A Locmou 51‘qu FOR A MICHIGAN FEED mumcwmm PLANT chsts for {'Em Dogma m§ M. 5 MECHEGAH STATE UNWERSETY Lowefl D. Hiil 1961 3 1 2 ii MW iiiziiiim L This is to certify that the thesis entitled A LOCATII‘LH’J STUDY FOR A MECHIGJ’AN FEED I'IAI‘CUFACTURING PLAE‘JT presented by Lowell D. Hill has been accepted towards fulfillment of the requirements for __M.._S._ degree MEL Major professor 0-169 LIBRARY Michigan State University NOV 2 6 H. f2 .134” ‘V ) ”a. Q) J— fir: ABSTRACT A LOCATION STUDY FOR A MICHIGAN FEED MANUFACTURING PLANT by Lowell D. Hill This study illustrates a method for locating a feed manufacturing plant at a point where total costs of transpor- tation would be minimized. Assuming a market area of the lower peninsula of Michigan, an analysis was made of the distribution of potential sales by projecting livestock numbers, and conducting a survey of feed manufacturing plants. The purpose of the survey was to ascertain the total manufactured feed sold in Michigan and classify it by kind of livestock and type of feed. The survey indicated that 19% of the total manufactured feed was sold as pellets and 20% was distributed in bulk. Considerable differences existed among classes of livestock in the proportion of protein supplements vs. complete mixed feed. For example, 64% of the turkey and other poultry feed was sold in the form of mixed feed and accounted for 55% of all complete feeds sold; while sheep feeds were composed of 77.5% complete feeds but Lowell D. Hill accounted for only 0.4% of all complete feeds. A large part of this study was involved with projecting livestock feed consumption to 1965 to obtain the demand pattern, by counties, for the State. With the limited historical data available on feed consumption in Michigan, no trend or basis for direct projection could be obtained. Therefore, livestock numbers were used to form a basis for the estimate. A linear regression was fitted to annual data obtained from Michigan Agricultural Statistics for the years 1947 through 1959, and an estimate for 1965 was extrapolated from this line. Broilers, turkeys, cattle on feed, and lambs marketed were not recorded by county in this publication so were approximated from other sources. Projected numbers of livestock for each county were then converted into tons of grain and tons of 44% protein supple— ment required per square mile. Using a gird overlay of the lower peninsula and algebraic formulas, the ton mile centers were found for feed usage by each individual class of live— stock and for all classes combined. Grain production was projected in the same way as live- stock numbers and the distribution and concentration studied. The ton mile center for each of four grains was determined 3 Lowell D. Hill from the estimated county production for 1965. The ton mile center for feed grains was found by combining corn and oat production into a corn equivalent figure. Using grain as an ingredient was found to have little influence upon the plant location, since grain and livestock concentrations are in the same general area. The distribution of grain sales indicated that an adequate supply could be obtained within a very small radius of any of the alternative plant locations. The formulas used for the ton mile centers were then expanded to include manufacturing ingredients and freight rates. The proportion of total feed consumption that would be produced by a hypothetical plant, and the kinds, amounts and sources of the various ingredients, were determined from the survey of feed manufacturers. Freight rates were based upon rail rate quotations to a specific plant. By using these figures the following points of minimum transfer cost were determined: 1. Fowler -- under the assumption that all transport rates are equal. 2. Three miles south of Holt -— under the assumption that transport rates per mile are unequal between products, but equal between locations. 4 Lowell D. Hill 3. Fowler -- using actual quoted rates for each ingredient between specified points. This study has dealt with only one aspect of the location problem. Its value is not as an answer to any specific location problem, but as a methodological approach to minimizing the transportation costs. Individual conditions within each plant would dictate the parameters to enter into the location formulas. Once these parameters are determined, this method involves only simple mathematical manipulation to determine the plant location which minimizes transportation costs. A LOCATION STUDY FOR A MICHIGAN FEED MANUFACTURING PLANT BY Lowell D. Hill A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1961 ii ACKNOWLEDGEMENTS I wish to express my appreciation to all who have made possible my work here at MSU. I am very grateful to the staff and faculty for their assistance and advice in selecting my thesis and accumulating the materials for it. I wish to thank Dr. Boger, head of the Agricultural Economics Department, for the financial assistance and personal encouragement which made possible my work toward the degree. A special thanks is due to my faculty advisor, Dr. Carleton Dennis, for his constant and willing contributions and supervision in completing this study. I know that I solicited many hours of his time from a busy schedule. A thank you is also in order to Mrs. King and members of the statistical pool for their time and effort in compiling the data used and to the members of the feed industry who cooperated in providing data without which I could not have completed this study. I can never express the depth of my gratitude to my wife, Betty, for all the understanding and effort she has put into the successful completion of my degree, nor to her mother, Mrs. Lila Carpenter, for her encouragement and support of my plans and decisions in continuing my study. iii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . V LIST OF FIGURES . . . . . . . . . . . . . . . . . . vi LIST OF MAPS . . . . . . . . . . . . . . . . . . . . vii CHAPTER I. METHODOLOGICAL APPROACH . . . . . . . . . . 1 Location Theory 1 Purpose of the Study 7 Determining the Point of Minimum Transportation Cost 8 Alternate Site Cost Computations 16 II. CONSUMPTION OF MANUFACTURED FEEDS IN MICHIGAN 18 USe of Sales Data for Determining Output of Manufactured Feeds 18 Obtaining the Data 18 Estimation of Total Feed Consumption 21 III. PROJECTION OF MICHIGAN LIVESTOCK FEED CONSUWTION O O O O O O O O O O O O O _ O O 2 9 Classification and Sources of Data 29 Method of Projection 31 Analysis of Livestock Distribution and Trends 34 Estimates of Projected Feed Consumption 48 IV. PROJECTION OF MICHIGAN FEED GRAIN PRODUCTION 54 Basis for the Projection 54 Analysis of Production Distribution and Trends 55 CHAPTER V. A LEAST-COST TRANSPORTATION ANALYSIS . . . . Requirements for the Analysis Determining the Ton Mile Center for All Feed Consumed Determining the Ton Mile Center for All Manufactured Feeds Determining the Point of Minimum Transportation Costs-Equal Transportation Rates Determining the Point of Minimum Transportation Costs—Linear Transportation Rates Determining the Point of Least Transportation Costs--Non-Linear Transportation Rates Summary VI. SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FURTHER STUDY . . . . . . . . . . . . . . Application to a Specific Plant Study Unsolved Aspectsof the Least—Cost Transportation Problem BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . APPENDIX A. APPENDIX B.’ Feed Research Questionnaire . . . . . . Wool Promotion Fund Deductions and Computations of Numbers of Lambs Marketed, by County in Michigan . . . . . . . . . . . . . APPENDIX C. Grain Production . . . . . . . . . . . . . . APPENDIX D. Concentration Maps of Livestock and Water Transportation . . . . . iv Page 65 65 66 69 75 80 83 90 93 93 95 99 101 104 110 131 LIST OF TABLES TABLE PAGE 2.1 Commercial Feed Sold in Midhigan by type of Feed and Class of Livestock . . . . . . 23 2.2 Commercial Feed Sold in Michigan by type of Feed, Size of Company and Location . . . 25 2.3 Bulk Feed Deliveries and Pelleted Feeds Sold as a percent of Total Feed, by Size of Company for 1959 and 1965 . . . 27 3.1 Computed R2 for Trend Lines for Selected Classes of Livestock Numbers and Grain Production . . . . . . . . . . . . . . . 47 3.2 Feed Allowances per Head of Livestock and a Comparison of Sources . . . . . . . . 49 5.1 Estimate of Manufactured Feed Sold, as a percent of Total Feed Consumed in 1965, by Class of Livestock and Type of Feed . . . . . . . . . . . . . . . . 71 5.2 Ingredient Locations, Tonnages Required, and Freight Rates used in Computing the Least-Cost Transportation Center . . 79 5.3 Total Cost of Transportation at Charlotte and Fowler Locations . . . . . . . . . . 