land planning is fe a s ib le to co n stru ct and run. The model a llo c a te s production requirements a t demand points among supply regions and a l l o ­ cates management s tra te g ie s over space. However, I t 1s d i f f i c u l t to con­ s tru c t and c o s tly to use. C ritic is m o f the Model The model used 1n the land e v alu atio n system can be applied to sev­ eral types o f s itu a tio n s : 1 ) management o f publically-ow ned land by a public land agency, 2 ) making recommendations f o r p riv a te landowners, given the o b je c tiv e s o f a p u b lic agency, and 3) p re d ic tin g land use p a t­ terns. Only the second and th ir d s itu a tio n s are re le v a n t in the Kalamazoo River Basin. little The f i r s t s itu a tio n is not considered because th ere is so publically-ow ned land 1n the Kalamazoo R iver Basin. the cu rren t USDA approach are reviewed. Problems o f S p a tia l aspects o f demand and the openness o f the economy are not considered. Land 1s the only l i m i t ­ ing fa c to r . Time is poorly considered. m inim izing. Im portant land management options are not considered. are some im portant data problems. ing. The o b je c tiv e fu nctio n is c o s tThere Data on a sub-county basis are la c k ­ The documentation o f data provided by the Forest Service f o r th is study was poor. Assumptions o f the id e a l model have im p lic atio n s fo r the usefulness o f the model. L in e a r ity , a d d it i v i t y , and independence n eg le ct economies o f scale so th a t the s iz e o f the o p eratio n has no impact on u n it costs. Non-add1t 1ve In te ra c tio n s and v a ria b le proportions are not considered. The assumption th a t landowners a c t as a s in g le entrepreneur 1s not v a lid . There are many landowners and th ere is no c e n tra l planning. Landowners do not seem to have id e n tic a l goals and do not appear to work to g e th e r. The model seems l i k e l y to be a poor p re d ic to r o f r e a l i t y because o f the 259 assumptions. The model seems to be best su ited fo r problems concerned with management o f publically-ow ned land or making recommendations to privatelandowners given agency goals. to make the model more r e a lis t ic . Some o f the assumptions were made They Include s p a tia l d is trib u tio n o f requirements, flows o f goods through space, openness o f the economy, and Inclusion o f tim e. Including space and time increases the s ize o f the 11 near program­ ming tableau. Computer core requirements increase as a re s u lt thereby increasing costs. I t is possible th a t computer core requirements could be increased u n til they exceed the lim its o f the computer. The assumptions used in the tested model also have im p lic a tio n s . The assumptions s im p lify behavior and could introduce bias in to the re ­ su lts. Conversions between classes o f lan d, such as between fo re s t and a g ric u ltu re , are not allowed to occur. Soil groups, condition classes, and management s tra te g ie s were aggregated. ment strate g ies are lim ite d . 1s assumed. Conversions between manage­ Even-aged management o f the tim ber resource Impacts on the ro ta tio n , merchantable s iz e , and c u ttin g cycle are not considered. not be r e a lis t ic . The planning period and discount ra te might The environmental d iffu s io n model and the m u ltip le land use assignment model were not included. Assumptions were made to overcome c e rta in data problems, since data were scarce. The assumptions could introduce bias in to the re s u lts . lack o f inform ation resu lts in estimates which are very im precise. creasing the amount o f data w ill increase p rec isio n . crease the accuracy o f the re s u lts . The In ­ Both problems de­ There is a s c a rc ity o f production and purchase data fo r timber and hunterdays. L i t t l e data are a v a ila b le to c a lc u la te supplies, excess su p plies, and tran sp o rt costs. The lack 260 o f data makes 1 t d i f f i c u l t to sp ecify and use p ro je c tio n models. assumptions s im p lify the economic and natural systems. ply do not in te r a c t to determine p ric e . The Demand and sup­ Regional advantages and d is ­ advantages do not change. The model 1s w ell su ited to some problems. Production requirements and management s tra te g ie s can be c o lle c te d over space. logical impacts o f land management can be stu d ied . Economic and eco­ The impacts o f eco­ nomic growth on land management and the impacts o f land management on economic growth can be considered. S p e c ific s it e problems and non-land management problems are not e a s ily handled. I t is d i f f i c u l t to lin k th is model o f the fo re s t sector to the model now used by the Economic Research Service because o f the way in which time is handled. I f a lte r n a tiv e land management plans are proposed com pletely o u t­ side o f the computer model by a planning group, a sim ulatio n model could be useful in studying impacts. A sim ulatio n model could be less c o s tly , have less r e s t r ic t iv e data requirements than lin e a r programming, and can be ta ilo r e d to the s p e c ific problem. More behavioral o r em pirical re la tio n s h ip s could be included in such a model. Needs fo r Further Research A lte rn a tiv e space-time models fo r use in planning the management o f fo re s t land should be developed. Two major suggestions are made. F ir s t , a recu rsive lin e a r programming model could be developed. Rela­ tionships concerning th e changes in the fo re s t resource over time r e s u lt ­ ing from land p ractices would have to be accounted fo r a f t e r the s o lu tio n fo r each time p erio d. Second, a sim ulatio n model could be developed. With th is model, a lte r n a tiv e land use plans could be form ulated by a planning groups outside o f the system. The production o f goods by a g rid 261 or region over time would be c a lc u la te d . The impact on econorny and the environment could be accounted fo r through a s e t re la tio n s h ip s Included 1n the model. E m p iric a lly tested re la tio n s h ip s should be used whenever possible. Research should be d irec ted to o th e r components o f the system. search is needed fo r the land inform ation system. resource classes should be developed. Re­ A standardized s e t o f A lte r n a tiv e geographic referen cin g systems should be In v e s tig a te d more deeply. R elationships to estim ate c o e ffic ie n ts f o r more products should be developed. Errors 1n land in ­ formation and in the estim atio n o f product c o e ffic ie n ts should be in ­ vestig ated. The desired accuracy o f land data and i t s Impact on the costs o f data c o lle c tio n should be In v e s tig a te d . size should be In v e s tig a te d . A lso, impacts on g rid c e ll Research in to the best softw are and storage methods to be used under d if f e r e n t s itu a tio n s should be undertaken. Further research is needed f o r the land e v a lu a tio n system. Rela­ tionships fo r the environmental d iffu s io n model need to be developed. More time should be devoted to determ ining re la tio n s h ip s to c a lc u la te product c o e ffic ie n ts . accuracy. used. R elationships should be s p e c ifie d and tested fo r These re la tio n s h ip s could be compared w ith those c u rre n tly C onstraints fo r erosion need to be developed. More data are needed. More time should be devoted to the s p e c ific a tio n and te s tin g o f regional models which p ro je c t demand and supply. The p ro je c tio n methods used in th is study were n e c e s s a rily very crude. D e fin itio n o f re la tio n s h ip s o f stand development over tim e in th is model needs to be improved. management s tra te g ie s should be developed. More Some suggestions in clu d e: 1) hunterday emphasis fo r d if f e r e n t game sp ecies, 2 ) sh o rt ro ta tio n f o r ­ e s try fo r d if f e r e n t sp ecies, and 3) changes in ro ta tio n length and stand 262 structure. More products should be Included in th is an alysis. C r ite r ia for developing o b jec tiv e function values fo r the land use assignment model should be developed. The use o f an o b jec tiv e function which maximizes p r o f it , b e n e fits , o r regional income in the production model should be investigated. Further research is needed to develop the co n stra in t generator. More time should be spent developing software fo r th is component. In v es tl gators should look in to new techniques fo r measuring mapped areas such as d ig itiz e r s . More computer graphics and p lo tte r routines should be surveyed, p a rtic u la rly those designed fo r computer systems o ther than the CDC 6500. Some time should be spent in in v e s tig a tin g what inform ation should be mapped w ith computer graphics. Conclusions and Reconmendations System S tructure Conclusions: 1. A lin e a r programming model including sp a tia l and temporal eco­ nomic and ecologic dimensions is fe a s ib le to construct and operate fo r purposes o f planning the fo re s t resource o f r iv e r basins. However, the model is d i f f i c u l t to construct and expensive to operate. 