:fi gt“ ‘1' L J) i‘flm‘fi Mn M—i, V 2mm. ,‘ VA OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circuIation records AN APPROACH TO THE DESIGN OF MANAGEMENT INFORMATION SYSTEMS WITH APPLICATIONS TO FAMINE RELIEF By AIIan Gerard Knapp A DISSERTATION submitted to Michigan State University in partia] fulfiilment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of E1ectrica1 Engineering and Systems Science 1980 6/243? 70 ABSTRACT AN APPROACH TO THE DESIGN OF MANAGEMENT INFORMATION SYSTEMS WITH APPLICATIONS TO FAMINE RELIEF By Allan Gerard Knapp Management Information System (MIS) design often fails to account for the effect that varying qualities of information and associated in— information costs have on the overall system performance. The focus of this dissertation is to develop an approach for ascertaining optimal in- formation quality levels for given budget constraints in large-scale systems. The methodology is applied to the problems encountered by a country experiencing a food shortage. The approach consists of three main components: a computer simula— tion, a cost function, and an Optimization procedure. The computer simulation models the background system in which the information system is imbedded; in this case, the demographic, consumption, and production characteristics of the famine-stricken area. A government decision— making component is also modeled to facilitate examination of policy structure. Overall system performance variables, such as reduction of fatalities and maintenance of high nutritional level, are defined to monitor the effects of changing policies or information quality. An information sampling component is added to the basic simulation model to enable the model's ”true” variable values to be disturbed with SPecific measurement error statistics. Sampling frequency, sampling Allan Gerard Knapp error, and processing delays are applied to model variables, thereby simulating surveillance sampling results received by system managers. The variables being measured in the famine context include nutritional level, consumption, and food storage level and location. The quality of information received by system managers is varied, using the sampling component, and corresponding results on overall system performance studied. The optimization stage can thus specify the ”best” information quality mix, in terms of expected outcomes. To tie the information quality to actual surveillance, processing and transmission design, a cost function is constructed. The design detail is restricted to this cost function development so that relief system simulation can be ap- plied at a macro level. Since increased costs are generally associated with improved information quality, the optimization is performed at several budget constraint levels. This provides comparisons of cost effectiveness of individual information quality parameters. The sampling component and the information quality concept are ef- fective tools for validation of the simulation model and policy struc— ture. Better information levels should lead to better overall system performance. If not, then faulty model or policy structure or the pre- sence of unexpected natural occurrences would be suspected. The approach provides an evaluation tool for determining useful real-world variables to monitor, desirable information quality levels and comparative performance of separate information quality parameters. It will also enable review of expected overall system outcomes in Allan Gerard Knapp situations where the level of crisis, policy structure and information quality are all subject to change. Several general principles for relief efforts emerge from the study: long-term versus short—term fatality reduction goals must be accounted for in distribution policies, the prevailing relationship between rates of consumption and storage patterns should be ascertained, andthelevel of the crisis must be estimated accurately for effective relief performance. The approach draws on techniques and concepts from many fields of study, including information filters and predictors, feedback control, optimal statistical sampling, simulation modeling, experimental design, statistical measurement and optimization algorithms. Portions of the methodology can be applied gainfully, particularly the computer simula- tion as an education tool and on-line decision aid. Modeling and solu- tion techniques are discussed which have general applicability to Management Information Systems. The dissertation concludes with major findings, advantages and disadvantages of the approach and a discussion of further research areas. DEDICATION To my wife, Diane ACKNOWLEDGEMENTS I first wish to thank Dr. Tom Manetsch for his wise counsel, gui- dance, and suggestions in my program and research. Without his timely comments, many unfruitful tangents would have been explored. I also express appreciation to the members of my committee for their teaching and cooperation. The research for this dissertation was funded in part through a research fellowship sponsored by the Midwest University Consortium for International Activities. My wife Diane has been a consistent source of strength and pa- tience. Her typing and editing skills are only a small part of what makes her invaluable to me. I also want to thank my parents and Diane's parents for their unfailing encouragement and support. And this dissertation could not have been completed without the consistent prayers of our many friends. Finally, I thank Barbara Reeves and her band of typists for the marathon project this tome has become. TABLE OF CONTENTS List of Tables ........................ List of Figures ....................... PART I: COMPUTER MODEL AND COST FUNCTION DEVELOPMENT Introduction . ..................... Chapter I: The Problem and the Approach ........ Information System Structure ............ Information for Planners .............. The Approach .................... Summary ...................... Chapter II: The Basic Survival Model .......... The Scenario: A Country Facing a Short Term Famine ............... Important Modeling Features ............ Nutritional Level ............... Death Rates .................. Grain Shortage ................ Emergency Aid to Relatives .......... Food Production ................ Price Level .................. Government Decision Points .......... Relief Strategies ............... Information for Managers ........... Summary ...................... Chapter III: Modeling an Information System ...... Modeling and Evaluation .............. Organization of the Government Component ...... Sampling Component ................. Model Variable Choice ..... _. .. ........ Additional Assumptions and Modifications ...... Summary ...................... Page viii Chapter IV: The Information System Model as an Aid in Policy Development and Model Verification . . ._ ............. A Changed Problem Formulation ........... Information Quality Validation ........ Policy Structure Additions ............. Increase Early Acquisitions .......... Reduce Harvest Acquisitions .......... Alleviate Transport Bottleneck ........ Modeling Changes .................. Principles for Change ............. Rural Consumption ............... Urban Class Consumption ............ Urban Private Storage ............. Famine Relief Implications ............. Chapter V: The Cost Function and Information System Design ................... Cost Function 6(5) ................. Policy Costs . ................... Information System Design ............. Information System Costs ........... Cost Function Characteristics ......... Simplifying Assumptions ............ Nutritional Surveillance Costs ........... Indicators of Acute Malnutrition ....... Relevant Social and Physical Factors in Bangladesh .......... Optimal Survey Costs ............. Consumption and Private Storage Surveillance Costs . Consumption Surveys .............. Private Storage ................ Equation Formats ............... Transmission and Processing Costs ......... Delay Parameter DELD ............. System Additions and Costs .......... Summary . ..................... Chapter VI: Information Filters for System Management Filters and Predictors ............... Testing the a—B Tracker .............. Evaluation Tools ............... Adding the Tracker to the Model ........ Testing by Sampled Variable .......... Testing by Population Class .......... Summary ...................... I07 I07 IIO II7 II9 I22 I23 I26 l27 I32 I34 I40 I40 I42 I44 I45 I46 I50 I53 I56 I60 I62 I64 I65 I74 -'_o' 1 Page Chapter VII: Model Validation ............. I76 Coherence Tests .................. I79 Price Level .................. I80 Conservation of Flow ............. I83 Sensitivity Tests ............... I84 Sampling Component Validation ........... I86 Crisis Level Variation ............... I89 Simulation Interval DT ............... l92 Summary ...................... I95 PART II: OPTIMIZATION APPLICATION .............. I99 Chapter VIII: Optimization Preliminaries ........ l99 Sensitivity Test Design .............. 20l Policy Parameters ............... 202 Test Methods ................. 206 Standard Sensitivity Tests ............. 2IO Performance Function ............. 2I3 Initial Optimization Vector .......... 2I5 Additional Base Vectors ............ 2l7 Observations ................. 2l9 Results .................... 220 Parameter Choice ............... 224 The Complex Algorithm ............... 226 Design Criteria .................. 229 Performance Function Substitute--PERTOT . . . . 229 Crisis Level Variability ........... 232 Algorithm Starting Points ........... 233 Optimization Results ................ 234 Conclusion and Summary ............... 239 Summary .................... 242 Chapter IX: Simulation Optimization .......... 243 The Optimization Problem and Solution Considerations .......... 244 Theoretical Optimization Difficulties ..... 245 Famine Relief and Approach Difficulties . . . . 248 Algorithm Choice Criteria ........... 250 Alternative Solution Methods ............ 25l Single Response Algorithm ........... 25l Regression Surface .............. 253 Search Algorithm ............... :54 Optimization Plan ................. 56 Optimization Constraints ........... 256 Complex Algorithm Parameters ......... Egg Optimization Results and Analysis ......... vi Page Model Validity ................ 265 The Complex Algorithm ............. 266 Translation to Information Quality Terms . . . 273 Policy Results ................ 277 Tracker Results ................ 278 Information System Results .......... 279 Information System Priorities ......... 282 Conclusions and Summary .............. 288 PART III: CONCLUSIONS .................... 29l Chapter X: Results and Summary ............. 29l Major Results ................... 29I Observations on the Approach and the Current Problem ............ 296 Advantages and Disadvantages of the Approach . . . . 297 Topics for Further Research ............ 30l Ties to Other Relief Components ........ 30l Simulation and Modeling ............ 303 Deeper Probles into Covered Topics ...... 306 Summary ...................... 309 Appendix A: Numerical Cost Coefficients ........... 310 Appendix B: FORTRAN Computer Program ............ 3I6 Bibliography ......................... 335 TT__T___TTTTTTTTTTTTTT_T_T_T_T__=TT_T_TTTT_TTIIIIIIIIIIIIIIIIIIIIIIIIIIEEgEEES3" LIST OF TABLES Information quality parameters used for prelimi- nary policy parameter sensitivity tests ...... Relationships among information quality, system alternatives, and costs ........... Error means and standard deviations with the a- B tracker for five Monte Carlo replications at various 8 values . . . . . . . . . .......... T-statistics and acceptance levels for hypothesis tests on means of Table 6.l, B=I.0 versus s=0.l . . . . a-B tracker results with distinct 8 values for five Monte Carlo replications . . . . ...... o-B tracker results by population class ..... Information quality vectors used in sampling compo— nent tracking test . ..... . ...... Original policy parameter list ............ Policy parameters to be used in sensitivity testing . Information quality parameter settings NJ . . Averages and standard deviations of objective values for good and poor information quality stochastic testing . . . . . . ........... . Policy parameter vector P$,. and preliminary sen- sitivity test results . . . . . Base parameters for sensitivity tests . Sensitivity number (STYNUM) results of one-at-a-time sensitivity testing . Complex method parameters and levels used for pre— liminary testing . . . . ............... viii I68 I7I I73 I87 207 208 2II 2I6 2I8 222 230 8.9. 8.l0a. 8.l0b. 9.I. 9.2. 9.3. 9.4. I0.I. A.I. A.2. A.3a. A.4. Optimization algorithm results at three dif- ferent information quality vectors . Policy parameters to be carried to final opti— mization stage ................... Fixed policy parameter values ............ Independent variable vectors 5_and E_with asso— ciated constraint vectors DJ, D2, E4, E2 ...... Complex algorithm parameters for final optimization . . Optimization results ................ Information quality parameters translated to sampling terminology ............ Comparative performance at five points in study . . . . Transmission and processing interpolation points Transmission and processing system cost components Relative cost and population percentages for surveillance calculations . ............. Standard error and per-unit sampling cost for surveillance calculations ........... Fixed cost parameters and variance for total cost calculations . . . ............... 238 238 25I 26I 264 275 294 3II 3II 3I3 3I3 3I5 2.I. 2.2a. 2.2b. 4.2. 4.3. 4.4. 4.5. 5.I. 7.I. 7.2. 7.3. 7.4. 7.5. 7.6. LIST OF FIGURES Page Information system for famine relief showing major functional groups and information linkages . . . 7 A methodology for design and evaluation of famine relief management information systems ........ l4 Food and information chains in preliminary survival model . . . . . . . . . . . ....... . . . . . 25 Rural food availability factor as a function of actual to desired storage ratio . . ......... 30 Urban food availability factor as a function of time availability of current stocks . . . . . . . . 30 Total deaths for different information quality vectors . . . .............. . . . 79 Deaths by rural and urban classes for different information quality sets . . . . ........... 82 Rural per-capita consumption before and after policy changes . . . . . . . . . . . . . ....... 90 Rural and government desired times of storage . . . . 94 Rural consumption after modeling changes ..... . . 98 Transmission and processing cost as a function of 147 information delay. . . . . . ........... Effect of price ceiling on rural sales rate ..... l82 Sampling component tracking test ....... l85 Total deaths as function of initial rural private 191 storage . . . . . . . . . . . . ........... Class fatality percentages as functions of 193 initial rural private storage ........ Total deaths simulated with varying DT values I96 Total nutritional debt simulated with varying DT 197 values . . . ................... 9.I. 9.2a. 9.2b. 9.3. 9.4. Nutritional debt versus deaths at varying budget levels ..................... Model performance variable output at each al- gorithm iteration--budget level I55 million won . . . . Model performance variable output at each al- gorithm iteration--budget level unconstrained ..... Performance versus cost ................ Performance-versus-cost measure H(C) ......... xi Page 267 27I 284 PART I COMPUTER MODEL AND COST FUNCTION DEVELOPMENT Introduction Famine is a real threat in many parts of the world today. Chronic malnutrition is widespread, leaving populations weak and susceptible to disease. A severe food shortage for even one season in such areas would lead to many deaths due to starvation. Relief efforts are handicapped when adequate knowledge of needs is not available. Each component of the relief system depends on communi- cation of information. These components include transportation units, field offices, and surveilance teams, as well as planners and decision makers. A Management Information System (MIS) is one way to provide the overall data communication needed. This dissertation is a proposed method for addressing the MIS design problem. Three major segments constitute the core of the approach. Part I defines the problem and approach, and it contains development of two major segments. First, a computer simulation of a country's experi— encing a critical food shortage is described along with an information System component that ties together surveillance data and information quality and their effect on relief system performance. Information filters, policy design, and model structure are all described in rela— tion to system management. The second major segment is a cost function that describes the resource commitments needed for various levels of information quality- In Part II, the third major segment ties the first two segments together by presenting an optimization problem. The goal is to maxi- mize performance of the overall relief system within a given informa— tion system budget. Chapters 8 and 9 explore optimization alterna- tives and likely approach outputs. Part III consists of Chapter IO, providing results and conclu- sions. Observations are given about the approach, the use of a compu- ter simulation, further research, and implications for famine relief systems. CHAPTER I THE PROBLEM AND THE APPROACH Famine poses a serious threat to many nations in the years ahead. In the last decade, food shortages have been caused by war, drought, natural disasters, and crop failure (46). Conflicts in Biafra and Bangladesh have resulted in destruction of food and disruption of nor- mal distribution lines. The Sahelian drought has damaged many coun— tries as the desert advances. Earthquakes, cyclones, and floods have caused food and water shortages in such diverse countries as Peru, India, and Iran. Successive crop failures led to a near catastrophe in the Bihar state of India during the late I960s (58, Chapter 2). Unfortunately, the probability of famine's striking has not been adequately reduced, even with the great strides made in food production capability. The problems of overpopulation, inadequate or nonexistent food distribution systems, economic inequality, greed, and corruption combine to create a well-established global system with food shortages a likely output. There is evidence that the earth is entering a period unfavorable to food production, adding a negative environmental input to the system (37). It will take a systematic and cooperative effort to prevent catastrophic famines. A food shortage has a devastating effect on individuals and on the stricken society. Weight loss and body wasting, apathy, decreased work output and self-centeredness are all common individual symptome. The generally weakened condition of the population leaves it highly 3 susceptible to epidemics. As food stores dwindle, rumors spread quick— ly, leading to large—scale migrations and hoarding. Crime, civil dis— turbances, and panic mount. Planning to meet or offset the consequences of a food shortage can encounter numerous obstacles. Political sensitivities sometimes cause a nation to withhold needed aid. It is also difficult for many coun- tries to acknowledge the existence of famine within its boarders for fear of the unfavorable impression it gives (49). There is little re— liable data from past famines. At least three factors have been noted for the scarcity of detailed recordkeeping. An adequate reporting policy has rarely been designed and used. Workers have consistently had a ”do" mentality, laboring diligently to aid victims but not taking time to record activities and results. The third factor is the fear that the extent of the disaster may reflect poorly on one's personal efforts, causing silence. Designs for famine relief sometimes come under the broader heading of disaster relief, which includes short~term encounters such as flood, fire, and earthquake. The special difficulties presented by famine in- clude its longer duration, its often widespread area, and its gradual overtaking of a weakened population. The dramatic intrusion of an earthquake or flood demands immediate and clearly substantial action. The requirements of famine relief are also substantial, but are not as early seen. However, the generally slower development of a food short- age allows prediction and time for planning to minimize the disaster's results. The need for preparation was recognized long ago in the earliest Indian Famine Codes: Proceed from the beginning on a comprehensive plan and publish it. Admist the manifold details of a Code, there lies a danger that the broad principles of famine relief may escape the notice of those who have to administer it. It is only on a knowledge of principles that the various incidents of famine administration settle into their proper places, and it is obviously of importance that all controlling offi- cers should understand the principles and bearings of what they have to do (53, p. l2). The main problem to solve in a food shortage is the distribution of food to those who need it. Many systems must interact fluidly. Planning decisions are needed on the goals of relief operations. Infor- mation must be acquired concerning the relative welfare of the popula- tion. Food transportation and storage logistics need to be examined. Field level programs of training, education, communication, and resource acquisition support systems are necessary. The problem is not simple, especially when the nations most prone to famine are underdeveloped and unorganized. The goals for a relief effort will vary by country and by crisis. Normally, the main priority is minimization of the death total (46). Other desirable results from the country's viewpoint could be to keep social disruption low and minimize foreign dependence. Humanitarian beliefs dictate that high nutritional levels, prevention of human per- formance impairment, and equitable food distribution are necessary goals. The major constraints preventing achievement of established ob— jectives are limited money, personnel, equipment, and time. A shortage of any one of these items can jeopardize an entire relief operation. Information System Structure The focus of this dissertation is on the information system needed for famine relief. The importance of information is easily realized by observing that any course of action will be based on available data. Knoweldge of the situation is necessary. The many links between the in- formation system and the transportation, field programs, system manag- ers, donors, and affected population subsystems will be examined here. But the thrust is to provide a systematic means of designing and imple- menting an efficient, accurate information system that leads to posi- tive results. Such a structure is often labeled a Management Informa- tion System (MIS). Figure l.l depicts the general structure of an information system for famine relief. The blocks represent the major groups involved in the relief process. The linkages are information flows, including plan- ning, training, communications, and evaluations. The expected scenario relating a real world food shortage to the structure of Figure I.l would be as follows: Planners start with the goals and objectives of the fa- mine relief system. They then provide the Teachers, Train- ers, and System Managers with the necessary system design, and work is done to prepare for disaster. As a good short— age strikes, the Affected People are observed by Data Col- lection teams. The surveillance results are tabulated by Data Processing and transmitted to the System Managers. De— cisions, based on planned policy and current observations, then flow to Government Programs, Relief Agencies, Field Of- fices, and the Transport System. Concurrently, Evaluations are made of relief activities, and the Media and Donors re— spond to the crisis. The cycle is closed as the Field Of- fices and Media provide the Affected People with needed food and reports on the extent of the shortage. Several of the component groups and linkages deserve further explan nation. The planners are responsible for the overall relief system, in- cluding the information system as one component. This dissertation is aimed at planners as an aid in the design and evaluation of data collec- tion, processing, and transmission alternatives. The complex Training Data Collection Program Availability, ’h Extent of Disaster RawI I— ______ I _________ TRé‘pFrt's— '[ Data I Program Field Data Evaluation Offices Processing I I \ -——r——-r—a r. IOperat1on , DirectivesI Teachers and Trainers Surveillance Affected People roce --Relief Design Base Data T'- Transport and Logistics Relief Agencies Government Programs .4 .5 D) _n. 3 .4. :1 LO l I | I I I I I I I I I I | I I I I I l : I | I I I Dresses Eesmmwations _______________ Statistics I l Extent of Disaster! IIIIIHHHHHEIIIIII Aid P romises : Aid Needs Program Goals Master Plan Planners Aid Requests ._______ Planning Link | l.-- ————— Monitored Link L——-- Figure l.l. Information System for Famine Relief Showing Major Functional Groups and Information Linkages. I I I I I I I | I I I | I I I I I | interrelationships among the many components allow a study of the infor- mation system to shed light on other subsystems. Thus, the approach discussed here also provides indications of policy, management, and training requirements. One planning element that ties directly to the information system is the need for on—going surveillance. The advantages of simultaneous consideration of long-term continuous and short-term crisis surveillance are numerous. Crop conditions, weather reports, food reserves, retail prices, and anthropometric measures can all serve as warning signals of an approaching crisis. Extant information on population size and dis- tribution, communication lines, and cultural and religious conditions will aid planners in efficient design of emergency operations. A trust and acceptance of survey procedures may develop as the surveys become more commonplace. Cost efficiency can be obtained as equipment and per- sonnel needs are evaluated. And possibly the greatest advantage is that disaster planning will occur well in advance. Advanced planning will provide relief system managers with a basic policy structure to guide decision—making. Knowledge of overall relief goals is a valuable aid in specific allocation and distribution judg- ments. This leads to the difference noted in Figure l.l between pre- planned and on-going information linkages. Planning can provide a poli— cy structure, training, and direction for emergency procedures and eval- uation. Once the crisis occurs, system management involves responses based on current available data. Training and the master plan are used to aid flexible, day-to—day decisions. Note that planners and managers may be the same individuals, as there are substantial overlaps in the distinguishable positions. The deciSion linkages pictured in Figure l.l will depend on the management structure of the affected area. One can envision a group effort with representatives of the transport, field programs, and in- formation systems serving in a guidance role. The literature suggests that one dynamic leader with broad powers has generally had positive results (45). A missing link in many past relief efforts has been the evaluation of the systems. The evaluation component in Figure l.l is needed to improve efficiency in system components, both during a crisis and in future planning. The information and material linkages between compo- nents should be singled out for frequent evaluation, to insure smooth transfers of responsibility. Two valuable assets outside the government system are relief agencies and the international communications media. Interantional groups, such as the Red Cross, CARE, United Nations organizations, and the World Council of Churches, have a great deal of experience and are able to draw on resources not available to the country itself. By presenting an accurate picture of the stricken nation's needs, the in- ternational press can help avoid senseless donations. The literature abounds with such incredible examples as winter coats sent to the equa- tor and building materials to starving countries. The actual ”relief“ work OCCurs at the field office level in Fig~ ure l.l. This is the system component where the most real-world data are available, on operation of food kitchens, health clinics, fair Price shops, etc. The other components can be thought of as support Systems for the relief work, but the support systems are vital. Mayer notes that "sooner or later, transport becomes the limiting factor in l0 relief“ (46). The transportation and logistics system includes entry, storage, and distribution points and all vehicles and personnel needed - to convey goods between the points. Thus, many operations are needed for successful fighting of a food shortage. The information system is central in that each component needs an understanding of its current milieu and its often-changing re- lationship to the other components. The information linkages have a great bearing on the efficacy of the overall effort. A note on the feasibility of the system outlined in Figure l.l needs to be made. Depending on the governmental structure, such a broad-based plan may not be implementable. Many countries define fam- ine relief as a nutrition problem, and the responsibility for handling nutrition has been split among several sectors or ministries in the government. The sectored bureaucracy is generally not amenable to a sweeping system design (l7). Planning must take into account even more factors than those pic- tured in Figure l.l. The issues of overall goals and policies must be addressed to provide a framework for implementation. And the govern- ment setting and bureaucracy already in place must be examined as one part of the practical implementation issue. Much wisdom is needed in meeting "soft" impediments--religion, cultural, political, and social obstacles. One alternative to planning for the existing bureaucracy is revol- ution (l7). Revolution can provide a quick path to a multi-sectored approach to the problem. But whenever revolution is more concerned with the system than with the people, the humanitarian goals of famine II relief are ignored. Witness the tragic famine and widespread malnu— trition in Cambodia during the past several years (2). A second opening for a systems approach may occur during an actual disaster. The-e seems to be a relaxing of restrictions during a cri- sis, allowing new constructs and implementations. This was the case in Bihar in I968 (58). It may be that one disaster is needed before a broad-based approach to coping with the next disaster can feasibly be implemented. Information for Planners The planners in Figure l.l desire an information system design that fits the real world situation, is economical, practical, and makes a real difference in relief results. We now examine the planners' in- formation needs in evaluating alternative information systems. The performance, costs, resource requirements, and critical con- straints of the alternative system designs will be of great interest to planners. Performance is related to the stated goals of relief, such as minimizing death or social disruption or the maximization of overall nutritional level. Costs and constraints measure the money, time, per- sonnel, and equipment allocations required. Several pieces of information could be useful in evaluating alter- native information systems. Recommendations for ”best” alternatives at several different cost levels would provide budgetary data and a shop- ping list of proposed systems. ”Best" refers to performance based on Goals. Additional aids would be an expected system performance level and degree of confidence in each of the recommended alternatives. A description of the minimum system necessary for relief operation is essential for comparison purposes. Knowledge of all possible undesir— able results for each alternative would also be helpful to planners. To help determine costs and performance, a list of the real-world variables to be monitored (nutritional level, food storage, water level, etc.) along with suggested measurement statistics is needed. The statistics would include desirable frequency and accuracy of sur— veys and allowable processing and transmission delays. Knowledge of the effects of varying