88 3.4 3.6 LIST OF FIGURES A Hypothetical Sales Map . . . . . . . . . . . A Grid Overlay on a Hypothetical Sales Map . . A Grid Map Showing Outbound and Inbound Quantities and the Least-Cost Transportation Center . . . . . . . . . . Alternate Site Locations . . . . . . . . . . . Trend of Numbers of Dairy Cattle in Michigan, from 1947 to 1959 and Projected to 1965 . Trend of Numbers of Sows Farrowed in Midhigan, from 1947 to 1958 and Projected to 1965 . . . . . . . . . . . . . . . . . Trend of Numbers of Hens and Pullets in Nfichigan, Jan. 1, 1947 to 1959 and Projected to 1965 . . . . . . . . . . . . Trend in Stock Sheep in Michigan, 1947 to 1959 and Projected to 1965 . . . . . . . . Trend in Lambs Marketed in Michigan 1947 to 1959 and Projected to 1965 . . . . . . . . Trend of Beef Cattle on Feed in Michigan Jan. 1, 1947 to 1959 and Projected to 1965 . . Trends of Total Dairy Cattle Concentrates Fed per Head, 1952 to 1960 and Projected to 1965 . . . . . . . . . . . . . . . . . . . Trends in Michigan Grain Production from 1947 to 1958 and Projected to 1965 . . . . Transportation Gradients for the Lower Mississippi Valley Area, 1939-1940 . . . . Operating Expenses Related to Volume of Feed Mixed O O O O O I 0 O O O O O O O O O O 0 vi Page 10 13 16 35 40 41 44 44 46 52 56 80 90 LIST OF MAPS Estimated Changes in Michigan Dairy Cattle Numbers, 1956-1958 to 1965, by Counties . . . . . . . . . . . . . . . . . Estimated Changes in Numbers of Sows Farrowed in Midhigan, 1956-1958 to 1965, by Counties . . . . . . . . . . . . . . . . . Estimated Changes in Numbers of Michigan Hens and Pullets, 1956-1958 to 1965, by Counties . . . . . . . . . . . . . . . . . Estimated Changes in Numbers of Michigan Stock Sheep, 1956-1958 to 1965, by Counties . . Estimated Changes in Michigan Corn Production, 1956-1958 to 1965, by Counties . . . . . . Estimated Changes in Michigan Soybean Production, 1956-1958 to 1965, by Counties . . . . . . . . . . . . . . . . . Estimated Changes in Midhigan Wheat Production 1956-1958 to 1965, by Counties . . . . . . Estimated Changes in Michigan Oat Production 1956-1958 to 1965, by Counties . . . . . . Grid Overlay Map of Lower Muchigan . . . . . . Grid Map Showing the Ton Mile Centers for Livestock Feed Consumption . . . . . . . . Grid Map Showing the Ton Mile Centers for Feed Grain Production . . . . . . . . . . . . . APPENDIX MAPS l. 2. Dairy Cattle. Density in Michigan Counties in 1959 C C O C O O O O O O O O O O O O 0 Dairy Cattle. Density in Michigan Counties Projected to 1965 (numbers per square mile) 0 o o o o o o o o o o o o o o o o 0 vii PAGE 37 39 42 45 58 61 62 63 67 70 77 PAGE 111 112 viii APPENDIX MAPS PAGE 3. Sows Farrowed, Density in Michigan Counties in 1958 (numbers per square mile) . . . . 113 4. Sows Farrowed. Density in Michigan Counties Projected to 1965 (numbers per square mile) 0 o o o o o o o o o o o o o o o o o 11.4 5. Hens and Pullets. Density in Michigan Counties in 1959 (numbers per square mile) . . . . . . . . . . . . . . . . . . 115 6. Hens and Pullets. Density in Michigan Counties Projected to 1965 (numbers per square mile) . . . . . . . . . . . . . . . . . . 116 7. Stodk Sheep. Density in Michigan Counties in 1959 (number per square mile) . . . . . 117 8. Stock Sheep. Density in Michigan Counties Projected to 1965 (number per square mile) . . . . . . . . . . . . . . . . . . 118 9. Lambs Marketed. Density in.Nfichigan Counties Projected to 1965 (numbers per square mile) . . . . . . . . . . . . . . . . . . 119 10. Cattle on Feed. Density in Michigan Counties Projected to 1965 (number per square mile) 0 o o o o o o o o o o o o o o o o o 120 11. Broilers. Density in Michigan Counties in 1959 (numbers per square mile) . . . . . . 121 12. Turkeys. Density in Michigan Counties in 1959 (numbers per square mile) . . . . . . 122 13. Corn Production Density in Midhigan Counties in 1958 (bushels per square mile) . . . . 123 14. Corn Production Density in Michigan Counties Projected to 1965 (bushels per square mile) . . . . . . . . . . . . . . . . . . 124 ix APPENDIX MAPS PAGE 15. Soybean Production Density in Michigan Counties in 1958 (bushels per square mile) . . . . . . . . . . . . . . . . . . 125 16. Soybean Production Density in Michigan Counties Projected to 1965 (bushels per square mile) . . . . . . . . . . . . . . . 126 17. Oat Production Density in Michigan Counties in 1958 (bushels per square mile) . . . . 127 18. Oat Production Density in Michigan Counties Projected to 1965 (bushels per square mile) . . . . . . . . . . . . . . . . . . 128 19. Wheat Production Density in Michigan Counties in 1958 (bushels per square mile) . . . . 129 20. Wheat Production Density in Michigan Counties Projected to 1965 (bushels per square mile) . . . . . . . . . . . . . . . . . . 130 CHAPTER I METHODOLOGICAL APPROACH Location Theory The location of agricultural industries is important in obtaining the optimum allocation of resources. From the view- point of the entrepreneur involved, it affects maximization of profits. From the viewpoint of the customer it is reflected in the price he must pay for the product. From the viewpoint of society, location is important in determining economic efficiency by providing the greatest possible output from a given set of resources. Despite early recognition by Von Thunen, Weber, and others, location theory has often been ignored or put aside in deference to problems with more specific and objective answers. This has been especially true in the case of English economists. Marshall and his followers concentrated on the variable of time and assumed space constant. Progress in this field was almost entirely limited to German writers, until Hoover's bodk in 1948.1 The leadership in the field was provided by lEdgar M. Hoover, Location of Economic Activity (New Yerk: McGraw—Hill, 1948). 2 Von Thunen, whose book in 18751 inspired and influenced other German economists. In many cases location is determined by intuition or accident. Only then does the entrepreneur consciously consider economic principles in maximizing profits. Successful industry location is often the end result of a process of elimination. As competition increases within an industry, firms less favorably situated find themselves unable to cover the higher costs which have resulted from their locational disadvantage, at the price set by their competitors. The less efficient, in terms of location, are forced out of the industry, While firms in an area of comparative advantage gain strength. Since the time of Von Thumen, location theory has tried to answer the two questions of EhéE,t0 produce and Where to produce it. Later writers have improved, refined, and broadened the theory, but the two basic questions remain what and where. In agriculture, the "where" is fixed in so far as land and its associated factors are given and can be adjusted, improved, and altered, but never moved. Physical mobility is more limited in agriculture than in other industries since properties of climate, soil, and topography are major lJohann Vbn Thunen, Der isolierte Stoat in Beziehung a3; Landwirtschaft and Nationalokonomie (Hamburg, 1826). determinants of production costs and output. Location in both agricultural and non-agricultural industries depends upon economic considerations since it would be physically possible to produce almost any crop under artificial environ- ment. However, most agricultural studies are oriented toward finding the most profitable product to produce at a specific location while non—agricultural location studies concentrate more on finding the most profitable location for production of a specific product. In this sense the difference between agricultural and non-agricultural location problems is the frequency in which "where" or "what" is the variable. Early in the nineteenth century, Von Thunen approached the agricultural location problem from the viewpoint of determining the production area for various agricultural products. He assumed a uniform plain of equal fertility and production possibilities, surrounding a city Which was the sole consumer. All transport costs were uniformly proportional to weight and distance. The production areas formed con- centric rings outward from the point of consumption according to the price of each product and its cost of transport. The limitations in this model are the assumptions of uniformity and its limited application to agricultural production only. Following Von Thunen, Weber attempted to present a more 4 general theory based on an evolutionary approach. Assuming a new, undeveloped economy, Weber illustrated how the various strata of society develop and locate. The minimum transfer point determines the basic location which is modified by other distorting influences of interrelationships within the society. The criticism of this method is primarily the lack of a common denominator to measure the total effect of the interrelationships and determine a net effect. In protest against partial analysis theories operating through time but ignoring spatial relationships, August Losch developed a static model of a space economy operating under conditions of monopolistic competition. His assumptions include a broad homogeneous plain, with a uniform distribution of markets and raw materials. Each producer would expand his circular market until all available markets were included. At that point the market area of each producer would be hexagonal as this is the figure nearest a circular, transpor- tation-miminizing shape which will completely exhaust the market area. The location is then determined by a set of equations from a mathematical model. This was the first attempt to include spatial relationships in a set of equations. From the standpoint of limitations, Losch's method is criticized for not including inequalities in raw material, labor, capital resources, and distribution of markets. The Leontief technique is more meaningful for a general equilibrium model in terms of input-output and price-cost relations, if it is constructed to include the factor of space. It consists of a set of simultaneous equations for minimizing total costs and maximizing revenue with transpor- tation included as a cost factor. It adapts well to linear programming, but is limited in the number of variables it can handle. Hoover approached location theory from the standpoint of profit maximization. His model attempted to minimize all costs while maximizing total revenue. He extended Weber's model by attempting to include factors of demand, competition, and unequal transportation costs. Greenhut attempted to integrate the theoretical approach of previous work with practical aspects of location. With the help of a series of empirical studies he illustrates the importance of personal influences, capital limitations, and other factors of reality.1 Although every author has his own list of relevant factors affecting location, the following classification includes The preceding comparisons are based largely upon the discussion by Walter Isard in Location and Space Economy. (New York: John Wiley, 1956), Chapter II. those pertinent to a feed mill location as treated in this study. 