2. Inclusion o f time in to a model o f the fo re s t resource makes i t d i f f i c u l t fo r i t to be lin ke d to the Economic Research Service model. The management strate g y concept is most compatible w ith pseudo-dynamic lin e a r programming since impacts o f management s tra te g ie s over time can be included. Recursive lin e a r programming is more compatible w ith the Economic Research Service model than pseudo-dynamic lin e a r programming. However,!t would be more d i f f i c u l t to include various time aspects o f management w ith recu rsive lin e a r programming than w ith pseudo-dynamic lin e a r programming. A model would be required outside o f the lin e a r pro­ gram ing model to generate impacts th a t occur 1n l a t e r time periods and input these to l a t e r stages o f the re cu rs ive program. namic lin e a r programming. With pseudo-dy­ These time impacts can be included in an a c t iv it y column. 3. T ransportation and environmental d iffu s io n components could be linked to the e x is tin g Economic Research Service model. 4. The land ev alu atio n system could be lin k e d to an Inform ation system based on a system o f g rid c e lls . 5. Management s tra te g ie s can, in tu rn , be a llo c a te d among a system o f g rid c e lls . Recommendations: 1. Production Component: a. The production model should be based on pseudo-dynamic lin e a r programming. b. The tra n s p o rta tio n and environmental d iffu s io n models should be incorporated in to the production model. c. A land assignment model should be used to a llo c a te manage­ ment s tra te g ie s among g rid c e lls . d. The use o f a gain-m axim izing o b je c tiv e fu nctio n should be in v e s tig a te d . 2. An e x p li c i t set o f re la tio n s h ip s to c a lc u la te product c o e f f i c i ­ ents based on resource d a ta , management o p tio n , and tim e should be de­ veloped. 3. Land Inventory System: a. Resource classes should be based on the m ulti-dim ensional 264 land type concept. These resource classes should be stan­ dardized fo r use in a l l r iv e r basins. The dimensions o f these resource classes are classes o f land inform ation im portant to making land management decisions. b. The g rid c e ll 1s recormeded as the basis o f inform ation storage because i t is commonly used and much technology is a v a ila b le to use th is type o f inform ation system. c. The g rid c e ll should be small enough to allo w c la s s ific a tio n o f only one resource. d. Research is needed to determine the desired p recisio n o f land Inform ation which in turn w ill a f f e c t the s iz e o f the g rid c e l l . e. Geographic referen cin g should be standardized and based on the Universe Transverse M ercator system. f. The amount o f data to be stored and the frequency o f access­ ing the data should determine the choice o f data storage technology and media. g. The in d iv id u a l data record fo r a g rid c e ll should contain lo c a tio n in fo rm a tio n , basic resource d ata, resource classes, and blank f ie ld s f o r inform ation added a t l a t e r tim es. 4. C o n stra in t Generator: a. I f many a lte r n a tiv e sets o f land management s tra te g ie s made outside o f the system are to be considered, a component to read acreages and co n strain the land e v a lu a tio n system should be Included. b. 5. More work is needed to develop th is softw are. Mapping Routines: 265 a. Algorithms chosen must be operable on the computer system used. b. More p r in te r and p lo tte r ro u tin es should be surveyed. c. P rin te r routines on the CDC 6500: 1) GRIDS and MIADS are best su ited to gridded inform ation resource d a ta , resource classes, output from the land assignment model. 2) SYMAP is best su ited to mapping la rg e , ir r e g u la r ly shaped areas. 6. Time should be spent to sp ecify and te s t re la tio n s h ip s which w ill p ro je c t requirements and production fo r regions. Data Conclusions: 1. The data system o f the Kalamazoo R iver Basin 1s in s u ff ic ie n t to support a gridded inform ation system because o f a lack o f s o il maps and sub-county fo re s t inventory d a ta , and a lack o f p rec isio n in remote sensing data in terms o f making management decisions. 2. There is a lack o f data to be used f o r p ro je c tin g requirements and supplies o f tim ber and hunterdays. More economic and physical data should be c o lle c te d to meet the needs o f the re la tio n s h ip s s p e c ifie d fo r p ro je c tio n . 3. Sources o f d a ta , d e fin itio n s , assumptions, and re la tio n s h ip s were not documented s u f f ic ie n t ly by U.S. Forest Service personnel when c a lc u la tin g product c o e ffic ie n ts thus making i t d i f f i c u l t f o r p riv a te researchers and c itiz e n s to in te r p r e t the data provided. 4. Assumptions made in co n stru ctin g the model s im p lify behavior and could introduce bias in to the model. 266 5. Im portant management options were neglected in developing the model thus introducing possible bias in to the model. Recommendations: 1. I f the data s itu a tio n o f the Kalamazoo R iver Basin is represent a tiv e o f o th er r iv e r basin s tu d ie s , much e f f o r t in inventorying and map­ ping data w il l be required i f a g rid system is to be implemented. 2. A standardized time se rie s o f production and consumption data o f various land products fo r d if f e r e n t regions should be estab lish ed i f b e tte r p ro jectio n s o f requirements and production are to be made. Col­ le c tio n o f o th e r data needed should also be standardized. 3. The U.S. Forest Service needs to improve documentation o f data submitted in r iv e r basin s tu d ie s. 4. More management s tra te g ie s should be developed such as hunter­ day emphasis and sh o rt ro ta tio n fo re s try . Usefulness o f the Model Conclusions: 1. The id e a l model is w ell su ite d to developing management plans on publically-ow ned land by a land management agency o r fo r developing land management recommendations fo r p riv a te landowners given the goals o f the p u b lic agency. 2. The id e al model is poorly su ited fo r p re d ic tio n o f land use p attern s . Recommendati ons: 1. I f a p re d ic tiv e model is d e s ire d , i t is recommended th a t in ­ v e s tig a tio n o f development o f a sim u latio n model based on observed behavorial patterns be undertaken. A lte r n a tiv e land management p o s s ib ili­ tie s could be developed and a llo c a te d to g rid c e lls outside o f the model 267 % The production o f commodities over time by g rid c e ll could be c a lc u la te d . These re s u lts could become Inp ut fo r s p a tia l economic and environmental Impact models. In v e s tig a tio n would be required to determine production and impact re la tio n s h ip s . An Inform ation system would have to be develop­ ed to sto re data f o r determ ination o f possible land management patterns and to provide inputs to the production and impact re la tio n s h ip s . Kalamazoo R iver Basin Land Use ConclusIons: 1. The fo llo w in g are Im portant fa c to rs a ffe c tin g a llo c a tio n o f management s tra te g ie s among regions: a. The most Im portant fa c to r 1s the le v e l o f requirements fo r commodities produced on the lan d . When le v e ls o f re q u ire ­ ments fo r a commodity are below a c e rta in c r i t i c a l le v e l, th ere is a s p a tia l d if f e r e n t ia t io n in the a llo c a tio n among regions o f management s tra te g ie s which produce th a t com­ modity. When the le v e ls o f requirements fo r a commodity are above a c e rta in c r i t i c a l le v e l, any s p a tia l d if f e r e n t ia ­ tio n in the a llo c a tio n among regions o f management s tra te g ie s which produce th a t commodity ceases to e x is t . That is to say, a l l tim ber producing lands must be managed in te n s iv e ly fo r tim ber when the c r i t i c a l le v e l is reached. b. There is an im portant tr a d e - o f f between development costs and tra n s p o rta tio n and im porting costs. Development costs in a region are incurred only when i t is cheaper to in v e s t in in te n s iv e management than to im port. c. The time d is tr ib u tio n o f production w il l be an im portant fa c to r . 268 d. The time period o f an alysis a ffe c ts the d e fin itio n o f which lands are tirriber producing and which are not and thus w il l have an e f f e c t on the p a tte rn o f land management. 2. OBERS demands fo r sawtimber cannot be met in time periods 1 and 3 given the s tru c tu re and assumptions o f th is model. 