surveillance frequency and accuracy on system performannce would be an invaluable aid. There is a need for a general, systematic approach to obtain the information for planners described above. There are lists of nutri— tional surveillance items with desirable frequency and error attri- butes (IO, 25). These are largely intended for the case of thorough, on-going surveillance and do not single out the most valuable informa- tion needs. General lists of possible variables to be monitored in a I food shortage also exist (7, 3l, 4l). But there is not a prioritized I crisis variable montoring list with suggested measurement attributes. Neither are there indicators of the relationship between list items and relief system effectiveness. To obtain such a result, the list must be based on information needed to make distribution and alloca- tion decisions. Certainly such a list will be peculiar to each country and crisis. But there probably are items that would be common to all I countries' needs. I A wide range of information systems has been mentioned in the I literature. A non-existent system resulted in a devastating famine in China during the l94OS; virtually no one, even in the capital, knew of the crisis (63, Chapter 4). At the other extreme, a rapid reporting I3 system designed by a New York consulting firm was a valuable aid in combating the Bihar, India, food shortage of I967 (6). But the most commonly voiced comment on relief data systems is the lack of re- liable and organized information. The Approach The diagram of Figure l.2 presents an approach to design that will systematically lead toward desirable information for planners: data on the real-world variables to monitor, data on measurement attributes for each variable, likely best system alternatives, and the costs and other constraints for each alternative. There are three major parts to the proposed GPPFOBCDI generation of information system alternatives, computer simulation of relief operation effects, and an optimization procedure to indicate good levels for system parameters. The generation of information system alternatives is a standard part of cost-benefit analysis. It leads to an understanding of the choices available. The common cost-benefit form converts all constraints and potential benefits to a monetary base for comparison purposes. Here, however, constraints §_could be measured in units of the limiting resource: man-hours, equipment units, etc. The key figures on the benefit side are information qual- ity statistics produced by the given alternatives. Information qual- ity is measured by a set of parameters K_including processing delays and frequency and error of surveillance. Each environmental variable to be monitored has its own set of K_parameters. Thus, system alter- natives can be characterized by the resources required and information Quality produced (§(K) and N). .msoume cowumELomcfi newsmmmcm z mow—om memEod mo :owuc:_e>m new cmvmwo cow awe—ovocpwz < .N.P acumen xow_om .mpmow _ u IIIIII m Empaagu m .m mcmuqmzu I. mwiumccwuz I m :0 32.5 m Lounge swomxm cowmeLoc ace :orppefipma “cocoasou m -:~ to =o_umem=mu . . . mew—asam suw_e:o b cowum=Co : m qugmcu mucwmguwcou mama—ed Im quamcu cowumscowcfi I fixvo coeoocsa a ucwecumcou wgwumEmcma o Lmunmzu xow_om mcwccm mcmmmcmz Emuman Ewumxm muzacH maocwmoxm 53% III i~€3%5 m_nwmmwd Aa.xvu _wco: vwvcmEEoomm mucmELoecmm m>_>L= Ewpmsm cmw_mz . , _ . m :o_umpzevm Ewumxm waFom m..m mammamgo Eu B saga 2.x: 3.25%: w .v mcmunwcu N Luggage covameswuqo mupamwm :o¢m_omo mmmooca ecu w>vumccqu< xomncwwd covumcw_w> xomnuwmu x_mx_4 Lo szum mcowumvcmEEouwm cowumcwao IS The major distinguishing feature of this approach is the use of a computer simulation to evaluate relief system performance. Computer models have often been used in the last three decades as tools in eval- uating alternative solutions to economic problems (I, p. 5). Examples of models related the famine relief problem are an agricultural sector simulation in Nigeria and a study of crop-related labor in Bangladesh (I, 2l). These studies unearthed some of the root causes of food shortages and some of the problems of food distribution. It should be noted that a computer simulation does have definite limitations. Not all the important factors affecting relief effective- ness can be included. Biological and physical interactions can be I modeled to the extent that the processes can be converted to numerical relationships. But psychological and cultural factors are very diffi- I cult to capture, due to the lack of numerical standards. Thus, a simu— I lation can only be one of the analyst's tools in design. There must be appropriate inputs on the role of such intangible or nonnumeric fac- tors as food habits, family ties, and village customs. The cornerstone of the current simulation effort is a model of the population undergoing a famine. Economic, demographic, and produc- tion components must be described. The model must be tuned to ade— quately depict the environment in which the relief system must operate. A macro view is necessary, at least initially, to adeQuately describe the scope of the problem. System management is modeled as a set of decision rules represent— ing policy structure. The rules are activated by the results from surveillance of several key variables. Thus, the intent of policy is to provide guidelines for action based on available information, a I6 Management Information System. It is assumed that the system managers know the background environment of the country and the goals and frame- work of the proposed relief system. The model decisions are limited to the rates and timing of relief operations. These policy parameters are dependent on the information received. The data provided to manag— ers are obtained through statistical sampling procedures and informa- tion filters. Modeling the sampling and filtering at a macro level allows the simulation of varying data quality without information sys- tem details. The links between alternative generation, system simulation, and optimization are the information quality parameters K) the policy rate parameters 3, and performance and constraint functions. The output of the computer model is a performance function 5(1gfi), where E is a vec— tor representing the measurable relief objectives. A constraint func- tion, §(K), is produced by system alternative generation. §_represents monetary, personnel, and equipment requirements. Off-line analysis work is done to select, for each K_vector, the information system that best allocates limiting resources. The functions f_and §_are the needed inputs for the third major component of Figure l.2, the optimization stage. As stated before, information system alternatives are characterized by a set of informa- tion quality parameters K_and a required resources function G, The simulation portion of the approach describes the effects that 5 will have on desired relief performance 5, The objective of the optimiza- tion phase is to maximize performance levels, subject to constraints on the required resources. This problem is difficult to define pre- cisely in the general case and still more difficult to solve l7 analytically. The goals and constraints must be well-defined, and assignment of relief system performance priorities is imperative for computerization. Valuable insights can be gained even before a precise optimiza— tion. By studying the values of model outputs, one can obtain likely results of particular decisions and policy structures. This provides a powerful analysis tool, both for the design of efficient operations and for validation of the computer model. The significant ties between policy structure and the information system, including key environment- al variables, can be examined. And simple sensitivity tests can indi- cate which information quality parameters are most important for sur— veillance purposes. Knowledge of component linkages and efficient policy structure is a valuable aid to planners that goes beyond basic information system specifications. The planning process is cyclical in nature as the chart in Figure l.2 indicates. Model results are continuously compared to real world data and expectations in a validation process. For the model to be a useful tool, system planners must have an understanding of environment- al and relief processes and must be satisfied that the model accurately portrays these processes. The model itself is updated, refined, and made more complete as the planning and testing proceed. The analysts' study of system performance leads to a better grasp of the monitoring function. This, in turn, leads to a better definition of policy and information quality parameters E_and K. An information system can provide crucial links between planning, implementation, and on—going operations. In fact, the three are very interrelated. Data capture and processing the data into a useful form I8 are essential for on-going operations and for system implementation. Setting up the machinery to gather and process the data is a planning and implementation function, but requires knowledge of basic opera— tions. This dissertation is mainly a planning tool; it concentrates on establishing a framework for tying a computer simulation to the de- sign of information systems. The operations descriptions are general, echoing the nature of the computer model. Accordingly, the specific data and level of aggregation used here is not immediately transfer- rable to specific country applications. But the framework for planning should be. The organization of this dissertation roughly parallels the se— quence of events leading to the development of the approach of Figure l.2. An application of the approach to a hypothetical country is fol— lowed through the individual steps, including major findings, pitfalls, and areas for further research. Part I covers the generation of in— formation system alternatives and relief system simulation, along with the validation process and a study of initial model results. Part II examines the optimization techniques applicable to the problem. And Chapter IO presents major results and conclusions, notes potential ad- vantages and disadvantages of the approach, and outlines several areas for further research. Chapter 2 describes the basic survival model designed by Dr. T. J. Manetsch (38). The addition of a sampling component to simulate infor— mation inputs to system managers is covered in Chapter 3, along with a detailed description of the K parameters used in the study. Initial model results and subsequent policy changes are discussed in Chapter 4. Information system alternatives with related costs and K_values are I9 examined in Chapter 5. The roles of the system manager and informa- tion filters are contained in Chapter 6. And Chapter 7 concludes Part I with a summary of model and approach validation techniques. The optimization section is divided into two chapters. The actual optimization work for the current application is covered in Chapter 9. Chapter 8 discusses pre-optimization work, methods for identifying the most sensitive K_and E_parameters. By limiting the number of parame- ters, optimization techniques are easier and less costly to apply. Considering the cyclical nature of this systems approach, the or— der of events in Part I described above is certainly not compulsory. The simulation and system alternatives sections can be developed simul- taneously, as can the components within the model. HoweVer, Part I completion should logically precede Part II. And the sensitivity work of Chapter 8 should precede the optimization of Chapter 9. Summary This approach is a proposed design. Much work is needed for im- plementation, this dissertation is only an initial pass. The approach is not a guaranteed solution to the whole problem of famine relief. The many complex interactions require well-defined objectives and tight coordination of efforts between the many subsystems depicted in Figure I.l. The question of whether famine relief efforts should be pursued is not specifically addressed here. It is assumed that man has an obliga- tion to relieve needless suffering where he can. Certainly a food shortage gives enough advanced warning that some sort of planning is imperative. CHAPTER II THE BASIC SURVIVAL MODEL The survival model discussed in this chapter was created by Dr. T. J. Manetsch and has been described by him elsewhere (38). A general description and many of the important modeling features are included here to provide necessary background material for the development of succeeding chapters. A computer simulation is an excellent tool for the systematic study of famine relief because the extremely complex nature of the problem requires analysis of several large, interconnecting, dynamic systems. Demographic, economic, transportation, communication, and system management components, and their interactions defy simple exami— nation. The computer allows the testing of many distinct strategies and system alternatives in a relatively short amount of time; perfor- mance can be estimated without experimentation in real food crises. And a simulation explores the process and structure of relief opera— tions and responses as well as providing numerical calculations. This survival model was constructed to study alternative strate- gies for combating a food crisis and to shed light on areas for further work. In particular, a rationing strategy and the question of optimum timing and quantities of international food aid were examined (38). SUQgested research areas included the impact of information quality on government decision making and the design of an overall information system tion. well a ficall tinues lowed a SIIOI exam inter 01‘ 01 are I done Ing " IUatI SII‘UI naul 2I system for famine relief, topics that are addressed in this disserta- tion. Chapter 3 contains a description of an information component as well as several modifications of the basic model to allow it to speci- fically address the information systems problem. This chapter con— tinues with an overview of the scenario and scope of the model, fol- lowed by a more detailed account of interesting modeling features and a short summary. The Scenario: a Country Facing a Short Term Famine The model describes a country on the brink of a food crisis and examines the demographic, economic, nutritional, and relief operation interactions over a one to two year time span. The important problems of overpopulation and underproduction, possible causes of the crisis, are not addressed. Rather, the scope is restricted to what can be done with available resources when a severe famine occurs. The model- ing is of a hypothetical country, so the simulation is not yet ade- quate for use in any specific nation. But the general processes and structures important to relief work can be discovered. The country has a regular food deficit and must import grain an— naully, but a balance of payments problem is assumed which restricts the amount of imports available on short notice. The particular cause (war, crop failure, natural disaster, drought, etc.) of the food short- age is not specified; the country begins the simulation in Janaury with storage levels well below the amount needed to feed the popula- tion through the next harvest period in mid-June. A second, larger harvest occurs in October. Thus, the severity of the crisis is set by the initial conditions on total grain storage, specifically the amount in run age on dltion- condit pond t values I rural. stocks smer. at In‘ class 22 in rural private storage (RSTOR). The real "crunch” of the food short- age occurs just before the first harvest. There are other initial con— ditions which influence system performance: population sizes, crop conditions, nutrition levels, etc. These values must be set to corres- pond to actual values in any specific application; currently, the values are estimated from South Korean data. Four population classes are included, three urban classes and one rural. The rural class is assumed to have most of the available food stocks, which it normally sells in the marketplace to the urban con— sumer. One class, the urban rich, is generally able to buy food, even at inflated prices. The urban poor constitute the remaining two classes and are divided into those with rural relatives and those with- out. In the event of food shortages, the poor with rural relatives can either migrate to the farms or receive aid from relatives. The poor without rural relatives are most vulnerable. The consumption patterns, nutritional requirements, storage levels and births and deaths peculiar to each population class are modeled dynamically. In addition, malnutrition levels and deaths due to mal— nutrition are calculated. These portions of life relevant to famine and famine relief work are simulated. The production component calculates the extent and timing of the harvests and increases rural private storage accordingly. The market component computes sales and prices based on supply and demand of the population groups. The government component interacts with each of the other model portions through decision rules on allocation and distribution of available grain. The decisions include the rates and ”triggers” to USE tor ove tio par for IIII re 23 use for emergency actions: acquisitions from the rural (hoarding) sec— tor, sales of government storage in the market, implementation of emer— gency feeding programs. The rules are constructed on the basis of an overall relief strategy, such as strong price controls or enforced ra- tioning of available food. An additional part of the government com- ponent is the data acquisition procedure needed to obtain necessary in- formation values such as nutritional levels, private storage levels and population size. The world outside the country is exogenous to the model, the only interactions coming through international food aid and grain imports received by the stricken nation. Each of the processes mentioned here has been modeled through the use of a wide range of techniques including distributed and exponen— tial delays, numerical integration, maximum functions, table functions, andarithmetic computations. Although the detailed operations may not be of general interest, the main equations and techniques are de: scribed in the next section and referred to in later chapters. Important Modeling Features The demographic, economic, nutritional, and production components are highly interconnected. Thus, the format of this discussion will be to follow the food chain through the model, beginning with nutritional and consumption considerations and moving to production, the market— place, and storage facilities. The information needed to monitor the food chain processes provides a natural link to the government data ga- thering and decision making component. Two distinct policy strategies and the information estimation structure will be described. Figure fl01 Nut mea OIIE tic IIII (I: r... .—J_ - III 24 2.l indicates the main components of the food chain along with the flows of food and related information. Nutritional Level A cornerstone in analyzing the effects of a food crisis is the measurement of nutritional level of the population. Certainly, this is one of the main areas of concern in evaluating famine relief opera- tions and is one of the information links between population groups and decision makers in Figure 2.I. The basic quantified form used in the survival model is that of accumulated, per-capita, nutritional debt (ANUTDP), which is calculated in Equation 2.l as the difference over time between required normal food intake and actual consumption. ANUTDPj(t) = ANUTDPj(O) + 75(RNUTPj(s) - PCONSj(s))ds (2.1) where: ANUTDP = accumulated per—capita nutritional debt (MT/person) RNUTP = current required nutritiOnal intake (MT/person—year) PCONS = per-capita consumption (MT/person—year) j = index on population classes. All food types are combined to give a ”total energy” viewpoint to the nutritional calculations. This eliminates unneeded complexity for the gross, macro problems addressed here, but obscures the vital de— tails of actual relief work: prescribing diets, ordering acceptable foodstuffs, etc. Quantities of food are converted to grain equiva» lents; the units used throughout the model are metric tons of grain equivalent. Outside World Outside Aid Food / Orders IAcquisitions I Rate . I Rural . I ’fi’ 5” Government Class I a Rural Sales I I Storage I I I I I I I I ,I ’,_.- Transport Rate I I I "' I I l ,/ I I/ / I Government “k, Government I Decision I Urban I Making R\ I“, T"‘ Storage l \ I I \ I A I x \ \ I I “" Sales Rate \ I I \ I \ \ Aid \ I f t' ‘I>? n orma ion R /,"’ System -atg_ Market / Stocks, I’ Sales, A I Deaths, PY‘ICE ‘ I Consumption, Nutritional . . X Level DeSired \ I LEmergency Aid \ Sales Purchases \\ . \ I Ald t \ I Relatayes [ I \ I . I I Urban Poor Urban Poor I I with Rural with no Urban I I Relatives Rural Relatives Rich | . I I. I ' ,’ \ ’1 \ / \ \\< \‘ \‘ ‘-.’4’ -------- 3’.’4/ ‘‘‘‘‘‘‘ \ N—’/ \\\\ “"-— "-’—-'/" Figure 2.I. Food and Information Chains in Preliminary Survival Model. rest Ieve nutr poi n phys IIICI Ir? 26 Two physiological facts form the basis for the modeling of the rest of the nutrition equations. First, as an individual's nutritional level drops (nutritional debt increases), weight drops, and required nutritional intake (RNUTP) decreases, up to a point. That is, up to a point, the less one weighs, the less one needs to eat. The second physiological fact is that the probability of death due to malnutrition increases with nutritional debt, It should be noted that rarely is death attributable directly to starvation. But malnutrition weakens the body and makes one highly susceptible to disease, especially dysen- tery and diarrhea (53). Deaths due to malnutrition are calculated here as those that occur above the normal death rate. Required nutrition falls as nutritional debt increases, as comput- ed in Equation 2.2. RNUTPj(t) = max(RNUTPN - UK4*ANUTDPj(t) , UK5) (2.2) where: RNUTP = required nutrition per person (MT/person-year) RNUTPN = normal required nutrition per person (MT/person-year) UK4 = parameter; rate of effect of nutritional debt on required nutrition (yr‘ ) UK5 = minimum life sustaining nutrition (MT/person-year) ANUTDP = accumulated nutritional debt (MT/person) j = index on population classes. Death Rates The assumption is made, baSed on the central limit theorem, that the probability of death due to malnutrition follows a cumulative nor- mal distribution on nutritional debt. This holds as long as the popu- lation starts with little or no malnutrition. Each urban and rural class has its own probability distribution. Specific numerical data dI‘eI SIIIIIEl Inc can cal< IIIIE 27 are estimated from controlled empirical studies (26). It is also as— sumed that deaths occur only when nutritional debt increases. The hu— man body adapts level of nutriti the case of retu Hence, long term to the chronic malnutrition represented by a constant onal debt. But the modeling is not yet adequate for rning to a malnourished state following recovery. (greater than two years) simulations will not be ac- curate. The probability functions, death rates and total deaths are calculated by Equations 2.3. ANTDPMj(t) = max(ANTDPMj(t- At), ANUTDPj(t)) (2.3a) PDTHj(t) = F2(ANTDPMj(t)) (2.3b) PDTHj(t - At) = F2(ANTDPMj(t - At)) (2.3c) DTHSMj (t) = max(( HPDTH -PDTH- (t - At)) * (POPJ- (t) + TDTHSM; (t) ), 6. 0) (2.3a) DRMJ-(t) = DTHSMJ-(t I /At (2.3e) TDTHSMj(t) = i DTHSMj(k * At) (2.3f) where: ANTDPM(t) = maximum per—capita nutritional debt in the interval (O,t) (MT/person) ANUTDP = accumulated nutritional debt (MT/person) PDTH(t) = probability of death due to malnutrition in the interval O,t F2 = cumulative normal distribution function DTHSM(t) = deaths due to malnutrition in the interval (t - At, t) (persons) POP = population (persons) DRM = death rate due to malnutrition (persons/year) TDTHSM = total deaths due to malnutrition (persons) 3 = index on population class k = index on discrete time intervals At in model. rat fec gr; C0 to 28 The malnutrition death rate, DRM, is added to the normal death rate to arrive at a total death figure. The birth rate is also af- fected by nutritional level, falling with consumption. Grain Storage Physiological modeling has the same form for all classes, but the consumption patterns differ for the rural and urban populations, due to their distinct food acquisition and storage habits. The rural popu- lation is self-sustaining and stores quantities to last through the beginning of the next harvest period. The urban classes, both rich and poor, buy supplies at regular intervals and expect to make their on—hand storage last for a much shorter time than do their rural coun- trymen. The difference in storage habits can be seen in Equations 2.4a and 2.4b, representing urban and rural private storage, respectively. USTOR (t) = USTOR (0) +.r§ (UPUR.(s) — cousu.(s) J 3 J J (2.4a) + EMFSLj(s) = EMFDGLj(s))ds RSTOR(t) = RSTOR(O) +.r§ (RH(s) - RSALES(s) (2.4b) - CONSR(S) - EMFSU(S) — GAQ(S))dS where: USTOR = urban private food storage (MT) RSTOR = rural private food storage (MT) UPUR = urban market purchases (MT/year) CONSU = urban market purchases (MT/year) CONSR = rural consumption (MT/year) EMFSU = emergency food sent to urban relatives (MT/year) EMFSL = emergency food received from rural relatives (MT/year) (EMFSL is lagged version of EMFSU) 29 EMFDGL = emergency food received from government programs (MT/year) RH = harvest yield (MT/year) RSALES = rural sales in market (MT/year) GAQ = government acquisitons from rural stores (MT/year) j = index on urban classes. Note that urban food sources are purchases and emergency relief, while harvests provide the only source for the rural class. Urban purchases and rural sales are results of market activity, to be dis- cussed later. Government acquisitions and emergency food programs are also described later, as part of the decision making component. Given the differing time scales of urban versus rural storage habits, it is clear that their consumption patterns are based on dif- ferent information inputs. Both groups have a desired base consumption level computed as the normal required nutrition rate (RNUTPN) plus a constant times current nutritional debt, to make up for past malnour~ ishment. But the desired level is tempered by a food availability fac- tor which differs substantially for urban and rural classes. The rural individuals know their consumption requirements and the expected time of the next harvest. They plan to stretch their food stocks accordingly. Thus, the rural food availability factor (FRl) is determined as an increasing function of the ratio (XFRl) of current storage to storage desired. The form of the function is given in Fig- ure 2.2a. Both XFRl and FRl are dimensionless variables. Note that if current storage exceeds desired storage, ratio XFRl is greater than one and consumption can proceed at desired levels. But for XFRl values below one, self-imposed rationing occurs to make FRl rural food avail- abil- ity factor FUl Urban food avail. abil. ity factor FRl rural food avail" abil- ity factor FUl urban food avail- abil- ity factor 30 FRl l.0 0.5. 0.5 1:0 1:5 actual storage XFRl = ————— desired storage Figure 2.2a. Rural Food Availability Factor as a Function of Actual to Desired Storage Ratio. l.0 0.5, 1.0 210 3.0 XFUl (weeks) Figure 2.2b. Urban Food Availability Factor as a Function of Time Availability of Current Stocks. stocks Chapt a sev of XF too 0 crisi the r as E ure the 3l stocks last. During the course of verification work, discussed in Chapter 4, it was discovered that the concave shape of this function is a severe impediment to minimizing total deaths. Especially for values of XFRl greater than 0.5, consumption is too great, depleting stocks too quickly and causing increased deaths in the latter months of the crisis. The time span for personally desired storage is much shorter for the urban classes, and no convenient time-frame exists for them as does time-until-harvest for the rural population. But given current urban private stocks and nutritional needs, one can determine, using Equation 2.5, the length of time (XFUl) before stocks will be exhausted. Then the food availability factor for urban classes (FUl) can be computed as a function of XFUl. The shape of the function is pictured in Fig- ure 2.2b. Note that virtually no consumption cutbacks are made unless the time availability of current stocks is less than one week. USTORi(t) XFUlj(t) = (2.5) RNUTPj(t) * POPj(t) where: XFUl = time availability of current stocks at current consump- tion rate (year) USTOR = personal storage (MT) RNUTP = current nutrition required (MT/person-year) POP population (persons) j index on urban population classes. 32 Emergency Aid to Relatives The emergency food sent from rural individuals to poor urban rela- tives, EMFSU, was mentioned in the discussion on private storage (Equa- tions 2.4). The amount of food sent is based on availability in the rural sector (using FRl again) and on the relative nutritional levels of the two groups. Aid will be sent at a rate proportional to the per- ceived difference in the groups' nutritional debts and the consumption level of the urban relatives. Equation 2.6 describes the process. The amount of grain actually received by the urban relatives (EMFSL) is computed simply as a first order exponential delay of the amount sent, to allow for transportation lags. The form of the delay is the same as described in Equations 2.l6. EMFSU (t) = max ((FRl(t)*(RKl*(PANUTD(t) - RNUTDP(t)) 2.6 + Wm) * Porzmr .o.o> ( ) dt where: EMFSU = emergency food sent to urban relatives (MT/year) FRl = rural food availability factor PANUTD = perceived per-capita nutritional debt of urban relatives (MT/year) RNUTDP = rural nutritional debt per-capita (MT/person) RKl, RK2 = parameters used to tune equation to real conditions POP2 = population of urban poor class with rural relatives (persons). Food Production The nutritional level of an individual is largely determined by consumption patterns, and these two items are at the end of the food chain. At the beginning is food production, which takes place in the rural areas the harm The d figure. 0 rated acre late the v in mid-Jun these desi input to a set of n f harvest re an nth-ore flou, nume estimate r Harv: duals the based on iered if Sales inc “ting to The hand dEpe Outside a WWW e) ”Ch, wir give" Ph rich are 33 rural areas. The model computes the total crop size, the timing of the harvests, and the distribution of the harvest over time. The different actual crops are aggregated into one grain-equivalent figure. Output is calculated as the product of yield per acre, culti— vated acreage, and a weather factor which could be randomized to simu- late the vagaries of agricultural production. Harvests are set to start in mid-June and October with the later crop‘s being the larger. At these designated times, the calculated grain output is fed as a pulse input to a distributed delay process (40, Chapter l0). The delay is a set of n first order differential equations whose output is a stream of harvest rates (see Equations 2.l8). The time series of rates follows an nth-order Erlang distribution. Since the delay process conserves flow, numerical integration of the delay rates produces an accurate estimate of total output. Harvested grain enters rural, private storage. The rural indivi- duals then sell grain on the market with quantities offered (RSUP) based on consumption needs and the price of grain. No sales are of- fered if the rurals realize they do not have enough for themselves. Sales increase with high prices, although rapidly rising prices, indi- cating food shortages, depress rural sales. The buyers in the market place are the urban classes. Their de- mand depends on desired consumption, price level, and the amount of outside aid received from rural relatives or government sources. When supply exceeds demand, all classes buy their desired amounts. But the rich, with higher disposable income, can pay higher prices and are given preference when demand exceeds supply. Once the demands of the rich are met, the remainder is split among the poor classes. Prism—‘- Price is dete' 2.7, a classical v. arrult) __ = cu dt * vhere: pra = food uoen = urban GSLSD = 90%" RSUP rural DEM 0 - avere till =markc j = inde: Government Decisir \ As seen in F foreign imports ( chases from the r stores as a price lization calculat 0f the pol icy str indicate that it S”lilies are exha GSLSD(t) = ( Where: 34 Price Level Price is determined by supply and demand levels as in Equation 2.7, a classical Walrasian market price mechanism (54). 