1. Production Factors (a) Labor and power '(b) Insurance, real estate, rent, and taxes (c) Capital facilities (d) Fire and police protection 2. Transportation Factors (a) Procurement cost of materials (b) Distribution costs (c) Freight rate patterns (d) Quantity and location of materials available 3. Demand Factors (a) Sales potential (b) Distribution of the consuming units (c) Competitive relationships 4. Personal Factors While many of the factors previously mentioned are important in determining location, most of them are of such a nature as to present a different problem for every firm. The demand for the product, the competitive situation, labor requirement, financial needs, and personal preferences all vary with each situation. For products such as feed and fertilizer that move in large volumes, transportation represents a major cost factor which presents a problem of similar characteristics for every firm in the industry. In most instances the general location of a manufacturing plant is determined by minimizing total transfer costs, and then adjusted on the basis of the other pertinent factors. Purpose of the Study The main purpose of this study was to present a method which could be used in locating the point of least transfer cost for agri—business industries. Only the transportation factors were considered: ignoring production, agglomeration, and personal factors. While a feed manufacturing industry was used as the example here, the method can be easily adapted to other industries with similar patterns of manufacture and distribution. Although a method of location was the primary objective, this study also determines a site of minimum transportation costs for a hypothetical feed manufacturing plant. In determining this it was necessary to analyze the trend in feed grains and livestock production, the feed consumption potential in Midhigan, and the centers of production of the classes of livestodk fed within the state. While the value of the specific point located in this study is limited by the required assumptions, it is only necessary to substitute the demand and supply factors of a specific plant to determine an actual location. Determining the Point of Minimum Transportation Cost If the source of raw materials were located at a single point and the market at another single point, the point of least transfer cost would generally lie at the market or at the supply, depending upon whether the product was weight- gaining or weight-losing; however, the market is not a point but an area, and the source of supply is either a series of points or an area. weber's location theory could not over— come this difficulty, and he was limited to a three-point triangulation analysis. Keefer,l in 1932, solved this problem by constructing a market area in a plane and placing BB shot at each market point in proportion to the weight of product shipped. The point at which the model could be balanced was the center for distribution. This did not allow for any variation in freight rates between inbound products. Other methods have also been applied to this problem and each has 1K. B. Keefer, "Easy Way to Determine the Center of Distribution," Food Industry, V61. 6 (October, 1934), pp. 450-51. its advantages and limitations. The grid analysis method used in this study is an alegbraic determination of a weighted average of all trans- portation costs for tonnages of inbound and outbound products. The factors needed to determine a minimum transfer cost point are: (l) the weight of inbound raw materials, (2) the weight of outbound finished product, (3) the transportation rate on the finished product, (4) the transportation rate on the raw materials, and (5) the location of supply and distribution points. To facilitate explanation of this method, a simplified example will be used, based upon a hypothetical market area and sales map. The sales map of Figure 1 shows the three sales territories and the respective tonnage of product delivered to each. A 55 Ton B C 75 Ton 60 Ton Figure 1.1 A Hypothetical Sales Map 10 Sales are assumed to be evenly distributed within each territory so that any subdivision would result in homogeneous areas within a territory. This market area map is then placed in the positive quadrant of a rectangular coordinate system and a grid overlay is placed upon it as illustrated in Figure 1.2. Y 1 2 3 4 2 25 30 5///// TM 25 I 15 35 .m 60 . /} 0 \\\Lv ' \\ ’// x Figure 1.2. A Grid Overlay on a Hypothetical Sales Map The size of a grid element1 is entirely arbitrary, but should be selected to correspond closely to the sales territory boundaries. More detail and exactness may be obtained from smaller grid elements, but the accuracy is limited by the detail available from the sales records. With the grid overlay 1The word grid is used to mean the entire system of' intersecting lines, while a grid element refers to the smallest area delineated by the grid lines. ll placed in the coordinate system, every point on the map may be located as a vertical and horizontal distance from the origin (0). In Figure 1.2, the grid elements are two miles square and the center of each grid element is one, three, five, or seven miles east and one or three miles north of the origin. By computing the sales, given in Figure 1.1, on a square mile basis, total sales‘for each grid element may be obtained on the assumption that distribution is uniform through- out each sales area. This figure is shown in each grid element in Figure 1.2, and for purposes of computation is assumed to be concentrated at the center of each. The ton mile center may now be found by the following formulas: A ZTRDR A ZIKDK H = ET and V - 2T R K where: A . . H = the Y coordinate of the pOint A . . V = the X coordinate of the pOint TR = the sum of the quantities in row R T . . . K = the sum of the quantities in column K D . . R = the Y coordinate of the center of each grid element D K = the X coordinate of the center of each grid element 12 Substituting the values from Figure 2 into the formula AH _ (5+25+30)3+(15+35+25+60)1 ’ 5 + 25 + 30 + 15 + 35 + 25 + 60 = 1.6 miles This is the distance from the origin to the horizontal axis of the ton mile center. Substituting values in the formula for determining the vertical axis gives: AV = (o + 15L 1 + (5 + 35) 3 + (25 + 25) 5 + (30 + 60) 7 _ 5 2 i o + 15 + 5 + 35 + 25 + 25 + 30 + 60 ‘ ° m This is the distance from the origin to the vertical axis of the ton mile center. The intersection of these two axes is the ton mile center (point m on Figure 1.2) where total cost of distribution is minimized. Introduction of a constant freight rate will not alter the point since it will multiply . both numerator and denominator of both formulas by the constant rate. The next step is to introduce the inbound quantities into the solution to determine the point where transportation in terms of ton miles is minimized for both inbound and outbound products. This is done by expanding the formula, using the lower case subscripts r and k to represent inbound quantities, as follows: E 13 AH _ 2TRDR + 2TrDr _ Z + TR ZTr AV - 2T‘KDIK + ZTka Z Z TK + T‘k Continuing with the example, Figure 1.3 shows inbound quantities plotted on the sales grid and represented by a circled number. Y] 1 2 3 4 5 25 30 n .p. 25 l 15 35 .m 60 Figure 1.3. A Grid Map showing Outbound and Inbound Quantities and the Least Cost Transportation Center. Substituting these values in the formula, the new ton mile center becomes: _ A = (5 + 25 + 30) 3+ (15 + 35 + 25 + 60) 1 + (500) 3 + (29) 1: H 5 + 25 + 30 + 15 + 35 + 25 + 60 + 500 + 20 180 + 135 + 1500 + 20 _ 1835 195 + 520 715 14 A _ 985 + 500 + 60 _ 1545 _ 2 2 v ‘ 195 + 520 " 715 ' ‘ This point is represented by "n" on Figure 1.3. In this example, the industry is a weight-losing industry, with distribution costs of less importance than costs of assembling raw materials. If more than one source of any raw material is available at competitive rates, it would be necessary to solve the location problem more than once using the alternative sources. In most cases, the best sources of the major ingredients that would be used in sufficient quantity to affect location can be determined by inspection of rates to the general area under consideration. If this cannot be ascertained, the center could be determined for each alternative source and a total cost computation could be used to determine which source would maximize profits. Ingredients located outside the market area are plotted at their point of entry into the grid system, and location determined as if they were purchased at the center of that grid element Where it enters. The remaining factor to be included in the formula is the rate at which the materials move to and from the manufacturing point. By multiplying each quantity by its particular freight rate ("C"), the preceding formula becomes: 15 ET D C. + 2T D C. A _ R R i r rgl H _ 2T c. ZTC. R i r j . + 2 D . A = ZTKDKcl Tk kCl + V ZTKCi ZTij Where Ci is the ton mile rate for outbound commodities and the Cj's are the respective rates for each inbound material. Using thirty cents/ton mile as the transportation rate on outbound materials, twenty cents/ton mile for the raw material located in grid “1,1," and twenty—five cents/ton mile for the raw material in grid "2,1" (Figure 1.3), the formula becomes: A _ (60) (3) (.30) + (135) (1) L30) + (500) (3) (.20) + (20) (1) H ’ (60) (.30) + (135) (.30) + (500) (.20) + (20) (.25) '25 = 399.5 = 2.4 miles (287 (.30) + (500) (.20) + (60) (.25) _ 419.5 Av = (195) (.30) + (500) (.20) + (20) (.25)“ 163.5 = 2'6 miles' Since transportation rate in this example was greater for the finished product than for the raw materials, the outbound product exerted a greater influence on the location than it did in the equal rates model. The center moved from a locus of (2.6, 2.2) to (2.4, 2.6). Referring back to Figure 1.3, this moves the center further from the raw materials and closer to the center of demand (point P, Figure 1.3). 