3. Small amounts o f commercial fo re s t lan d , conversions o f fo re s t land to urban use, and c h a ra c te ris tic s o f land tenure l i m i t the p o s s ib il­ it ie s fo r growth in output in tim ber-using in d u s trie s . a. As a re s u lt: Growth in output from the Menasha Corporation appears to be lim ite d by a comparative disadvantage r e la t iv e to o ther p u lp m ills in Michigan. This pulpm ill is r e l a t i v e ly d is ta n t from the la rg e pulpwood resource o f the northern lower peninsula o f Michigan when compared to o th e r p u lp m ills , which are located in th a t a re a . However, o th e r fa c to rs might make the distance from the pulpwood resource less lim itin g : a v a i l a b i l i t y o f la b o r and c a p it a l, economies o f s c a le , new technology, and sh o rt ro ta tio n poplar c u ltu re on sub-marginal farmland. b. Growth in output o f small m ills which use hardwoods can be accommodated. In te n s iv e management could improve the qual­ i t y o f tim ber and fu rth e r improve the growth p o te n tia l o f these o peratio ns. 4. I t is d i f f i c u l t to apply the re s u lts o f th is study to o th er r iv e r basins because o f the unique lo c a tio n fa c to rs o f each r iv e r basin. Recommendati ons: 1. A ll lands capable o f producing merchantable tim ber during the time period o f an a ly sis should be converted to in te n s iv e management as 269 soon as possible to meet requirements In an economically e f f i c i e n t manner. 2. The fo llo w in g recommendations are made fo r lands not capable o f producing merchantable tim ber during the time period o f a n a ly s is : a. A ll adequate condition class lands should be converted to in te n s iv e management as soon as p o ssible. b. Forest land classes which are in the non-adequate condition class have the lowest p r io r it y fo r in te n s iv e management. In te n s iv e management is concentrated on c e rta in key land classes in regions 2 , 3, and 4. Conversions to in te n s iv e management can occur l a t e r in tim e. APPENDICES APPENDIX A FLOWCHART SYMBOLS 1 1 A -l ,N Begin Do Loop from 1 to N End Do Loop Input/O utput I n i t i a l i z e Elements o f Array to Zero Assign Value to V a riab le Decision o CUD S tart/E n d Connector > X < ------- Y Flow Arrow V a ria b le X 1s assigned the value o f Y 270 APPENDIX B PURCHASES OF SAWLOGS AND VENEER LOGS Table B -l.--P u rc h a s e s o f Veneerlogs and Sawlogs by County (MCF) County Allegan Barry B errien Branch Calhoun Cass C linto n Eaton G ra tio t H ills d a le Ingham Io n ia Jackson Kalamazoo Kent Lake Mecosta Montcalm Muskegon Newaygo Osceola Ottawa S t. Joseph Van Buren 1972 1969 1965 709.4 2068.9 235.9 737.2 26.6 111.9 705.5 1112.3 107.9 426.0 947.8 1593.6 190.6 187.1 1721.1 407.4 585.2 530.6 196.7 930.2 450.1 924.7 450.3 1206.6 52.7 9 1 .2 763.7 1023.5 116.7 112.7 1522.8 420.6 363.1 507.3 1279.3 896.5 2669.0 combined w ith B errien 731.0 1210.7 combined w ith C lin to n 398.6 315.2 758.5 conbined w ith Calhoun 183.2 1130.2 380.4 - 408.9 994.7 1184.6 824.8 81.7 10.7 152.0 - 761.2 827.2 1450.3 463.4 50.0 8 .3 5 3 .3 271 - 683.1 815.7 924.2 265.6 combined w ith Muskegon combined w ith B errien 120.5 APPENDIX C PROPORTIONS OF COUNTY CONSUMPTION ALLOCATED TO REGIONS Table C - l . — Proportions o f County Consumption A llocated to Regions County Allegan Barry Berrien Branch Calhoun Cass C linto n Eaton G ra tio t H ills d a le Ingham Ion ia Jackson Kalamazoo Kent Lake Mecosta Montcalm Muskegon Newaygo Osceola Ottawa S t. Joseph Van Buren Proportion Region 0 .1 8 0 .8 2 0 .0 7 0 .9 3 0 .5 0 .5 2 4 2 7 3 10 9 0.86 0 .1 4 1 0.59 0.41 1 1. 1. 1. 1. 1. 1. 1. 1. 0 .6 7 0 .3 3 1. 1. 1. 1. 1. 1. 1. 1. 1. 0 .5 5 0 .4 5 272 9 8 7 7 12 9 10 7 1 2 9 6 11 11 11 5 11 12 5 9 3 4 APPENDIX D DEMAND MULTIPLIERS USING TREND OF FIRST DERIVATIVE Table D - l . — Demand M u ltip lie r s a t 1970 R e la tiv e Prices Product 1970 1980 1990 2000 2010 2020 Sawlogs Veneer Pulpwood Total 1.0 1 .0 1.0 1 .0 1.36 1.22 1.77 1.39 1 .6 3 1.44 2 .7 4 1 .8 3 1.81 1 .6 7 3.91 2.32 1.90 1.90 5.2 0 2.86 1.90 2 .1 3 6.85 3.45 Source: U.S. Forest S e rv ic e , 1973. Table D -2 .— Demand M u ltip lie r s a t R ising R e la tiv e Prices Product 1970 1980 1990 2000 2010 2020 *Sawlogs Veneer Pulpwood Total 1.0 1.0 1.0 1.0 1.18 1.00 1.70 1.30 1.27 1.05 2.50 1.60 1.27 1.3 3 3.40 1 .9 0 1 .2 7 1.77 4 .4 0 2.20 1.27 2 .3 8 5.50 2.50 Source: U.S. Forest S e rvic e, 1973 *Trend p red icts a decrease in demand a f t e r the ye ar 2000, th is was assur ed not to occur. Table D -3 .— Demand M u ltip lie r s a t R e la tiv e P rices Above 1970 Product 1970 1980 1990 2000 Sawlogs Veneer Pulpwood Total 1.0 1.0 1.0 1.0 1 .1 3 1 .2 2 1 .6 2 1.28 1.31 1.44 2.49 1.66 1.54 1 .6 7 3.61 2.14 Source: U.S. Forest S e rv ic e , 1973 273 ’ 2010 2020 1.82 1.90 4 .9 8 2.72 2.15 2 .1 3 6 .6 0 3.40 . APPENDIX E REQUIREMENTS FOR SAWLOGS, VENEER LOGS, AND PULPWOOD Table E -1 .— Requirements fo r Sawlogs and Veneer Logs w ith 1970 R e la tiv e Prices (Mcf) Region 1 2 3 4 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 872 828 201 227 913 1455 3198 542 1125 859 2103 671 1177 1117 271 306 1233 1964 4317 732 1519 1160 2839 906 1412 1341 326 368 1479 2357 5181 878 1823 1392 3407 1087 1569 1490 361 409 1643 2619 5756 976 2025 1546 3785 1208 1657 1573 382 431 1735 2764 6076 1030 2183 1632 3996 1275 1666 1581 384 434 1744 2799 6108 1035 2149 1641 4017 1282 Table E -2 .--•Requirements fo r Sawlogs and Veneer Logs w ith Rising R e la te Prices (Mcf) Region 1 2 3 4 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 872 828 201 227 913 1455 3198 542 1125 859 2103 671 1020 969 235 266 1068 1702 3742 634 1316 1005 2461 785 1098 1043 253 286 1150 1833 4030 683 1418 1082 2650 845 1107 1052 255 288 1160 1848 4061 688 1429 1091 2671 852 1134 1076 261 295 1187 1892 4157 705 1463 1117 2734 872 1160 1101 267 302 1214 1935 4253 721 1496 1143 2797 892 274 275 Table E -3 . --Pulpwood Requirements w ith 1970 R e la tiv e Prices (C c f) Region 2 5 1970 1980 1990 2000 2010 2020 41673 119271 73761 211109 114184 326802 162941 466349 216699 620209 287515 817006 Table E -4 .— Pulpwood Requirements w ith Rising R e la tiv e Prices (C cf) Region 1970 2 5 41673 119271 1980 1990 2000 70844 202761 104183 298177 141688 405521 2010 183361 524792 2020 229202 655991 APPENDIX F ROUNDWOOD REQUIREMENTS Table F - l . — Roundwood Requirements w ith 1970 R e la tiv e Prices (M cf) Region 1 2 3 4 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 872 4995 201 227 12840 1455 3198 542 1125 859 2103 671 1177 8493 271 306 22343 1964 4317 732 1519 1160 2839 906 1412 12759 326 368 34159 2357 5181 878 1823 1392 3407 1087 1569 17884 361 409 48278 2619 5756 976 2025 1546 3785 1208 1657 23242 382 431 63756 2764 6067 1030 2138 1632 3996 1275 1666 30332 384 434 83445 2799 6108 1035 2149 1641 4017 1282 Table F -2 .— Roundwood Requirements w ith R ising R e la tiv e Prices (M cf) Region 1 2 3 4 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 872 4995 201 227 12840 1455 3198 542 1125 859 2103 671 1020 8053 235 266 21344 1702 3742 634 1316 1005 2461 785 1098 11461 253 286 30967 1833 4030 683 1418 1082 2650 845 1107 15221 255 288 41712 1848 4061 688 1429 1091 2671 852 1134 19412 261 295 53666 1892 4157 705 1463 1117 2734 872 1160 24021 267 302 66813 1935 4253 721 1496 1143 2797 892 276 APPENDIX G PROPORTIONS OF COUNTY TIMBER PRODUCTION ALLOCATED TO REGIONS Table G - l . — Proportions o f County Timber Production A llo cated to Regions County Allegan Barry B errien Branch Calhoun Cass C linto n Eaton G ra tio t H ills d a le Ingham Io n ia Jackson Kalamazoo Kent Lake Mecosta Montcalm Muskegon Newaygo Osceola Ottawa S t. Joseph Van Buren Proportion Region 1.00 0.36 0.64 0.20 0.80 1.00 0.69 0.31 1.00 1.00 0.24 0.76 1.00 0 .1 2 0 .8 8 1.00 1.00 0 .2 4 0.76 0.61 0.39 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.24 0.76 1.00 0.89 0.11 2, 4 2 7 3 8 9 1 9 8 7 1 7 12 1 9 10 7 1 10 2 9 6 11 11 11 5 11 12 4 5 9 2, 3 8 277 APPENDIX H SAWLOG PRODUCTION IN OUTSIDE REGIONS Table H - l . — Sawlog Production from Outside Regions by County (Mcf) Region 5 6 7 8 9 10 11 12 County 1972 1969 1965 Muskegon Ottawa Kent Ion ia Barry Eaton C li nton B errien Cass Van Buren S t. Joseph Branch Kalamazoo Calhoun Hi 1ls d a le Ingham Jackson Lake Mecosta Newaygo Osceola G ra tio t Montcalm 887 197 1363 1745 817 577 925 168 408 30 254 277 123 76 314 814 409 594 46 1219 914 636 717 255 242 930 1131 576 520 573 161 660 220 137 460 140 172 238 973 358 906 149 1621 651 1059 706 446 153 859 827 364 498 647 259 455 36 223 403 110 170 218 925 395 650 317 1206 292 706 772 278 APPENDIX I VENEER LOG PRODUCTION IN OUTSIDE REGIONS Table 1 - 1 .— Veneer Log Production by Region and County (Mcf) Region County 5 Muskegon Ottawa Kent Io n ia Barry Eaton C lin to n B errien Cass Van Buren S t. Joseph Branch Kalamazoo Calhoun H ills d a le Ingham Jackson Lake Mecosta Newaygo Osceola G ra tio t Montcalm 6 7 8 9 10 11 12 1972 19 5 32 30 46 12 0 37 43 10 6 9 6 6 11 4 13 25 0 25 0 0 13.5 1969 6 0 3 4 8 33 0 30 43 9 26 29 12 1 31 30 18 0 16 0 24 3 7 APPENDIX J EXCESS SUPPLIES OF TIMBER Table J - l . — Excess Supplies o f Timber w ith 1970 R e la tiv e Prices (M cf) Region 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 -11853 -365 -702 354 22 464 3244 875 -21356 -874 -1821 165 -372 150 2508 640 -33172 -1267 -2685 19 -676 -69 1940 459 -42290 -1529 -3260 -79 -878 -233 1562 338 -62770 -1674 -3580 -133 -991 -309 1351 271 -82457 -1709 -3612 -138 -1002 -318 1330 264 Table J - 2 .