3 dPFdD‘t(t_) = CMW ’3 UDEM-(t) — GSLSD(t) — RSUP(t) ) i=1 J (2.7) * PFD(t) / DEM0 where: PFD = food price (monetary unit/metric ton) UDEM - urban food demand (MT/year) GSLSD government desired domestic sales (MT/year) RSUP = rural sector desired sales (MT/year) DEM0 average aggregate demand (MT/year) CMl market price response coefficient j = index on urban population classes. Government Decision Points As seen in Figure 2.l, the government acquires food either through foreign imports (GIMP), emergency food aid (EMFINT), or direct pur~ chases from the rural sector (GAQU) Sales are made from government stores as a price control mechanism. Equation 2.8 describes the stabi- lization calculation used. Price control is the main feature of one of the policy strategies to be discussed later, and simulation results indicate that it is an effective allocation measure until government supplies are exhausted (38). GSLSD(t) = (PFD(t) — PFDD) / PFDD + GNSLS (2.8) where: GSLSD = gavel PFD = corn PFDD = desir GllSLS = name CEP = polic Grain storage simulation. Equat ing the levels of rated into rural a Rural storage is g than that of short levels of governme transportation lir government decisic GSR(t) = GSRl - Rl GSU(t) = GSU where: GSR = gov GSU = gov GIMP = im; EMFINT = in“ GAQU = 90‘ REMFDG = em GSRU = gr hm 35 GSLSD = government desired domestic sales (MT/year) PFD = current food price (monetary unit/MT) PFDD = desired food price (monetary unit/MT) GNSLS = normal level of government domestic sales (MT/year) CGP = policy control parameter (dimensionless). Grain storage is a vital component of the food chain in any dynamic simulation. Equations 2.4 have described the inputs and outputs affect- ing the levels of personal storage. Government grain stocks are sepa- rated into rural and urban components, dependent on physical location. Rural storage is generally long term and, thus, its capacity is higher than that of short term urban stores. Equations 2.9 calculate the levels of government storage, based on input and output rates. The transportation links between rural and urban sites involve an important government decision, the rate of movement of grain (see Equation 2.lO). t GSR(t) = GSR(O) + f (GIMP(s) + EMFINT(s) + GAQU(S) 0 (2.9a) - REMFDG(s) - GSRU(s))ds t GSU(t) = GSU(0) + r (GFRRU(s) - GSLS(s) - EMFDG(s))ds (2.9b) where: O GSR = government rural grain storage (MT) GSU = government urban grain storage (MT) GIMP = imported grain (MT/year) EMFINT = international emergency aid (MT/year) GAQU REMFDG = emergency food aid to rural sector (MT/year) governmental acquisitions from rural sector (MT/year) GSRU ‘ grain sent from rural to urban storage (MT/year) GFRRU = 9m GSRI GSLS = gov; EllFDG = gave The general i rural sector; impo place determined is rate and governmen level. Then a foo sector hoards its Hithout substanti a depleted as it mus prices soar, and t rural relatives re and many die. Relief Strategies The governmer response to such i been simulated am used is to minimi sible. A second 9 end of a year, is 36 GFRRU = grain arriving at urban storage (lagged value of GSRU) (MT/year) GSLS = government domestic sales (MT/year) EMFDG = government emergency aid to urban poor (MT/year) The general food chain is modeled to include production by the rural sector; imports by the government sector; sales in the market place determined by consumption needs, prices, supply, and demand; pri- vate and government storage; consumption; and the resulting nutritional level. When a food crisis occurs, the chain breaks down. The rural sector hoards its small supplies, not offering grain in the market. Without substantial international aid, the government's supplies are depleted as it must sell grain to keep prices down. Sales decrease, prices soar, and the urban poor are unable to buy food. Those with rural relatives receive some aid, but the poor with no relatives starve and many die. Relief Strategies The government decision making component simulates strategies of response to such a food crisis. Two particular relief designs have been simulated and tests run to check their performance. The objective used is to minimize total deaths. Other objectives are obviously pos- sible. A second goal, that of minimizing total nutritional debt at the end of a year, is considered in later chapters. the plan for Equation 2.8 to 01 prices are too his large murder of d program is ineffec price control alsc government wants 1 the price stabiliz which increases de nutritional debt 1 The second are spreading nutritic equalization of nu of needing less fr be much more effec The decision is to be done, whv five activities w the rural sector, urban poor, forei rural to urban si ger" used to decl The approact strategy has great noted and comparu difference dete commonly called 37 One plan for relief is to allow the price control mechanism of Equation 2.8 to operate, providing free emergency aid to the poor when prices are too high. Unfortunately, this strategy does not reduce the large number of deaths in the urban poor classes. The emergency aid program is ineffectual since the lack of grain signaling the failure of price control also precludes distribution of free food. So when the government wants to aid the poor, it cannot. The main computation in the price stabilization strategy is a modification of Equation 2.8 which increases desired government sales (GSLSD) with perceived urban nutritional debt (TPUND). The second modeled strategy is based on rationing available food, spreading nutritional debt evenly across all classes. Rationing and equalization of nutritional debt are based on the physiological process of needing less food as weight drops. This strategy has been shown to be much more effective than the price control scheme above (38). The decision rules to implement a relief plan must stipulate what is to be done, when to do it, and at what rate. Figure 2.l indicates five activities which the government can influence: acquisition from the rural sector, sales from government stocks, emergency aid to the urban poor, foreign import orders, and the transportation rate from rural to urban sites. An additional item to be discussed is the “trig- ger” used to declare existence of a food crisis. The approach used in constructing decision rules for the rationing strategy has great generality. Key information quantities are esti— mated and compared to desired values. The direction and size of the difference determines the type and level of relief response. This is commonly called a closed loop feedback control (55, Chapter 6). A lF""____________—______""_______"______—_'__—______________________________________________::lllli!5;’l l.2-E siuple example sl port of governroen trol loop is inst storage (GSRD). and compared with since government values, and there difference (GSR - rate at which the to insure non-neg GSRU(t) = ma where GSRU = gover GSR = gover GSRD = desi r CG] = param Recall that Thus, if GSR is g ence. If GSR is stores to increas Government ‘ control loop. Tl orders is comparu If Supplies excel the country cann storage and impo t 38 simple example should help explain the concept. Rural—to—urban trans— port of government grain must take place at some rate. A feedback con— trol loop is instituted by setting a desired level of government rural storage (GSRD). The size of actual rural storage (GSR) is ascertained and compared with GSRD. (The model assumes perfect knowledge of GSR, since government supplies are well known compared to other estimated values, and there are procedures extant for their measurement.) The difference (GSR - GSRD) is multiplied by a parameter designating the rate at which the gap will be narrowed. A maximum function is included to insure non—negative transport rates. The result is equation 2.l0. GSRU(t) = max (CGl*(GSR(t) — (GSRD), 0.0) (2.l0) where GSRU = government rural-to-urban transport rate (MT/year) GSR = government rural storage (MT) GSRD = desired government rural storage (MT) CGl = parameter determining rate of transport (year't). Recall that increasing GSRU decreases GSR, from Equation 2.9a. Thus, if GSR is greater than desired, GSRU works to reduce the differ- ence. If GSR is less than desired, no food is sent, allowing rural stores to increase through imports and acquisitons. Government import orders are determined using a similar feedback control loop. The total amount of government storage plus previous orders is compared to desired storage plus the expected amount of sales If supplies exceed demands, no orders are made. But, in general, since the country cannot produce enough to feed itself, demand exceeds actual storage and imports are ordered. Declaration 0 relief operations warning signals ex capita storage def age level, subtrac difference by the given in Equations level, an emergenc runs, although a 1 erosrclt) = mm = a eorcttl . (E where: erosrc - est crsrn . es, Educ . €51 TTSH = tir SF = Sd‘ error . es. RNUTPN e no ElMP = es GSR e go GSU = 90 ERSTOR . es 39 Declaration of a famine is an important timing consideration, since relief operations will begin with the announcement. Numerous early warning signals exist (25, 53). The "trigger” used here is the per- capita storage deficit. It is calculated by computing a desired stor- age level, subtracting estimated actual total storage and dividing the difference by the estimated population total. The computations are given in Equations 2.ll. If the final figure (EDPC) is above a pre-set level, an emergency is declared. (The level 0.0 was used in simulation runs, although a small negative value may be better.) ETDSTG(t) = (TTSH(t) + SF)*ETPOP(t)*(RNUTPN-EIMP(t) / ( ) 2.lla ETPOP(t) ) 3 ETSTG(t) = GSR(t) + GSU(t) + ERSTOR(t) + '2] USTORj(t) (2.llb) J: EDPC(t) = (ETDSTG(t) - ETSTG(t) )/ETPOP(t) (2.llc) where: ETDSTG — estimated total desired storage (MT) ETSTG = estimated total storage (MT) EDPC = estimated storage deficit per—capita (MT/person) TTSH = time until start of next harvest (years) SF = safety factor for time of harvest (years) ETPOP = estimated total population (persons) RNUTPN normal nutritional requirement (MT/person-year) EIMP = estimated imports (MT/year) GSR government rural storage (MT) GSU government urban storage (MT) ERSTOR = estimated rural private storage (MT) cusroa estir j inde: Notice that d new cr0p is ready, capita consumption at the time of des tion work, as expl The aim of tt across population government can use iood programs (EMT nutritional debts and the average a' back control l00p: RRRUT is cal amount of availab and across the t1 Cluded since thos ”59 0t TTSH and a conditions. RRNUltt) = ( where; RRNUT = aver Rear SF : Safe 4O EUSTOR = estimated urban private storage (MT) j = index on urban population classes. Notice that desired storage is the product of the time until the new crop is ready, the estimated number of people, and the desired per- capita consumption rate. The use of TTSH plus a constant safety factor at the time of desired storage is too crude an estimate for optimiza- tion work, as explained in Chapter 4. The aim of the rationing strategy is to equalize nutritional debt across population classes. The three main control activities that the government can use are acquisitions (GAQU), sales (GLSLDU), and free food programs (EMFDGU). The specific decision rules use accumulated nutritional debts, private storage levels of the population classes, and the average available rate of nutrition per-capita (ARNUT) in feed- back control loops. ARNUT is calculated in Equation 2.l2 by estimating the total amount of available food and dividing it equally among the citizens and across the time until the next harvest. Estimated imports are in- cluded since those supplies are expected. As mentioned earlier, the use of TTSH and a constant SF does not work well under optimization conditions. ARNUTtt) = (ETSTG(t)/(TTSH(t) + sr) + EIMP(t))/ETPOP(t) (2.12) where: ARNUT = average available per-capita nutrition rate (MT/person- year) ETSTG = estimated total storage (MT) TTSH = time until harvest start (years) 5F = safety factor for harvest timing (years) HR? = estim ETPOP = estin If all popula equal nutritional would insure equal levels are unequal emment calcul ate: on ARNUT and know used as target le debt across class is used to equali sales rate evens some of the urban food program is u poor classes. No hack loops and AR GAQU(t) = ma GSLSDU (t) = enroeuj (t) ‘E: - ;:1' 4l EIMP = estimated imports (MT/year) ETPOP = estimated total population (person). If all population classes started with equal levels of storage and equal nutritional debt levels, consumption of food at the rate ARNUT would insure equalization of the rationing strategy. But since initial levels are unequal, additional control variables are needed. The gov- ernment calculates desired private storage levels for each class based on ARNUT and knowledge of consumption habits. These desired values are used as target levels in one feedback loop. Comparison of nutritional debt across classes forms a seond feedback loop. The acquisition rate is used to equalize rural versus average urban nutritional debt and the sales rate evens the debts for rich versus poor urban classes. Since some of the urban poor receive aid from rural relatives, the emergency food program is used to equalize nutritional debt across the two urban poor classes. Notice in Equations 2.l3, 2.l4 and 2.l5 the use of feed- back loops and ARNUT. GAQU(t) = max(GC30*(ERSTOR(t) — GRSTRD(t)), 0.0) + CG36*(AEUNDP(t) — ERNTDP(t))*PR(t) (2.l3) GSLSDU(t) = ARNUT(t)*(PU3(t) + CG3l*(PU1(t) + PU2(t)) EATNDP1(t) + EATNDP2(t) (2.l4) + CG32*(EATNDP3(t) - 2 0 *PU3(t) + CG34*(GUSTRD3(t) - EUST0R3(t)) EMFDGU. t = ARNUT t * PU-(t) J( ) ( ) J EATNDP1(t) + EATNDP2(t) 2.0 (2.15) + CGZ7*(EATNDPj(t) — cscsou = g EHFDGU = ERSTOR = EUSTOR = GRSTRD = GUSTRD = ERNTDP = EATNDP = AEUNDP = ARNUT = C630 ,CG34 = C636 ,CG32 3 C627 = Each of the are used to adju etc.) so that th ences between co fl'Slures are used values (to be di where: GAQU GSLSDU EMFDGU ERSTOR EUSTOR GRSTRD GUSTRD ERNTDP EATNDP AEUNDP ARNUT PR PU ll II II ll CG30,CG34 = CG36,CG32, CG27 ll 42 *PUJ.(t) + CG34*(GUSTRDJ-(t) — EUSTORj(t)) government acquisitions from rural sector (MT/year) government desired domestic sales (MT/year) government emergency food (MT/year) estimated rural private storage (MT) estimated urban private storage (MT) government desired rural private storage (MT) government desired urban private storage (MT) estimated rural nutritional debt (MT/person) estimated urban nutritional debt (MT/person) average estimated urban nutritional debt (MT/person) average available rate of nutrition (MT/person-year) rural population (persons) urban population (persons) control parameters for private storage feedback loops (year-l) control parameters for nutritional debt feedback loops (year-l) index on urban population classes (j=l signifies poor with no relatives, j=2 signifies poor with relatives, j=3 signifies rich class). Each of the control loops contains a population multiplier. These are used to adjust the units of the control parameters (CG36, C034, etC-) so that the parameters represent the rate at which the differ- ences between compared values will be narrowed. The exact population figures are used in these basic model equations although estimated values (to be discussed next) would give a more accurate portrayal of the decision proce will be dependent are added. Information for Ma In any relief known Uncertaint certain their effe Three estimation types of processe interval between similar delay wit of data acquisiti simulate large gm Once a deciS‘ tions, government implement the dec each variable and 2.16. This type food aid sent to VARL,” (t) = where: VARL = lagg VARU = unla DEL = aver A t = time 'TP*"—"""""""""‘TT‘T"T""'—'T_——"______—________________________‘ 4~—~IIIIIIE§§fi 43 the decision process. Note also that the control parameters' values will be dependent on each other because the distinct feedback loops are added. Information for Management In any relief activities, very few information items are perfectly known. Uncertainty and error are introduced in the model to help as- certain their effects on performance and make the model more realistic. Three estimation forms are used to allow for simulation of different types of processes. A first order exponential delay describes the time interval between the making of a decision and its implementation. A similar delay with randomness models the lag time and measurement error of data acquisition. And an nth—order distributed delay is used to simulate large grain shipments. Once a decision rule is invoked, desired values of grain acquisi- tions, government sales, etc., go to the programs that will physically implement the decision. The organizational and communication Tags for each variable and class (if necessary) are represented by Equation 2.16. This type of delay is also used to simulate the transport lag of food aid sent to urban relatives (Equation 2.6). VARL,j(t) = VARL,j(t — At) + ___AE;__.* (VARUijtt) DELij (2.l6) - VARL,j(t - At) where: VARL = lagged implemented value of variable VARU = unlagged desired value of variable DEL = average implementation delay (years) A t = time increment of discrete modeling process (years) i = index i = index Information private storage 1 variable, by clas and measurement e variable RR cause time increment A rors are added ov effect on EST is error is compound ESTqJ-(t) = where: EST = estima NEW = actual DEL = averac SD = RR = At, 1‘, J' = In transpor 90 at its destin value. This is tions 2.18 (40 C 44 i = index on variables j = index on population classes. Information items required by system managers include population, private storage levels, and nutritional debt. Each sampled population variable, by class, is estimated with appropriate transmission delays and measurement error, according to Equation 2.17. The uniform random variable RR causes a zero mean uniformly distributed error term at each ‘ time increment A't. And since At is small, many such independent er- rors are added over the course of a simulation run. So the cumulative ‘ effect on EST is a zero mean, normally distributed random error. This error is compounded by the deviation from NEW caused by the delay term. EST1j(t) = EST,j(t _ at) + ((1, + SD1*RR)*NEW1j(t) At (2.17) - EST1j(t — At)) t_______ DEij where: EST = estimated information value NEW = actual information value DEL = average delay time in information transmission (years) SD standard deviation of measurement error (same units as NEW) RR uniformly distributed random variable (-1/2, 1/2) A t, i, j = as in Equation 2.16. In transporting large quantities of grain, the arrival of the car- go at its destination will be distributed in time around some mean value. This is modeled by the series of first order differential Equa~ tions 2.18 (40 Chapter 10). The two specific distributed delays in the quennent compon grain and the arri ing procedure is u rent. The input i dr]j(t) = dt drzi (t) dt 1 dt where: rK = output NEW = grain d r]...rK = arr K = order DEL — averag i = index The basic su in evaluating str areas for future facing a short te 45 government component are for rural-to-urban transport of government grain and the arrival of foreign imports. Recall that this same model- ing procedure is used to produce harvest rates in the production compo- nent. The input is a one—time pulse in the case of harvests. 3_ = (NEW,ct) - rqjctll (2.l8a) dt DEL. l dr21-(t) K1 ___;;___ = ________ (r,j(t) - r2,(t)) (2.l8b) dt DELi =' (r .(t) — r .(t)) (2.18c) dt DELr Kr'1" Ki 1 where: rK = output of delay = grain arrivals (MT/year) NEW = grain dispatched (MT/year) r]...rK = array of intermediate rate variables of the delay K = order of the delay (describes the distribution) DEL — average transportation time (years) i = index on variables. item The basic survival model described here was constructed as an aid in evaluating strategies for famine relief and identifying fertile areas for future research. The model describes a hypothetical country facing a short term food crisis and simulates the dynamic demographic, i economic, producti model is highly ag ‘ country, but it sh life operation. A discussed in Chapt tion system compon 46 economic, production, and decision-making processes over time. The model is highly aggregated and does not adequately detail a specific country, but it sheds light on important issues to be faced by any re— life operation. Additions and modifications to the basic model are discussed in Chapter 3 where the model is augmented with an informa— tion system component. To allow evalr performance of fam‘ basic survival mode chapter describes a component. An approach t aspecific applica component to the be cific application, ernment component ' imq modeling links and decision making aggregation as the on information qua' Sampling frequency details of surveil' avoided. The last Wrtant modeling pr It is importa 1" the overall inf CHAPTER III MODELING AN INFORMATION SYSTEM To allow evaluation of the effects of information quality on the performance of famine relief efforts, appropriate modifications of the basic survival model of the preceeding chapter are necessary. This chapter describes a general approach to modeling an information system component. An approach to assessment of information systems is described and a specific application is considered with the addition of a sampling component to the basic model. Much of the material refers to this spe- cific application, but the approach should be clear. The model‘s gov- ernment component is organized for information system addition, provid- ing modeling links among surveillance, data processing, communication, and decision making functions. To keep additions at the same level of aggregation as the basic model, a sampling component is devised based on information quality. The important concepts of measurement error, Sampling frequency and processing delay are included while the complex details of surveillance technique, communication networks, etc., are avoided. The last section of the chapter covers several small but im- portant modeling problems often met in simulation work. Modeling and Evaluation It is important to realize the context of a computer simulation in the overall information system for famine relief (see Figure 1.1). 47 i The model is one purpose is to pr: to be encounterec examines specific and very simplifi programs, and out data processing a tion network. Ti variables can nev tion system inclu relief work, tog quality. The system oqraphic, product system perfomanc tionships between ity. Important): having most effec fect), optimal le straints, and the structures. Two performa minimization of t both observed at because they spec Volved. The mair 0Rhosed to addit‘ 48 The model is one of many tools to be used by the system planners. Its purpose is to provide insight into the processes and structure likely to be encountered during a food crisis. The basic model of Chapter II examines specific aspects of the affected people, the system managers and very simplified versions of transport and logistics, government programs, and outside aid. Our attention now turns to the surveillance, data processing and communication components; the heart of the informa— tion network. The problem becomes one of estimation, since many dynamic variables can never be known perfectly. The evaluation of an informa— tion system includes learning how precise the data must be for efficient relief work, together with the cost of obtaining the desired data quality. The system evaluation is largely a sensitivity analysis. The dem- ographic, production, and market components are fixed, objectives of system performance are defined, and observations are made of the rela- tionships between system performance and changes in information qual- ity. Important problems to solve include determination of data items having most effect on policy performance (and those having least ef- fect), optimal levels of information quality with given cost con- straints, and the interrelationships between data items and policy structures. Two performance objectives are used in this study. These are minimization of total deaths and total accumulated nutritional debt, both observed at the end of one year (T=T.0). These goals are chosen because they specifically measure the well-being of the people in~ volved. The main damage of a food crisis is to the population, as Opposed to additional economic and facilities losses incurred by war i or natural disasi the population tc how well preparec Many other ( minimization of e The goals used he optimization stuc jective to two ar many. It is assr give needed gener Second, each cou the fact that be for judging fami A third typv nutritional debt functional relat out considerable examining the co tional debt. An ers. Since tota per-capita consu tritional debt. crease in nutrii level must be me which time most choosing one yer 49 or natural disasters. The time frame of one year is chosen to allow the population to move through one complete harvest cycle and to assess how well prepared the people are to face another possible crisis. Many other objectives are possible: maximization of storage, minimization of economic loss, minimization of social disruption, etc. The goals used here are limited to two for several reasons. First, in optimization studies, the technique changes needed in going from one ob— jective to two are generally more difficult than in going from two to many. It is assumed that several objectives may be used and two will give needed generality without introducing unneeded complications. Second, each country must choose its own performance objectives, and the fact that both deaths and nutritional level are standard measures for judging famine extent provides a general case (46). A third type of generality achieved by choosing deaths and total nutritional debt as criteria is that they are inversely related. Any functional relationship between them is too complex to determine with— out considerable effort. The inverse relationship is easy to see by examining the combination of processes that lead to deaths and nutri- tional debt. An increase in the number of deaths means fewer consum- ers. Since total available foods is fixed, fewer people means higher per-capita consumption, causing higher nutritional level, or lower nu- tritional debt. Similarly, a decrease in deaths is followed by an in— crease in nutritional debt. Since this is a dynamic process, the debt level must be measured significantly after the initial harvest, by which time most deaths have occurred. (This is another reason for choosing one year as the measurement point.) The single 9 situation. Throu very small death population weak a to provide genera fects of famine 0 Two benchmar the information 5 information stan the best possibl specifically desi involves price c0 mrch use of addit informational qua specific famine r The availability ture as the clair policies and impe two boundaries. The quality meters: the stan error is assumed and the delay tin for system manag world activities the model. As a are transmitted 50 The single goal of minimizing deaths can lead to a precarious situation. Through a similar chain of events as described above, a very small death rate will cause a large nutritional debt, leaving the population weak and vulnerable to disease. So two criteria are chosen to provide generality and to give a comprehensive measure of the ef— fects of famine on the population. Two benchmarks are easily identifiable to judge the performance of the information system. The worst possible case, from a quality—of— information standpoint, would be continuation of normal policy, and the best possible case would be the use of perfect information in specifically designed relief activities. Normal policy in the model involves price controls to determine food allocation, does not make much use of additional nutritional data, and will be little affected by informational quality. This ”worst” case represents operation without specific famine relief information and will be the minimal cost system. The availability of perfect information is referred to in the litera- ture as the clairvoyant case (22). System performance using relief policies and imperfect information should fall somewhere between the two boundaries. The quality of a given data system is modeled here with four para- meters: the standard deviation and bias of measurement error (the error is assumed to be normally distributed), the sampling frequency, and the delay time between measurement and availability of information for system managers. The parameters can be varied to account for real world activities, but the activities themselves are not included in the model. As an example, a decreased delay time is possible if data are transmitted by telephone rather than messenger. To account for this change, the the cause. Agai ity. Specific c cal methods will try, and would 0 of model develo sub-systems as p The four ch generality. The data processing, in an actual app sate for long la meter follows th convenient base surveillance cos reporting observ ganization, mach used in studying duced by the sta sumed to be norm sumed because tl private storage through the errc the central l i or average value a 51 this change, the delay parameter is decreased; no mention is made of the cause. Again, this approach is taken in the interests of general- ity. Specific communication devices, sampling techniques and statisti- cal methods will differ in cost and applicability from country to coun— try, and would only add complexity that is unnecessary at this stage of model development. Chapter V does probe into some of the specific sub—systems as part of cost analysis. The four chosen parameters provide a great deal of flexibility and generality. The delay term represents the sum of all surveillance, data processing, and communication lags. To achieve a given delay time in an actual application, adjustment can be made in one area to compen— sate for long lags in another. The use of a sampling frequency para— meter follows the real world data acquisition process and provides a convenient base for determining the amount of data generated and the surveillance costs. Bias is included to account for regular errors in reporting observations. Possible causes would be bureaucratic disor— ganization, machinery errors, or corruption. This parameter is not used in studying the current model. Random measurement error is pro— duced by the standard deviation parameter; error distributions are as— sumed to be normal with mean equal to the true value. Normalcy is as— sumed because the variables estimated (accumulated nutritional debt, private storage, etc.) are averages derived from many samples. Al- through the error term of each individual sample may not be normal, the central limit theorem guarantees that the distribution of the average value approaches normalcy as the number of samples increases. Policy stru sired policies d information help policies. In ge and leads to mo the planning sta be estimated val of probable vari using a computer streams are typic two. The modeling and the productio tions follow the r "true" variables. for actual governr roan-made decision: Many simulation a can assume that e the error is smal the difference be ably the most imp The organiza events present in cessing functions is depicted in Fi 52 Organization of the Government Component Policy structure and information gathering are intertwined; de— sired policies dictate the types of data needed, and the quality of the information helps determine the likelihood of success of implemented policies. In general, better data allows more knowledgable decisions and leads to more successful outcomes. It is important to realize in the planning stage that the only data available during the crisis will be estimated values of actual dynamic variables and g_pfjgri_knowledge of probable variable movement. This is especially significant when using a computer simulation, because both the actual and estimated data streams are typically present. Care must be taken to differentiate the two. The modeling of the rural and urban populations, the market sector and the production component is done using actual values. The calcula- tions follow the natural relationships