16 Alternate Site Cost Computations These computations were made on the basis of constant linear freight rates on each commodity. If this assumption is relaxed, the center becomes only an approximation of the optimum location and provides a basis for determining total transportation costs. From this point a method of "total cost at alternate sites" must be used to establish an exact point where transportation is minimized. Starting at the approximate point located previously, a move is made into the next freight rate area in any arbitrarily selected direction. Total cost is computed at each alternate site in one direction until a minimimum is reached. Then successive moves are made along an axis perpendicular to this point until total cost is minimized on this axis. This method is continued until a point is reached where a move in any direction will increase total costs. Referring to Figure 1.4, this method would proceed as follows: Let A be the ton mile center. Compute total transportation cost using actual rates. Move to position B and compute total transportation costs again. D L A >e B 4%C “F— E ° 1: "El-)6) Figure 1.4. Alternate Site Locations 17 If this figure is smaller, move to C. If total cost increases at C, then B is the minimum point on this axis. Move to position D along a perpendicular and compute total costs again. If it is higher, reverse along the same axis through B to E. Continued moves and computations will finally move the location to Point I. Any further moves in any direction would increase total cost of transportation. While this method appears clumsy, in actual situations it is quite simple. First, because freight rates are fairly constant over large areas and rates tend to be a function of distance. Secondly, visual inspection of a rate map will usually determine only a few feasible alternative locations for which to compute total cost of transportation. Once the ton mile center is computed it would only be necessary to determine total costs at that point and then for a few alternate sites which afford possible rate advantages.l 1The method and formulas shown in this chapter were obtained from Smykay, Bowersox, and Mossman, Physical Distribution Management (New Ybrk: McMillan Co., 1961). 18 CHAPTER II CONSUMPTION OF MANUFACTURED FEEDS IN MICHIGAN Use of Sales Data for Determining Output of Manufactured Feeds Determination of the demand center for manufactured live- stock feeds required an analysis of present distribution and demand patterns in Michigan. Since the relationship between feed consumption and livestock numbers is normally consistent, past sales records are basic determinants of future demand patterns. Although livestock distribution and numbers are constantly changing, fluctuations are not from zero to maximum but follow a gradual and fairly consistent pattern. There- fore, an analysis of past feed production and sales was needed to be used as a guide for establishing feed consumption patterns and trends. Then by analyzing livestock concentrations and distribution throughout the State, a potential feed market could be established and projected to 1965. Obtaining the Data An attempt was made to obtain a yearly summary of Michigan feed sales from the Feed Registration Department of the State Department of Agriculture. However, all feeds in Michigan are licensed by brand only and no record is kept of feed l9 tonnages. All major feed associations and publications were also contacted, but no information was available that had been sufficiently classified or accurately compiled. There- fore, a survey questionnaire1 was prepared to obtain this information directly from the feed manufacturers. It was designed to provide the following information: 1. The amount of commercial feed manufactured by plants in Michigan. 2. The amount of commercial feed sold in Michigan. 3. The amount of grain purchased outside Michigan and resold as feed within the State. 4. A classification of all feed sold indicating the proportion of complete feeds and protein supplements2 produced from each class of livestock. 5. The present situation and future expectations, by the feed manufacturers, regarding the per cent of feed sold as pellets vs. meal, and bulk vs. bag. 6. The concentration of feed sales by county areas. 1See Appendix A. 2“Protein supplement" includes all commercially prepared feed containing more than 20% protein and used to supple- ment the grain in livestock rations. "Complete feed" or "mixed feed" refers to commercially prepared feeds containing both grain and protein supplements. 20 Prior to mailing the questionnaires, personal interviews were conducted with ten plant managers as a means of refining the questionnaire structure and determining the attitudes of plant managers toward the various questions and the study in general. As a result of the interviews, the questionnaire was altered to clarify the questions, simplify the necessary computations and adapt the questionnaire to the bookkeeping methods of the firms being contacted. A list of four hundred seventy companies was compiled from the records of the Feed Registration Department, Michigan Department of Agriculture,1 showing the address and number of brands registered for each company. The list was then divided into twentyefive large companies and four hundred forty-five small ones on the basis of the number of brands licensed. While this criterion was proven to be not entirely accurate, by the returned questionnaires, it still provided an approximate division to facilitate handling and classifi- cation. After adjustments were made in this classification a total of twenty companies remained as major contributors to Michigan feed production and four hundred fifty in the group of smaller plants. lBrand registration records for 1959 from William Geagley Laboratories, East Lansing, Michigan 21 A personal letter was sent with each questionnaire to the twenty-five major companies, and a follow-up letter to the non- reSpondents was used in an attempt to obtain 100% response. However, only fifteen of the twenty companies on the list, were willing to provide the necessary data.1 Of the four hundred fifty questionnaires sent to the smaller companies, there Was a total response of seventy-one. Sixteen of these were discarded due to inadequate, or obviously inaccurate or incomplete information. The remaining fifty—five valid returns, representing a twelve percent response, were assumed to be an accurate sample of the entire group. This assumption was strengthened by the observation that there was a geographical distribution of sales throughout the State in an approximate relationship to the numbers of livestock in each area. Also, the reports indicated a cross section of the various size- strata ranging from an annual production of less than 100 tons to more than 4,000 tons. Estimation of Total Feed Consumption In order to determine the total feed produced for Michigan consumption, the results of each questionnaire were recorded 1One other company replied after tabulation was completed. Their figures compared closely enough to the estimate made for them so that no change in totals and averages were necessary. 22 and totaled by class of feed for each of the two categories of plant size. From these totals, averages were obtained for the large plants by class of feed, and multiplied by the twenty plants in this group. The averages, in the small plant category, were multiplied by four hundred fifty, giving an estimated total for each class of feed by small and large plant categories. These two sets of totals were then combined to obtain an estimated total tonnage of feed produced for Michigan by type of feed and class of livestock as shown in Table 2.1. The distribution of feed, shown in Table 2.1, indicates that turkey feeds and other poultry feeds account for 7.4% and 38.1%, respectively, of all feeds, for a total of 45.5% for all poultry. Dairy feed ranks next with 23.3% of all feeds being sold as dairy feed. Hog feed and beef cattle feed follow in that order with 16.9% and 11.8% respectively. The remaining 2.2% is made up of specialty feeds and sheep feeds. Due to high concentrate requirements and industry specialization, poultry (including turkeys) comprise over half of the market for complete mixed feeds. This indicates that the market for manufactured complete rations will be near the areas of poultry concentrations. The relationships of other classes of livestock feeds may be seen in Table 2.1. 23 . .,-....