- - -Excess Supplies o f Timber w ith R ising R e la tiv e Prices (M cf) Region 5 6 7 8 9 10 11 12 1970 1980 1990 2000 2010 2020 -11853 -365 -702 354 22 464 3244 875 - 20357 -612 -1246 263 -169 318 2886 761 -29980 -742 -1534 214 -271 241 2697 701 -40725 -758 -1565 209 -282 232 2676 694 -52679 -802 -1661 192 -316 206 2613 674 -56261 -845 -1757 176 -349 180 2550 654 280 Appendix K REQUIREMENT FOR DEER HUNTERDAYS, 1970 Table K - l . — Requirements fo r Deer Hunterdays by County and Region, 1970 Region 1 2 3 4 5 6 7 8 9 10 County Calhoun Eaton H ills d a le Jackson A11egan Barry Kalamazoo B errien Van Buren Allegan Ottawa Van Buren Muskegon Ottawa Kent Io n ia Barry Eaton Cl inton B errien Cass Van Buren S t. Joseph Branch Kalamazoo Calhoun H ills d a le Ingham Jackson DNR zone 17 14 17 17 18 18 18 18 18 18 13 18 13 13 13 13 18 14 14 18 18 18 18 17 18 17 17 14 17 Population 128437 15437 2666 12419 49303 12458 172457 50518 24057 13115 52311 23200 157426 73311 411044 45848 25708 53455 48492 113357 43312 8916 47392 37906 29093 13526 34505 261039 130855 281 Requirements 15926 2161 331 1540 7691 1943 26903 7881 3753 2046 5859 3619 17631 8211 46037 5135 4010 7484 6789 17684 6757 1391 7392 4700 4538 1677 4279 36545 16226 Appendix L REQUIREMENTS FOR HUNTERDAYS Table L - l . — Requirements fo r Deer Hunterdays Regions 1 2 3 4 5 6 7 8 9 10 1970 1980 1990 2000 2010 2020 19958 36537 11634 11526 25842 46037 23418 25832 22587 52771 21953 40191 12797 12676 28426 50641 25760 28415 24846 58048 23930 43808 13949 13817 30984 55198 28078 30973 27082 63272 25307 46329 14752 14612 32768 58375 29694 32755 28640 66914 26684 48850 15555 15408 34551 61552 31310 34537 30199 70555 28061 51371 16357 16203 36334 64728 32926 36320 31757 74196 Table L - 2 .- -Requirements fo r Small Game Hunterdays Regions 1970 1980 1990 2000 2010 2020 1 2 3 4 5 6 7 8 9 10 70735 104227 33186 39438 102678 182915 77209 73685 72278 174393 77809 114650 36505 43383 112946 201207 84930 81054 79506 191832 84811 124968 39790 47287 123111 219315 92574 88348 86661 209097 89692 132160 42080 50009 130196 231936 97901 93433 91649 221130 94573 139352 44370 52730 137281 244557 103228 98517 96636 233163 99453 146543 46660 55451 144365 257179 108556 103601 101623 245197 282 Appendix M GAME KILLS IN REGIONS OUTSIDE OF THE RIVER BASIN Table M - l . — Game K ills Per County 1n Regions Outside o f the R iver Basin Region 5 6 7 8 9 10 County Muskegon Ottawa Kent Io n ia Barry Eaton C linto n B errien Cass Van Buren S t. Joseph Branch Kalamazoo Calhoun H ills d a le Ingham Jackson DNR Region Deer 13 13 13 13 18 14 14 18 18 18 18 17 18 17 17 14 17 440 369 736 490 238 283 372 303 328 45 337 335 147 143 344 364 356 S q u irre l 14283 11984 23887 15907 10079 11984 15769 12823 13898 1926 14225 14228 6214 6076 14594 15411 15080 C o tto n ta il 22587 18952 37775 25155 15939 18952 24937 20278 21978 3046 22543 22500 9826 2608 23079 24371 23847 Appendix N HUNTERDAYS SUPPLIED IN REGIONS OUTSIDE OF THE RIVER BASIN, 1970 Table N - l . — Hunterdays Supplied by Counties 1n Regions Outside o f the Basin, 1970 Region County 5 Muskegon Ottawa Kent Ion ia Barry Eaton C lin to n B errien Cass Van Buren S t. Joseph Branch Kalamazoo Calhoun H ills d a le Ingham Jackson 6 7 8 9 10 Deer 16456 13801 25095 18326 8901 10584 13921 11332 12267 1683 12604 12579 5498 5348 12866 13615 13315 284 S q u irre l 22139 18576 37025 24656 15622 18575 24442 19876 21542 2985 22095 22053 9632 9418 22621 23887 23374 C o tto n ta il 40657 34114 67995 45279 28690 34114 44887 36500 39560 5483 40577 40500 17687 17294 41542 43868 42925 Appendix 0 EXCESS PRODUCTION OF HUNTERDAYS BY OUTSIDE REGION Table 0 - 1 . — Excess Production o f Deer Hunterdays Region 5 6 7 8 9 10 1970 1980 1990 2000 2010 2020 4415 -20942 28314 -550 26258 -25841 1831 -25546 25792 -3133 23999 -31118 -727 -30103 23654 -5691 21763 -36342 -2511 -33280 22038 -7473 20205 -39984 -4294 -36457 20422 -9255 18646 -43625 -6077 -39633 18806 -11038 17088 -47266 Table 0 -2 . — Excess Production o f Small Game Hunterdays Region 5 6 7 8 9 10 1970 1980 1990 2000 2010 2020 12507 -77895 159056 52261 171141 -40339 2539 -96187 151335 44892 163913 -57878 -7626 -114295 143691 37708 156758 -75043 -14711 -126176 138364 32513 151770 -87076 -21796 -139537 133037 27429 146780 -94109 -28880 -152129 217709 22345 141796 -111143 285 APPENDIX P MILES TRAVELLED ON EACH CLASS OF ROAD IN EACH REGION Table P - l . — M iles T ra v e lle d on Each Class o f Road in Each Region Class 1 2 3 4 5 6 Trunk 3 .5 2 .3 .6 .3 7.3 6 .5 2 1 .3 12.2 11.6 8 .2 18.9 8 .6 NonTrunk 3.9 5 .7 4 .0 5 .4 5 .8 4 .7 4 .3 3 .0 4 .9 4 .6 5.6 4.1 I .6 .3 .2 .2 .4 .5 .1 .1 .4 .2 .2 .6 II .1 .2 .0 .1 .1 .1 .3 .1 .2 .1 1 .5 .4 III .1 .2 .1 .3 .2 .1 .4 .0 .1 .1 .2 .6 IV .0 .0 .0 .1 .0 .0 .1 .0 .0 .0 .1 .1 V .5 .5 .4 .5 .4 .5 .5 .4 .4 .4 .6 .5 286 7 8 9 10 11 12 APPENDIX Q MILEAGE TRAVELLED ON THE TRANSPORTATION NETWORK IN EACH REGION Table Q -l.--M ile a g e T ra v e lle d on the T ransportation Network 1n Each Region Subarea 1 2 3 4 5 6 7 8 9 10 11 12 Longest Distance (Road M ile ag e/4) 16.7 23.7 21.0 19.5 16.8 17.8 17.94 16.38 28.45 20.55 24.13 19.5 287 Average Distance (D is ta n c e //IT ) 11.81 16.76 14.85 13.79 11.88 12.59 12.69 11.58 20.12 14.53 17.06 13.79 APPENDIX R TIMBER TRANSFER COSTS BETWEEN REGIONS, 1970 Table R - l . — Timber T ra n s fe r Costs Between Regions ($ /C c f ) , 1970 Route Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 O rig in D estination 1 2 1 3 1 4 2 3 2 4 3 4 1 5 1 6 1 7 1 8 1 9 1 10 2 5 2 6 2 7 2 8 2 9 2 10 3 5 3 6 2 1 3 1 4 1 3 2 4 2 4 3 5 1 6 1 7 1 8 1 9 1 10 1 5 2 6 2 7 2 8 2 9 2 10 2 5 3 6 3 288 Cost 9.6 5 8 .6 3 9 .5 0 10.79 11.86 13.03 7.4 3 8.3 9 7.34 9.0 9 8 .5 3 7.84 18.26 18.26 15.29 14.84 9.8 9 10.90 12.53 13.76 7.38 8 .9 7 9 .2 3 9 .1 2 11.42 11.43 9.7 6 8.6 4 13.54 15.34 10.25 8.40 9 .7 8 13.17 14.66 15.07 13.28 12.86 14.03 12.29 289 Table R - l . ( c o n t 'd .) Route Number 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 71 72 73 74 75 76 77 78 O rig in D estination 3 7 3 8 3 9 3 10 4 5 4 6 4 7 4 8 4 9 4 10 1 2 3 4 11 11 11 11 12 12 12 12 7 3 8 3 9 3 10 3 5 4 6 4 7 4 8 4 9 4 10 4 1 2 3 4 1 2 3 4 1 2 3 4 Cost 17.81 18.64 7.79 7.34 11.94 13.49 16.80 14.88 8.65 7.58 8.35 8.10 12.43 13.72 8.98 13.55 18.09 17.46 18.29 17.57 5.08 5.83 5.01 17.57 25.03 19.08 22.49 17.63 15.44 12.82 16.23 11.30 APPENDIX S WEIGHTS ON EACH YEAR'S CAR CLASS Table S - l . — Weights on Each Year's Car Class Year 1974 A t t r it io n Weight Production Weight 1.0 Total Weight 1.0 1.0 1973 .945 1.29 1.22 1972 .89 1.24 1.10 1971 .96 1970 CO CO r^. • • 1.16 .93 .74 1969 .73 1.08 .78 1968 .67 1.09 .73 1967 .62 1.09 .67 1966 .56 1.09 .61 1965 .50 1.09 .54 Source: Motor Vehicle Manufacturers Association o f the U .S ., I n c ., 1974. 290 APPENDIX T PROPORTIONS OF EACH CAR CLASS PRODUCED Table T - 1 .— Proportions o f Each Car Class Produced Source: Year Standard Compact 1974 .509 .242 .248 1973 .573 .179 .248 1972 .619 .151 .230 1971 .617 .157 .226 1970 .631 .199 .170 1969 .720 .164 .116 1968 .746 .150 .104 1967 .746 .150 .104 1966 .746 .150 .104 1965 .746 .150 .104 Subcompact Motor V ehicle Manufacturers A ssociation o f the U .S ., I n c ., 1974. 291 Appendix U TRANSFER COSTS FOR BIG AND SMALL GAME HUNTERDAYS, 1970 Table U - l . — T ran sfer Costs fo r Big and Small Game Hunterdays, 1970 Route number O rigin D estin atio n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1 2 1 3 1 4 2 3 2 4 3 4 1 5 1 6 1 7 1 8 I 9 1 10 2 5 2 6 2 7 2 8 2 9 2 10 3 5 2 1 3 1 4 1 3 2 4 2 4 3 5 1 6 1 7 1 8 1 9 1 10 1 5 2 6 2 7 2 8 2 9 2 10 2 5 3 Cost Big Game Small Game (D o lla rs ) (D o lla rs ) 2.85 3.60 4.19 3.52 5.41 4.84 2.84 2 .1 8 3.21 2.12 2.51 2.92 2.17 2.61 6.49 6 .7 6 3 .6 8 4 .1 8 5.96 5.22 3.01 2.33 3.26 2 .7 4 4.67 4.41 3.15 3.4 8 6.16 5.66 2.96 4.0 9 5.37 3.70 6 .5 9 6.22 5.41 5.59 292 4.06 5.14 5.97 5.02 7.72 6.94 4.05 3.11 4.57 3.03 3.58 4.17 3.10 3.71 9.25 9.6 4 5.24 5.96 8.50 7.44 4.3 0 3.33 4.64 3.91 6 .5 7 6.29 4.50 4.96 8.79 8 .0 8 4.22 5.84 7.65 5.28 9.39 8.86 7.72 7.96 293 Table U - l . ( c o n t 'd . ) Route number O rig in D e stin a tio n B1g Gara^0S tSmall Game (D o lla rs ) 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 3 6 3 7 3 8 3 9 3 10 4 5 4 6 4 7 4 8 4 9 4 10 1 2 3 4 6 3 7 3 8 3 9 3 10 3 5 4 6 4 7 4 8 4 9 4 10 4 1 2 3 4 5.06 6.00 8.0 2 8.57 2.37 2.51 5 .5 4 4.7 6 6 .4 8 7.55 2.47 2.97 2.72 2.79 5.26 5.51 5.8 4 3.15 7.77 8 .2 5 7.99 8 .3 6 1.37 1.75 1.36 1.38 (D o lla rs ) 7.22 8 .5 6 11.43 12.22 3 .3 8 3.57 7.90 6.79 9 .2 4 10.77 3.51 4 .2 3 3.87 3.9 8 7.49 7.86 8 .3 3 4 .4 8 11.07 11.76 11.39 11.92 2.13 2.49 1.95 1.99 Appendix V RANGES OF FIBER PRODUCTION Table V - l . — Ranges o f F ib e r Production by Resource Class, Management Strategy and Stand Size Class Resource Class Management S trateg y cu IM CU IM CU IM CU.IM CU IM CU IM S tand.S ize Class NS ss PT ST SS PT ST NS SS PT ST SS PT ST NS SS PT ST SS PT ST NS SS PT ST NS SS PT ST SS PT ST NS SS PT ST SS PT 294 Average (c f/y r ) 8 32 64 40 41 89 52 8 26 57 32 33 73 41 2 13 49 28 17 63 37 0 0 0 0 3 13 49 31 14 63 31 3 8 43 20 10 55 Low (c f/y r ) 8 27 63 37 36 84 47 8 21 46 22 28 61 30 2 11 42 22 14 57 32 0 0 0 0 2 7 37 19 14 49 25 2 5 33 17 7 44 High (c f/y r ) 8 37 76 46 46 95 54 8 31 68 34 39 85 54 2 15 56 34 19 70 42 0 0 0 0 4 22 58 30 18 70 37 4 10 50 22 12 62 295 Table V - l . (Cont'd) Resource Class Management Strategy 7 CU, IM 8 CU, IM 9 CU IM 10 CU IM 11 CU,IM 12 CU IM 13 CU IM StandhS1ze Class ST NS SS PT ST NS SS PT ST NS SS PT ST SS PT ST NS SS PT ST SS PT ST NS SS PT ST NS SS PT ST SS PT ST NS SS PT ST SS PT ST Management S tra te g ie s CU = Current Use Management S trateg y IM = In te n s iv e Management S trategy Average (c f/y r ) 25 0 0 0 0 0 0 0 0 3 23 86 42 30 112 54 3 23 70 34 23 90 44 0 0 0 0 6 18 65 45 23 84 55 4 12 43 31 16 55 40 NS SS PT ST = = = Low (c f/y r ) 23 0 0 0 0 0 0 0 0 2 17 57 31 23 77 41 2 17 53 27 19 71 36 0 0 0 0 5 12 57 35 11 75 47 4 10 33 24 13 44 32 High (c f/y r ) 28 0 0 0 0 0 0 0 0 4 31 103 59 39 129 74 4 31 92 43 26 115 54 0 0 0 0 7 24 84 56 30 105 70 4 16 53 37 20 60 46 Stand Size Class Non-Stocked S eedling-S apling Poletim ber Sawtimber APPENDIX W AGE DISTRIBUTION OF FOREST TYPES IN THE SOUTHERN LOWER PENINSULA Table W-l.