and clearly call for the use of ”true” variables. The same is true of the bookkeeping equations needed for actual government storage and imports. But the introduction of man-made decisions requires a second stream of values, the estimated. Many simulation applications, such as queueing or inventory models, can assume that estimated and true values of information are equal, if the error is small or unimportant to the problem being considered. But the difference between in—hand data and real world conditions is prob- ably the most important concept in information system evaluation. The organization introduced here follows the logical sequence of events present in any information system. The inputs to the data pro— cessing functions are the true values of the variables to be estimated. As depicted in Figure l.l, data are collected, processed, and cormrmrnicated. A calculations and timrated, stochas Since the i parameters, the as one unit. It sible for the i described in th pling frequency of the rest of 1 quence. The requirl computation, an asampling comp other means. T rates of change gate statistic cannot be compc and a computed of the calcula in the decisio food rates, be A partic example of th information 5 sitions, sale uses the exac fi 53 communicated. Along the way, measurement errors are introduced and calculations and transmission time cause natural delays. Lagged, es— timated, stochastic variables are used in making decisions. Since the information stream is being represented by data quality parameters, the surveillance and communications components are modeled as one unit. It is assumed that these are the functions most respon— sible for the introduction of errors and delay. The sampling component described in the next section provides for error, delay, and the sam— pling frequency. This forms the core of the modeling additions; much of the rest of the organization needed involves correct computation se- quence. The required order of calculation is simple: estimation, complex computation, and decision rule use. Variable estimates are made with a sampling component, an exponential delay (see Equation 3.l), or some other means. Then calculations can be made to determine target levels, rates of change, and aggregated statistics. An example of an aggre— gate statistic is the average available nutrition rate (ARNUT), which cannot be computed until estimates of imports, storage, population, and a computed figure for time of desired storage are known. The form of the calculation is given in Equation 2.l2. ARNUT can now be used in the decision rules for determining allocation, sales, and emergency food rates, because it is an estimated variable. A particular change of the basic model is mentioned here as an example of the need for consistent calculations when evaluating the information system component. The Equations 2.l3-2.l5 determine acqui- sitions, sales, and emergency food levels in the basic model. Each uses the exact population figure, a practice that is perfectly acceptable excep the problem bein has been added a the new form. A simple me to a simulation. approaching inf is to avoid the munication methc real delays, mea The randomized 6 Equation 3.l) at of the calculat' at each time in: ESTk(t) = l where: EST = esti 54 acceptable except when the precision of the inexact variable is part of the problem being studied. Thus, an estimate of each population class has been added and used in the revised model. See Equation 3.8 for the new form. Sampling Component—-SAMPL and VDTDLI A simple method is needed to introduce data quality parameters in— to a simulation. Simplicity is desirable, since one of the reasons for approaching information system evaluation through the use of parameters is to avoid the detail of describing particular surveillance and com- munication methods. At the same time, the method must approximate the real delays, measurement error and sampling frequency in the system. The randomized exponential delay of the basic model (repeated here as Equation 3.1) accounts for delay and measurement error, but the form of the calculation assumes constant sampling; a new input is processed at each time increment of the model At EST (t) = EST (t—At) + * ((l. + SD * RR) *NEN (t) k k DEL k k k (3.l) — ESTk(t-At) where: l EST - estimated value of variable NEW true value of variable DEL = parameter; average delay (years) SD = error parameter RR = uniform random variable ('— ,~- ) 2 2 rt =tlfi£l index 7';— II Certainly t theinformation butbecause of t mst;mnre sampl exponential dela asmt of percen systematic bias The followi generality then thespecified ir achml variable distributiori fur teras the mode thesamPle serv F” the Periods due to attempt SCheme holds th interval. The detail culatlon in the ‘ t in more detail 55 at = time increment of discrete model (years) k = index on variables. Certainly the sampling frequency is an important characteristic of the information system, not only from the standpoint of data quality, but because of the direct relationship between sampling frequency and cost; more sampling implies higher costs. A further drawback of the exponential delay is that there is only one measurement error parameten a sort of percentage standard deviation. A parameter representing systematic bias in the observations is also desirable. The following routines are quite easily implemented and allow more generality then Equation 3.l. A sampling frequency is given and, at the specified intervals, random measurement error is introduced. The actual variable, plus or minus a bias term, serves as the mean of the distribution function. The sampled value is then stored in the compu— ter as the model advances through a given delay period, after which the sample serves as the estimated value to be used in decision rules. For the periods between sampling points, some form of filtering can be done to attempt to follow the actual variable. The simplest filtering scheme holds the sampled value as a constant estimate throughout the interval. The details of sampling component (SAMPL and VDTDLI) modeling features are now presented. The description follows the order of cal— culation in the routines. A complete listing of the FORTRAN code is contained in Appendix B. These routines are described and validated in more detail in Chapter VII. The discrete linto a specific simple counter (T occurs. The com checked against ‘ of desired varia! that SAMPT can b NSAMPk = SA where: NSAllP = nun SAMPT = sar m = sir k = in: The meaSur lectiOn, l'S sin don Standard er depending on u EStlmation Com; second method 9 dard deviation ESlk(ST) ESTleT) whtte: EST = e5 VAL ‘ ti 56 The discrete model translates the sampling interval parameter of k_into a specified number of simulation cycles, using Equation 3.2. A simple counter (NCNT) is set to zero each time the sampling procedure occurs. The counter NCNT is incremented by one each cycle DT and is checked against the sampling interval size NSAMP. Thus, measurement of desired variables takes place only at specified intervals. Note that SAMPT can be dynamic. NSAMPk = SAMPTk / DT + .5 (3.2) where: NSAMP = number of simulation cycles in sampling interval SAMPT = sampling interval (years) DT = simulation cycle increment (years) k = index on variables. The measurement of a desired variable, corresponding to data col- lection, is simulated in SAMPL with the introduction of bias and ran. dom standard error parameters. Two estimation equations are possible, depending on the characteristics of the true variable. One method of estimation computes an error term proportional to the true value. The second method generates a normally distributed error with fixed stan- dard deviation. The equations used are 3.3 and 3.4 respectively. ESTk(ST) = VALk(ST) * (l. + SDk * Y) * BlASk (3.3) ESTk(ST) = VALk(ST) + SDk * Y * BIASk (3.4) where: EST = estimated value of variable VAL = true value of variable BIAS = “1935 ST = samp Y = star k = inde Straightfor estimates in bot etmnte varian< mi * soi whil: cah E(Yl = 0.0 tnbuted errors isin the stand true value; the The form 0 Shme the stand ht hns methoc cuniderably or t10n 3.3 depenc hatheasuremer The Choice Series data TOT DOSSTny fm‘ S ramnfm.uu COTTCelVable th Per‘capit 3"1Slllce the 57 BIAS = measurement bias ST = sampling time Y = standard normal random variable k = index on variables. Straightforward calculations show that the expected value of the estimates in both equations is the true value plus the bias term. The estimate variances differ: Equation 3.3 produces a variance equal to VALi * SDE while the variance of EST from Equation 3.4 is SDE. (Re- call E(Y) = 0.0, var(Y) = l.) Both calculations produce normally dis— tributed errors, since Y is a normal random variable. The difference is in the standard deviation of the error: one is proportional to the true value; the other is fixed. The form of Equation 3.3 is preferable for discussion purposes since the standard deviation can be described as X% of the true value. But this method becomes an inaccurate model if the true values vary considerably or approach zero. Since the size of the error in Equa— tion 3.3 depends on the size of the variable, the implication would be that measurement techniques get better as the variable decreases. The choice of error estimators is based on examination of time series data for true variable values. Private storage levels vary considerably but the low values stay comfortably away from zero except Possibly for short periods just before harvest time. An additional reason for using Equation 3.3 for storage levels is that it would be conceivable that with less grain to measure, error would be reduced. Per-capita nutritional debt estimation must be done with Equation 3.4 since the true values are small (on the order of lO‘ZMT/person) and can be either are also small (ay: only during the mc Subroutine S! The estimates are tine, VDTDLI. The boxcar routines ( changes in the de to telephone serv current study, bu problems enc0unte Aboxcar del string 01‘ railroa the train empties With the latest 5 9act car moves f. £958. The equat CARn = In where; CART = ith IN : inpl i : llldi N i num and can be either positive or negative. Per-capita consumption rates are also small (approximately 2*l0'7MT/person—year) but approach zero only during the most dire emergencies. Subroutine SAMPL produces estimates values for sampled variables. The estimates are then used as inputs to a discrete, variable delay rou- tine, VDTDLI. The form of the delay follows that of familiar discrete boxcar routines (35). VDTDLI has the added capability of handling changes in the delay rate, as might occur with a change from messenger to telephone service. The variable delay capability is not used in the current study, but is described here as an indication of the particular problems encountered with information flow. A boxcar delay routine is so named because it operates much like a string of railroad cars on a circular track. The car at the front of the train empties its load at the designated output point. A new car wibi the latest supplies (or information) joins the train‘s tail. And each car moves forward One position. Equations 3.5 describe this pro— cess. The equations must be solved in the order presented. OUT = cAR, (3.5a) CARi_1 = CARi, for i=2,3,...,N (3.5b) CARN = IN (3.5c) where: OUT = output of routine CARi = ith car in the array IN = input to routine 1 = index on cars N = number of cars. The delay pal number of array pt tion is simply do Nk = DELAYk/ where: N = size DELAY = dela DT = Sllllt k = inde Notes that ‘1 the array, or tr. an input and out Changes in tion from the ta in increased del od. Equations 3 Equation 3.5c. Where 3 = inde mm . new N = old on . an, A dECreaSe information und 59 The delay parameter of information quality is related to N, the number of array positions, by the simulation increment UT. The calcula- tion is simply done in Equation 3.6. Nk = DELAYk/DT + .5 (3.6) where: N = size of delay array DELAY = delay parameter in 5 (years) DT = simulation increment (years) k = index on variables. Notes that the relationships of Equations 3.5 and 3.6 require that the array, or train, be updated each simulation cycle. There must be an input and output each cycle DT. Changes in delay time always cause addition or deletion of informa— tion from the tail of the train; the newest data values are affected. An increased delay causes the newest data to be held for the extra peri- od. Equations 3.5a and 3.5b are retained, but Equation 3.7 replaces Equation 3.5c. CARJ- = 1m , for j=N,N+l,N+2,...,NNEN (3.7) where j = index on new cars in array NNEN = new size of delay array N = old size of delay array CAR = array element. A decreased delay does not cause loss of data. Rather, the newer information under the old delay scheme is superseded by new data from the new scheme. cannot force the only modification the new, shorter ion in modeling i The output c used in decision an input and pros model. SAMPL ca' val, so additiona is to retain a 54 throughout the 3 Chapter 2) will Offer three Oppo dUTGS. Filteri n Sum 0f Previou £955: POlynomia VDTDLI between 5 We C10591i the variable Observe estimation prob‘ “‘9 Problei Mdehng patter! Each varia tinct infOTma ti 60 the new scheme. This implies that implementation of the new methods cannot force the old information through the system any faster. The only modification to Equations 3.5 is that N is recalculated to fit the new, shorter delay. Note that conservation of flow is not a criter- ion in modeling information transfer. The output of VDTDLI is a lagged, randomly measured estimate to be used in decision rules of the government component. The routine needs an input and provides an output at each time interval of the discrete model. SAMPL calculates a new estimate only once each sampling inter- val, so additional inputs to VDTDLI are necessary. The simplest scheme is to retain a sampled value from SAMPL as a constant input to VDTDLI throughout the sampling interval. This common zero—order hold (ll, Chapter 2) will be the base method used in this study. SAMPL and VDTDLI offer three opportunities for further estimation or filtering proce- dures. Filtering techniques can be used in SAMPL to include the re- sults of previous measurements of the variable in the estimation pro- cess. Polynomial smoothing or similar methods can predict inputs to VDTDLI between sampling points which, hopefully, will track true values more closely than the zero-order hold. And a_prig:i knowledge of the variable observed can lead to modified estimation procedures. This estimation problem is discussed in more detail in Chapter 6. Model Variable Choice The problem of the particular variables to be estimated with the modeling pattern of SAMPLE and VDTDLI is now examined. Each variable included has the potential of generating four dis- tinct information quality parameters. Thus, too many variables could result in complex sensitivity and or with less than th balk at more than age requirements with the number c only the estimate tion system will computer outputs sults by the 9]“. He turn to ber of variables timated is dicta catetloties based famine Many it Population, 90% already monitors system f0y~ Tamil ables not yet 8; storage are deC this second cat called fOr by t ables to es tlma scheme WOul d be \\\\““‘-~_ * quadratic lear, Pirame fii—WW T 6T result in complexities too great for standard analysis. Most of the sensitivity and optimization literature on computer simulations deals with less than three or four parameters, and the more powerful routines balk at more than fifteen parameters (60). Computation costs and stor— age requirements for optimization work seem to increase factorially with the number of parameters.* An additional consideration is that only the estimated values directly linked to a famine relief informa— tion system will be examined in studying data precision. Generation of computer outputs with too many data items can obscure important re- sults by the glut of numbers produced. We turn to real world conditions for a means of limiting the num- ber of variables and parameters. The total number of values to be es- timated is dictated by policy structure. The variables fall into two categories based on need for additional sampling specifically during a famine. Many items are included in existing information systems. Population, government storage levels, crop and harvest conditions are already monitored in almost all countries. Design of an information system for famine relief will be especially concerned with the vari- ables not yet sampled often enough. Nutritional debt and private storage are decision variables from the current model that fall into this second category. These are the generally unknown data items called for by the policy design. Another criteria for choosing vari- ables to estimate in a sampling component (the alternative estimation scheme would be an exponential or similar delay) is the rate at which 3. *As an example, a standard least squares regression including lin- lear, quadratic and interaction terms for n variables requires l+2n+(§) Parameters and the inversion of a square matrix of that size. the variable varie normally tend to T levels. In gener. mfficult More f niques may not ca An alternati parameters to be estimations and s mation system eve point made in the world conditions allowing concent‘ Per-capita variable, to be rESulting form 0 Equation 3.8, S "Dd“ have simil rural consumptic values are used GMUM) = l Where; GAQU - ERSTOR = e GRSTRD = S the variable varies with time. Population levels and crop conditions normally tend to change slowly, relative to consumption and nutritional levels. In general, more rapid changes make the estimation process more difficult More frequent sampling is required, and simple modeling tech- niques may not capture real world behavior. An alternative approach for limiting the number of variables and parameters to be analyzed would be to use the sampling component for all estimations and select only the most sensitive variables for the infor— mation system evaluation. This is certainly a valid process. The point made in the previous paragraph is that examination of the real world conditions and objectives can eliminate much needless analysis, allowing concentration on the items perceived to be most crucial. Per-capita consumption has been added as a decision rule control variable, to be used in much the same manner as nutritional debt. The resulting form of the government acquisitions decision rule is given in Equation 3.8. Sales and emergency food rate equations of the basic model have similar alterations. Note that acquisitions increase when rural consumption is greater than average urban consumption. Estimated values are used throughout. GAQU(t) = CG3O * max (ERSTOR(t) - GRSTRD(t)) (3,8) + CG36 * (AEUNDP(t)-ERNTDP(t)) * EPR(t) + C835 * (EPCONR(t)—AEUPCN(t)) * EPR(t) where: GAQU = government acquisitions from rural sector (MT/year) ERSTOR = estimated rural private storage (MT) GRSTRD = government desired rural private storage (MT) ERNTDP = es EPCONR = es AEUPCN = a P EPR = e C630, CG36 Per-capita of nutritional decision rules sunption provid differences in on relative nut an overshoot , sunption level recently receiv allocation to t The addit“ where policy 5* the change. Tl of the decisio have been reco Nations, which tional surveil elements are T levels and die by real world AEUNDP = average estimated urban per-capita nutritional debt (MT/person) ERNTDP = estimated rural per-capita nutritional debt (MT/person) EPCONR = estimated rural per-capita consumption (MT/person-year) AEUPCN = average estimated urban per-capita consumption (MT/ person-year) EPR estimated rural population (persons) CG30, CG36, CG35 = control parameters. Per-capita consumption forms part of the rate of change process of nutritional debt, providing a sort of derivative control for the decision rules (ll, Chapter 2). In practical terms, knowledge of con— sumption provides a tool to help avoid serious overcompensation for differences in nutritional level. That is, when allocation is based on relative nutritional debts, sustained allocation priority can cause an overshoot, a reversal of roles between the two classes. The con— sumption level takes account of the differences in amounts of food recently received by the two classes and proportionately decreases the allocation to the class that is eating more. The addition of consumption level as a control variable is a case where policy structure and real world conditions coincide to dictate the change. The derivative control was needed to increase the power of the decision rules. Consumption rates as well as nutritional level have been recognized as important pieces of information by the United Nations, which is encouraging all nations to adopt some form of nutri- tional surveillance (25). It should be noted that many other data elements are needed for comprehensive famine relief, especially water levels and disease incidence. Consideration of these items is prompted by real world conditions, but they fall outside the scope of the preliminary m0 food as a mean distribution a nutritional mo Three var sampling compo variable, per- ates four esti data quality exists. Fort time streams The time requ assumed to be one delay par data are assun so one sampli! for each of tl of the samplir common sampli surveys are t There ar of rural vers last until tl classes desii parameters Till classes can : 64 preliminary model used here. The current focus is on allocation of food as a means of equalizing nutritional levels. Eventually water distribution and health care may be added to the policy structure and nutritional modeling. Three variable types have been chosen as inputs to the current sampling component: nutritional debt, private storage, and the new variable, per-capita consumption. Each variable type actually gener— ates four estimates, one for each population group. Given the four data quality elements, a total of forty—eight possible parameters exists. Fortunately, similarities in the processes modeled and the time streams of the variables allow considerable numerical duplication. The time requirements of surveillance and transmission processes are assumed to be similar for each variable type, allowing the use of just one delay parameter. The sampling error of nutritional and consumption data are assumed not to vary significantly across population classes, so one sampling frequency, standard deviation and bias are postulated for each of these variable types. The assumption relies on the ability of the sampling teams to measure different groups equally well. The common sampling frequency corresponds to a real world situation where surveys are taken of all population groups simutaneously. There are substantial differences in the size and rate of change of rural versus urban private storage. Recall that rural storage must last until the next harvest (nine months at the longest) while urban classes desire stores that last one to three weeks. Thus four separate parameters must be used for rural private storage, although the urban classes can share four parameters. These econom thirteen: one d deviations, and are not used in the causes of hi area for further lative ease of a The nine re inputs that will mization work. assigning it a v quality paramete Addi The three p allow evaluation tions are presen for this dissert nificance, they the changes are the next chapter edge of the typc simulation of a An assumpt outside aid bey of this model i resources. Thl' 65 These economies in parameter use have reduced the total needed to thirteen: one delay and four each of sampling frequencies, standard deviations, and biases. It was mentioned earlier that bias parameters are not used in this study. The main reason for this deletion is that the causes of bias will be specific in each country and are left as an area for further research. A secondary but important reason is the re— lative ease of analyzing nine parameters instead of thirteen. The nine remaining data precision elements form a set of variable inputs that will be used extensively for sensitivity analysis and opti- mization work. The importance of this parameter set is underlined by assigning it a vector representation, 5, the vector of information quality parameters. Additional Assumptions and Modifications The three previous sections cover the major additions needed to [ allow evaluation of the information system. Several further modifica- i tions are presented here that apply specifically to the modeling effort for this dissertation. Although the particulars are not of general sig- l nificance, they are discussed for two reasons. The assumptions behind the changes are noted to provide background for results described in the next chapter. And it is hoped that the reader will gain some knowl- edge of the types of problems and subtleties inherent in a computer simulation of a famine. An assumption made throughout the study is that there will be no 1 outside aid beyond the purchased government imports. A main purpose of this model is to examine efficient means of allocating available resources. This allocation problem exists even with substantial fi international a' need for efficir that includes rr no i nternati ona' aid is availablw crisis conditior easily adapted i of the simulatir There is n( food distributic has almost enoug feeding would i r However, any rel particularly the tion as the urba zation purposes, and emergency pr tinction of rur mots, although Due to ini parameter sets to zero. This tive nutritional causes the cons fairly quick equ as planned for b Sales is highly 66 international aid; the aid changes the level of crisis, but not the need for efficient policies and a good information system. Planning that includes reliance on outside help may be disastrous if there are no international reserves at the time of the famine. In the event that aid is available, there will be a time interval between recognition of crisis conditions and food arrival. So the approach used here could be easily adapted to include outside food aid by limiting the time horizon of the simulation and setting a level of expected aid. There is no provision in current policy structure for emergency food distribution to the rural class. The defined ”rural“ population has almost enough food initially. So the addition of rural emergency feeding would involve buying food and giving it back, a wasted effort. However, any relief program will involve aid to those in rural raeas, particularly the landless poor who would be in roughly the same situa— tion as the urban poor classes of this model. Indeed, for conceptuali- zation purposes, the rural poor can be combined with the urban poor, and emergency programs for both groups labeled EMFDG. The class dis- tinction of rural and urban might better be labeled the haves and have- nots, although the physical location may be an important distinction. Due to initial values assigned the urban classes, certain control parameter sets can force the level of government desired sales (GSLSDU) to zero. This typically occurs when the wealthy urban class has nega- tive nutritional debt; they are overfed. The withholding of sales causes the consumption level of the rich to plummet, and there is fairly quick equalization of nutritional debt across the urban classes, as planned for by the policy structure. However, the event of zero sales is highly unrealistic. There is some food available, especially fi at the onset of a cutoff of the is contrary to ' practical reaso mainly by the r of available fo may be infeasib economic reason level of sales, (ARNUT). Then Another si occur in the rv incorrect way ‘ to force a non flow problems tion used here output is ter] The thre gency food ha storage (RSTO tivity cutoff cision variab able. Then 5 to zero. Unl of delays; an shortage hits variables sir 67 at the onset of the crisis (when GSLSDU is most likely to hit zero) and a cutoff of the supply to one particular class even for a short period is contrary to the humanitarian purposes of famine relief. A more practical reason for non—zero sales is the fact that purchases are made mainly by the rich, and the rich will probably get at least their share of available food, assuming that power goes with wealth. In fact, it may be infeasible to limit sales at all to the rich for political or economic reasons. Thus, the assumption is made that there is a minimal level of sales, proportional to the average available nutrition rate (ARNUT). The minimum proportion is set at seventy-five percent. Another situation that occurs in the modeling world but cannot occur in the real world is having a storage level dip below zero. One incorrect way to combat negative storage is to use a maximum function to force a non-negative value. But this can lead to conservation of flow problems if output rates remain larger than input rates. The solu- tion used here follows the actions that would occur in a real case; output is terminated if storage drops too low. The three government activities of acquisitions, sales, and emer- gency food handouts could cause direct depletions of rural private storage (RSTOR) or government urban storage (GSU). Two levels of ac— tivity cutoffs are used, one large storage level for the unlagged de- cision variables and a smaller value for the lagged, implemented vari— able. When storage drops below the designated setting, the rate is set to zero. Unlagged cutoffs are set higher in keeping with the nature of delays; anticipation of a shortage should occur before the actual shortage hits. Quite small storage levels are used to cut the lagged variables since they are slow to rebuild, especially with the use of exponential del model stability Two uses 0 mral-to-urban Since the delay transient respo lay (two months tained by using non-zero. One— both transport are set equal, mediate rates case where inp conserve materi The final rather than moc volving random which are base for obtaining ‘ parameter set different rand distribution 0 calculated fro 396 requiremer variance recur stored values O‘l CD exponential delays. Lagged variable cutoff could cause a shock to model stability. Two uses of distributed delays are mentioned in Chapter II, for rural-to-urban transport of government grain and for import shipments. Since the delays are initialized with zero values in the basic model, a transient response occurs, lasting approximately the length of the de— lay (two months in the case of imports). Smaller transients can be ob- tained by using non-zero initial values for initial rates, and it is logical that import and government shipment rates would normally be non—zero. One-half the maximum was chosen as the starting value for both transport rates. The inputs and outputs of the distributed delays are set equal, making intermediate rate initialization easy; all inter- mediate rates are identical to the common input-output rate. In the case where input does not equal output initially, care must be taken to conserve material flow in the delay (40, Chapter TO). The final modification to be discussed has to do with computer use rather than modeling. The stochastic results of simulation runs in- volving random variables call for statistical evaluations, many of which are based on sample means and variance. The standard technique for obtaining the desired statistics is Monte Carlo simulation. A parameter set is fixed and several separate model runs are made using different random values (29). Each run produces one sample from the distribution of a given variable. The desired statistics are then calculated from the samples, using well known formulas. Computer stor- age requirements are reduced considerably by calculating the mean and variance recursively, according to Equations 3.9. Note that only two stored values, 7 n and Sn, are required for each variable. Another advantage of t available afte ing hypothesis X] = X], — _ l Xn ' nu" Hi Sn = n- where: n = numb xn = nth In = samp 5n = samp Several p modifications. scope of the mc needed to inch And recursive e tion aid. This chapl tion systems us economic, and p Objectives are its effect on ! Ci to advantage of the recursive calculation is that current statistics are available after each run, providing a convenient structure for conduct- ing hypothesis testing with a minimum number of computer runs. X] = X], S] = 0 (3.9a) T =1(( UT + )' <2 (3 9b) n U‘ n- ’n-l xn ’ n- - fl 1 _ 2 < Sn : “-1 * Sn_] + E (Xn_] - Xn) ; n- 2 (3.9C) where: n = number of samples X 3 I ' nth sample Xn = sample mean of n samples U) H n sample variance of n samples. Several purposes can be distinguished in the above assumptions and modifications. Types of aid present are noted to limit and define the scope of the model. Initial value and situational modeling changes are needed to increase the correspondence between real world and model. And recursive equations for sample mean and variance provide a calcula- tion aid. Summary This chapter presents a general approach to evaluation of informa- tion systems using computer simulation techniques. The demographic, economic, and production components of the computer model are fixed, Objectives are defined, and information precision is varied to determine its effect on system performance. four data qual veillance and The probl sensitivity an is discussed. effort are pre problems and 5 With the for verificati ination of sim several unexpe requiring subs modeling struc the use of the larities. 