-1-.._._.r=;., .ctmt mo>use on. Scum ooozoauo .oum_m oar no“ :qoiol do aafluno 0:5 one sonsmHm awoswu .mgwnmflo a Loqconm uozio was spousoa now moo .znww .-MLJou .uusiorus --;. - .. --1+- :--.siiuiiiil s.~3 cos sow.esm can mes.hmm oos muh.hnm “some use n.54 N.N -4.Ns o.m smm.s m.m sum.m «guano m.ha N.o eam.s s.o cam . 3.0 oNo.H amass e.h~ m.ss oas.ee. $.45 som.ws 5.5 cam.ms News s.se «.mm nom.sma m.m~ nna.a~ a.mw ohm.em sauna o.mm a.o~ Hoe.mm 5.5N one so “.41 Dem am no: n.ae s.sm esm.msm N.mm moa.aoH 5.33 shm.eos anussoa Lasso s.an e.m msa_se a.“ sga.ns m.s5 mnm 3N assess tomb amCOH mszoamaumsm emcee oomw .zsoo occcH some c.6sasoo ii: 3. O6.L z in ca at e as.oe.mo N we ”Hem zoom «0 m.w :.woom H DoH mucosoflamdm :wououm 22mm enoaaaou Moo. o>w4 mo unsflm secumo>wg mo mango was poem uo mama so sst£0wz a“ uaom pooh HmwuueEEoo H.N mamcg 24 Complete feed for each class of livestock is computed as a percent of total feed manufactured for that class and is shown in Column 7, Table 2.1. It is noteworthy that 57.8% of all turkey feed is in the form of complete rations. Hog and beef feeds rank lowest with less than 30% of the feed being sold as a complete ration. Sheep feeds have the largest proportion, with 77.5% of all commercial feeds sold being in the form of a complete feed. Technical difficulties of feeding sheep, balancing their rations, and controlling entertoxemia, are partial explanations of this high figure. The survey also indicated that the feed produced by the major companies was composed of a larger proportion of protein supplements than was true for the minor companies. Since all but five of the larger companies were located outside the State of Michigan, transportation costs on bulky feeds placed them at a marketing disadvantage compared to the locally operated plant using local grains. The feed production for Michigan was also classified according to its source--within the State or outside the State. These results, shown in Table 2.2, indicate a large proportion of Michigan feed products are manufactured outside the State. None of the companies located outside Michigan reported purchasing grain from Michigan; therefore, either 25 -lv '.'C|'\1‘!>5Jfi newssoEoo Had newcomEou owned Lowscofioo Hgmfim nauseous assuage newsmzaou Hg< newcomeoo owumg newsmmsoo damsw aawaauuz cases: mecca swv .mwuwmddowuuosv tosusnou can so oouuooou nowuwucmsv aoDOO can L L I: mmm.sea ~n¢.¢m oam.oms Nno.m ems n35.6s nsm.mu som.~m woo.~s mam.HsH sam.mm sao.s~s ~o¢.e can use.ss Hwe.a~ L mus.~n sma.0s sam.w wan oom.~ mas 0 mm an we 3~N.s am3.~s mes.mm Nem.m~ Ham ans oaa.o oo~.¢s sma.m Haa.mm Nae.- amn.aH nnH.H~ m. «an esm.H oao.m em~.~ amm.oN ma~.am mos.NN mas.hs new Am o~n.m «so.ss mo~.s nme.ns mpuom .onasm «poem ouoHosoo swououm Ham .HH4 -< umaua- momma ovum:- ausma mama; anusnoa - coaumuoa was .hsmnaou we onwm .oomh we mohk an unawanuwz aw oaom poem flewuuussoo N.N mqmcH - i a .1 .1 iii.- il ii. . _ onwm can sowumUOMN 26 the grain moves from Michigan to manufacturing points in an indirect manner, or the large Michigan exports of feed grains1 move into markets other than livestock feed. The survey replies also indicated a definite upward trend in sales of both pelleted and bulk feeds. The averages for the two groups are listed in Table 2.3 indicating an expected increase by 1965 from 18.6% to 32.0% in pelleted feed sales, and an increase from 19.7% to 47.5% in bulk feed sales. Estimates for 1965 by the major companies ranged from 7% to 70% for pelleted feed, and from 10% to 90% for bulk feeds. The smaller companies gave estimates for 1965 ranging from 0% to 100% to be sold as pelleted feed and 0% to 95% sold in bulk. There was a much wider dispersion of estimates in the small companies than in the large ones and a higher percent of the large companies responded to the question than did the small ones, indicating, perhaps, a greater awareness and concern of future adjustments and pending changes. 1U.S. Census data shows 43,891,000 bu. of corn sold in 1959 excluding inter-farm sales. This was a 70% increase over the amount reported in the 1954 census report. 27 TABLE 2.3 Bulk Feed Deliveries and Pelleted Feeds Sold as a Percent of Total Feed, by Size of Company, for 1959 and 1965 Size of Company Pelleted Bulk 1959 1965a 1959 1965a Large Companies 24.3 37.3 28.0 46.5 Small Companies 12.8 26.8 11.4 48.5 pverage of Above Categories 18.6 32.0 19.7 47.5 aEstimated by survey respondents. In so far as possible, data were compared with estimates from other sources such as the Feedstuffs table1 and USDA figures2 to obtain an indication of the plausibility of the computed totals. The only major deviation appeared to be in the complete rations for cattle on feed which showed a dis- crepancy throughout the study. This quantity was far above the expected figure for cattle on feed. No error could be found in the data but some of the firms might have reported complete feeds that were custom ground or mixed for the 1Reprints from Consumption of Formula Feeds. Feedstuffs Magazine, Miller Publishing Company, Minneapolis, Minnesota. Table from 1952-58 with breakdown of totals and types of feed consumed by States. 2U.S.D.A. Production Research Report No. 21. Consumption of Feed by Livestock, 1909-1956. 28 farmers. Since the number of companies reporting feed sold for beef cattle was small, it is possible that the estimates are not as reliable as for the other classifications. Since no concrete justification could be found for altering this figure, it was accepted as reported. 29 CHAPTER III PROJECTION OF MICHIGAN LIVESTOCK FEED CONSUMPTION Classification and Sources of Data The preceding chapter presented an estimate of the actual manufactured feed sold in Michigan in 1959. The purpose of this chapter is to project this figure to 1965 as a basis for a market oriented location study. Composition and distribution of feed consumption for the State will not remain static while a location study is made, a site selected, and a plant built and put into operation. A business organized on yesterday's demand patterns would be out of date before it was completed. An actual study must be based on future expectations with sufficient versatility to adjust to a continuing change. A projection period of six years was chosen for this study on the assumption that underlying conditions would not radically change and present trends would continue. This period is short enough to be comparatively stable while providing sufficient time to develop a planned program. The first step was to select the livestock that exert an influence upon the manufactured feed industry and classify it into types. It was necessary that data be available for 30 these livestock classes by counties on an annual basis. The following classes were selected: 1. Dairy cattle 2. Cattle on feed 3. Other cattle 4. Sows farrowed 5. Lambs marketed 6. Stock sheep 7. Hens and pullets 8. Broilers marketed 9. Turkeys raised. Michigan Agricultural Statistics was used as the main source of data for livestock on hand January 1 of each year. The exceptions to this source were cattle on feed, lambs marketed, broilers, and turkeys. Since these classes were not recorded by county, other sources had to be used to approximate their population. The total numbers of cattle on feed and lambs marketed for the State, were taken from Michigan Agricultural Statistics but county distribution was determined on a percentage basis by using approximations from a confidential sample survey on beef cattle and wool marketings from feeder lambs. Broiler and turkey numbers were obtained from Census data. 31 Method of Projection After determining the classifications and sources of data for each, livestock numbers were projected for the six- year period from 1959 to 1965. The ideal would have been a prediction of numbers, of each classification, for 1965 using a multiple regression equation with several independent variables; such as, livestock prices, feed prices, feed grain supplies, and present level of production. However, no prediction of this type was available, and the research and computation necessary for making one by counties was beyond the scope of this study. Regardless of the complexity of the predicting equation, it would not have retained the same accuracy for every county, since the independent variables which determine livestock production would be different in number and weight for different areas. The straight-line projection was selected as an objective and consistent method, with full knowledge of the limitations and broad assumptions required by this procedure. No attempt was made to adjust the computed figures on the basis of cycles, reversing trends, or knowledge of possible external forces acting contrary to the mathematical projection. Data for the twelve-year period from 1947 to 1959 were used to determine the projected numbers for 1965. In using this linear regression the assumption had 32 to be made that livestock population was a linear function of time. Empirically, this is not completely accurate, but it is a good approximation. Other assumptions necessitated by this method are: that technology of livestock production will improve at a constant rate; that governmentalerograms will involve no major changes; that world situation and demand conditions will be consistent with previous situations; and that the organization of farming will continue at the present rate of advancement. Each class of livestock was projected individually and, so far as possible, on an equivalent basis with every other class. Dairy cattle, as defined by Michigan Agricultural Statistics