~Age Distribution of Forest Types in the Southern Lower Peninsula (1000 Acres) Forest Type 296 White-redjack pine jack pine red pine white pine scotch pine Spruce-Fir white spruce white cedar tamarack Oak Elm-AshCottonwood Maple-BeechBirch Aspen-Birch All Ages 0-20 12.1 36.5 24.0 36.2 16.1 10.1 20.5 1016.5 10.7 29.2 11.6 31.9 20-40 40-50 50-60 60-70 70-80 80-90 90-100 100-120 120-140 1.6 7.3 .4 6.5 5.6 4.3 16.1 5.5 8.5 6.1 347.3 133.4 4.6 5.9 71.9 81.9 75.7 86.9 32.8 14.8 130.2 41.6 719.4 337.2 102.9 54.9 62.7 25.5 35.8 44.3 25.9 19.6 10.6 501.6 429.4 149.8 80.6 301.5 108.3 58. 6.8 23.9 5.1 23.4 7.7 21. 32.5 56.3 44. 12.1 APPENDIX X ACRES OF COMMERCIAL FOREST LAND BY STAND SIZE CLASS IN THE SOUTHERN LOWER PENINSULA Table X - l . — Acres o f Commercial Forest Land by Stand S ize Class in the Southern Lower Peninsula (1000 Acres) Ecosystem Total Sawtimber Conifer Oak Elm-AshCottonwood Maple-BeechBirch Aspen-Birch 149.3 1016.5 26.1 4 3 2.3 719.4 501.6 429.4 Seed-Sapling Non-Stocked 27.1 237.1 84.1 259.4 11.6 8 7 .7 191.2 185.2 227.0 116.0 239.8 14.5 103.6 126.8 145.6 253.9 12.6 34.2 P o le tin b e r 297 APPENDIX Y PRODUCTION ACTIVITIES A c tiv itie s to be Included in resource classes where adequate and TSI condition classes are d iffe r e n tia te d : A cti vi ty c Stand S ize Class S eed lin g -sap lin g CU, EE IM.CU to IM a t the present3 CU to IM a t SS-PT ju n c tu re 3 CU to IM a t PT-ST ju n c tu re 3 CU-TSI to IM-AD a t the presentb CU-TSI to IM-AD a t SS-PT ju n c tu re b CU-TSI to IM-AD a t PT-ST juncture^ Poletim ber CU.EE IM - c u rre n t3 CU to IM a t the present3 CU to TSI to IM-AD a t PT-STb Sawtimber CU EE,CU to EE a t the present IM - c u rre n t3 CU to IM before c u ta CU to IM a f t e r cu ta CU-TSI to IM-AD Non-stocked CU CU to IM a t the present CU to IM a t 2000 anot in TSI class ^not in adequate class cCU = c u rre n t use EE = environmental emphasis IM = in te n s iv e management A c tiv itie s to be included when TSI and Adequate co n dition classes are not d iffe r e n tia te d : 298 299 A cti v lt y Stand Size Class Seed-sapling CU.EE* IM -cu rrent CU to IMa t the present CU to IMa t th e SS-PT ju n ctu re CU to IMa t the PT-ST ju n ctu re Poletim ber CU,EE* IM -cu rren t CU to IM a t the PT-ST ju n ctu re Sawtimber CU EE.CU to EE - present IM -cu rren t CU to IM before cut CU to IM a f t e r cut Non-stocked CU CU to CU to IMa t the present IMa t the y e a r 2000 *separated w ith aspen-birch A c t iv itie s to be included when no merchantable tim ber is produced Stand Size Class A c t iv ity Seed-sapling CU,,EE IM--cu rren t CU to IM a t the CU to IM a t the CU to IM a t the Poletim ber CU,,EE IM-■current cu to IM a t the Sawtimber cu,,EE, CU to EE IM-■current cu to IM Non-stocked cu CU to IM a t the CU to IM a t the APPENDIX Z MULTIPLIERS FOR PRODUCT COEFFICIENTS Table Z -l .--C o n if e r Ecosystem Stand S ize Class Time Period Seed-sapling Poletim ber Sawtimber Timber M u lt ip lie r fo r sawtimber class 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Mul t i p l i e r 3 . 66SS + . 34PT .1 7SS + .83PT .83PT + .1 7ST .34ST + . 66PT 1.0ST l.OST .89PT + .11 ST •67PT + . 33ST .28PT + .72ST 1 .OST l.OST 1 .OST .89ST + .11SS .67ST + . 27SS + .06PT .56ST + . 22SS + . 22PT .56ST + .39PT + .06SS . 66ST + . 34PT .89PT + .11 PT .22ST 0 0 0 0 .25 Stand S ize Classes SS = S eed lin g -sap lin g PT - Poletim ber ST = Sawtimber 300 Table Z - 2 .— Oak Hickory Ecosystem Stand Size Class Seed-sapling Poletim ber Sawtimber, cu rren t use Timber m u ltip lie rs fo r sawtimber c la s s , c u rre n t use Sawtimber, in te n s iv e use Timber M u ltip lie r s fo r sawtimber c la s s , in te n s iv e use Time Period 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 M u lt ip lie r . 66SS + . 34PT .17SS + .83PT .83PT + . 17ST . 66PT + .34ST l.OST l.OST . 88PT + .1 2ST •64PT + .36ST .41PT + .59 ST .15PT + .85ST l.OST l.OST .89ST + .11SS . 70ST + .25SS + .05PT .61 ST + . 18SS + .21 PT .56ST + .10SS + . 34PT .42ST + .16SS + .42PT .46ST + .14SS + .40PT .232ST .142ST .034ST .072ST .19ST .1 56ST .98ST + .02SS .94ST + .05SS + .01PT .84ST + . 12SS + .04PT . 7ST + . 19SS + . 12PT .61ST + .16ST + .23PT .58ST + .lo s s + .32PT .044ST .044ST .142ST .142ST .034ST .034ST 302 Table Z - 3 . — Elm-Ash-Cottonwood Ecosystem Stand Size Class Time Period Seed-sapling Poletim ber ..... Sawtimber, c u rren t use Sawtimber, in te n s iv e management 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 M u ltip lie r . 66SS .17SS .83PT . 34ST l.OST l.OST .91PT .74PT .58PT .25PT l.OST l.OST .95ST .89ST .81 ST .65ST .47ST .38ST .99ST .96ST .93ST . 88ST .81 ST .67ST + + + + .34PT .83PT .17SS . 66PT + + + + .09ST .26ST .42ST .75ST + + + + + + + + + + + + .05SS .09SS + .02PT .11SS + .08PT .2SS + .15PT .25SS + .28PT .23SS + .39PT .01SS .03SS + .01 PT .05SS + .02PT .06SS + .06PT .1SS + .09PT . 2SS + .13PT 303 Table Z - 4 .— Maple-Beech-Birch Ecosystem Stand Size Class Seed-sapling Poletim ber Sawtimber Timber m u ltip lie rs Time Period 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 Mul t i p H e r .75SS + .25PT . 25SS + .75PT . 75PT + .25ST .25PT + .75PT l.OST l.OST .91PT + .09ST . 66PT + .34ST .34PT + . 66ST .14PT + .86ST 1 .OST 1 .OST .98ST +.02SS .95ST + .05SS .87ST + .11SS .75ST + .20SS .54ST + .33SS .32ST + .44SS .032ST .032ST .1 2ST . 12ST . 30ST .16ST + + + + .02PT .05PT .13PT .24PT Table Z - 5 .— Aspen-Birch Ecosystem Stand Size Class Seed-sapling, in te n s iv e .u s e Poletim ber, in te n s iv e use Sawtimber, in te n s iv e use Timber m u ltip lie r s , in te n s iv e use Seed-sapling, cu rren t use P oletim ber, cu rren t use Sawtimber, cu rren t use Timber m u ltip lie r s , cu rren t use Time Period 1 2 3 4 S 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 M u lt ip lie r . 66SS + . 34PT .1 7SS + .83PT .83PT + .17ST .33PT + .50ST + .17SS .33ST + .67SS -66SS + .34PT .9PT + .1ST •69PT + .21ST + .1SS .29PT + .4ST + . 31SS .29ST + .51SS + .2PT .34ST + . 66PT .9PT + .1ST 1.0ST 1 .OSS .5SS + .5PT 1 .OPT 1 .OPT 1 .OST 1 .OST .2PT .22PT .58PT fo r poletim ber .33SS fo r seed-sapling . 66SS 1 .OST . 66SS + .34PT •5SS + .5PT .83PT + .17ST .34PT + .64ST .83ST + .1 7SS .34ST + . 66SS .9PT + .1ST .69PT + .31 ST .29PT + .61ST + .1SS .69ST + .26SS + .05PT .29ST + .51SS + ,2PT .34SS + . 66PT . 66ST + .34SS .17ST + .67SS + .16PT .42SS + .58PT .09SS + .91PT . 66PT + . 33ST .1 7PT + .83ST . 66ST .34 ST .10PT 305 Table Z -5 . (c o n t’ d .) Stand Size Class Time Period 4 5 6 M u lti p li e r .1 1PT .29PT f o r poletim ber .33SS fo r seed-sapling . 66SS APPENDIX AA AGE CLASS AS A PROPORTION OF STAND SIZE CLASS BY ECOSYSTEM Table AA-1.—Age Class as a Proportion o f Stand Size Class by Ecosystem Ecosystem Coni fe r Oak Age Class 0-10 10-15 15-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110 110-120 0-10 10-15 15-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110 Proportion o f Age Class Seedling-Sapling Poletimber Sawtimber .67 .33 .56 .22 ,22 .52 .01 .25 ,22 .67 .33 ,21 .23 22 .34 .18 .16 .19 .07 .03 .14 .14 .03 110-120 120-130 130-140 Elm-AshCottonwood 0-10 10-15 15-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 .01 .67 .33 ,50 ,16 ,16 18 .28 ,11 .16 .19 ,12 306 307 Table AA-1. (c o n t'd .) Ecosystem Proportion o f Age Class Age Cl ass S eedling-S apling Maple-BeechBirch Aspen-Birch 100-110 110-120 120-130 130-140 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110 110-120 120-130 130-140 0-10 10-15 15-20 20-30 30-40 40-50 50-60 60-70 70-80 Poletim ber Sawtimber .04 .04 .02 .02 .5 .5 ,24 ,24 .36 .15 .13 .11 .16 .29 .12 .12 .03 .03 ,67 .33 .41 ,30 .29 .35 ,26 39 APPENDIX BB COSTS OF PRODUCTION ACTIVITIES, 1970 Table BB-1. — C o n ife r Ecosystem, S oil Group 1 Stand S ize Class A c t iv ity 9 Cost Condition Class Seedling-sapl1ng Poletim ber Sawtimber Non-stocked CU.EE IM.CU to IM, present CU to IM a t SS-PT CU to IM a t PT-ST CU-TSI to IM-Ad a t present CU-TSI to IM-Ad a t SS-PT CU-TSI to IM-Ad a t PT-ST CU.EE IM CU to IM, present CU-TSI to IM-Ad a t PT-ST CU EE,CU to EE, present IM CU to IM, before cut CU to IM, a f t e r cu t CU-TSI to IM-Ad, a f t e r cut CU CU to IM, present CU to IM, 2000 Adequate (D o lla rs ) TSI (D o lla rs ) 0 0 0 0 * * * 0 0 0 ★ 5089.31 0 16843.42 13353.14 5089.31 0 * * * * i t * 50 32.60 12.93 0 * * 2.4 5 4116.29 0 * * * 10528.26 0 64.50 11.62 A cti vi ty CU = Current Use Management S trateg y EE = Environmental Emphasis IM = In te n s iv e Management Strategy CU to IM , present = Convert from Current Use to In te n s iv e Management a t the Present CU to IM a t SS-PT = Convert from Current Use to In te n s iv e Management a t the ju n c tu re between seedling-sapl1ng and poletim ber CU to IM a t PT-ST = Convert from Current Use to In te n s iv e Management a t the ju n c tu re between poletim ber and sawtim ber CU to IM, 2000 * Convert from Current Use to In te n s iv e Man­ agement in the y e a r 2000 308 309 CU to IM, before cut - Convert from Current Use to In te n s iv e Management before harvest CU to IM, a f t e r cut = Convert from Current Use to In ten sive Management a f t e r the harvest CU-TSI to IM-Ad a t present - Convert from Current Use re q u ir­ ing tiiriber stand imporovement to In te n s iv e Management 1n adequate condition a t the present CU-TSI to IM-Ad a t SS-PT - Convert from Current Use re q u irin g tim ber stand Improvement to In te n s iv e Management in adequate co n dition a t the ju n ctu re between s e ed lln g sapling and sawtimber CU-TSI to IM-Ad a t PT-ST = Convert from c u rre n t use re q u irin g tim ber stand Improvement to in te n s iv e management in adequate co n dition a t the ju n c tu re between poletim ber and sawtimber CU-EE, present - Convert from Current Use to Environmental Emphasis a t the present Table BB-2.