70 The decision making component must be well-organized to match real world behavior. Particular attention is paid to maintaining correct calculation sequence and using only estimated values in decision rules. A sampling component, consisting of two FORTRAN subroutines, is described. The routines model variable estimation through the use of four data quality parameters, avoiding the details of particular sur— veillance and communication system alternatives. The problem of choosing the variables and parameters for use in sensitivity and optimization work is examined, and a general principle is discussed. Several of the assumptions used in the current modeling effort are presented to provide needed background and a feel for the problems and subtleties likely to be encountered. With the addition of a sampling procedure, the model is now ready for verification and validation, using sensitivity analysis and examin- ination of simulation outputs. The model described here produced several unexpected and, in some cases, undesirable numerical results, requiring substantial changes in the policy rules and the nutritional modeling structure. Chapter 4 describes the problems, the changes, and the use of the information system component in detecting the irregu- larities. Hi consist with an tion sy several set by meters. tency a prices, tual da behavio change Th and set expecte lead t< shorten System set fm sultin. CHAPTER IV THE INFORMATION SYSTEM MODEL AS AN AID IN POLICY DEVELOPMENT AND MODEL VERIFICATION With the completion of Chapters 11 and III, the simulation model consists of the basic demographic, economic, and government sections with an added sampling component. Before evaluations of the informa- tion system can take place, the model needs to be ”fine tuned" and several verification procedures conducted. Parameter limits can be set by observing allowable output changes due to changed input para- meters. Verification involves, among other things, checking for consis- tency and reasonableness. Simulation output values for population size, prices, etc., should be sensible and, if available, should track ac- tual data. The model should be consistent with assumed and observed behavior; a known input change should either produce an expected output change or provide clues to the incorrectness of the expectation. The information component can be a useful aid in the verification and sensitivity testing process. A basic assumption is made about the expected effects of changing data quality: better information should lead to better system performance. “Better” information refers to shorter delays and sampling intervals and smaller measurement errors. System performance is defined by the objectives (minimize deaths, etc.) set forth by decision makers. So, by observing performance changes re- sulting from variation of the information parameter vector 5, the 7l soundness adequacy Each tions and mulation An evoluti expected The nation sy policy st felt that ations um Hence, thv nathemath a cost co Mini‘ subj where : E l>< [m soundness of the problem formulation and policy structure and modeling adequacy can be tested. Each of the next three sections of this chapter describes correc— tions and additions to the basic model and to the original problem for- mulation as required by violations of information quality assumptions. An evolutionary process unfolds as the model behaves more and more like expected real world activities. Several general conclusions become apparent about efficient famine relief. These conclusions are presented in the last section. A Changed Problem Formulation The intended research path of this study was to examine the infor- mation system effects apart from all other considerations, particularly policy structure. Because of the general ”approach” nature here, it was felt that specific policy structures, crisis levels, and cultural vari- ations would be better studied at the time of actual application. Hence, the desire for an efficient and economic information system was mathematically formulated as a multiresponse minimization problem with a cost constraint, as in Equation 4.1. Minimize EA!) subject to §fl§)5 g, and 51ij Where: E_ = system performance vector (total deaths, total nutritional debt) E = cost function vector X _ ‘ information quality vector (delays, sampling intervals, measurement errors) 9] H" 9192” This form questions, the validity of co can be done wi two or three d effect observe stricted to th However, ent fonnulatic is sensitive t be included wi case that, as sented in the BefOre CC “on quality, policy StructL di'l'ections on Should follow to enuanze m C0“Sists of ai ings‘ The .001 meswhich C16 is an Example: affecting 90W 73 C1 = resource constraint vector QT’QZ = constraints on information quality. This formulation has several advantages. By avoiding all policy questions, the information system can be examined directly. To test validity of conclusions acorss policy structure changes, optimizations can be done with distinct government decision components. Similarly, two or three different crisis levels can be simulated and data decision effect observed. The scope of each optimization problem is nicely re- stricted to the parameters of the §_vector. However, there is no a_prigri evidence for accepting this conveni- ent formulation. If the optimal performance level of a policy parameter is sensitive to changes in data precision, then that parameter should be included with §_in optimization studies. It could easily be the case that, as information quality improves, stricter constrols (repre- sented in the model by large parameters) can be instituted. Before continuing the discussion of policy sensitivity to informa— tion quality, distinctions should be drawn among relief strategies, policy structure, and policy parameters. The structure consists of directions on what_to do, the decision rules themselves. Structure should follow from the overall strategy. In this study the strategy is to equalize nutritional debt across the population; the policy structure consists of allocation through acquisitions, sales, and emergency feed— ings. The policy parameters are the specific variables of the decision rules which determine the timing and rates of the various activities. As an example, the Equation 3.8 is a defined part of policy structure affecting government acquisitions (GAQU). The parameters C636, C835, and C630 determ hidden paramete activities by 5 refer to policy the vector 3. Policy par formance. Asi bility. Distir be sufficient). tor. The tests elaborate exper 0f the sensitii fixed l Note for a given h, Sistem will val 0litimal policy Sensitivity cal in I For infl is by far more variation is p' Used. But if Numemug fixed I Values n . \ . ‘*0pt~ima] . We“ 0litima] 74 and C630 determine the rate at which acquisitions are made. A somewhat hidden parameter (CGZl) determines the start and end of acquisition activities by signaling a state of emergency. "Policy” will henceforth refer to policy structure. The policy parameter set will be noted by the vector 3, Policy parameters P_may have an effect on information system per- formance. A simple set of sensivitity tests can check for this possi- bility. Distinct values for §_are chosen (two or three vectors should be sufficient). Sensitivity tests on E_are made for each fixed 5_vec— tor. The tests can be one parameter variation or can involve more elaborate experimental design and optimization techniques. The intent of the sensitivity analysis is to move toward an "optimal"* P_ at each fixed N. Note that two types of sensitivity will be present. First, for a given 5, policy parameter changes will affect performance. The system will vary in sensitivity to the individual E_ parameters. Once optimal policy parameters are chosen for each 5, the second type of sensitivity can be examined, the sensitivity of E. values to changes in X, For information system evaluation, the second type of sensitivity is by far more important. If only the performance sensitivity to.E variation is present, the assumed formulation of Equation 4.l can be used. But if.fi varies with 5, a new problem statement is needed. Numerous sensitivity simulation runs were made at three different fixed_§ values. The information vectors chosen are listed in Table 4.l as ”clairvoyant,” ”good,’l and ”poor” data quality. The clairvoyant \M . *Optimality is complicated by the multiresponse nature of the ob- Jective function, B_ may consist of many vectors, each producing a pareto optimal response. Table 4 Preli XParameters Delay (weeks) Nutrition Sampling Consumpti Sampling Private S Sampling Standard Devig has Table 4.1. Information Quality Parameters Used for Preliminary Policy Parameter Sensitivity Tests Data ualit Sets X Parameters Clairvbyant Good Delay (weeks) 0.2 1.0 Nutritional Debt Sampling Interval (weeks) 0.l l.0 Consumption Sampling Interval (weeks) 0.l l.O Private Storage Sampling Interval (weeks) 0.1 2.5 Standard Deviation 0.0 0.0 Bias 0.0 0.0 Poor 2.0 4.0 4.0 6.0 0.0 0.0 vector assumes the so-called data precision exercise. The nal Eparamete costs can be i tic portions l intervals for the discrete ' Fourteen involved iden variations in vector. lota with total m The resc fourteen para and six were results. Till Volated in t tElltative f0 WAG and pr MG) used i this Chitter IPEl‘fomanc tiined in Cl 76 vector assumes near—perfect knowledge of available information, while the so-called good and poor vectors represent successive degradation in data precision. Note that measurement error terms were not used in this exercise. The purpose of the sensitivity tests is to determine if opti- mal P_parameters are sensitive to §_changes. A savings in computation costs can be realized if E_is shown to be sensitive to the non-stochas— tic portions of 5, It should also be noted that the delay and sampling intervals for the clairvoyant case are the smallest values possible with the discrete model and sampling component constraints. Fourteen P_parameters were chosen for sensitivity tests. The tests involved identifying a base vector, observing results of ten percent variations in each parameter singly, then moving toward a better base vector. Total death count was used as the main criterion of choice, with total nutritional debt secondary. The results of the crude optimization process showed that of the fourteen parameters, three were definitely sensitive to §_variation and six were not. The remaining five parameters produced inconclusive results. Thus, a tentative conclusion was drawn that E_and §_are inter— related in their effects on system performance. The conclusions are tentative for two reasons. First, the sensitivity tests described are crude and produced, at best, likely local paretg_gptima. Second, the model used for the tests was not completely validated; the rest of this chapter contains numerous modifications that could affect P_versus X performance. A more thorough study of the sensitivity problem is con tained in Chapter VIII where the conclusion is drawn that policy para- meters do interact with information quality parameters in influencing system performa wfll also be gi A new prob the effect of l athn informati policy paramete Minimize f subject tc av were: E = s 9 = c I = T E = s E = c 5&ch E13E2=c Note that WWW, the the COHStrajn costs. The cost SONS. FiLSt, 77 system performance. A more complete description of sensitivity testing will also be given at that time. A new problem formulation is proposed in Equation 4.2. Because the effect of §_on P_is the only sensitivity type of interest in evalu— ating information system work, the P_in Equation 4.2 consists only of policy parameters whose optimal values change with N, Minimize E(N,E) (4.2) subject to g(x) 5 C and Q1 5 5.: 92 5153532 where: E_ = system performance vector E_ = cost function vector 5_ = information quality vector E_ = sensitive policy parameter vector 9_ = constraint vector 21,92 = constraints on information quality Eq,§2 = constraints on policy parameters. Note that the cost constraint remains a function of §_only. Theo— retically, changes in E_will affect program administration and could cause substantial cost and manpower variation. This would imply that the constraining function should become §(§,E) to account for policy costs. The cost function is left as g([) for several very practical rea— sons. First, the policy costs will greatly exceed information system ‘W': costs. Adding in infonnatiov team in charge only with the". of programs, a affect the sut are not incluc sideration is sis, a factor tic nature. Possibly POVCY costs i All. Dependi n be in critical illocation of formation syst StPaints in th "I“ l‘estrict and Constructi Inf - W The resul the basic info sents graphs 0 lllth clairvoya] better than DOT 78 costs. Adding policy and information expenses would obscure changes in information cost during optimization work. Secondly, a planning team in charge of infonnation system design will likely be concerned only with their own budget and other resource constraints. The costs of programs, although important in the overall relief system, will not affect the subsystem planners. Similarly, transportation system costs are not included in the information system optimization. A third con- sideration is that policy parameters are affected by the level of cri- sis, a factor that cannot be explicitly planned for due to its stochas- tic nature. Possibly the most important reason for not adding information and policy costs is that monetary restrictions may not be the limiting fac— tor. Depending on the stricken area, equipment, personnel, or time may be in critically short supply. The major decisions would then involve allocation of trained people, trucks, and radios to programs, the in- formation system, or transportation work. The objective of the con- straints in the problem formulation should be to identify factors which will restrict optimal system performance. Chapter V examines the form and construction of g, lflfgrmation Quality Validation The results of preliminary sensitivity work were disconcerting: the basic information quality assumption was violated. Figure 4.l pre- sents graphs of total deaths through time for the three sets of x_and E vectors. The curves increase as expected through the first half year, with clairvoyant data working better than good data, which are, in turn, better than poor data. The leveling off of deaths after the first Total Deat (Millions Figure 4.]. ' 79 Total Deaths (Millions) 6 Poor“\N 5 . ‘Clairvoyant \Good 4 f 3 2 1 First Second Harvest Harvest Time 4 n _1 A; J L L /\ 1 k 1 (YearS) A .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 Figure 4.l. Total Deaths for Different Information Quality Sets. harvest indicai combined to cre some situation T: (.5 years, rapidly, shoot ing the total Several p culated P val cies, the poli natural phenom Non. Further bination of al curves in Fig formation has plained. The prob‘ information h likely cause lar equations is known; it P0pulat10n gr and lower tot model are knc should Indice 80 harvest indicates that the reduced population and good harvests have combined to create a more stable nutritional climate. But a trouble- some situation occurs just before the first harvest, in the period T = (.5 years, .6 years). Deaths in the clairvoyant case mount most rapidly, shooting above results from the "good" data and almost reach- ing the total from the "poor“ data. Several possible causes exist for the observed behavior. The cal— culated_E values may not be optimal, the model may have inconsisten— cies, the policies may not be correctly formulated, or there may be a natural phenomenon occurring which is obscured by non-perfect informa- tion. Further work described in the next sections reveals that a com— bination of all the above factors is responsible for the shape of the curves in Figure 4.l. The key fact uncovered here is that better in— formation has produced worse results; this inconsistency must be ex- plained. Policy Structure Additions The problem exhibited in Figure 4.l is quite fundamental: better information has produced worse results. The steps in discovering a likely cause for this vexation involve moving back through the particu- lar equations that lead to the problem. The overall relief strategy is known; it is desired to spread nutritional debt evenly across all population groups. This should equalize death rates for all classes and lower total deaths. Simulated time series for all variables in the model are known. Comparison of desired results and simulated variables should indicate a direction for problem solution. Figure 4. classes for th are such that rural popution deaths almost outperforms th much closer fc after the harv and urban conc case, the urbe is narrowed or available fooc Relating be seen that 1 exclusively by mUCh 0f the i l habits of ture increase near the harvest s Plies at that The dist harsh reality co"sumption m population ex the harvest. ii Crunch," pre 81 Figure 4.2 depicts the breakdown of total deaths by urban and rural classes for the clairvoyant and poor data sets. Because initial values are such that the total urban population is approximately equal to the rural popution, the desired policy reSult is to have rural and urban deaths almost equal. By this criterion alone, the clairvoyant data set outperforms the poor quality data. Rural and urban death totals are much closer for the better data case, particularly in the stable region after the harvests (T > .7). But there is a large gap between rural and urban conditions during the early crisis. Even for the best data case, the urban deaths lead rurals by as much as l.2 million. The gap is narrowed only at the height of the crisis when presumably no one has available food. Relating Figure 4.2 to the total death curves of Figure 4.l, it can be seen that the large initial jump in total deaths is caused almost exclusively by urban suffering, while the rural population accounts for much of the increase immediately preceding harvest time. The different habits of rural and urban classes account for the larger rural death increase near the harvest. Rural consumption is tied more directly to the harvest start, so the rurals are more likely to exhaust their sup— plies at that time. The distinct shapes of the urban and rural death curves suggest a harsh reality. With a limited amount of food available, more early consumption means much worse conditions at the crisis peak. The rural population exhausts its supplies early and suffers greatly just before the harvest. The urban group, on the other hand, eats too little in the early portion of the famine but is then not as affected by the ”crunch,“ presumably because there are fewer people to feed. The Deat (llilli 3.5 . 3.0 - 2.5 . 2.0 , 0.5 . Fig ‘82 Deaths (Millions) 3.5 . ”Poor,” Urban \ 3.0 " n ' II Clairvoyant Urban,\ 2.5 . &\ ”Clairvoyant“ Rural 2.0 . &\."Poor" Rural l.5 r 1.0 _ 0.5 . _ J_ A; L_g4i, Time .l [2 .3 .4 .5 .6 .7 .33 .9 1.0 (Years) Figure 4.2. Deaths by Rural and Urban Classes for Different Information Quality Sets. advantage of 5' especially in 1 port requi remei more is availa stark: short- Increase Early lncreasin should serve a based on its r should eventua nation of the Parameter is ; government urt that with gove are PFOtected increasing thf hood of em), Unfortuni Initial Condi- lS negative; . 0facouisitio ChdSes are ma h POlicy adequateh’ to once thuisit Policy mods f1 83 advantage of slowly increasing nutritional debt can be clearly seen, especially in relation to the rural class. By consuming less, life sup— port requirements are less, to a point. Thus, less food is needed and more is available at the worst times. The conclusions is chillingly stark: short-term gains can lead to long-term disaster. Increase Early Acquisitions Increasing acquisitions from the rural sector early in the crisis should serve a dual purpose. The rural class should reduce consumption based on its reassessment of storage levels. And the urban classes should eventually benefit from the increased government stocks. Exami- nation of the policies shows a possible immediate remedy. A cutoff parameter is part of the acquisitions policy to stop purchases when government urban storage is too high. The reasoning for the cutoff is that with government storage above a certain level, the urban classes are protected and acquisitions would unfairly hurt the rural class. By increasing the cutoff value or eliminating it altogether, the likeli— hood of early acquisitions increases. Unfortunately, a second hindrance to early acquisitions exists. Initial conditions are such that average urban nutritional debt (AEUNDP) is negative; the urban rich are overfed. This reduces the desirability of acquisitions according to Equation 3.8, so that little or no pur- chases are made. A policy addition is needed. The former policies are unable to adequately control results since parameter changes alone cannot influ- ence acquisitions. Several loose guidelines can be set for allowable Policy modifications. A well-defined policy objective is needed that is in line witl explicit timing especially for policy's worth Here, the the rural sect: control becausi rural personal an emergency h. average nutrit since the regu reasoning lead tion 4.3, if a) a and b) A then anon Where; anou . ll ERSTOR GRSTRD = AEUNDP = C645 — ~ Addition rule is snooty Rural deaths c 84 is in line with the overall relief strategy. Parameters should provide explicit timing and rate controls. And simplicity is highly desirable, especially for assessment of policy effectiveness. The final test of a policy's worth is its ability to positively influencesystemperformance. Here, the desired policy must increase government purchases from the rural sector early in the harvest. Nutritional debt is not a good control because the urban average figure is initially negative. But rural personal storage is still a possible control. And the fact that an emergency has been declared can serve as a starting signal. Urban average nutritional debt greater than zero can serve as an ending signal since the regular policy of Equation 3.8 can then take over. The above reasoning leads to a simple proposed early acquisitions policy, Equa- tion 4.3. If a) an emergency has been declared and b) AEUNDP : 0.0, then GAQU(t) = max(CG45*(ERSTOR(t) — r‘RSTRD(t)),0.O) (4.3) where: GAQU = government acquisitions (MT/year) ERSTOR = estimated rural private storage (MT) GRSTRD = government desired rural private storage (MT) AEUNDP = average urban nutritional debt (MT/person—year) CG45 = rate parameter (year'1). Addition of Equation 4.3 to the model does increase the early ac~ quisitions rate, and the transition to the normal purchase decision rule is smooth. But the effects on death rates are not as desired. Rural deaths do increase slightly at the beginning of the emergency. However, the tr ban population acquisitions be These new large increase rural class exl area cause, a for transporta‘ help the urban tor. The poss storage as the that governmen W Thus, the the harvest. maximum functi tion policy (E htest of this hill. Unfort m to harm th without the ru heuisitions f The Secon because Common nodel perform when hUl‘al c0“ I. However, the toll at the crisis peak is higher than ever. And the ur- ban population shows no improvement until several weeks after the early acquisitions begin. These new results lead to an examination of the causes of the large increase in rural deaths just before harvest time. Clearly, the rural class exhausts its food stocks. Perhaps, excessive acquisitions are a cause, along with overconsumption. It appears that the lag times for transportation and policy implementation restrict the ability to help the urban classes through government purchases from the rural sec— tor. The possibility arises that grain is piling up in government storage as the rural class starves, since a time series analysis showed that government rural storage is consistently greater than desired. Reduce Harvest Acquisitions Thus, the next policy to address is reduction of acquisitions near the harvest. Two solutions suggest themselves. First, dropping the maximum function on the rural private storage control of the acquisi— tion policy (Equation 3.8) should decrease purchases when stocks drop. A test of this modification showed that acquisitions do fall dramati- cally. Unfortunately, the main effect is not to help the rural class, but to harm the urban classes, because government stocks are exhausted without the rural grain. Evidently, there are causes beyond excessive acqUisitions for the large rural death toll. The second method for reducing government purchases is implemented because common sense dictates its inclusion. The effect on current model performance is negligible, but a different set of initial condi— tions could change its importance. The policy is to stop acquisitions when rural consumption falls below the minimum life—sustaining level. At this point, broken down an expended to tr people is wast If EPCONF where : GAQU EPCONR UK5 = Transport effectiveness. ies analysis < a thorough stl desiom‘ng eff Policy modifii 0i informatim “mlwereunco. total . The Satu “hk causes a nent pupa] st tion that is that of a 9rd hides (truck 86 At this point, the reasoning behind nutritional debt equalization has broken down and disaster is inevitable without outside aid. The energy expended to transfer food from rural starving people to urban starving people is wasted. Thus, the inclusion of decision rule Equation 4.4. If EPCONR(t):iUK5, then GAQU(t) = 0.0 (4.4) where: GAQU = government acquisitions (MT/year) EPCONR = estimated rural consumption (MT/person—year) UK5 = minimum life sustaining nutrition (MT/person—year). Alleviate Transport Bottleneck Transportation lags were mentioned earlier as a hindrance to policy effectiveness. Several implications have been derived from a time ser- ies analysis of the transport process in the current model. Certainly, a thorough study of transport and distribution systems is needed in designing efficient relief efforts. The following observations and policy modifications are included as examples of the interrelationships of information systems, transportation systems, and policy structure. Theywereuncovered as possible contributions to the huge rural death total. The saturation of the rural—to-urban government transportation link causes a serious bottleneck. This occurs when inputs to govern— ment rural storage exceed outputs, causing stocks to mount in a loca- tion that is not immediately accessible. The problem is similar to that of a grain-handling seaport where the grain is offloaded from Ships into dockside storage silos and then onto appropriate land ve— hicles (truck or train). Results of previous simulation work on seaport Operat put rate from the expected i adequate trans is essential f Two simple increase outpu for in the fol' government stor low. The ”trig levels at which Port delays. T aslight modifi 1ISSThPly obtai (€525) whose va If (GSU(t) then GSRU(‘ If (esele) then (soggy there; GSU _ go GSR = go GSUD = 90 GSRD = 90 GSRUlix = ma. GAQU - - 90‘ 87 seaport operations indicate that to avoid excessive buildups, the out— put rate from silo to land transport must be considerably larger than the expected input rate of grain in ships (30). The implication is that adequate transportation (ship to storage or between storage locations) is essential for the operation of any allocation policies. Two simple ideas exist for alleviating the transport saturation: increase outputs or decrease inputs. Both possibilities are arranged for in the following policy additions. Increased outputs from rural government storage (GSR) are desired when urban storage (GSU) falls too low. The “trigger” level of GSU must be considerably larger than the levels at which emergency programs are stopped, to account for trans- port delays. The parameter GSUD serves as the trigger in Equation 4.5, a slight modification of Equation 2.l0. The increased transport rate is simply obtained by multiplying the normal rate (CGl) by a factor (C025) whose value is greater than one. If (GSU(t) : ssup), then GSRU(t) = min(GSRUMX, max(CGl*CGZS*(GSR(t)—GSRD),0.0) (4.5) If (GSR(t) : GSRD), then (GAQU(t) :_GSRUMX - EIMP(t) (4.6) where: GSU = government urban storage (MT) GSR = government rural storage (MT) GSUD = government desired urban storage (MT) GSRD = government desired rural storage (MT) GSRUHX = maximum transport rate (MT/year) GAQU = government acquisitions (MT/year) EIMP CGi = C625 Equation current model sitions so the (GSRUHX). In was tried in l GAQU, causing in Equation 4 Four pol of model outp better l0f0rn testing. Unf data quality led to only a worsened the Slhption time the ThTOrmat' ca”59$ discus The Sam duces worse modified to whid the inc 88 EIMP = estimated imports (MT/year) CGT = normal transport parameter (year’T) CGZS = crisis transport increase parameter (dimensionless). Equation 4.6 represents a limit placed on inputs to GSR. In the current model all increases in GSR are due to either imports or acqui- sitions so that inputs to GSR cannot exceed maximum possible outputs (GSRUMX). In an alternative formulation, current transport rate (GSRU) was tried in place of GSRUMX. This placed too great a restriction on GAQU, causing urban class suffering. The GSR restriction is included in Equation 4.6 to allow rural storage to increase it if falls too low. Four policy additions have been made based on time series analysis of model outputs. The investigation was suggested by the fact that better information was producing worse results in initial sensitivity testing. Unfortunately, the policy additions have not eliminated the data quality inconsistency. Recall that increased early acquisitions led to only a small early increase in the rural death rate and greatly worsened the death toll at the ”crunch." Analysis of per—capita con- sumption time series in the next section reveals a modeling cause for the information system trouble, in addition to the policy and natural causes discussed already. Modeling Changes The sampling component has revealed that better information pro- duces worse results using the basic model. Policy structure has been modified to provide additional control over the processes leading to~ ward the inconsistencies in total death figures. The policies have not produced the desired changes; especially disappointing is the lack of results from s the puzzle is rate, per-capi rural per-capi policies from effect of the : Two parts ral population acquisitions ii the pe0ple are sistently overc Til is the osci Peak is explain following deep Pecially Since question. Thes Undesirabi Period of time Peasming relief the and the pri Thin work, my. Piter Search is rural permapi ta government acQui nodeh‘ng leading 89 results from substantial early acquisitions. The next step in solving the puzzle is an examination of the variable responsible for the death rate, per-capita consumption. Figure 4.3 contains time series plots of rural per-capita consumption both before and after the addition of policies from the previous section. By comparing the two curves, the effect of the new decision rules can be seen. Two parts of the curves in Figure 4.3 are curious. First, the ru— ral population does not appreciably change its consumption habits when acquisitions increase at the beginning of the crisis. It appears that the people are not adequately planning for the future since they con- sistently overconsume during these early stages. The second peculiar— ity is the oscillatory behavior during the harvests. The consumption peak is explainable as the result of the incoming harvest. But the following deep decline in eating does not match expected activity, es— pecially since personal storage levels are high during the period in question. These two behaviors indicate a possible modeling problem. Undesirable consequences abound if the model is incorrect. The period of time around the start of the first harvest is crucial for measuring relief effort performance. The crisis hits a peak at that time and the probability of disaster is at its greatest. In optimiza- tion work, poor modeling could lead to distorted results if the para— meter search is trapped by a model inconsistency. The fact that the rural per-capital consumption curve does not respond to persistent government acquisitions could cause rejection of a wise policy, if the modeling leading to such results is wrong. Per Capita C (MT/perso .45l .40- .35 .30 .25 .20 90 Per Capita Consumption (MT/person—year) ‘45i .40, l .35F .30- Basic Model .25- .20- .l5 .l0 “zzFirst Harvest Start y- . 