was taken directly from the bulletin as the number on hand January 1 of each year. The projection was made for each county and recorded as the number on hand January 1, 1965. Hens and pullets, stock sheep, and cattle other than dairy, were done in a similar manner. Broilers marketed, and turkeys raised were not available on a county basis in Michigan Agricultural Statistics so had to be obtained from Census data. Considering the rapid changes that have been taking place in these two industries, it was decided that no realistic trend could be established on the basis of the Census data. Instead, future production was 33 assumed to be more accurately represented by the 1959 situation than by a trend line over the past ten years with only three observations during the period. The number of birds in each county in 1959 was used as the number for 1965. Since broilers and turkeys have a rather small role in total feed consumption, and that in only a few counties, this assumption will have little effect upon the results of the study. Cattle on feed were not recorded by county, but a trend was indicated in the yearly figures for the State. For this reason, a 1959 county survey of cattle on feed was used to determine the proportionate number in each county. Cattle on feed was then projected on a State basis and the previously determined percent for each county was applied to the 1965 State estimate. This precluded any possibility of a change in county distribution, but did take account of the upward trend in numbers of fed cattle. Lambs marketed were similar to cattle on feed in that no county information was available on this classification. The only available indication of the distribution by county was the Production Marketing Association records of wool incentive payments made on slaughter lambs.1 By using the pounds of 1Appendix B. 34 wool eligible for payment in 1959, the county concentration was determined as a percent of the State figure. Lambs marketed and home slaughter for the state were combined and projected to 1965. This figure was then distributed over the state on the basis of the predetermined percent for each county. Sows farrowed were selected to represent the number of hogs consuming feed on farms, because data were available on a county basis and would give a more accurate picture of feed consumption than would a yearly count of numbers on hand January 1 of each year. After dairy cattle and cattle on feed were projected, all cattle remaining were grouped together as other cattle. It would have been possible to have separated beef cows from this group and further subdivided the remaining categories. However, the improvement in feed consumption figures due to further refinements was offset by greater inaccuracies and computational difficulties resulting from less adequate data on these groups. Analysis of Livestock Distribution and Trends The projection of dairy cattle numbers (Figure 3.1) shows a steady decline in numbers, despite some fluctuation above 35 amma ou mama ousuasoapw< «o uaoauuuaoa suwusoqz mofiumwuwum HonsuH50fluw< cmwflnofiz "sumo oflmmm mo ouusom mama ou emuomnoum can mnma on Nina.” EOHM nfldeLOHE #3.” 0Huufi0 hHHflQ MO muwflgz m0 UCQHH oaom OHDth .3. ..... ”L ...Q .1 , .L 7,. 1f .. J 3.. {a "\nu mph (3,... _..u Of 7.... mg n we?“ I i 1.1 l 4 S i J‘ 1 <_ 4 1 .1 + “O 100K inXum .Onm 1nXuo .mfimo Aunoi MOZwq «o N m mmA.muwsqom >91. -v- r a0 mmmdu seam undo names mood ouasdumm eousesou nomad coca :H upwEEoo .umm ofiom pooh Mo meow m~0m comm mo mach muoneaz x00u3c>ua I "§!.-I‘$ D it!!! P'IIV-‘.I comm no make cam xuoumobwq mo mango ha .momfl a“ wasnmcoo boom demon mo ucmu Ham 4 m4 mgom comm vousuumwmcm: mo mumEuumm ~.n uAnwd me couzilooa moumuuzoucou :aououm mo .9 ooo.¢n au«3 moon Hduoa mo .8 coo.maa mo :wuuo cc com: canons aumuusQusoo cwououm mo .9 ooo.o~¢ sues moon «snow mo .8 coo.o~n mo and «use as 20m: semi“: homum Dumam Eoum mucfiuuaid moooe moon: woa.c no¢.-~ 3:3.omm Henna ovum mousuuomszuz ume.~ wme.a nme.~ oc¢.om oas.mea deuce muoseoum guess 93.¢N ooosu n~.~ mum.m ooo.;~ «.m menace moapsaom a «no: name 3a.; an.» as.“ Nam.“ asc.~a a.“ mousse o=0umuxna on.“ om.k .mo.m a¢..m oea.a~ k.s onuuueu Lao: amamwz< a -- s -- mn~.o qeu.m ooo.ou e.e esaeummeaa seas muamwu< Lao: segue Om.o~ Omom coon mmw.m 009.6a ¢.¢ awouuon minnow anon 056.220“. 5 -u a s: e~.n one.u ooa.ua m.« oneuaeo mommeeor om.“ an.“ m~.n sea.os om~.am s.ma onmufieo same smashes gee a I: s It boom omN.m coo.o~ m.m onduwzo onwammogm fidfioamUwQ H603 :UUSHQ :ou. om.mw amok» n~.n wmn.wN can.~m~ ¢.am oncognu chfiavnar Moon Mao cmoemom Non modesdom muoaafiuuwn mum“ ow non“ :« anneaueeo meson .um use: coexausoo .wmz some «0 .nmz some unease cheese azmHammcmH an on cues anemone you you has has Manon «soa\oumm o=0H\muma mamas“; omovooz mGOH nmooooz @309 m wo R. .uouneo coHuoDHOQmacuH uuoo momma pseusafioo aw .aoumm ugmwoum one .wmuwsvom mowmssou .uco«umooq acoqmounau .u.n mqn<fi coma 80 Determining the Point of Minimum Transportation Cost-Linear Transportation Rates The next step in relaxing assumptions was to let trans- portation rates vary between products and between location, but require them to be linear through the origin. While this assumption is seldom strictly correct in the real world it is approximated. While not linear, rates are usually an increasing function of distance, tending to increase at a decreasing rate with a positive intercept. The exact shape of the transportation function depends upon the medium under consideration and the distance range over which the function is plotted. Figure 5.1 is a graphic presentation of the three main modes of transportation. 30 25 TRUCK 20 . RAILROAD 15 10 —-—'“" 0 100 200 300 400 500 Figure 5.1. Transportation Gradients for the Lower Mississippi Valley Area, 1939 to 1940.1 Edgar M. Hoover, Location of Economic Activity (New York: McGraw-Hill, 1948). Figure 2.1, p. 23. 81 Since no quoted rates were available as rates per ton mile, an approximation was made by dividing ton rates by the mileage over which they applied. These figures are Shown in Table 5.2. Computing the point of minimum transportation cost under these assumptions provided a location six miles west of Charlotte in Eaton County. The effect on the location of the inbound materials, resulted in movement south and west of the ton mile center of distribution. The tonnages and their locations, which were used in the computation, are shown in Table 5.2. All ingredients located outside the State were plotted at the center of the grid element at which they entered, and transportation rate was based upon the computed ton mile rate shown in Table 5.2. Transpor- tation costs of feed grain ingredients were computed from the ton mile center of feed grain equivalent shown on map 5.3. Transportation rates on grain products and processed feed were obtained by computation from the previously mentioned plant study and were linear approximations rather than existing, effective rates. The use of the ton mile center as the location of grain ingredients, requires the assumption that purchases of grain will be proportional to grain production in every grid element. This assumption is very unrealistic in view of the quantity 82 of grain sold in each county. In most of the south central counties, producers in an area twenty-four miles in diameter would sell more grain products than would be needed by the plant.1 If this plant succeeds in purchasing only 25% of the total grain sold it would have to enlarge its purchasing market to thirty-six miles in diameter. If only 10% of the total grain sold can be taken by this plant then it requires an area with a diameter of one hundred miles. This was computed on the basis of a Fowler location and the exact mileage would vary with each location. The production per square mile is sufficient in every county in this area to provide the necessary grain products within a relatively small distance. If grain products are considered an ubiquitous substance, and thus of no consequence in the location, the ton mile center is changed so slightly as to have no importance. Instead of being 85.5 miles north and 92.4 miles east of the origin as it is when including grain products, the least- cost transportation center is located 85.2 miles north and 91.1 miles east with grain excluded. 1Grain sales: 1959 Census of Agriculture 83 Determining the Point of Least Transportation Cost —- Non—Linear Transportation Rates Only one assumption remains to be relaxed in this study. Linear transportation rates on ingredients are unrealistic in most cases and can usually provide only a general area for location. The preceding steps in which one assumption was relaxed at a time, were necessary to limit the scope of the problem to manageable dimensions. Transportation rates were changed from linear estimates to quoted rates and the problem then became one of determining the minimum total cost of transportation at alternate sites at the effective rate for each area. While rates on processed feeds and grain are usually based on zoning areas, the actual cost to the company for delivery of a given tonnage must be a direct function of distance. In other situations, the feed is priced as delivered to the retail outlet. This only means that the cost is absorbed by the distributing firm, averaged out over all deliveries, and reflected in the price of the feed. Grain products present a similar situation when purchased locally and delivered by company owned facilities. It was as realistic to assume a ton mile rate for delivery of feed and grain as to assume a constant charge regardless of distance or area freight rates. Therefore, the same freight 84 rate for processed feed was used in computing total costs, as was used under the previous assumption of all rates linear. As explained previously,l grain products were not considered to affect location and total costs could not be determined without knowing the exact point where grains would be pur- chased, so no charge was made for grain movements. The possibility of transportation reduction by back hauls was also ignored since it would have required a more detailed study of location and routings than is feasible here. The situation in ingredient transportation was entirely different. Here the cost to the manufacturing firm was not a direct function of distance. Many factors take precedence over mileage in determining transport costs. Transit privileges and balances, competitive facilities, accessi- bility of the location, and many other factors function to set freight rates. The freight charges used for ingredient products at alternate locations were obtained by special permission from a feed manufacturing firm which had received bids on moving various ingredients between several locations. While this material cannot be reproduced here these rates were selected 1Page 83. 