— C o n ifer Ecosystem, S o il Group 2 A c ti v1ty Stand Size Class Seed-sapl ing Poletim ber Sawtimber Non-stocked CU.EE IM CU to CU to CU to CU EE,CU IM CU to CU EE,CU IM CU to CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST to EE, present IM a t PT-ST to EE, present IM, before cut IM, a f t e r cut IM, present IM, 2000 Cost ($) 0 0 50 32.60 12.93 0 0 0 2.45 3419.38 0 13857.71 9868.87 4045.66 0 64.50 11.62 310 Table BB-3.— C o n ifer Ecosystem, S o il Group 3 Stand Size Class Seed-sapling Poletim ber Non-stocked A c tiv ity CU.EE IM CU to CU to CU to CU.EE IM CU to CU CU to CU to Cost ($ ) 0 0 50 32.60 12.93 0 0 8 .6 7 0 64.50 11.62 IM, present IM a t SS-PT IM a t PT-ST IM, IM, present IM, 2000 Table BB-4.— Oak Ecosystem, S oil Group 1 Stand Size Class A cti vi ty Cost Condition Class Adequate (D o lla rs ) Seed-sapling P oletirrber Sawtimber Non-stocked CU,EE IM,CU to IM, present CU to IM a t SS-PT CU to IM a t PT-ST CU-TSI to IM-Ad, present CU-TSI to IM-Ad a t SS-PT CU-TSI to IM-Ad a t PT-ST CU.EE IM CU to IM a t PT-ST CU-TSI to IM-Ad a t PT-ST CU EE,CU to EE, present IM CU to IM, before cut CU to IM, a f t e r cut CU-TSI to IM-Ad CU CU to IM, present CU to IM, 2000 0 0 0 0 * * * 0 0 0 * 3856 0 16719.36 14231.04 3856 * •k * k TSI (D o lla rs ) 0 * * * 30 33.98 1.07 0 * ★ 4 .7 3 3416.35 0 ★ * * 11428.75 0 61 8 .1 3 311 Table BB-5.— Oak Ecosystem, S oil Group 2 Stand Size Class Seed-sapling Poletim ber Sawtimber Non-stocked A c t iv ity CU.EE IM CU to CU to CU to CU,EE IM CU to CU.EE IM CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST IM a t PT-ST IM IM, present IM, 2000 Cost ($) 0 0 30 33.98 1.07 0 0 4 .7 3 O 0 13.08 0 61 8 .1 3 Table BB-6 . — Elm-Ash-Cottonwood Ecosystem A c it v ity Stand S ize Class Seed-sapling Poletim ber Sawtimber Non-stocked CU.EE IM CU to CU to CU to CU.EE IM CU to CU.EE IM CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST IM a t PT-ST IM IM, present IM, 2000 Cost ($ ) 0 0 28 19.50 3.24 0 0 7 .7 3 0 0 0 0 61 8 .1 3 312 Table BB-7.--M aple-Beech-Birch Ecosystem, S o il Group 1 Stand Size Class Cost Act1vi ty Condi tio n Class Adequate (D o lla rs ) Seed-sapling Poletim ber Sawtimber Non-stocked CU.EE IM,CU to IM, present CU to IM at.SS-PT CU to IM a t PT-ST CU-TSI to IM-Ad CU-TSI to IM-Ad CU-TSI to IM-Ad CU, EE IM CU to IM a t PT-ST CU-TSI to IM-Ad a t PT-ST CU EE,CU to EE, present IM CU to IM, before cut CU to IM, a f t e r cut CU-TSI to IM-Ad, before cut CU CU to IM, present CU to IM, 2000 TSI (D o lla rs ) 0 0 0 0 * ★ * 0 0 0 * 7076.18 0 14739.68 10965.74 7076.18 * * * * 0 •k * * 30 16.04 3.24 0 * * 3.91 5738.79 0 ★ ■k * 9417.25 0 61 8.1 3 Table BB-8 . — Maple-Beech-Birch Ecosystem, S oil Group 2 Stand Size Class Seed-sapling Poletim ber Sawtimber Non-stocked A cti vi ty CU.EE IM CU to CU to CU to CU,EE IM CU to CU,EE IM CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST IM a t PT-ST IM IM, present IM, 2000 Cost ($ ) 0 0 30 16.04 3.24 0 0 3.91 0 0 3.24 0 61 8.13 313 Table BB-9.— Aspen-Birch Ecosystem, S oil Group 1 Stand Size Class Seed-sapling Poletim ber Sawtimber Non-stocked A cti vi ty CU EE IM CU to CU to CU to CU EE IM CU to CU EE,CU IM CU to CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST IM a t PT-ST to EE, present IM, before cut IM, a f t e r cut IM, present IM, 2000 Cost ($ ) 1278.5 0 3918.47 3924.95 3819.01 3200.23 1454.83 0 8584.65 7280 15243.49 0 32732.61 25942.12 15250.95 0 0 0 Table BB-10.— Aspen-Birch Ecosystem, S o il Group 2 Stand S ize Class Seed-sapling Poletim ber Sawtimber Non-stocked A cti vi ty CU EE IM CU to CU to CU to CU EE IM CU to CU EE,(CU IM CU to CU to CU CU to CU to IM, present IM a t SS-PT IM a t PT-ST IM a t PT-ST to EE IM, before cut IM, a f t e r cut IM, present IM, 2000 Cost ($ ) 863.23 0 2677.64 2585.34 2188.56 2684.12 980.25 0 6035.67 4927.18 10279.44 0 22193.52 17439.50 10287.27 0 0 0 APPENDIX CC QUANTITIES OF GOODS PRODUCED OUTSIDE OF THE MODEL Table CC-1. — Q u a n tities o f Outputs Produced on Forest Land Converted to Urban Use Time Period 1Region Product 1 2 3 4 1 Timber (CF) Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 3261 176 549 500 18654 854 2495 2108 7468 434 1305 1142 18669 739 2493 2034 2 Timber (CF) Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 4236 170 632 470 13459 601 2339 1532 4073 269 1102 761 12257 587 2176 1700 3 Timber (CF) Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 8898 148 602 411 27084 365 1498 1071 10915 190 711 628 26682 391 1449 1927 4 Tinfcer (CF) Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 6907 111 485 308 13244 173 766 519 5385 82 353 240 13254 562 790 536 5 Timber Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 8543 79 285 193 9209 98 455 304 3989 46 206 138 16787 103 486 339 6 Timber Big Game Hunterdays Small Game Hunterdays Erosion (T o n s /a c re /y r) 2300 25 100 66 3809 32 153 96 2188 14 66 45 4191 36 164 110 314 Table C C -2 .--Q u a n titie s o f Outputs Produced on Lands C u rren tly 1n In te n ­ sive Management and Environmental Emphasis Time Period 1Region Product 1 2 3 4 1 Timber (CF) 167050 Big Game Hunterdays 3572 Small Game Hunterdays 7449 Erosion (T o n s /a c re /y r) 5246 266481 5048 10627 7620 214710 2790 5702 3647 177470 3701 7683 5017 2 Timber (CF) 44260 Big Game Hunterdays 3561 Small Game Hunterdays 6999 Erosion (T o n s /a c re /y r) 4891 200930 5285 12116 10673 156780 2641 5841 3521 120370 3599 7610 4709 3 Timber (CF) 109460 Big Game Hunterdays 3494 Small Game Hunterdays 7923 Erosion (T o n s /a c re /y r) 4898 253960 5210 11024 7133 204450 2680 5733 7009 180830 3574 8555 4314 4 Timber (CF) 189160 Big Game Hunterdays 3707 Small Game Hunterdays 8274 Erosion (T o n s /a c re /y r) 4670 293580 5304 11109 7202 196628 2693 5966 2656 251260 4511 8386 4953 5 Timber (CF) 392660 Big Game Hunterdays 4467 Small Game Hunterdays 8813 Erosion (T o n s /a c re /y r) 8273 674240 6778 14531 7126 573610 3559 6184 3117 499882 3833 8690 4996 6 Timber (CF) 340140 Big Game Hunterdays 4454 Small Game Hunterdays 8778 Erosion (T o n s /a c re /y r) 8273 426762 7505 14426 7027 310030 3548 6123 3180 289129 3836 9295 4998 APPENDIX DD ACREAGES ALLOCATED TO MANAGEMENT STRATEGIES IN LINEAR PROGRAMMING SOLUTIONS Table DD-1. — Run A Stand Size Class*1 Management Strategy3 1 Ecosystem: C onifer SS PT ST Ecosystem: C o n ifer C onifer SS ST NS C onifer SS PT PT ST 319 1 S oil Group: S o il Group: Oak S o il Group: CU-IM, present CU-IM a t PT-ST CU-IM, present CU-IM, before cut 316 51 - - - 451 - Condition Class: 519 691 - 159 2005 573 96 568 285 4 Adequate - 169 369 Needs TS1 1900 664 - - - - 191 - 95 95 2 275 291 - 95 1423 182 - - - 97 473 191 483 95 569 192 - 87 87 94 1275 - 643 - 270 97 3 CU CU CU-IM, present CU CU ST NS SS - CU CU-IM, a t PT-ST CU CU-IM, a t PT-ST CU-IM, before cut CU PT Ecosystem: S oil Group: Condition Class: 375 CU CU CU-IM, before cut CU-IM, a f t e r cut CU NS Ecosystem: 1 CU-IM, present CU-IM, present CU-IM, before cut SS PT ST Ecosystem: S oil Group: Region 2 3 1 189 - 176 92 - - 96 - - 92 - - 97 - - - Condition Class: — 2568 472 6101 1312 2474 13405 502 Adequate 4657 - - 2254 3600 2485 7614 317 Table DD-1. (c o n t'd .) Stand Size Classb Management S trategy3 Region 2 3 1 Ecosystem: Oak SS PT SS PT ST NS Ecosystem: SS PT ST NS Ecosystem: 1 CU CU CU-IM, present CU-IM, before cut CU ST NS Ecosystem: Soil Group: Oak S oil Group: CU CU CU-IM, present CU CU Elm-Ash-Cottonwood 1833 3773 14237 7322 - - 1143 1440 2165 6390 1466 1951 2002 1332 2926 - 1502 2842 1328 Needs TSI 6136 3072 - 1289 3819 2 - - 2894 587 2378 1143 564 - 564 1028 189 5520 - 359 76 6553 10832 - 5335 - - 9490 8097 4746 5335 3694 Soil Group: 259 76 l S oil Group: CU CU-IM a t PT-ST CU CU-IM, a t present CU-IM CU Maple-Beech-Birch Condition Class: 1 4794 3450 - 4536 2344 — 5621 - 4956 3278 Condition Class: quate SS PT ST Ecosystem: SS PT ST NS Ecosystem: SS PT ST NS CU-IM, present CU-IM, present CU-IM, before cut Maple-Beech-Birch Soil Group: CU CU CU-IM, before cut CU Maple-Beech-Birch CU CU CU CU 553 668 2802 877 1169 975 195 711 311 6041 1 625 - 3329 1846 373 5167 Condition Class: 6296 2375 3230 765 1412 947 369 283 3420 1190 1205 371 1045 373 1233 191 475 193 850 176 90 169 Soil Group 2 875 873 1460 94 - - Needs TSI 318 Table DD-1. (c o n t'd .) Stand Size Classb Management S trateg y3 1 Ecosystem: SS PT ST NS Aspen-B1rch S oil Group: SS PT ST NS Aspen-Birch S o il Group: CU-EE CU-IM a t PT-ST CU-IM, before cut CU 4 1 CU-EE CU-IM a t PT-ST CU-IM, before cut CU Ecosystem: Region 2 3 3222 758 185 194 6468 2561 387 1233 2496 648 93 467 3407 1195 279 35 3322 775 192 192 4955 2193 187 756 2429 745 188 282 2796 1084 183 537 2 aRefer to Appendix BB, Table BB-1 on page 308 f o r the d e fin itio n o f symbols 1n the management s tra te g y column. bStand S ize Classes NS SS PT ST = = = Non-Stocked S eedling-Sapling Poletim ber Sawtimber 319 Table DD-2.