1 - - -—4. . Time .T .2 .3 .4 .5 .6 .7 .8 .9 .l0 (Years) Figure 4.3. Rural Per~Capita Consumption Before and After Policy Changes. A few wc the current n tions. while sented in the principal mee volves testir havior (29). empirical, Cil study actual famine) to 91 relection of Sistencies t' to affect. Mass an model varia tions, these T- Doe pre 2~ Doe the 3. Doe of hh example c redPotion ir the first ar CUSSed b8) Oil 9T Principles for Change A few words are needed here on procedures for determining whether the current model is accurate and whether to accept proposed correc— tions. While a more complete discussion of model validation is pre- sented in Chapter VII, the verification method is mentioned here as a principal means of determining model corrections. Verification in- volves testing whether proposed equations match expected real world be- havior (29). In the current case, expected behavior is reasoned, not empirical, due to a lack of data. This, of course, implies a need to study actual behavior (in this case, consumption habits preceding a famine) to ground the model in the real world. An obvious reason for rejection of a particular model occurs when there are persistent incon- sistencies that parameters and applicable policy structure are unable to affect. Mass and Singe give three criteria for determining whether one model variable is dependent on another (44). With slight modifica- tions, these criteria can be applied to a modeling change involving several variables: l. Does the modeling change lead to desirable changes in predicted numerical values of the system? 2. Does the modeling change lead to a desirable change in the system behavior mode? 3. Does the modeling change lead to a desirable changed view of preferable policies? An example of the second criterion in the present problem would be a reduction in consumption oscillations during harvest time. Examples of the first and third criteria come to light as modeling changes are dis- cussed below. W Calculat in Equations - of Equation 4 presents curr expected stor last. Thus, w the harvest w form of Equat crease with t of desired cc nomal requii Note that cor The intent o: senses an app XFRl(t) mun . Pcowsm where : XFRl FRl F2 RSTOR PR EHFsU Rural Consumption Calculated rural consumption habits of the basic model are given in Equations 4.7, 4.8, and 4.9. The numerator on the right hand side of Equation 4.7 is actual private storage, RSTOR. The denominator re— presents current desired storage. It is computed as the product of the expected storage depletion rate and the time over which stocks must last. Thus, when XFRl is less than one, storage will be exhausted before the harvest without consumption cutbacks or outside aid. The functional form of Equation 4.8 is given in Figure 2.2a, where FRl is seen to in- crease with the ratio XFRl. Per-capita consumption is an FRl fraction of desired consumption. Equation 4.9 computes desired nutrition as the normal requirement (RNUTPN) plus a recovery portion of nutritional debt. Note that consumption cannot go higher than four-tenths MT/person—year. The intent of these equations is to describe a rural population that senses an approaching shortage and reduces consumption accordingly. XFRl(t) = RSTOR(t)/((RNUTPR(t)*PR(t) + EMFSU(t))* (TTSH(t) + SF)) (4.7) FRl(t) = F2(FRl(t)) (4.8) PCONSR(t) = min(.4, (RNUTPN + RK6*RNUTDP(t))*FRl) (4.9) where: XFRl = ratio of current to desired rural private storage (dimensionless) FRl = rural food availability factor (dimensionless) F2 = consumption habit function (depicted in Figure 2.2a) RSTOR = rural private storage (MT) PR rural population (persons) EMFSU emergency food to urban relatives (MT/year) 'IJTY'vQ .' RNUTPR = RNUTPN = RNUTDP = PCOHSR = TTSH = SF = RK6 = Examinat cularities of due to the 0 tion F2 in F1 93th acquisi The cult variable its} harvest star' Creases inst. real world 5 want l0 have end! The co time Oh harv vagaries of more and mor Teeter. wan decreaSe wit hnewi CUTVe (a) 0‘ l i 93 RNUTPR = current nutritional requirements (MT/person—year) RNUTPN = normal nutritional requirements (MT/person-year) RNUTDP rural nutritional debt (MT/person) PCONSR = rural per—capita consumption (MT/person-year) TTSH = time until start of next harvest (year) SF harvest time safety factor (year) RK6 recovery rate parameter (year—T). ll Examination of Equations 4.7-4.9 shows possible causes for the pe- cularities of Figure 4.3. The denominator of Equation 4.7 provides a clue to the oscillatory behavior near the harvests. The shape of func- tion F2 in Figure 2.2a suggests the non-repsonsiveness of rurals to early acquisitions. The culprit in Equation 4.7 is the time ofdesired storage. The variable TTSH is computed as the difference between the time of the next harvest start and current time. Thus, TTSH is discontinuous; it in- creases instantaneously at the two harvest starts (T=.55, T=.75). If real world storage desires matched this variable, the rural class would want to have more grain stored at the beginning of a harvest than at the end! The constant safety factor SF also produces inconsistencies. The time of harvest is only approximately known early in the year, due to vagaries of weather. But as the harvest approaches, the farmer knows more and more precisely when crops will be ready. Thus, the safety factor, which represents a safeguard in case of a late harvest, should decrease with TTSH. A new functional form for time of desired storage is pictured in Curve (a) of Figure 4.4. It is based on certain assumptions concerning lime (Yea‘ Time (Years) Curve(b) Government GTDSTO Curve(a) Rural .2 _ TDSTO ./" . . 444, a , . . a . . Time .T .2 .3 .4 .5 .6 .7 .8 .9 1.0 (Years) Figure 4.4. Rural and Government Desired Times of Storage. arural indiv He expressly the harvest. sired storage harvest and t incorporates harvest time. The June months. The thought is g" and-a-half it sold. After as this crop Curve (i function has. curve is def; Randomized h tions by the inclusion in The lac function F2 flection Sta Thus, the re tightening. is availab]e mod“ descm' 95 a rural individual's assessment of his/her needs and harvest timing. _ We expressly assume that people forward plan and space out food until the harvest. The expected time until harvest forms the base for de- sired storage time in the long period between the end of the second harvest and beginning of the first. A linear equation is given which incorporates a decreasing safety factor. The major changes occur at harvest time. The June crop brings the first new supplies in at least eight months. The crisis is over, assuming that harvests are good. Little thought is given to storage buildup until near the end of the month- and-a-half long harvest period. Then grain is gradually stored or sold. After the start of the second harvest, storage begins in earnest, as this crop must last for another eight month period. Curve (a) of Figure 4.4 represents a continuous, approximated function based on the assumed conditions of the basic model. The new curve is deterministic because the harvest times of the model are. Randomized harvest times would call for estimation of the crop condi- tions by the rurals. Such estimation is considered too detailed for inclusion in the current study. The lack of rural response to early acquisitions is related to function F2 in Equation 4.8 and Figure 2.2a. The normal consumption fraction stays much too high, especially for XFRl values above one~halfi Thus. the result of early acquisitons is not to produce desired belt- tightening. Instead, rural stocks are exhausted more quickly and less is available at the crunch. (See Figure 4.3). Apparently, the basic model describes a population not well prepared for meeting a crisis. It is po eliminating f Because of ti greater than nendous overt the distinct conservation for acquired Equation 4.9 consumption hon for the for good tin Equations 4. XFRl (t) FRl(t) PCONSRI where; TNTO= FRl The us 4T2 shOUic Showed a tE Penis) was 96 It is porposed to relate XFRl directly to desired consumption, eliminating function F2. There is a drawback to this scheme, however. Because of the new desired storage time function, XFRl often is much greater than one. Using the ratio indiscriminately could lead to tre- mendous overconsumption. This problem can be avoided by considering the distinct consumption desires in times of abundance versus times of conservation. Nhen food is plentiful, the individual wants to make up for acquired nutritional debt, similar to the desired consumption of Equation 4.9. But during crisis times, sensible planning limits the consumption base to required nutrition. XFRl is the availability frac- tion for the lean times, while one (l.0) must be the maximum fraction for good times. The new rural consumption modeling is summarized in Equations 4.l0, 4.ll, and 4.l2. XFRl(t) = RSTOR(t)/((RNUTPR(§)*PR(t) + EMFSU(t))* TDSTO(t ) (4.l0) FRl(t) = min(XFRl, l.0) (4.ll) PCONSR(t) = min(.4, RNUTPN*XFRl(t), (RNUTPR(t)*RK6*RNUTDP(t))*FRl) (4.l2) where: 'HBTO = time of rural desired private storage (year) FRl = food availability factor in good times XFRl = food availability factor in lean times All other variables as in Equations 4.7-4.9. The uses of RNUTPN and RNUTPR for desired consumption in Equation 4.l2 should be noted. Model testing with various variable combinations showed a tendency toward underconsumption when RNUTPR (current require- ments) was used for lean time desires. Similarly, overconsumption exists when RT results are n: are mentioned Figure 4 above model c of Figure 4.3 sumed. The; sumably due 1 tually improi tightening 0' al modeling significant ing fact to tion again f the hypothet ThPortance c creased. AS men marked 1mm. fitted mini similar Cha reveaTed an recall fro" till of f0, 97 exists when RNUTPN (normal requirement) is used in good times. These results are not highly significant in overall system performance, but are mentioned as possible further research areas. Figure 4.5 presents the rural consumption curve resulting from the above model changes. Note that the harvest time oscillatory behavior of Figure 4.3 is reduced, leaving only the peak as first crops are con— sumed. The plunge before the harvest has also been eliminated, pre- sumably due to more careful rationing. In fact, rural conditions ac— tually improve just before the crisis hits. This suggests further tightening of acquisition controls. And, in fact, without the addition- al modeling changes described next, the urban classes suffer much more significant losses than the rurals. There is one additional interest— ing fact to be derived from Figure 4.5. Note that per-capita consump— tion again falls below RNUTPN after the harvests. This indicates that the hypothetical country of the model is chronically food-deficit; the importance of total nutritional debt as a performance objective is in— creased. Urban Class Consumption As mentioned above, changed rural consumption modeling produced marked improvement in the rural death toll, but the urban classes bene- fitted minimally. Perhaps the urban consumption equations require similar changes. Time series analysis of average urban consumption revealed an oscillatory behavior similar to that of Figure 4.3. But recall from ChapterII that urban consumption is based more on the quan- tity of food available than on the desired storage time. Urban classes rely on frequent purchases (or handouts) to replenish their supplies. Per Capita (MT/pers .40 .35 .30 .25 .20 Flgu 98 Per Capita Consumption (MT/person-year) .40 . .35 e .25 . .20 L .15 i .10 f .05 - Figure 4.5. Rural Consumption After Modeling Changes. Normal Required ----- Nutrition RNUTPN Time (Years) The possibil timal use of would be tha quantities. when storage tion curves Urban c ties. The s is. The urt during the c on average a tion 2.12. changed forr replaces (T‘ the same os< tion GXNTDTT been include 0rdecrease: Pally. cool dl'tions or 1 Several IES‘ wwwmi Where: CGBT ARNUT RNUTPN 99 The possibility exists that urban groups in the model do not make op- timal use of available food at the peak of the crisis. The reason would be that the FUl curve of Figure 2.2b goes to zero with storage quantities. But a modeling change to insure ”hand-to-mouth” feeding when storage hits a given low point did not significantly alter consump- tion curves or system performance. Urban consumption modeling is not the cause of urban inconsisten— cies. The same storage time calculation that plagued rural consumption is. The urban classes depend on government sales and feeding programs during the crisis. The decision rules for these actions depend heavily on average available per-capita nutrition (ARNUT), calculated in Equa- tion 2.12. The new proposed form is given here as Equation 4.13. The changed form has a limit on the maximum value of ARNUT, and GTDSTO(t) replaces (TTSH(t) + SF). The discontinuous TTSH and constant SF caused the same oscillatory behavior in ARNUT and urban per—capital consump- tion exhibited by rural consumption. A control parameter, C081, has been included in this equation to allow exploration of slight increases or decreases in the government calculations of usable nutrients. Nor- mally, C081 would equal one. But it may be that continual slight ad- ditions or cutbacks in ARNUT will produce better overall results. Several test computer runs showed that C081 should stay at one. ARNUT(t) = C081 * min(RNUTPN, (EIMP(t) + ETSTG(t)/GTDSTO(t))/ETPOP(t)) (4.13) where: C081 = control parameter ARNUT = average available nutrition (MT/person-year) RNUTPN = normal required nutrition (MT/person—year) EIMP ETSTG = GTDSTO = ETPOP = Two pos first is par that discuss 4.4. The gc 10810 (a). a larger sai first harves storage for should the . Still in f0 hRHUT. lhi outs. Equa increased. the 10810 a ”0i VTOTent tTOPS shoul The se VTPP was ti timates ma the next h Proddce an TOO EIMP = estimated imports (MT/year) ETSTG = estimated total storage (MT) GTDSTO = government desired time of storage (year) (curve (b) in Figure 4.4) ETPOP = estimated total population (persons). Two possible solutions to the ARNUT problem were examined. The first is part of Equation 4.13, a time—of~storage function similar to that discussed earlier. The storage time curves are graphed in Figure 4.4. The government curve, GTDSTO (b), is consistently above the rural TDSTO (a). This represents the assumption that the government desires a larger safety factor. The largest curve divergence occurs during the first harvest. The government desires a considerable increase in storage for two reasons. First, stores will be desperately needed should the second crop fail. And, since the crisis declaration is still in force, the government wants to curb overconsumption by reducing ARNUT. This sh0u1d increase acquisitions and decrease sales and hand- outs. Equation 4.13 indicates that ARNUT will decrease if GTDSTO is increased. Note that if the assumptions leading to the divergence of the TDSTO and GTDSTO curves are correct and if the rural population is not violently opposed to government activity, then government acquisi- tions should be easiest during the first harvest. The second solution explored for reducing oscillatory ARNUT beha- vior was to match the discontinuities of TTSH by augmenting storage es- timates with crop size estimates. TTSH represents the total time until the next harvest. Adding an estimated output figure to storage should produce an idea of total food available until the next harvest. (Note that estimated imports are already a part of Equation 4.13). This second approe formation sys The firs Trying to ma‘ in instantan: of crop size how long to will be avai actual food Recall ing acceptai above have 1 modes. The 0i the cons holy impro possible ca dead after “ith Perfec hPProximatE and hiOdeli r The mc criteria b3 the) varia] "hht sales 101 second approach has the appealing feature of connecting extant crop in- formation systems to the famine relief system. The first method was chosen for its continuity and simplicity. Trying to match discontinuity to discontinuity would invariably result in instantaneous jumps in ARNUT not expected in the real world. The use of crop size presents a complicating calculation; one needs to estimate how long to hold present stores based on how soon replacement stores will be available. The lag time between the technical harvest start and actual food availability must be estimated. Urban Private Storage Recall the three criteria given early in this section for determin— ing acceptance of proposed model change. The alterations described above have caused improvement in numerical values and system behavior modes. The behavior criterion is obvious, as the severe oscillations of the consumption and ARNUT curves have been removed. The most strik- ingly improved numerical value is the total death figure. The worst possible case, the extended price control policy,leaves 10.5 million dead after one year of an initial population of thirty—four million. With perfect data, the basic model was able to reduce the toll to approximately five million. With no parameter optimization, the policy and modeling changes produced a further drop to 3.5 million. The modeling alterations also satisfy the third change acceptance criteria by removing urban private storage (USTOR) as a desirable con- trol variable. Recall that the basic model decision rules for govern- ment sales and emergency feedings make use of the difference between estimated am 2.15.) The' Estimatl information crisis, sinc cal values i components 0 be difficult places. A 1 control var" sistentl y se back contro' a common p0 Positi deaths sinc Time series catoes over Contrast, d duces grade ter prepare Classes to overinduigé SlStem per- “‘0“ of th. death tota The q ducing the l02 estimated and desired private storage values. (See Equations 2.l4, 2.l5.) The relevant control parameter is C634. Estimated urban private storage is not a likely candidate as an information system control variable. Storage is minimal during the crisis, since food is hard for the urban classes to obtain. The numeri- cal values in the model are consistently tiny when compared to the other components of total storage. From a real world standpoint, USTOR would be difficult to measure because there would be small quantities in many places. A further drawback is the performance of urban storage as a control variable. Even with large CG34 values, desired storage is con- sistently several times greater than actual storage. Desirable feed— back control behavior would have actual and desired storage move toward a common point. Positive CG34 values should have a negative impact on total deaths since urban consumption is tied directly to storage levels. Time series analysis shows that in mid-crisis, C634 greater than zero causes overconsumption and early exhaustion of government stores. By contrast, deletion of the urban storage control (C634 equal zero) pro— duces gradually decreased consumption, leaving the population much bet- ter prepared for the ”crunch." The larger CG34 has allowed urban classes to consume more than their allotted (ARNUT) portion. And this overindulgence continues until government supplies run out. However, system performance of the basic model was more sensitive to C634 than most of theotherparameters. Positive CG34 invariably produced lower death totals than a zero value. The question arises why urban overconsumption was helpful in re- ducing the basic model death toll. One plausible explanation is that the increase time oscilla TTSH increas and feeding keep the go» peak. Ands works poorl) The moc and the abi' next sectior tions of th- of problem . One poi fring poten tem compone It can be u and economi tion needed SYStem perf thi‘OUgh Whe l. pc 2. pC 3~ Ir 103 the increased storage parameter was needed to counteract the harvest time oscillation of the old ARNUT variable. At the harvest start, TTSH increases dramatically, decreasing ARNUT at the time when sales and feeding programs are most needed. A large C634 would be needed to keep the government programs at acceptable levels during this crisis peak. And since the parameters are time invariant, the large C634 works poorly early in the crisis. The modeling changes have greatly improved both numerical results and the ability of the model to match real world expectations. The next section concludes the chapter with a discussion of the implica- tions of this study for general relief work and the relative importance of problem formulation, policy structure, and modeling accuracy. Famine Relief Implications One powerful use for computer simulations is as an aid in identi- fying potential bottlenecks in real world systems. The information sys— tem component has a similar task in modeling famine relief efforts. It can be used to determine proper modeling of demographic, nutritional and economic components and to design optimal policies. The key assump- tion needed is that better information quality should produce better system performance. There are several possible causes to search through when the basic assumption is violated: l. Policy parameter values not satisfactory 2 Policy structure too weak 3. Inaccurate modeling 4 A natural phenomenon unaccounted for A natur harsh realii tion early ' incurred lea the future. peak, given mouths to ft with the shr alive as lo: efforts for Short term i similar pat' tritional d1 dicator of . harsh reali‘ likelihood . Cannot be a- not easy ma. The la sumption mo 50%] conse is WhEther . facing a to do not favo lamlChed to tin“ Wit, ”9'5 habit l04 A natural phenomenon very prominent in the current study is the harsh reality of long term versus short term goals. Decreased consump- tion early in a crisis has several desirable results. The weight loss incurred leads to lower nutrient needs, so less food is necessary in the future. Less food eaten early means more available at the crisis peak, given a limited total supply. And more early deaths means fewer mouths to feed and better health among survivors. Hence, the conflict with the short term (two to three months) goal of keeping as many people alive as long as possible. This phenomenon plagued current modeling efforts for several months before it was realized that the effects of short term optimization must be planned for in a long term problem. A similar pattern occurs when a famine extends beyond one year; total nu- tritional debt at the end of the first harvest cycle is a crucial in- dicator of ability of the population to withstand a new crisis. Other harsh realities must be taken into account. The political climate, the likelihood of outside aid and cultural and religious responsibilities cannot be avoided by ignoring them in the planning process. These are not easy matters to deal with; there is no free lunch. The largest improvement in system performance attendant to con— sumption modeling changes has definite educational implications. Per— sonal conservation is a desirable goal. An important area for study is whether consumption habits naturally adhere to desirable limits when facing a food shortage. Two possibilities exist if cultural conditions do not favor conservation. A long term educational program can be launched to inform citizens of the benefits of moderation. Or a dis— tinct policy structure can be designed to attempt to work around peo— Ple‘s habits. Wise allocation policies are needed to insure that recipient gr evidence tha aid and reje Pre-pla tion. The r ability of 5 system desig dwious. The pla mecialties. abounds in d biography3 go dsoinvolve DFOject's ge‘ Perhaps discern impo. Aledger 0f . tvochapters Wmtfinmt, eXPEHded 0n ( Sampl 1 ns lllln( attempts wi ti witl Witt l05 recipient groups do not eat their allotment too quickly. There is some evidence that excessive outside aid can cause complete dependence on the aid and rejection of centuries-old famine food sources (32). Pre—planning is basic to the approach espoused in this disserta— tion. The revised problem formulation of Equation 4.2 depends on the ability of system planners to examine policy structure and information system design concurrently. The interrelationships between the two are obvious. The planning procedure calls for a team of persons with varying specialties. Just the portion of the famine relief topic examined here abounds in diversity: rural psychology, nutritional measurement, de- mography, government structure, communications, etc. The team must also involve the right amount of government interaction to assure the project‘s getting off the ground. Perhaps the most important personal attribute needed is wisdom to discern important points from among a multitude of obscurant details. A ledger of the study time spent in securing the results of the past two chapters provides an excellent example of the need to separate the wheat from the chaff. Four research items and the approximate effort expended on each is listed below: sampling component addition and minor modifications: two person-months attempts to reconcile inconsistencies: with problem reformulation and parameter variation: two person—months with policy structure; one—quarter person—month with modeling changes: one-quarter person-month The latter 1 time. Certa standing of was not knov 106 The latter two avenues produced the biggest impacts and took the least time. Certainly, earlier efforts paved the way by providing under- standing of the system processes, but a major roadblock to progress was not knowing what to look for. The pr information 5.). Theg of the cost from the su ability to real world and the Opt Mi nimi SUbjec Where: [-71 CHAPTER V THE COST FUNCTION AND INFORMATION SYSTEM DESIGN Cost Function 6([) The preceding chapter describes a mathematical formulation for the information system design problem which is repeated here as Equation 5.l. The goal of this chapter is to describe a process for generation of the cost function 6(5). The analysis for obtaining 6 is done apart from the survival model which produces performance function f, The ability to adequately describe 6 is crucial, for this function links real world system designs to the simulation of the preceding chapters and the optimization work of later chapters. Minimize fix,5) (5.1) subject to 6([)_: C El< Ef-Ez where: F = system objective vector (F = total deaths, " F2 = total nutritional debt) G = cost function (monetary units) X = information quality vector (sampling frequency, _ measurement error, time lag) P = policy parameter vector (rates and triggers) 91:92,§J,§2 = parameter constraints C = budgetary constraint. lO7 Recall personnel, l information This would noted in Eq ployed here stage does in the foll Further dis nature of f The 56 source allc liminary wc completed. will do the Priorities A non: can be valr traditiOna Preach wil AS de formation in the 5am derived fr Costs, dEn infemetic comPUtatjc l08 Recall that constraints on relief system performance will include personnel, equipment, time, and money limitations. To obtain maximum information, each of these constraints should be explicitly noted. This would cause a vector gtof optimization constraints and was so noted in Equation 4.2. A single-valued monetary cost function is em— ployed here for three reasons. First, the level of complexity at this stage does not warrant separation. The system alternatives described in the following sections are very crude, a result of lack of data. Further disaggregation would not lead to significant results about the nature of famine relief resource allocation. The second reason for adopting a single cost value is that the re- source allocation problem for relief work is better analyzed after pre- liminary work on all subsystems (transportation, education etc.) is completed. System planners wish to place scarce resources where they will do the most good. The particular situation may dictate allocation priorities, making further analysis unnecessary. A monetary function 6 is chosen because personnel and equipment can be valued in money terms. Money equivalents are often assigned in traditional cost-benefit analysis work. Note that a true systems ap- proach will examine each constraint separately ifthe situation warrants. As described in Chapter Tm it is theoretically possible that in- formation system costs and famine relief policy costs can be considered in the same optimization problem. The two are distinct and would be derived from different sources in the current methodology. The policy costs, denoted 62(3), are generated by the survival model, while the information costs are a product of off~line analysis. The off-line computations are the main considerations of this chapter. The first section dc could be d possible 9 considerat consists l gency prog Appendix B The 9 portant li second sec needs anal; describes g tem costs, fifth sect' exa“idles cc food consun and Process The er Sion that . Proach is e Iddesh. T) process and any aPDlica QEOgraphy, ”ent Syste fuller flav because i ts l09 section does, however, contain a description of policy costs as they ”could be derived from the survival model. The purpose is to provide a possible guide for further research; policy costs will not be a major consideration in succeeding chapters. The policy cost function 62(3) consists largely of bookkeeping equations, tracking the costs of emer- gency programs, grain storage, and transport. The computer model in Appendix B allows printing of the policy-related costs. The generation of the information system cost function is the im- portant link between real world designs and simulated performance. The second sectionof this chapter discusses the initial stepsof design work needs analysis and the productionofsystem alternatives.The sectionalso describes general necessary conditions for the relationships among sys-. tem costs, and the information quality parameters 5. The third through fifth sections present examples of implementations of the approach. The examples cover cost functions for the surveillance of nutritional debt, food consumption and private storage, and for information transmission and processing. The last section summarizes the approach. The emphasis here is on a methodology for information system de- sign that could be useful in many parts of the world. Although the ap- proach is emphasized, the discussion will focus on the country of Bang- ladesh. There is a danger that a general discussion would obscure the process and the amount of work needed to derive the cost function. In any application, detailed data on the country's demography, culture, geography, and economy will be needed in producing feasible and effi— cient system design. So a specific country is chosen to provide a fuller flavor of the proposed approach. Bangladesh is a good example because its weather and economy make it vulnerable to famine. A note on currenci Bangladesh There response 0 Thfbwo the rural from the r rich at a emergency buy in the An ac able by t) actual far acquisiti. areas and The grain tra Denses wo tifv thos 0f t desIgned Costs of PTOgram c the relic Selling . lllcur~red llO on currencies is appropriate here. The base model uses the Korean won. Bangladesh has the takka. The won is used throughout this dissertation. Policy Costs There are three main government programs in the simulated famine response of the survival model: acquisitions, sales, and emergency aid. The flow of food in the model is generally from those with a surplus in the rural sector to the urban sectors. The government purchases grain from the rurals at a set, normal price. It then sells to the urban rich at a market price that is high due to small available supply. The emergency feeding programs are for the urban poor who cannot afford to buy in the market. An additional food source is the small amount of imports afford- able by the government. International food aid might be expected in an actual famine, but is assumed to be negliglble here. The imports and acquisitions from the rural sector arekeptin government rural storage areas and shipped to the smaller urban storage areas as the need arises. The costs to be examined are for operation of the three programs, grain transport and storage, and government imports. Some of the ex- penses would be incurred in normal operation; the goal here is to iden- tify those portions attributable to famine relief operations. Of the programs, acquisitions and emergency aid are specifically designed for famine relief, while market sales is an on-going activity. Costs of operating the former programs are relief expenses, while sales program costs are not. Grain costs and receipts must be included in the relief accounts. The government could use any profits made from selling to the rich at high prices to help cover the program expenses incurred elsewhere. There are normal average levels of transportation and storage But the exc should be c lmhonu trade balar grain is a: must be in) grams. with costs are the amount obtained t famine. l onom EMFTT GSLTI GIMT EMTR EMST Where; GAQi GAO) EMF‘ EMFI lll and storage whose costs are covered outside of the famine relief budget. But the excess activity generated by increased stockpiling and transport should be charged to the relief account. The survival model assumes a limit on the imports available to the country, due to a disadvantageous trade balance. Thus, the cost of locating and transporting imported grain is assumed to be a normal expense. The cost of the grain itself must be included, since this grain is sold or distributed in other pro- grams. With the above as background, the equations for calculating policy costs are now presented in some detail. The first task is to compute the amounts of grain involved in each activity. The grain totals are obtained by integrating the appropriate rates over the duration of the famine. The rates are model variables, presented in Equations 5.2—5.7. 