85 upon the basis of their reality. Any company contemplating location would face the specific rates and situations appli— cable in each case. Water rates were originally believed to offer an opportunity for freight reductions and at the beginning of the study were expected to influence the location. Replies were received from eleven different sources as the result of a request for information from all the major barge and overseas water freight companies, as well as Port Authorities, Interstate Commerce Commission, and others. In all cases the replies indicated that water transport would not be feasible without a volume three or four times the estimated tonnages of ingredients needed. An information sheet in Appendix D summarizes the major points of all the replies. It was included in a letter from the Tennessee Valley Authority and was prepared by their Navigation Economics Branch. The freight rate chart indicated no rate advantage to any of the alternative sites except Charlotte. Here the advantage was on only a few items and by only a few cents per hundred- weight. Since the Fowler location minimized distribution costs, an alternative site must have a sufficient rate advantage on ingredients to overcome its distribution cost disadvantage. Since Charlotte was the only point having any rate advantage 86 it was only necessary to compute total costs at Fowler and compare them with total costs at Charlotte. The distance from Fowler to the center of every grid element was multiplied by the estimated tonnage of feed from that grid element. The summation of these figures was the total ton miles of distribution of manufactured feed. Total cost of distribution was computed by multiplying ton miles by the freight rate of four cents per ton-mile. In most cases ingredients were assumed to be shipped from the point with the minimum rate to Fowler.2 One exception to this was the case of 44% soybean oil meal from Rossford, Ohio. Here the differential in rates was sufficient to have an effect upon location. Investigation of this showed that price quotations from Rossford were sufficiently higher to more than make up this difference and in fact very little soybean meal is shipped into this area from Rossford. Therefore, a Chicago rate was used even though Rossford offered what appeared to be a rate advantage. Other ingredients were also considered to be shipped from the logical point of lowest rate, even though there might have been other impractical shipping points with lower rates. 1This rate is the computed estimate shown in Table 5.2. Rates were given to St. Johns but were identical to Fowler rates so far as could be determined. 87 Total transportation cost was computed for inbound products by multiplying the tonnage of each group of ingredients by the respective rate per ton. Total costs of inbound added to total costs of outbound products, gave the total cost of transportation1 for a plant located at Fowler. These figures are shown in Table 5.3. As the only alternate location offering a rate advantage, Charlotte was used as an alternate site and total transpor- tation costs were computed in the same way as for Fowler. As shown in Table 5.3, the effect of decreased freight rates on ingredients was more than offset by the increase in distance from the plant to distribution-consumption points. If soybean meal had been priced at Rossford on an equal basis with the Decatur plant price the rate advantage on soybean oil meal shipped to Charlotte would have been sufficient to force the least—cost location to Charlotte rather than Fowler. With the rate structure as used in this study, however, the ton mile center of distribution was the determining factor in the final location. This analysis has provided a plant location where total lY'Total cost of transportation" means total of all transport costs considered to affect the location. As mentioned previously (page 83) grain ingredients were omitted as were several minor ingredients. 88 .mcou scum Museum meawzu:09 we madman many 0 om.“ magma Ecuma .muumu mason .um ou amuuucoow whoa mouse uoasomm (H. mmo.~muw ou~.eo»w uaou uuoamsmuw Amuoy smm.sn am.qw s-.m as-.om no.q~ oku.m «possess; scum Ham: ends ano.aa as.» ~nn.~ mm.ma om.s Nam.“ moneys scum meanness; nua.s~ am.m mem.m oun.eu on.k nem.m omeowso gone Saws «mamma4 ken.sn o“.sa smo.n ans.mm ah.m smm.m awesome scum magnum use: ommufiso souwuamos mno.eaz am.“ «us.mz mmo.¢aa om.“ Ne.ms saunas .amua ..mnuez nnz.osa an.“ moo.- mms.goa on.“ moo.- .ouauuso zone «on HNH.kHH om.k eso.sa ~«~.NHH on.“ seo.sa omauuso scum gee ado: somehow moon mounuommssmz mok.uanw so. » omso.man.k nea.konw so. a omkm.aks.k «a nodussuuumen umou amuoe asoaxoumd :09 umoo “muck soH\mumm mcoa a A a . m ; eummmuuenow .um usoMumqu awaken can «Ducaumsu um acaumuuonmseua mo umoo "muck 89 costs of transportation would be minimized. The hypothetical plant used for the example was producing 112,400 tons of livestock feed to be distributed over the lower peninsula in proportion to the livestock population. No consideration has been given to a multiple plant location, or the conflict between economies of scale and diseconomies of distribution costs from a single location. A study done by Bresike and Askew1 indicates a rapidly declining average operating cost curve from O to 10,000 tons of annual output. After this point the curve tends to flatten out and much less economy to scale is available at higher levels of output (Figure 5.2). If average total costs are considered rather than average operating costs a similar curve is obtained which indicates that most of the scale economies are achieved in plants of about 40,000 tons of output. Phillips2 computed both long run and short run average total cost curves from budget data obtained in the Brensike and Askew study. Many factors of bias are built into this model, such as age of plant, relative capacity of operations, etc., but it serves 1 . . . V. John BrenSike and William R. Askew, Costs of Operating Feed Mills, U.S.D.A. Marketing Research Report No. 79 (Washington, D.C., 1955). 2 . . . . . . Richard Phillips, Empirical Estimates of Cost Functions For Mixed Feed Mills in the Midwest, Journal Paper J-2860, Iowa Agricultural Experiment StatiOn, Ames, Iowa, 1956. 90 to indicate that more than one plant is an economic possibility for a large market area such as that used in this study of Michigan's lower peninsula. $ Per Ton 50 40 30 20 10 0 20 40 60 80 Thousands of Tons Mixed Per Year Figure 5.2. Operating Expenses Related to Volume of Feed Mixed Source: Brensike and Askew, op.cit., p. 23. Summary In this chapter a step by step procedure was followed to determine the minimum transportation location of a hypothetical feed plant. The necessary assumptions that correspond to the final solution are: 1. One plant producing 20% of the anticipated 1965 feed. 91 2. Demand for this firm's product is uniformly and equally distributed over the entire lower peninsula in a constant ratio to total feed consumption. 3. Equal proportion of the market for all classes of livestock. 4. Outbound transportation rates are linear through the origin with respect to distance. 5. Grain products needed will not affect location of a plant of this size. The ton mile center was first computed for distribution of the finished product. Inbound ingredients were then included and the site of minimum tran8portation costs was determined on the basis of linear freight rates. Actual freight rates were then used to determine total costs of transportation to the ton mile center at Fowler and at the alternate site of Charlotte. Since no other locations offered a freight rate advantage, it was deemed unnecessary to compute total cost for more than the one alternate site. The increase in cost of distribution due to movement from the ton mile center makes the system fairly sensitive to locational changes even over small distances. In lieu of knowledge of any large advantages in freight rates in any other locations, Fowler was accepted as the point where total 92 transportation was minimized with the data used in this study. As mentioned previously, any data used in this study is applicable to very few specific cases. Every firm considering location would have its own market distribution, its own source and list of ingredients, its own speciality classes of feed, and its own specific freight rates on all products. 