— Run B, Changes in Acreages A llocated to Management S tra te g ie s as Compared to Run A Stand Size Class Management S trategy 1 Ecosystem: C o n ifer Ecosystem: Oak SS Ecosystem: Ecosystem: SS Ecosystem: SS Ecosystem: SS S oil Group: 95 1 CU-IM, present CU-IM a t SS-PT Elm S o il Group: Maple S oil Group: S oil Group: Soil Group: CU-IM, present Condition Class: 643 Adequate 2585 1312 5520 10832 4657 6553 4794 1 Condition C lass: Adequate 711 625 1846 3222 6468 2494 3407 3322 4955 2429 2796 553 1 CU-IM, present Aspen-Birch 2.98 84.02 2 CU-IM, present CU-IM a t PT-ST Aspen-Birch 182 502 CU CU-IM a t PT-ST SS 4 S oil Group:- 2 CU CU-IM, present PT Region 2 3 2 Table DD-3.--Run C, Changes 1n Acreages A llo cated to Management S tra te g ie s as Compared to Run A Stand Size Management S trateg y Region 2 3 1 Ecosystem: C onifer Oak SS Ecosystem: Oak Ecosystem: SS Ecosystem: SS 1 S o il Group: Elm S o il Group: S o il Group: 1 S o il Group: - S oil Group: CU-IM, present 1312 502 - 7322 - « 92 Adequate - 4657 Needs TSI 3072 1502 - 2 1466 - 1951 - 2002 - 259 564 - 1332 — 564 76 1 5520 - 1 10832 - 6553 4794 Condi t i on C lass: — 553 711 - 625 - - Adequate 1846 - 1 CU-IM, present Aspen-Birch 96 Condition C lass: 3773 CU-IM, present CU-IM a t PT-ST Aspen-Birch •• 192 Condition Class: 2586 CU CU-IM a t PT-ST Maple — - CU CU-IM a t PT-ST CU CU-IM, present SS SS S oil Group: Oak PT Ecosystem: - CU CU-IM, present SS Ecosystem: S o il Group: 95 CU-IM, present CU-IM a t SS-PT PT Ecosystem: 3 CU CU-IM a t PT-ST PT Ecosystem: S o il Group: 4 3222 6468 2494 3407 3322 4955 2429 2790 2 Table DD-4.— Run D, Changes in Acreages A llo c ate d to Management S tra te g ie s as Compared to Run A Stand Size Class Management S trategy 1 Ecosystem: C o n ife r PT Ecosystem: Oak Oak Ecosystem: SS Ecosystem: SS 1 S o il Group: Elm S oil Group: S oil Group: 1 S oil Group: S o il Group: CU-IM, present 1312 4657 Condition Class: 3773 1083.9 6238.1 1502 1466 2002 Needs TSI 3072 259 564 1951 1332 564 76 1 5520 6553 10832 4794 1 Condition C las s: Adequate 711 625 1846 3222 6468 2494 3407 3322 4955 2429 2790 553 1 CU-IM, present Aspen-Birch Adequate 2 CU-IM, present CU-IM a t PT-ST Aspen-Birch 92 502 CU CU-IM a t PT-ST Maple 96 Condition Class: 2586 CU CU-IM a t PT-ST CU CU-IM, present SS SS S oil Group: Oak PT Ecosystem: 192 CU CU-IM, present SS Ecosystem: 95 CU-IM, present CU-IM a t PT-ST PT Ecosystem: S o il Group: 4 3 CU CU-IM, present SS Ecosystem: S o il Group: Region 2 3 2 322 Table DD-5.— Run E, Changes 1n Acreages A llo cated to Management S tra te g ie s as Compared to Run A Stand Size Class Management Strategy 1 Ecosystem: Oak SS SS Elm S o il Group: CU CU-IM a t PT-ST 4 2 CU CU-IM a t PT-ST CU CU-IM a t PT-ST PT Ecosystem: S o il Group: Region 2 3 1466 - 1951 - 2002 - 259 564 - 1332 564 10832 4794 - 76 1 5520 — 6 1 8.3 5934.7 APPENDIX EE SURPLUSES AND DEFICITS Table E E -1.— Surpluses and D e fic its in Receipts Derived 1n L inear Pro gramming Solutions Run A B C D Product Timber Timber Timber Timber Uni ts Region CF 1 4 2 Days 4 5 5 2 3 4 5 6 3 2 3 4 5 6 3 4 6 2 3 4 5 6 1 Days 4 Days 4 CF CF CF 1 2 1 2 B C D Small Game Hunterdays Small Game Hunterdays Small Game Hunterdays Time Surplus 662,217.8 1 ,7 8 4 ,6 0 6 .8 - D e f ic it _ - 1 ,3 7 4 ,2 6 9 .7 4 ,4 5 8 ,1 5 2 .5 4 ,6 9 3 ,1 0 7 .4 2 ,5 2 4 ,8 7 7 .6 1 4 ,2 3 9 ,3 1 3 .4 31,444.1 2 ,3 0 4 ,5 6 9 .7 5 ,5 6 5 ,0 1 0 .0 6 ,1 6 9 ,4 0 7 .4 4 ,6 9 3 ,1 7 7 .6 1 6 ,0 4 5 ,0 1 3 .4 869,411 .6 26 4 ,1 69 .3 47 5 ,1 5 7 .3 3 ,1 4 5 ,5 6 9 .7 8 ,2 1 2 ,1 1 0 .9 11,168,238.1 1 0 ,8 4 0 ,6 7 7 .6 24,602,456.1 353 - 1 357 - 1 354 - 323 APPENDIX FF RIVER BASIN PRODUCTION Table F F -1 .— R iver Basin Production Output3 1 2 3 4 5 6 Run A TIM BHD SHD ERO 4545602 63333 179076 127636 3042430 61262 185868 128540 3366448 58487 186403 127686 4421147 61582 195080 120470 8969125 66799 200568 123374 6145187 68632 201052 122367 Run B TIM BHD SHD ERO 4545602 62083 182705 127677 3042430 60561 189691 128261 3366448 59808 188308 126940 6663993 61843 198888 119744 13477522 66232 214723 122699 6145187 68016 226270 121734 Run C TIM BHD SHD ERO 4545602 62420 182779 127671 3042430 50361 189242 128387 3366448 60366 188557 127148 6663993 63917 199383 120296 13477522 68679 215324 123046 6145187 70371 209581 122081 Run D TIM BHD SHD ERO 4545602 62380 184768 122714 3042430 61239 194229 128367 3366448 60117 196130 127115 6663993 63906 199302 120251 13477522 71459 204660 122992 6145187 70021 209489 122027 Run E TIM BHD SHD ERO 4545602 64185 176163 127289 3042430 62143 186215 128274 3366448 46860 186434 127651 6663993 62312 195263 120631 13477522 68272 192422 123098 6145187 72021 201492 122120 aOutputs TIM BHD SHD ERO = = = = cubic fe e t o f tim ber big game hunterdays small game hunterdays tons per y e a r o f erosion 324 APPENDIX GG DEFINITION OF TERMS A g ric u ltu ra l land: A g ric u ltu ra l land includes th a t land used fo r the ra is in g o f liv e s to c k and crops. Conversion o f Land Use: A change in man's a c t iv it y on the land from one category, such as a g ric u ltu r e , to another, such as urban. Forest land: Forest land includes th a t land which is a t le a s t 10 percent stocked by fo re s t trees o f any s iz e . I t excludes land c u rre n tly d evel­ oped fo r n on -forest use such as urban or th ic k ly s e ttle d re s id e n tia l or re s o rt areas, c it y parks, orchards, improved roads o r improved pas­ tu re land. Unproductive fo re s t land incapable o f y ie ld in g crops o f in d u s tria l wood because o f adverse s it e conditions are excluded. Pro­ ductive fo re s t land withdrawn from commercial tim ber use through s ta tu te or a d m in is tra tiv e re g u la tio n . Growing-stock tre e s : tre e s . Hunterday: A ll liv e trees o f any s iz e except rough and ro tte n One person hunting a game animal fo r a p ortio n o f one day. Inland w ater: Inland w ater includes the surface area o f a l l w ater bodies w ith in the s ta te boundaries, excluding the Great Lakes. Land areas underlying lak es , streams and ponds are included. In te n s iv e management: Intension management involves investment in fo re s t stands through the a p p lic a tio n o f c u ltu ra l p ractices to increase wood y ie ld s and economic re tu rn s . Recreation land: P u b lic a lly owned land used p rim a rily fo r re c re a tio n purposes. Includes nation al and s ta te fo re s t campgrounds, nation al parks, s ta te parks, game areas, re c re a tio n a l areas, p u b lic fis h in g s it e s , public water access, and county and township re c re a tio n areas. Roundwood: Logs removed from the stump and limbed. Stand size clases: Sawtimber tre e s : Live trees o f commercial species containing a t le a s t a 1 2 -fo o t saw lo g . Softwoods must be a t le a s t 9 .0 inches in diameter a t breast height and hardwood a t le a s t 11.0 inches. Poletim ber tre e s : Live trees o f commercial species a t le a s t 5 .0 inches in diameter a t breast height but sm aller than sawtimber s iz e , and o f good form and v ig o r. S eedling-S apling tre e s : Live trees o f commercial species less than 5 .0 inches in diam eter a t b reast h e ig h t. 325 326 Stocking: The degree o f u t il i z a t i o n o f land by trees as measured 1n terms o f basal area and/or the number o f trees required to u t i l i z e f u l l y the growth p o te n tia l o f the land. Stocking Classes: W ell-stocked stands: growing-stock trees Stands 70 percent o r more stocked w ith Medium-stocked stands: growing-stock trees L ig h tly stocked stands: growing-stock trees Stands 40 to 69 percent stocked w ith Stands 10 to 39 percent stocked w ith Non-stocked areas: Forest land less than 10 percent stocked w ith growing-stock trees Transportation land: T ransportation land Includes land devoted to pub lic highways, roads, r a ilr o a d s , and a ir p o r ts . C ity and v illa g e s tr e e t are considered to be urban land. Urban land: Land in the fo llo w in g ca teg o ries : a. A ll incorporated c it ie s and v illa g e s over 2,500 in h ab itan ts b. Incorporated c it ie s and v illa g e s between 1,000 and 2,500 in h a b ita n ts , providing t h e ir density was g e n e ra lly g re a te r than 1,000 in h ab itan ts per square m ile . c. Unincorporated places over 1,000 in h ab itan ts as id e n tifie d by the U.S. Census Bureau, providing t h e ir d en sity is over 1,000 in h a b ita n ts per square m ile . LITERATURE CITED LITERATURE CITED Published Books DENNIS, R. 1974. Clambering in to the e ig h tie s , a n atio n al economic pro­ je c tio n re p o rt. National Planning A sso ciatio n, Report no. 7 4 -N -l. 70 pp. LOCKWOOD PUBLISHING CO. 1970. Lockwood's d ire c to ry o f the paper and a l l i e d tra d e s , 95th e d itio n . Lockwood Publishing C o ., New York. RUSSELL, CLIFFORD S ., AND WALTER 0. SPOFFORD, JR. 1972. A q u a n tita tiv e framework f o r re sid u a ls management d ec is io n . In Kneese and Bower (e d s .), Environmental q u a lity a n a ly s is : theory and method in the so c ia l sciences. Johns Hopkins Press, New York. 115-179. Journal P u b licatio n s DAY, J .C . 