6AQTOT(t) = f5 GAQU(s)ds (5.2) EMFTOT(t) = f5 EMFD6(s)ds (5.3) 6SLTOT(t) = If, GSLS(s)ds (5.4) GIMTOT(t) = r5 GIMP(s)ds (5.5) EMTRAN(t) = r5 (GSRU(s) - GNSLS)ds (5.6) EMSTOR(t) = f3 (osn(s) + asu(s) - GSN)ds (5.7) where: GAQTOT = total government acquisitions (MT) GAQU = acquisitions rate (MT/year) EMFTOT = total distributions for emergency aid (MT) EMFDG = emergency aid distribution rate (MT/year) GSLTOT GSLS GIMTOl GIMP EMTRAT GSRU GNSLS EMSTO GSR GSU GSN O,t The e is useful flture (Gr cause the rural stov average 5. use. The 0“ govern GSN Where; GSN GSUT GSRT CG6! GSLTOT GSLS = GIMTOT GIMP ' EMTRAN = GSRU GNSLS EMSTOR = GSR GSU GSN O,t ' llZ total government sales (MT) sales rate (MT/year) total imports (MT) import rate (MT/year) excess grain transport due to famine (MT) urban to rural transport rate (MT/year) normal government sales rate (MT/year) excess storage due to famine (MT/year) government rural storage (MT) government urban storage (MT) normal government storage (MT) time limits on duration of famine. The equations are all straightforward, but a word of explanation is useful for Equations 5.6 and 5.7. The non-famine government sales figure (GNSLS) is used as proxy for the normal transportation rate be- cause the grain sold in the urban market must first be shipped from rural storage. 80 the average transport rate should be close to the average sales rate to avoid frequent shortages or inefficient vehicle use. The normal storage amount, GSN, is computed in Equation 5.8 based ' ' on government target storage levels. where: GSN = GSUD = GSRD = 0660 = GSN = C660 * (GSUD + GSRD) normal government storage (MT) desired government urban storage (MT) desired government rural storage (MT) storage parameter (dimensionless). Unit c total costs pnce (PFDR priate calc puted simil grain purct sector is c distributic The amount tions (EMF' Equation 5 CGAQ(' CEMFD where: CGAQ PFDRN CGAP GAQTO CEMFD CGFP EMFTC PWLD ER Extra Wide range ll3 Unit cost parameters are multiplied by grain totals to ascertain total costs. Acquisition expenses are based on a fixed grain unit price (PFDRN) plus an average program cost per unit (CGAP). The appro- priate calculations are in Equation 5.9. Emergency aid costs are com- puted similarly, but care must be taken to avoid double-counting the grain purchases. It is assumed that grain acquired from the rural sector is distributed through the emergency aid program. Additional distributions beyond the rural acquisitions must come from the inputs. The amount will be the difference between distributions and acquisi- tions (EMFTOT-GAQTOT). The price is the current world price PWLD. Equation 5.lO contains the emergency aid cost function. CGAQ(t) = GC6I * (PRDRN + CGAP) * GAQTOT(t) (5.9) CEMFD(t) = CG62 * (CGFP * EMFTOT(t) + PWLD*ER*(EMFTOT(t) - GAQTOT(t))) (5.IO) where: CGAQ = acquisitions cost (won) PFDRN = fixed purchase price for acquisitions (won/MT) CGAP = acquisitions program cost (won/MT) GAQTOT = total government acquisitions (MT) CEMFD = emergency aid cost (won) CGFP = emergency aid program cost (won/MT) EMFTOT = total emergency aid (MT) PWLD = world food price (S/MT) ER currency exchange rate (won/$). Extra factors (C66l and C662) are included to account for the wide range of feeding programs possible. Some sources note that gra— tuitous relief should be avoided, as it has a demoralizing effect on recipients done on gov tion. An 5 sixty-nine (58). Thu: ful plannir are used to relief. through we The s the differ and buying in Equatic integrand, CGSLE where; CGSLS PFD GSLS The 5 Price C9]- fest tota a Price 0 by Compet and ODIN) 0n non-go ll4 recipients (53). An alternative proposal is to pay with food for work done on government organized projects, such as road or well construc- tion. An account of the Bihar, India, famine of 1967-68 claims that sixty-nine percent of the relief costs were spent for productive work (58). Thus, the drain on the total budget can be alleviated with care- ful planning and well organized projects. The parameters CG6T and C662 are used to compute the proportion of program cots attributable solely to relief. So C66l = T.O would indicate that no benefits were derived through work-for-food programs. The sales program actually generates revenues. The net income is the difference between selling at the inflated domestic market price and buying on the unaffected world market. Total income is calculated in Equation 5.ll. Note that the food price is included as part of the integrand, as it varies with time. CGSLST(t) = f5 PFD(s) * GSLS(s)ds (5.11) where: CGSLST = receipts from government sales (won) PFD = domestic food price (won/MT) GSLS = government sales rate (MT/year). The sales revenue depends heavily on food price. Any type of price ceiling will greatly affect government income. It will also af— fect total death figures, as discussed later in Chapter VII. Setting a price ceiling is an important government decision area, influenced by competing considerations of inflation, equitable food distribution, and opinions of the populace. Such a ceiling is difficult to enforce on non—government sales. Because revenues are greatly affected by a decision the will be kept sibhity do: very high p' for relief I The t0‘ mtions pro! Equation S.‘ CPROG(t) = l Were: CPROG = CGAQ : CEMFD = One adc Pa“0f the 99nses in E< AUQS to 0th Concern here “310“ Consi b0Ughtatt) cou-en whEre; CGIMP PWLD ER GIMTOT ll5 decision that lies outside the direct focus of this study, the revenues will be kept separate from the policy costs 62(3). An interesting pos- sibility does suggest itself here. By selling grain to the rich at very high prices, the government may be able to use the revenue to pay for relief programs. Sucha plan is worth considering. The total program cost will be the sum of emergency aid and acqui- sitions programs, since the sales program is to be counted separately. Equation 5.l2 presents the required summation. CPROG(t) = CGAQ(t) + CEMFD(t) (5.l2) where: CPROG = total program cost (won) CGAQ = acquisitions cost (won) CEMFD = emergency aid cost (won). One additional program cost is noted, that of government imports. Part of the import cost enters the calculation of emergency aid ex! penses in Equation 5.l0. The rest will be deducted from sales reve- nues to obtain a net sales figure. Since revenues are not of major concern here, the total import cost is presented as an important de- cision consideration outside the scope of the model. The grain is bought at the prevailing world price, as computed in Equation 5.l3. CGIMP(t) = PWLD * ER * GIMTOT(t) (5.13) where: CGIMP = import total cost (won) PWLD = world food price ($/MT) ER = currency exchange rate (won/S) GIMTOT = total imports (MT). The t derived in reflect th less than CGSRL CSTOF where: CGSRl CRUT EMIRT CSTO CHI EMST The Not rectl y d Wide) 3 W ll6 The transportation and storage costs are straightforward and are derived in Equations 5.l4 and 5.l5. A maximization function is used to reflect the fact that the relief account would not be credited when less than normal levels are shipped or stored. CGSRU(t) = max(0.0, CRUT * EMTRAN(t)) (5.l4) CSTOR(t) = max(0.0, CHI * EMSTOR(t)) (5.l5) where: CGSRU = famine transportation cost (won) CRUT = unit transport cost (won/MT) EMTRAN = grain transport due to famine (MT) CSTOR = famine storage cost (won) CHI = unit storage cost (won/MT—year) EMSTOR = storage due to famine (MT—year). The policy cost function is now derived in Equation 5.l6 by sum- ming the totals from Equations 5.l2, 5.l4, and 5.l5. 62(3) = CPROG + CGSRU + CSTOR (5.l6) where: 62 = policy costs (won) 3‘ = policy parameter vector CPROG = program costs (won) CGSRU = transportation costs (won) CSTOR = storage costs (won). Note that none of the equations described in this section is di- rectly dependent on P, The parameters affect the rates in the survival model, which enter the cost function through Equations 5.2-5.7. The of dard nutri this disse discussed monograph systems sh expands ti limit the The c of a systv Chapter 2 limits an is define tive meth posed. A ble for p be to eva alternati tl0!) errc by intuit and SYStT world 0“. An use of a mum ROd COSt ll7 Information System Design The objective of this section is to examine the place of the stan- dard nutritional surveillance design process in the overall approach of this dissertation. The process for continuous surveillance has been discussed in several places, notably a World Health Organization (WHO) monograph (TO, 25). The WHO recommends that famine relief information systems should be a special case of on-going surveillance. This greatly expands the possible scope of system design, but we will continue to limit the discussion to the case of severe food shortages. The contents of the WHO monograph can be placed in the context of a systems approach to the design of a surveillance system (40, Chapter 2). The first step is to analyze information needs. The limits and components of the system are identified, then the problem is defined based on the real world variables to be estimated. Alterna- tive methods forcollecting and communicating the information are pro- posed. An initial screening eliminates alternatives that are infeasi- ble for political, cultural, or physical reasons. The next step should be to evaluate the economic and financial feasibility of the remaining alternatives. This evaluation is generally done by minimizing informa— tion error for a given budget cost. Variables to be sampled are chosen by intuition and experience. The performance of the selected variables and system alternatives is evaluated through time by observing real world outcomes. An altered approach is suggested in the current methodology. The use of a computer simulation allows initial evaluation of system alter~ natives using both costs and performance criteria. The system design and cost analysis phases are done off—line from computer performance model and c the cost a) meter vect 5.l7. Not cost alter than for ( Re Ponents cessing assessr tollec RUirem questi SUDGrv Stati DTOgr ADIOS ll8 model and optimization work. An additional qualification is added to the cost analysis, minimizing costs for the information quality para- meter vector X. The process is described mathematically in Equation 5.l7. Note that the members of §_are continuous variables, so minimum cost alternatives are chosen for regions of the vector space, rather than for discrete vectors. G(_X,) = mlgimum caiq) (5.17) subject to E4 < 5,.ifig .— where 6 = information system costs _.§ = information quality parameter vector a, = ith system alternative, i=l,2,...,K C = cost of a1, dependent on_§ E],E2 = information quality constraints. Recall the information system identified in Figure l.l. The com- ponents to consider in the design phase are data collection; data pro- cessing and transmission; program evaluation and the interpretation, assessment, and storage of data at the system manager‘s level. Data collection involves the methods, number of samples, and personnel re- quirements from the sampling design; the format of data reports and questionnaires; training for surveillance teams; and provision for supervision and quality control (25). The processing component must statistically analyze the accumulated raw data. Microcomputers or programmable calculators may be powerful pieces of appropriate tech- nology for use here. Data transmission design depends on the institutior sonnel avai munication. The s; need to as They must large and ters as ar cussed in Data including managemen Alte data wil' are dete' data iter stages C lnformat Cos The ”lair sampie exDense cost tc SPECia) “9) cos Trainh ll9 institutional structure of the country and on equipment and per- sonnel available. The structure dictates the needed lines of com- munication, while physical resources determine thecommunicationmmthods. The system managers are not just programmed decision makers; they need to assess conditions based on numerous pieces of information. They must be able to interpret the significance of tables, charts, large and small changes in variables, etc. The use of information fil- ters as an aid to system managers in assessing true conditions is dis- cussed in Chapter VI. Data storage is vital to evaluation of overall relief activities including policies, the information system, and the field programs. A management decision needs to be made on the use ofcomputers for storage. Alternative system designs must include not only the stages that data will follow, but the data items themselves. The information needs are determined along with policy structure. Once specific desired data items are known, the collection, transmission, and processing stages can be tailored to fit requirements. Information System Costs Costs of separate processes and stages are difficult to identify. The main variable expenses will be due to personnel, equipment, and sample design. Generally, the total salary or purchase price for an expense is known. The difficulty comes in assigning a portion of the cost to the relief account. If the famine surveillance system is a special case of regular surveillance, then total equipment and person— nel costs can be shared by the similar functions. Some expenses, like training and planning, may be incurred long before an actual famine. Some of the the famine, and the pa' will be al tions will of the cos In 96 The impor‘ developed informati alternati informati It s 0f the r) quality DOnent. the) n cal Cost As sengers 1a9 tim telepho large n cost Wt ment d. for mi l20 Some of the equipment expenses are fixed regardless of the extent of the famine, while other items vary both with the severity of the crisis and the particular design chosen. Another complication is that costs will be allocated differently in different countries. Several assump~ tions will be discussed later in this section to better define the scope of the cost analysis for this dissertation. In generating the cost function 6(5), three items must be linked. The important middle link is the set of specific system alternatives devel0ped in the design process. The other two links are the costs and information quality related to the alternatives. One starts with the alternatives and develops the 6 function by minimizing costs for given information quality. It should be useful at this point to examine Table 5.l finrexamples of the relationships among system alternative components, information quality parameters and costs. The key to the table is the System Com— ponent. The §_Parameters (sampling frequency, measurement error, lag time) likely to be affected are given in the second column. The Typi- cal Cost Significance column describes ties among the three links. As an example, two possible communication devices would be mes- sengers or telephones. The primary §_parameter affected would be the lag time, unless common carelessness introduces significant error. The telephone alternative would have high initial costs and would incur large maintenance expenses for the first years of use. But the total cost would, hopefully, be shared by many businesses and other govern~ ment departments. The telephone (or something similar) would be needed for minimal delays. System to Sample de Data col‘ Personne‘ Travel arrangem Communic equpmer Communit Personnl Data St) l2l Table 5.l. Relationships Among Information Quality, System Alternatives, and Costs. Typical Cost System Component Parameters Significance Sample design Sampling frequency, Error affects number delay, sampling of observations; error ” cost = # surveys * cost/survey; cost/ survey = cost/obser- vation * observation/ survey; processing techniques may intro- duce bias Data collection Delay, error More personnel re- Personnel duces delay, but costs more Travel Delay Faster travel re— arrangements duces delay, costs more Communication Delay, error Technical equipment equipment reduces delay, costs more; reliability costs more Communication Delay, error Training cost impor- personnel tant Data storage Sampling frequency, More sampling means error, delay larger storage; fas- ter retrieval re- duces delay The n done to de number of telephone- al altern telephone vetted The useful. formatio ternativ tified w problem through nents a) "best" . dated. System Tw functic tives v dividil than t will ) lines. Timits |22 The main messenger cost would be for personnel. Studies could be done to determine the optimal design for quick service with a minimum number of messengers. This is likely to be much less expensive than telephones, but the delay time is increased. Note that several addition- al alternatives could be generated as combinations of messenger and telephone use levels. Cost Function Characteristics The function 6(5) will have several characteristics if it is to be useful. There must be a well defined relationship between specific in- formation quality parameter values 5_and the unique optimal system al- ternative that provides that quality level. Each vector 5_must be iden- tified with one alternative, since the solution of the optimization problem of Equation 5.l will be an 5 vector. It would be useless to go through the optimization process and derive a vector whose delay compo- nents and error components indicate competing alternative systems as the "best" choice. Another necessary attribute of 6(_) is that it be vali- dated. That is, some testing must be done to insure that the chosen system alternatives actually do provide the cited information quality. Two statements can be made about the probable form of any 6(5) function. The first has been mentioned previously: system alterna- tives will be optimal for whole regions of the 5_vector space. The dividing lines will be hyper—planes in the space of one less dimension than the vector 5, A second statement on the form of 6(5) is that it will likely not be differentiable but may be continuous at the dividing lines. Discontinuities could occur when one alternative reaches the limits of its physical constraints. An example is the necessary minimal dc mission. discontinr The . complexit necessary be cyclic tify gene sequent c quality 2 Then a 5: defined - §1991j111 Sev rest of Positior the man) second, to the Th has bee and is ables C sumpti( in Cha) INTOrml l23 minimal delay inherent in the use of messenger service for data trans— mission. A further decrease in delay time may require a substantial discontinuous jump in costs. The 6(5) function can be constructed at many different levels of complexity. A general guideline to follow is to use only the complexity necessary at each stage of the design process. The overall project will be cyclical in nature. A first pass at the cost function should iden— tify general costs to allow an idea of the tradeoffs to be faced. Sub- sequent optimization work will give estimates of desired information quality and should eliminate some of the original system alternatives. Then a second, more specific cost analysis can be done with more well- defined objectives. Simplifying Assgmptions Several assumptions are presented here to focus the study of the rest of this chapter. There is a twofold purpose for making these sup~ positions. First, they will provide needed limits on the discussion; the many possible cases to explore would fill numerous volumes. And second, it is hoped that the assumptions will provide some insight in- to the kinds of decisions faced in actual cost analyses. The first assumptions have already been mentioned. Bangladesh has been chosen as the region to study. This country is famine-prone and is much like other endangered areas in Southern Asia. The vari- ables on which data will be collected are nutritional debt, food con— sumption, and rural private food storage. These variables were chosen in Chapters III and IV as the survival model was modified to include information system evaluation. tion tions ties in ti to 0‘ syst othe coll beti tiox zen: to l24 Several suppositions are made about the portions of the informa— tion system (see Figure l.l) to be included in cost function considera- tions. Specifically, the evaluation component, data storage capabili- ties and communications back to the affected peoples will be excluded in the Current study. It is felt that these items are heavily linked to other systems and to planning outside the famine relief information system. Program evaluations will be made using much data collected for other purposes. The chief costs should then be for personnel and the collection of quality control data. The evaluation component would be better considered along with specific program design (feeding, sanitam tion, health, etc.). Similarly, although it is important to keep citi— zens aware of famine extent and relief development, this ties closely to the operation of relief programs. Data storage capabilities must be large enough to include many pieces of information distinct from famine relief. Since the famine records will not be useful without further planning for future food shortages, the storage function should be studied as part of a long range continuous surveillance system. System manager salaries are an important cost, especially if the administrative heads are given special responsibilities for the dura— tion of the famine. But this expense is considered to be part of over— all relief, not assignable to information system cost. However, the procedures of the managers, discussed in Chapter VI, will influerce the vector 5, which will indirectly affect the cost function. The preceding limiting assumptions have focused attention on costs for collection, processing, and transmission of nutritional debt, consumption,and private storage data. The interrelationships of these tasks allow several simplifications in translating the system alternat‘ processir sampled additive and proc of measx in infor A the sam is, the survey: of des relate S cation avoide transr tion) chara line defir time tiOn than ties the l25 alternatives to information quality parameters. Data collection and processing can be considered together for error purposes. The various sampled variables can be transmitted through the same channels to avoid additive costs. The sample design should cover both data collection and processing. These two operations will constitute the main source of measurement error. So for cost function purposes, the error terms in information quality vector 5 will apply only to the sample design. A point to build from in constructing the cost function is that the sampling frequency can be separated from measurement error. That is, the total surveillance cost equals the product of the number of surveys and the cost per survey. The cost per survey is a function of desired measurement error, while the number of surveys is inversely related to the sampling frequency. Sampling frequency will affect transmissions only if the communi— cation channels are overloaded. If we assume that such practices are avoided, then the delay parameter of 5_is the only one affected by the transmission component. It is further assumed that two—way communica- tion between the field programs and system managers is a necessary characteristic of system design. The delay parameter of.5 provides an example of the use of off— line analysis to simplify later optimization work. The total delay is defined as the lag between the time test observations are made and the time that system managers receive summarized reports of the observa- tions. The lag can be roughly broken into a measurement delay and a transmission delay. These delays are related to two separate activi- ties, so that the desired final optimum is the “best” combination of the activities. There are two ways of handling the combination problem As pa rt cmtcmn delay le that the overall the off- of para) the der survey ' paramet versus which i ll teams I tions, Proces one-ti Equati where l26 As part of the cost function optimization, one can find the minimum cost combination of measurement and transmission methods for each total delay level. 0r two separate delay parameters can be assigned in 5_so that the optimal delay combination is discovered as a by—product of the overall optimization. We assume here that the decision is handled with the off—line cost function analysis. This helps to minimize the number of parameters needed in the final optimization. Note, however, that the derivation of the cost function can become extremely complex. The survey method affects not only the delay parameter, but also the error parameters. There may be tradeoffs in providing smaller delay costs versus smaller error costs. A smaller error requires more observations, which increases the delay time. Nutritional Surveillance Costs To collect data on the nutritional level of the population,trained teams of observers will conduct sample surveys. The number of observa— tions, the villages to visit, recording techniques, and statistical processing are all part of the sample design. With the inclusion of one-time fixed expenses, a crude cost function can be derived as in Equation 5.l8. Note that SDND, DELD, and SAMPT are all members of 5, CNS(TF, SDND,TDELD, SAMPT) = CFIXN + TF * CSURN(SDND, DELD)/SAMPT (5.18) where: CNS = cost of nutritional surveillance (won) CFIXN = fixed cost of nutritional surveys (won) CSURN = cost per nutritional survey (won/survey) SDND = nutritional debt measurement standard error incur be pr leve' Seve' tica surv port _l_ndi cal , sub; have gem rap- mor. vit tat (23 dis Prc cr- 127 DELD = delay (years) SAMPT = nutritional sampling interval (years/survey) TF = time duration of famine (years) The problem now is to determine the fixed costs and survey costs incurred when measuring nutritional debt. Background information will be presented on methods commonly used for assessment of nutritional level and on relevant social and physical conditions in Bangladesh. Several natural methodological choices present themselves. A statis— tical sampling technique is then presented which allows an estimate of survey costs based on the chosen measurement methods. The result is a portion of the information system cost function. Indicators of Acute Malnutrition There are four nutritional measurement types: clinical, biochemi- cal, tissue, and anthropometric (23). In general, clinical tests are subjective and highly variable, while biochemical and tissue tests have extensive time, facility, and personnel requirements. There is a general consensus that anthropometric measures are most efficient for rapid assessment of acute malnutrition. The other methods have been more useful in evaluating long term, chronic malnutrition involving vitamin and other deficiencies. Children (to the age of ten) are almost always taken as represen- tative of the entire population for acute malnutrition surveillance (23). The young, with their high growth rates and susceptibility to disease, are the first to show appreciable signs of malnourishment. Protein-calorie malnourishment (PCM) is the main concern in a food crisis. Vitamin and other deficiencies are secondary in the short run. A cat the T pattl of m is t rovi tive pro) SET for to Cl” Cd 128 A caution in using children as representative is to determine whether the particular society has preferential in-family food distribution patterns that would bias results. Eleven clinical signs have been identified as possible indicators of malnutrition (T4). The main objection to quick clinical examinations is the inherent subjectivity. However, it could be possible to have roving teams of clinicians each sampling in several areas for compara— tive purposes. Such an approach has not surfaced in the literature, probably because of the common call for standardization. Typical biochemical tests would be for amino acid imbalance, serum albumin, and urinary creatinine. The practical aspects of sample pre- servation, personnel, and equipment make such tests highly infeasible for quick work. In addition, the results are often unsatisfactory due to wide variability in PCM syndromes. Tissue measurements are probably also impractical for use during crises. It is claimed that ”hair root diameter is the first morphologi— cal adaption to experimental protein deprivation” (9). But the most rapid hair root measurement calls for a microscope and relatively care— ful sample collection, both of which are generally scarce commodities in thefield. Anthropometry includes several quick and reliable nutritional in— dicators. The so-called "big six” are weight, height, arm, head, and chest circumferences and triceps fat fold. A common indicator is de— rived from taking the ratio of measurements for two distinct body ele— ments. One element must be sensitive to recent periods of low consump- tion (arm circumference, body weight) while the other should be little affected by short term conditions (height, head circumference). The most tios back trar ing iab‘ etc ext ter tap 01‘ 129 most widely used indicators are weight, arm circumference, and the ra- tios of these two with height. Weight measurement requires an appropriate scale. Possible draw- backs of a scale for fieldwork are required maintenance, testing, and transport. A study of the causes of measurement variability in obtain— ing body weight of children attributes ninety-nine percent of the var— iability to short term variation in the child (bladder, gut contents, etc. (66). The same study concluded that weight alone could identify extreme cases of protein-calorie malnutrition but is not useful in de- termining mild to moderate PCM. Limb and other circumferences are easily obtained with a simple tape. The best tape is narrow fiberglass to avoid fraying, breaking, or stretching the tape or breaking the skin of the subject (24). A fairly recent invention of the Quaker Service Team in Nigeria allows measurement of arm circumference (AC) and height and a quick calculation of their ratio (4). The so-called QUAC (Quaker Arm Circum~ ference) stick is a height measuring stick which is marked off in arm measurements rather than height. Cutoff values for a specified percent of expected AC for the given height are marked on the stick. If a child is taller than the level on the stick