93 CHAPTER VI SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FURTHER STUDY Application to a Specific Plant Study The preceding chapters have presented a method for locating a feed manufacturing plant at a point where total transportation costs are at a minimum. In order to illustrate this method, the location was determined for a hypothetical plant. Since this plant was defined by a set of assumptions specifying market distribution, purchasing policies, plant size, competitive forces, products manufactured, etc., the conclusions resulting from this analysis cannot be accepted for any actual plant. It was used only to facilitate illustration of the complete procedure used in locating the point of minimum transportation cost. An actual feed manufacturing plant considering location or relocation would have to determine the five factors for the formula,1 as they apply to the firm being located. The quantity of outbound materials would be determined by analysis and projection of present or expected sales information. The boundaries of the market would have to be delineated, 1Page 9, Chapter I. 94 the sales potential determined, the effect of competition (in light of the anticipated location) studied, and the type of feeds and potential users analyzed. With the aid of this information, the feed manufacturing firm could prepare a grid map of the projected market as illustrated in Chapter V. Using this sales data, the necessary plant capacity and the total amount of each ingredient needed could be determined. Substitute ingredients and alternative formulas would have to be considered in relation to their effect upon total transportation cost. Transportation rates on processed feed would be partially determined by administrative policy. If common carrier rates are to be used, they can be found by bids from the carriers involved. If delivery by the consumer is to be the policy, delivered costs by competitors must be analyzed to find the effect upon market boundaries. The cost to the manufacturing firm would be in terms of lower prices which must be offered to maintain the volume of sales. If the feed is priced as delivered to the consumer, actual costs of delivery can be used as the rate and will approximate a linear rate per ton mile as discussed in Chapter V. Ingredient transportation rates would have to be determined by a study of freight rate structures and estimates by the 95 carriers involved. The sources of ingredients would depend on not only freight rates but on purchase prices too. When total cost at alternate sites is computed1 it may be necessary to replace freight charge per ton, by total delivered price per ton, if visual inspection is not sufficient to determine the most economical source. Purchases of grain ingredients could be ignored as done in the example2 in Chapter V, unless the ton mile center indicated an area with insufficient local grain supplies. With a grid map of the distribution of the finished product and ingredients, and transportation rates for all products, the formula would determine the least-cost transportation center. This would be only one factor in location and many other facts would have to be taken into consideration besides transportation. Unsolved Aspects of the Least-Cost Transportation Problem Several facets of the least—cost transportation problem have not been dealt with adequately in this study and would require additional analysis before the problem could be completely solved. 1As illustrated in Chapter I, page 16 and Chapter V, page 87. 2See Chapter V, pages 85 and 86. 96 l. A detailed transportation cost study. Transit privileges were completely ignored and could have resulted in selection of a different source of ingredients and a different optimum location of the plant. Transit privileges are not uniform to and from all points and are not in effect in many locations. If the need arises they are usually made available, however. Future changes in transportation rates should also be analyzed. A location on a spur or with only one transport facility, runs the risk of future rate increases in order to maintain a little-used line. A second or third mode of transport to the same location greatly enhances the competitive position of the feed plant. Backhauls within or outside the company should also be given considerable study. Movement of ingredients and finished feed over the same route could result in considerable change in rate structure. 2. Competitive relationships within the market. This factor becomes important in both purchasing and selling aspects of the firm. Size of purchases could influence price in smaller ingredient processing firms and affect the source of supplies. The policies and position of competitive firms becomes a very relevant factor in determining the sales 97 area and distribution. Competition must be considered in the present situation as well as the anticipated changes and retaliatory actions when the new plant is located and put into operation. 3. Multiple plant location. This study was based upon the assumption of one market area served by one plant. It is not only possible but very probable that a company producing 20% of the State feed consumption would minimize total costs by producing at two or more plants. A study of feed mill costs1 indicates that little decrease in average total costs results from expansion above 40,000 tons per year, but the transportation differential would be large with three plants compared to one. Linear programming could probably then be used to determine the optimum combination of plant size and distance of transport. The most economical size of plant might have greater total costs than a smaller plant, if cost distribution increased at a faster rate than the decrease in costs due to larger scale of operations. Profits would be maximized by equating marginal net returns between production costs and transportation costs. lRichard Phillips, Empirical Estimates of Cost Functions for Selected Mixed Feed Mills in the Midwest, Journal Paper J-2860, Iowa Agricultural Experiment Station, Ames, Iowa. 98 While many factors of location have been omitted in this study, the method presented provides a simple, objective evaluation of the major problem of location. Location by this method provides the point where total cost of transpor- tation is miminized. Its major advantages are the ease of computation, applicability to large market areas, and the ability to handle any number of products and freight rates. 99 BIBLIOGRAPHY Books Dunn, Edgar, The Location of Agricultural Production. Gainesville: University of Florida Press, 1954. Greenhut, Melvin L. Plant Location. Chapel Hill: University of North Carolina Press, 1956. Hoover, Edgar M. Location of Economic Activity. New York: McGraw—Hill, 1948. . Location Theory and the Shoe and Leather Industry. Cambridge: Harvard University Press, 1937. Isard, Walter. Location and Space Economy. New YOrk: John Wiley, 1956. Losch, August. The Economics of Location. (Trans. 2nd Edition, revised), New Haven: Yale University Press, 1954. SmYkay, Bowersox, and Mossman, Physical Distribution Management. New York: McMillan Company, 1961. Bowersox, Donald. A Study of Theoretical and Practical Procedures in Plant Location (Unpublished MJA. Thesis, MiChigan State University, 1958). Periodicals and Reports Askew, W. R., Vosloh, C. J. and Brensike, V. J. Case Study of Labor Costs and Efficiencies in Warehousing Formula Feed, Marketing Research Report No. 205, United States Department of Agriculture, November, 1957. Brensike, V. J. and Vosloh, Carl J. Price Spreads for Formulated Poultry Feeds in Illinois. Marketing Research Report No. 378, United States Department of Agriculture, 1960. 100 Phillips, Richard. Empirical Estimates of Cost Functions for Mixed Feed Mills in the Midwest. Journal Paper J-2860, Iowa Agriculture Experiment Station, Ames, Iowa. Volvanis, Stefan. "Losch on Location," American Economic Review, Vbl. 45, Part I, 1955, pp. 637—644. Vosloh, C. J., ASkew, W. R., and Brensike, V.J. Custom Feed Milling in the Midwest, Marketing Research Report No. 273, United States Department of Agriculture. lOl APPENDIX.A Feed Research Questionnaire Used in the Survey of Feed Manufacturing Plants in Michigan Feed Research Questionnaire CONFIDENTIAL Name of Business 102 Business Address 1. How much of the total tonnage of feed manufactured at your plant in 1959 was sold in Michigan as: Complete feed Concentrates (grain and concentrate mixture only POULTRY: Turkey tons tons Other tons tons HOGS tons tons DAIRY tons tons BEEF tons tons SHEEP tons tons OTHER tons tons 2. How many tons of ingredients were sold in 1959? (Do not include concentrates given in question 1.) KIND (indicate total only if available Soybean meal Meat & Bone scraps TOTAL tons tons tons tons tons tons tons -2- 103 3. From what firms did you purchase manufactured feeds in 1959? NAME.AND LOCATION QUANTITY 4. Did you purchase any grain outside Michigan in 1959 for resale as feed How much? CORN tons (or Bu.) OATS tons (or Bu.) BARLEY tons (or Bu.) WHEAT tons (or Bu.) 5. What is your estimate of the proportion of your total feed sold in Michigan as pellets in 1959 ? 1965 7 6. What is your estimate of the proportion of your total feed sold in Michigan, in bulk in 1959 ? 1965 ? 7. Indicate the approximate area of your retail market on the enclosed map of Michigan. 104 APPENDIX B Wool Promotion Fund Deductions and Computations of Numbers of Lambs Marketed by County in Michigan. 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