1972. A recu rsive programming model fo r n o n -s tru c tu ra l flo o d damage c o n tro l. Water Resources Research (6 ):1 2 6 2 -1 2 7 1 . HARDY, E .E ., AND R.L. SHELTON. 1970. Inventorying New Y ork’ s land use and n atu ral resources. New York's Food and L ife Sciences 3 ( 4 ) : 4 - 7 . ISARD, WALTER, AND DAVID J. OSTROFF. 1960. General In te rre g io n a l eq u i­ lib riu m . Journal o f Regional Science 1 1 (3 ): 67-74. KING, R. A ., AND W. R. HENRY. 1959. T ran spo rtatio n models in the study o f in te rre g io n a l com petition. Journal o f Farm Economics (1 4 ): 997-1011. LACATE, DOUGLAS L. 1961. A review o f landtype c la s s ific a tio n and mapping. Land Economics 3 7 ( 3 ) :271-278. TAKAYAMA, T . , AND G. G. JUDGE. 1964. E q u ilib riu m among s p a tia lly sepa­ rated markets: a re fo rm u la tio n . Econometrica (3 2 ):5 1 0 -5 2 4 . Government P u b lic a tio n s , Data and Inform ation BLYTHE, JAMES E ., ALLEN H. BOELTER, AND CARL W. DANIELSON. 1975. Primary products in d u s try and tim ber use, M ichigan, 1972. U .S .D .A ., Forest Service B u lle tin NC-24. North Central Forest Experiment S ta tio n , S t. P aul, Minn. 45 pp. 327 328 BULL, LEN, AND JOHN SUTTON. 1974. The a p p lic a tio n o f m u lti-o b je c tiv e resource evalu atio n to r iv e r basin s tu d ie s. NRED-ERS-USDA, August, 1974, East Lansing, M i. 30pp. BUREAU OF THE CENSUS, U.S. DEPARTMENT OF COMMERCE. 1972. County and c it y data book. Washington, D.C. 1020pp. CHASE, CLARENCE D ., AND RAY E. PFEIFER. 1970. The growing tim ber resource o f Michigan, 1966, u n it 1 - eastern upper peninsula. Forestry D iv is io n , Michigan Department o f Natural Resources, Lansing, M i. 66pp. CHASE, CLARENCE D ., RAY E. PFEIFFER, AND JOHN S. SPENCER, JR. 1970. The growing tim ber resource o f Michigan, 1966. North C entral Forest Experiment S ta tio n , U .S .D .A ., Forest S e rvic e, Resource B u lle tin NC-9, S t. P aul, Minn. 62pp. DIVISION OF RESEARCH, GRADUATE SCHOOL OF BUSINESS ADMINISTRATION, MICHIGAN STATE UNIVERSITY. 1974. Michigan s t a t is t i c a l a b s tra c t, 10th e d itio n . 705pp. FISH AND WILDLIFE SERVICE, U.S. DEPARTMENT OF THE INTERIOR. 1971. 1970 National survey o f fis h in g and hunting. Washington, D.C. 150pp. FORESTRY DIVISION, MICHIGAN DEPARTMENT OF NATURAL RESOURCES. 1974. 1974 D ire c to ry o f primary wood using plants in Michigan. Lansing, M i. 43pp. FORESTRY DIVISION, MICHIGAN DEPARTMENT OF NATURAL RESOURCES. 1969. Michigan commercial sawlog, veneerlog, and lumber production by county, 1969. Lansing, M i. 5pp. FORESTRY DIVISION, MICHIGAN DEPARTMENT OF NATURAL RESOURCES. 1966-1973. Michigan pulpwood production. Lansing, M i. 5pp. FORESTRY DIVISION, MICHIGAN DEPARTMENT OF NATURAL RESOURCES. 1965. Sawlog and lumber production, M ichigan, 1965. Lansing, M i. 5pp. HAWN, LOUIS J . 1974. Michigan small game k i l l estim ates, 1973. Michigan Department o f Natural Resources. Surveys and S t a t is t ic a l Report no. 138. Lansing, M i. 6pp. MICHIGAN DEPARTMENT OF STATE HIGHWAYS AND TRANSPORTATION. 1975. 23rd Annual progress re p o rt, re p o rt no. 162, lo c a l government d i v i ­ sio n. Lansing, M i. 247pp. PFEIFFER, RAY E ., AND JOHN S. SPENCER, JR. 1970. The growing tim ber resource o f Michigan, 1966, u n it 3 - the northern lawer peninsula. F orestry D iv is io n , Michigan Department o f Natural Resources, Lansing, M i. 112pp. 329 RYEL, L. A. 1974. The 1973 deer seasons. Michigan Department o f N atural Resources, Surveys and S t a t is tic a l Report no. 135. Lansing, M l. 6pp. STATE PLANNING DIVISION, MICHIGAN DEPARTMENT OF NATURAL RESOURCES. 1972. Land use c la s s ific a tio n system as recommended by the s ta te plan­ ning d iv is io n f o r the s ta te o f Michigan. Working D r a ft. Lansing, M i. 29pp. SPENCER, JOHN S .,J R ., AND RAY E. PFEIFER. 1970. The growing tim ber resource o f M ichigan, 1966, u n it 2 -th e western upper peninsula. F orestry D iv is io n , Michigan Department o f Natural Resources, Lansing, M i. 72pp. U.S. BUREAU OF LABOR STATISTICS. 1974. Monthly labor review . Washington, D.C. June 2, 1974. Government Documents FOREST SERVICE, U. S. DEPARTMENT OF AGRICULTURE. 1973. The outlook fo r tim ber in the United S ta te s . Forest Resource Report No. 20. Washington, D.C. 367pp. NATIONAL MATERIALS POLICY COMMISSION. 1974. Timber: the renewable mate­ r i a l . Washington, D.C. 100pp. WATER RESOURCES COUNCIL. 1973. Water and re la te d land resources, estab­ lishm ent o f p rin c ip le s and standards fo r planning. Federal R e g is te r, Volume 38, Number 174. Monday, September 10, 1973. Washington, D.C. 89pp. WATER RESOURCES COUNCIL. 1974. P rin c ip le s and standards In te r e s t r a te . Federal R e g is te r, Volume 39, Number 158. Wednesday, August 14, 1974. Washington, D.C. Ip . U.S. DEPARTMENT OF AGRICULTURE. 1973. USDA in te rim procedures fo r p lan­ ning w ater and re la te d land resources. D r a ft. 80pp. Government Research Papers AMIDON, ELIOT L. 1964. A com puter-oriented system fo r assembling and d is p la yin g land management in fo rm atio n . U .S .D .A ., Forest Service Research Paper PSW-17.34pp. FEDERAL HIGHWAY ADMINISTRATION, U.S. DEPARTMENT OF TRANSPORTATION. 1972. Cost o f operating an autom obile. Washington, D.C. 15pp. GINGRICH, SAMUEL F. 1962. Adjusting s h o rtle a f pine volume tab les f o r d if f e r e n t lim its o f top u t i l i z a t i o n . U .S .D .A . Forest S e rv ic e , Central States Forest Experiment S ta tio n , Technical Paper 190, September, 1962. 10pp. 330 LEUSHNER, WILLIAM A. 1972. P ro jec tin g the aspen resource in the lakes s ta te s . U .S .D .A ., Forest S e rvic e, North Central Forest Experiment S ta tio n , Research Paper NC-81. S t. P aul, Minn. 32pp. MURRAY, T . , R. ROGERS, D. STINTON, C. STEINITZ, R. TOTH, AND D. WAY. 1971. Honey H i l l : a systems an alysis fo r planning the m u ltip le use o f c o n tro lle d water areas. Corps o f Engineers, In s t it u t e o f Water Resources, Report 7 1 -9 , Washington, D.C. 403pp. SHLAGEL, BRYCE, E. 1971. Growth and y ie ld o f quaking aspen 1n north c e n tra l Minnesota. U .S .D .A ., Forest S e rv ic e , North Central Forest Experiment S ta tio n , Research Paper NC-58, S t. P aul, Minnesota. 10pp. U n iv e rs ity Research Papers MANTHY, ROBERT S ., LEE M. JAMES, AND HENRY A. HUBER. 1973. Michigan tim ber production - now and 1985. Michigan S ta te A g ric u ltu ra l Experiment S ta tio n , Natural Resources Research Paper 192. East Lansing, M i. 23pp. MICHIGAN STATE UNIVERSITY, COOPERATIVE EXTENSION SERVICE. 1973. County and regional fa c ts . Regions I I , I I I , IV , V I , and V I I I . East Lansing, M l. PATTERSON, R. L. 1972. A p p licatio n s o f lin e a r in te g e r programming to problems o f land use a llo c a tio n . U n iv e rs ity o f Michigan, Sea Grant Program (M ichU-SG-72-213), Ann A rbor, M1. 36pp. WYND, WILLIAM R ., AND ROBERT S. MANTHY. 1971 Transporting pulpwood from M ichigan's upper peninsula. Michigan S ta te U n iv e rs ity , A g ric u ltu ra l Experiment S ta tio n , N atural Resources Report 128, East Lansing, M i. 15pp. YOUNG, C. 1972. SYMAP. Computer In s t it u t e f o r Social Science Research, Michigan S tate U n iv e rs ity , Technical Report no. 100. Revised by D. Dugger and R. W ittic k . East Lansing, M1. 47pp. Presentations a t Meetings POMPI, LOUIS W. AND DANIEL E. CHAPPELLE. 1974. Linking the fo r e s tcentered economic and ecologic systems o f western Montana: a prog­ ress re p o rt. Presented a t the Economic Models f o r Management o f N atural Resources Workshop, Big Sky, Montana. 56pp. SHELTON, R. L. AND TA LIANG. 1973. Land inven tory systems (th e Cornell exp erien ce). Presented a t the Inter-A m erican Meeting on Science and Man 1n the Americas, Mexico C ity , Mexico. 12pp. 331 PRIVATE ORGANIZATIONS MOTOR VEHICLE MANUFACTURERS ASSOCIATION OF THE U .S ., INC. 1974. Motor veh icles and energy. S ta tis tic s Department. January, 1974.D e tr o it, M i. 16pp. Unpublished M a te ria ls DULLER, 0. H. 1965. P ro fita b le adjustments on selected Michigan tre e f r u i t farms. Ph. D. Thesis. Michigan S ta te U n iv e rs ity , East Lansing, M i. 130pp. DUVICK, R.D. 1970. A lte rn a tiv e methods o f financin g growth on Michigan d a iry farms. Ph.D. Thesis. Michigan S ta te U n iv e rs ity , East Lansing, M i. 151pp. JORDAN, TOM, AND A. J. BAKER. 1973. The development o f m u lti-p ro d u c t c o e ffic ie n ts f o r the fo re s t resource in r iv e r basin stu d ies. U .S .D .A ., Forest S e rv ic e , S ta te and P riv a te F o re s try , Upper Darby, Pa. 26pp. POMPI, LOUIS W. 1975 Linking the fo re s t-c e n te re d economic and ecologlc systems o f western Montana: a problem a n a ly s is . Ph.D. Thesis. Michigan S tate U n iv e rs ity , East Lansing, M i. 384pp.