where his/her arm circum- ference is found, the child's arm is thinner than the average child of his/her height and is judged to be malnourished. By observing only walkers, one avoids the problem of defining correct baby length mea- surement. With a simple modification, the tape can be used as a record— ing device to be analyzed later (69). The QUAC stick has been used to identify two or three levels of malnutrition, generally given as percentages of a standard value. The QUAC dual chi l tati shov and the bin' and of I Call tecl wid ind her men DdC sex tie giv Sec Pi) 130 QUAC can also be used as a screening device to identify specific indivi- duals in need of extra care. Since the stick's figures are set and a child's AC changes very slowly (compared to weight), the critical limi- tation on measurement variability is correct technique. Studies have shown an average three percent variation in one measurer‘s results (24) and a maximum of eight to ten percent variance between observers (3,36) To obtain a skinfold measurement, calipers are needed. These have thecHsadvantage of being hard to use and relatively expensive. By com- bining skinfold and AC measurements, the cross sectional areas of fat and muscle can be determined (43). This allows an estimate of the type of PCM prevalent. As in many of the anthropometric measures, edema can be a complicating factor here. Several difficulties are inherent in the use of anthropometric techniques. In the countries where acute malnutrition is likely to be widespread, exact age levels are seldom known. This requires age- independnet indicators. A nutritional survey can be best interpreted if baseline data exists and a normal desired status is defined. The hereditary effects on body dimensions must be separated from environ— mental malnutrition. Factors other than malnutrition which have an im- pact on body dimensions include socioeconomic status of the parents, sex and birth rank of the child, climate, seasonal variation, infec- tions, parasites, and psychological factors (23). Recent reports of nutritional assessment in areas of known famine give strong support for the use of the QUAC stick. A study in Biafra, Sponsored in part by the United States Center for Disease Control, ex- plored various methods for determining relief allocation quantities. Pilot surveys were conducted using six indicators: kwashiorkor hair cha hei tec WOT ter pre chi the qui two not as the was 131 changes, edema, clinically established malnutrition, estimated age/ AC, height/ weight, height/ AC. These represent a broad range of available techniques. The QUAC stick ratio of height/AC was chosen for later work because it is: l. Reproducible and accurate 2. Simple enough to be performed by unskilled workers under supervision 3. Economical 4. Able to yield three levels of malnutrition (mild, mod- erate, severe) 5. Rapidly performed 6. Based on objective rather than subjective standards (15) The above survey covered sixty villages in one month without in- terrupting routine relief activities. A team of three people (inter- preter, secretary, measurer) could survey a minimum of seventy-five children of a village in one to three hours. A similar use was made of the QUAC stick in a different region of Nigeria (36). By using a quicker (and probably less accurate) sampling technique, an average of two hundred children were examined by two people in one hour. This did not include sample selection or travel times. In addition to serving as a basis for mass feeding allocations, the method was used to screen the severely malnourished for later examination by a physician. Quac stick measurement of more than 8,000 children in Bangladesh was followed eighteen months later by a study to determine the indivi- duals' fates. A clear picture emerged as those in the lowest percen- tiles of AC/height stood the greatest risk of dying (62). The study concluded that the QUAC stick provides an accurate measure of nutri- tional level. It also provided evidence that the predictive value of th 90 pe of th La 132 the measurement decays with time. That is, old information is not as good as new information. One article does report on the use of the weight/height ratio dur- ing a food crisis (20). A brief clinical exam and questioning on mor- tality rates were also included. The survey lasted ten weeks. The main result was a change in the food distribution patterns to cover more thoroughly those regions furthest from the capital. It is not clear whether this long—term survey was able to accommodate emergency situations. Relevant Social and Physical Factors in Bangladesh Several factors will greatly influence the success of any system implemented in Bangladesh. The country is one of the most densely pop- ulated and poorest in the world. Approximately seventy—five million people live in a land area the size of Louisiana. There are an average of one thousand people per square mile. Fifteen to thirty percent of the land mass is flooded during the monsoon months from May to August. Land communication and transportation are sorely lacking (57). Ninety-five percent of the people live in small villages. Most live in extended households, and there are generally two or three fac— tions or household groupings in each village (68, Chapter 5). Sharing of food is common within factions and often within the entire village. Generally heads of households receive the largest food portions, as a mark of their positions. The p0pulation is largely undereducated and illiterate; many graduates migrate to the cities. It is clear from the above explanatory material that the QUAC stick can be very useful in the assessment of malnutrition in expel forma the ( invo‘ of 81 range 0i 0) abunc Smal' the c from as a the ) TTaVe r____zx 133 Bangladesh. The method fits the population in that it is relatively nonthreatening to the subjects being measured and it can be administered without a great deal of training. There is the additional advantage that the QUAC can be used as a screening device to reduce costs in feeding and health programs. Finally, the QUAC stick can be used to develop an objective and comparative nutritional index across geo- graphical and economic classes. This is in accord with the equaliza- tion policy structure of the survival model. The assumption is made here that the QUAC stick will be the least expensive assessment tool for any feasible range of the applicable in- formation quality parameters. This allows several simplifications in the cost function analysis. The cost per survey variable CSURN will involve only one technique; there is no need to determine the levels of SDND and DELD that separate distinct system alternatives. A whole range of SDND and DELD values can be constructed on the basis of number of observations and personnel use. The QUAC stick technique is quick and simple,and there is an abundance of subjects available. Measurement time will likely be very small, as long as a sufficient number of survey teams are used. Thus, the delay parameter, DELD, of 5_will have a negligible contribution from nutritional debt surveillance. This allows us to consider CSURN as a function of SDND only (see Equation 5.18). Optimal Survey Costs As mentioned earlier, the cost of a sample survey is related to the number of observations to be made. Equipment, personnel, and travel expenses can be summed and divided by the number 0f UNIT samples to th pr re C0 As wh Cd 134 to obtain a cost per observation figure. A general statistical fact is that the number of observations required is inversely related to the measurement variance. In sample surveys, stratification of the subjects is often done to provide subgroups that are homogeneous. The g_p:ig:i_groupings help to reduce the expected sampling error. For nutritional surveillance, common bases for stratification have been geographical area, population group, and biological status (age, sex, etc.) (25). If the survey cost can be stated in a simple form, it is often possible to obtain a sample design with Optimal cost and variance. Assume that costs are of the form of Equation 5.19. L CSUR = C0 + h§1 Chnh (5.19) where: CSUR = survey cost (won/survey) CO = fixed survey cost (won/survey) Ch = sample cost, stratum h (won/sample) "h = number of observations, stratum h L = number of strata. Given such a linear cost function, it is possible to compute a minimal cost for specified variance (13, Chapter 5.5). The necessary calculations are given in Equations 5.20-5.22. 1 L nh = v‘* (mhsh/ fEE) * ( Z whsh “5%) (5.20) h=l _1_ L 1 /_ n = V -k ( 2 thh M) * ( X thh/ Ch) (5.21) h=1 h=1 1 L csun = C0 + v * ( z whsh (E;)2 (5.22) h=1 whe mate of ( dSS root form nutr cabl nUSt lain) Took Bang) 135 where: nh number of observations, stratum h total observations 3 II CSUR - survey cost (won/survey) Wh = population proportion, stratum h Sh = population standard deviation, stratum h Ch = sample cost, stratum h (won/sample) L = number of strata C0 = fixed survey cost (won/survey) V = variance of survey mean. Note that stratum size and population standard error must be esti— mated along with the observation cost of the strata. The optimal number of observations in each stratum increases as stratum size increases or as stratum internal variability increases. The information system standard error parameter SDND is the square root of the survey variance V, relating cost (Equation 5.22) to the in- formation system. To determine whether this form can be used for the nutritional survey problem, the form of Equation 5.19 must be appli— cable and the parameters Wh, Sh, Ch, and CO from Equations 5.20—5.22 must be available. The population proportions Wh can be easily ob- tained from census materials (12). The other items require a further look at likely conditions in Bangladesh. Let us first examine the state of the communications network in Bangladesh as of 1973. The capitol, Dacca, is connected to each of the other regional centers by modern microwave facilities. Each region has five or six "base“ towns connected to the regional center by an ti de wi av on ta su Ch POI RBI 9)" of rec adc 136 old UHF network. The ”bases" are natural choices for surveillance headquarters. A survey team operating out of each base town would be responsible for a small region of the country. Given the transporta- tion obstacles present in Bangladesh, the use of many teams seems pru- dent. This also supports the assumption that measurement delay time will not be significant. The nutritional survey teams would then be available for other types of surveillance. It will be assumed that one team operates out of each base town and that one survey can be com— pleted in one to three days. Note that this assumption bypasses the important problem of optimal surveillance personnel use. The use of many survey teams leads to relatively small transpor- tation costs. This is important for the use of Equation 5.19 since substantial travel expenses require a different formulation (13, Chapter 5). The remaining consideration is estimation of the nutritional debt population standard error Sh. This should not be confused with measure- ment standard error SDND. 5% represents the variation inherent in the given stratum. Baseline studies can help to estimate this quantity. Estimates are also available if the range and approximate distribution 0f possible values are known. The variance problem here is twofold. First, the survival model requires the variance of per-capital nutritional debt requirements. An additional error is introduced in translating QUAC stick measurements to nutritional debt levels. Based on successful past experiences with the QUAC stick, it appears that the needed translation can be done and that increased sample size reduces the expected error. For the purposes of the current model, initial estimates of Si values will be made according to Cochran (13, Chapter 4.7). The form of this estimate is given in Equation 5.23. It will be assumed that maximum and minimum per-capita nutritional debt values are known and that the distribution in the population is similar to an isoceles tri- angle. The nutritional debt variance estimate will be increased to reflect the randomness inherent in Quac stick use. The amount of in- crease is set to provide reasonable results, based on descriptions of QUAC surveys in the literature. 52 = RAN6E2/24 (5.23) where: 52 = nutritional debt variance in population RANGE = difference between maximum and minimum nutritional debt values. An additional consideration that could be examined in later stud- ies is the effect of measurement variance among observers on the opti- mal number of survey teams. This has been avoided here by the assump- tion of one team at each base. If the variance among observers is known and a cost function can be constructed as in Equation 5.24, then the number of observers and unit samples to minimize costs can be de- termined for a given variance (56, Chapter 8.5). CSUR = C0 + c1 * n + c2 * m (5.24) where: CSUR = survey cost (won) C0 = fixed cost (won) C1 = unit sample cost (won/sample) : :ch four tner whe 138 C2 = observer cost (won/observer) n = number of samples m = number of observers. The survival model requires nutritional debt estimates for each of four economic classes, each estimate having the same variance. Thus, there are only fOur strata representing the nutritional standard error of the population. It will be assumed that the classes are spread even— ly across the four regions, so that four population strata will suffice. Costs vary by region and by class. With these definitions, the nutri- tional debt surveillance costs are summarized in Equations 5.25 and 5.26. One further note is that CSURN is computed with the assumption that each population class represents a separate survey and the four re- gions are the statistical sampling strata. The reason for this break- down is the possibility that different error rates could be allowed for different classes, particularly a rural and urban breakdown. This gen- erality is not used in the current study. CSN(TF,SDND,SAMPT) = CFIXN + TF * CSURN(SDND)/SAMPT (5 25) 1 4 4 y——- csuww(sowo) = on + * ( z sNZ 2 wh cwhj)2 (5.25) 0 some2 i=1 3 h=l where: CSN = nutritional surveillance cost (won) CSURN = nutritional survey cost (won/survey) TF = time duration of emergency (years) SDND = nutritional debt measurement standard error SAMPT nutritional survey frequency (years/survey) CFIXN fixed nutritional surveillance costs--training and equipment (won) Apper dixl comp equi incu wher men) CTUl Sid and CNh CN0 = fixed nutritional survey cost--equipment (won/survey) Wh = population proportion, stratum h SN = population nutritional standard error CN = nutritional unit sample cost (won/sample) j = index on population classes h = index on statistical strata. The exact parameter values used in modeling work are explained in Appendix A and can be located in the FORTRAN computer program in Appen- dix B. The following designations have been made to simplify numerical computations. Surveillance fixed cost CFIXN includes training and equipment (QUAC sticks). The fixed equipment and training costs are incurred once. The form used for calculating the fixed cost function is given in Equation 5.27. CFIXN = TEAMS * (TRAINN + EQN * PMNT) (5.27) where: CFIXN = fixed nutritional surveillance cost (won) TEAMS = number of survey teams TRAINN = training cost (won/team) EQN = equipment cost (won/team) PMNT = % maintenance expense. The survey costs are for travel expenses, personnel salaries and equip- ment that is not reusable (reporting forms). Equipment costs are in- cluded in fixed survey expenses CN Travel time varies between re— 0. gions. and personnel use varies with the number of needed observations and travel time. These two items are included in the unit sample cost CNhj. ——_—_‘ di llb 140 Consumption and Private Storage Surveillance Costs Much of the framework has been built in the previous section for discussion of food consumption and rural private storage costs. The ”base“ town observation teams are avilable for surveillance duty. A possible cost minimization routine is available. And background mater- ial on Bangladesh is known. The remaining task is to examine possible surveillance techniques and determine if Equations 5.25-5.26 can be adopted. Consumption Surveys Common methods for assessing food intake are divided on the basis of purpose of the sampling. The distinct uses are for obtaining group averages versus individual screenings. Assessment of individual con- sumption is generally done either on the basis of an interview to de- termine intake in the last twenty—four hOurs or by a three-to-seven day observation of a household's actual consumption. The methods are referred to as recall and observation, respectively. Determination of group average consumption levels involves the use of several pieces of information. Some individual sampling is done, and food ”disappearance” estimates and family food patterns are used (67). Advantages of the group survey are smaller required time, cost, cooperation, and degree of precision. The twenty-four hour recall method of individual sampling is most efficient for group average use. In computing consumption levels during a food crisis, several pieces of data will be available apart from the surveillance function. Harvest and storage estimates will tell the total food amount that has "disappeared” through consumption, sales, gifts to poor relatives. or ho til qu ho to cl no ca si no Ev wo cl an on or Th ta 141 hoarding. Reports from feeding programs will indicate food distribu- tion to a sizeable portion of the population. The main data item re- quired of consumption surveillance is an estimate of individual (or household) intake. A typical recall interview in a developed country may take twenty to twenty—five minutes and cover a wide range of food items (42). This is too long and too detailed a process for famine relief work. Simple, clearly defined questionnaires are needed that can be administered by non-technical personnel. Foods can be classified in three or four categories to reduce the amount of paperwork and statistical proces- sing (64). Such categorization would be especially applicable in Bang- ladesh where at least two-thirds of the daily diet consists of rice and much of the remaining intake is in the form of curries and pulses (50). Even with short questionnaires, it is doubtful that consumption surveys would be practical during a famine. Consumption sampling will be in- cluded in the current study for demonstration purposes. It will be assumed here that surveillance for consumption levels will take place using a short questionnaire. The survey teams will have the same coverage areas as the nutritional observation teams of the previous section and will consist of the same personnel. Since the interviews are expected to be short and travel requirements are again small, delay time due to measurement requirements is assumed negligible and the cost function form of Equation 5.19 will be used. One differ- ence between QUAC stick measurements and food intake interviews is crucial. The interview techniques will require extensive training. The skill of the observer is the most important consideration in ob- taining accurate results (18). co: aPl ha1 lei met any pli of for sto Cha) meas m Dercr Alla) disc) --_..__.a- -x-.._ A- . _. __ _.. . 142 Private Storagg Before examining the specific form of consumption surveillance costs, rural private storage surveillance is discussed. Storage can be approximated by deducting estimated consumed amounts from the estimated harvest. A more accurate method would be to measure actual storage levels by "eyeballing" or more sophisticated techniques. Probably both methods will be needed to assess the degree of hoarding present. In any event, the grain stores will probably be held by households. Sam- pling of individual household stocks should be quick since the amount of grain involved will be small. More detailed observation methods must be determined elsewhere. For the current study, it is assumed that food consumption and private storage surveillance will be conducted separately. As a result of Chapter IV findings, only the holdings of the rural class will be measured. Equation Formats Assumptions will be made concerning statistical strata, population classes, per unit costs, and standard errors that are very similar to those made for nutritional surveillance. The standard error and per unit costs vary by class and by region. Population proportions vary by region only. The only major difference concerns the use of measurement standard errors SDRC and SDRS for consumption and storage respectively. As discussed in Chapter III, the model assumes that these errors are percentages of the true consumption and storage levels. The cost mini- mization of Equation 5.22 treats the variance as a true variance. This discrepancy is easily resolved. Observation of model outputs indicates avere dard ing 1 5.28 wher are (CFi inc and tio ful CS Wh. 143 average values for consumption and storage. The model percentage stan- dard deviations are converted to true standard deviations by multiply- ing by the average values. The computation is indicated in Equation 5.28. SOT; = SDPi * VAV6, (5.28) where: SDT = true standard deviation SDP = percent standard deviation VAVG = average variable value i index on variable (consumption, rural private storage). Costs for food consumption and rural private storage surveillance are now given in Equations 5.29-5.32. Again, fixed surveillance costs (CFIX) cover training and durable equipment; fixed survey costs (CO) include replaced equipment; unit sample expenses (Chj) are for travel and salaries. In computing unit sample costs both here and for nutri- tional surveillance, it is assumed that survey team members have gain- ful employment in non-survey times. The cost parameters CC, CN, and CS cover one survey day for each team. CSC(TF,SDRC,SMPRC) = CFIX + TF * CSURC(SDRC)/SMPRC (5.29) CSS(TF,SDRS,SMPRS) = CFIXS + TF * CSURS(SDRS)/SMPRS (5.30) 1 4 4 CSURc(SDRc) = ccO + * z (2 whsc. (och-)2 (5.31) soRc2 j=l h=l 3 3 4 1 CSURS(SDRS) = cs0 + * ( z whss dosh)2 (5.32) soRs2 h=l where: Tn mi fi 144 CSC = consumption surveillance cost (won) CSS = storage surveillance cost (won) SDRC = consumption measurement standard error SDRS = storage measurement standard error SMPRC = consumption sampling interval (years/survey) SMPRS = storage sampling interval (years/survey) TF = time duration of emergency (years) CSURC = consumption survey cost (won/survey) CSURS = storage survey cost (won/survey) Wh = population proportion, stratum h SC = consumption standard error of population SS = storage standard error of population CFIXC = consumption fixed surveillance cost (won) CFIXS = storage fixed surveillance cost (won) CCO = consumption fixed survey cost (won/survey) CSO = storage fixed survey cost (won/survey) CC = consumption unit sample cost (won/sample) CS = storage unit sample cost (won/sample) h = index on strata j = index on population class. Transmission and Processing Costs Previous simplifying assumptions have made the cost of data trans- mission the main link to the delay parameter of 5, Transmission is de- fined here as whatever methods are used to transform (and process) the field-acquired measurements into reports usable by system managers. reg eac gio tha be: ex‘ til si tr ti 145 The extant communication network in Bangladesh discussed earlier is a logical starting point. Efficient microwave channels connect the regional centers to the capital, Dacca. Five or six small towns in each of the four regions serve as "bases." These are linked to the re— gional center by an old and *inefficient UHF network. Other facilities that may be useful include several mobile UHF base units which have been used for emergency work, primarily during floods. Telephones exist only in the largest cities and are not reliable. Surveillance procedures previously discussed call for one observa- tion team's Operating out of each base town. We will assume that the single team can handle the three types of surveillance. Thus, the transmission process involves team reports to the base town, where ini- tial processing takes place; UHF or other communication with the region- al centers; and additional processing and microwave transmission to Dacca, where final reports are prepared. Messenger service from base towns to regional centers may be required, depending on the UHF network status. Delay Parameter DELD The delay parameter, DELD, from the survival model represents the average amount of time needed to complete the above process. It may well be that urgent messages can be sent very quickly, but the desired figure here is the normal time needed over the course of the food cri- sis. Costs include personnel training, salaries, equipment purchase, and maintenance. For the purposes of this study, the existing system in Bangladesh will be considered the overall minimum cost, maximum delay alternative. 146 Reductions in the average delay time will require improvements to the current structure. The cost function will be constructed by citing three feasible system additions in order of priority. Costs and delay time improvements will be estimated for each addition. Then, four points on the cost function curve will be calculated by successive ad- ditions to the basic system. The functional shape is indicated in Fig- ure 5.1. Linear interpolation will be used to estimate costs for delay times among the four designated alternatives. This allows generation of a transmission cost for any delay level DEL within parameter con- straints. Note that the costs are additive; alternative III includes the cost of alternatives I and II, etc. The monetary conversion rate used here is four hundred won equal one dollar. It should be noted that the won is the monetary base in Korea, the country modeled in the original simulation (38). The takka is the currency base for Bangladesh. §ystem Additions and CoSts As mentioned, the first alternative is the existing system, in- cluding the microwave and UHF network and the personnel and equipment needed ixioperate the base stations. It is also assumed that a high level computer is available at Dacca for computation, analysis work, and storage. This base alternative is point number I in Figure 5.1. The first addition to the basic system (point II in Figure 5.1) is a set of two-way transceivers for each base, observation team, and re- gional center. These radios would allow rapid reporting to the base so that processing is not delayed while teams return from surveillance. The transceivers would also be a back-up for the UHF system. Some 147 CDEL (100 million) won 2.0L IV 1.8 L UHF Renovation 1.6 - III 1 4 _ Base ' Microcomputers 1.2 - II I Base Transceivers Existing System 1.0 - 0.8 > 0.6 0.4 r 0.2 r 44 —L —4 . DELD 0.5 1.0 1.5 2.0 (Weeks) Figure 5.1. Transmission and Processing Cost as a Function of Information Delay. 148 effort has been expended on the design and construction of radios that are inexpensive, reliable, and able to transmit and receive over fairly long distances (65). The resulting unit reportedly has a broadcast range of 160 miles and costs approximately one hundred dollars. The predicted range should cover each surveillance area and most base—town- to-regional—center links. The next suggested improvement (in addition to radios) is a micro- computer to speed the processing task at base locations. The computa- tional power needed at the base level consists mainly of means and standard errors from survey results. A programmable calculator with printer should provide the necessary power and a hard copy for error checks. Additional personnel are assumed to be needed for operation of the new computers. The last improvement considered is the renovation of the UHF net— work. This would be advantageous for many purposes beyond famine re- lief. Costs for each of the above improvements are assigned to the fa- mine relief information system based on estimated purchase price, main- tenance expense, depreciation percentage, usage level for famine relief, yearly salaries, duration of the emergency, and number of equipment and personnel units required. This breakdown of cost components is helpful in assigning total cost. The breakdown also allows analysis, using sensitivity tests to indicate critical cost considerations. Equipment costs are computed for each alternative using the form of Equation 5.33. This applies to the initial equipment, microwave, UHF, radios, and calculators. The number of units times the price per unit gives the base cost. Percentage maintenance and depreciation are factc assig will maini where wher 149 factored in, as well as a usage proportion, to arrive at a yearly cost assignable to famine relief. Maintenance and depreciation factors will be high in Bangladesh due to high humidity, theft, and few trained maintenance people. CEQi = UEQi * WEQi * (MAINTi + PDEPi) * PUSi (5.33) where: CEQ = equipment cost (won/year) UEQ = units of equipment WEQ = equipment purchase price (won/unit) MAINT = percent maintenance cost PDEP = percent depreciation PUS percent equipment usage for relief 1 index on equipment items. Equation 5.34 contains the form used for calculating personnel expenses for transmission of famine relief data. Two costs are in- cluded, for salaries and training. Per person costs are multiplied by the number of personnel. Because the operators may work on projects other than the relief effort, a parameter (PRPUS) is included to re— flect percentage time spent on relief. CPRj = UPRj * (NPRj + TPRj) * PRPUS:j (5,34) where: CPR = personnel cost (won/year) UPR = number of personnel (persons) NPR = salary (won/person—year) TPR = training cost (won/person—year) and very avai for to ) The cos len ger wh 150 PRPUS percent personnel time for relief index on personnel type. Ll. II The exact parameter values used are in the tables of Appendix A and in the FORTRAN code in Appendix 8. Estimation of the parameters is very crude since little exact cost information from Bangladesh is available. The information quality parameter DELD is the independent variable for function CDEL of Figure 5.1. The value obtained is the yearly cost to provide information transmission with the given average delay time. The relief information system expense is computed by multiplying yearly cost by the length of the food crisis, as in Equation 5.35. Emergency length is easily obtainable in the model by observing the crisis trig- ger described in Equations 2.11. CDELF(DELD,TF) = CDEL(DELD) * TF (5.35) where: CDELF food crisis transmission cost (won) CDEL = yearly transmission cost (won/year) TF = length of crisis (years) DELD = information delay parameter. Summary The surveillance and transmission cost equations of the last three sections are cast in a form where they are solved once for a given in- formation quality vector and simulation run. This corresponds to pro— posed calculation of the cost function in an analysis off-line from the survival model performance function. Cost parameters then represent 6V9 COS add whe CUT) Spe do: to on 151 average figures over the crisis duration. The total information system cost in this modeled off-line analysis is obtained in Equation 5.36 by adding the transmission and surveillance costs. 6(5) = CDELF(DELD,TF) + CSN(TF,SDND,SAMPT) (5.36) + CSC(TF,SDRC,SMPRC) + CSS(TF,SDRS,SMPRS) where: 6 = information system cost (wen) 5_ = information quality parameter DELD = information delay (years) SDND = nutritional debt measurement error SDRC = consumption measurement error SDRS = private storage measurement error SAMPT = nutritional debt sampling interval SMPRC = consumption sampling interval SMPRS = private storage sampling interval CDELF = transmission and processing cost(won) CSN = nutritional surveillance cost (won) CSC = consumption surveillance cost (won) CSS = storage surveillance cost (won) TF = food crisis duration (years). An alternative cost modeling procedure would be to dynamically ac- cumulate costs as the simulation proceeds. Costs would be assigned to specific events, such as sampling, transportation, etc. Each time the designated events occur, a cost would be generated (perhaps randomly) to augment the expense total. Note that this would require more detail on the separate components of system alternatives than the current model provides. CC dology is an The func odology by it discusses the mation qualii the G functiv function com) As discr monetary con: requirements ment and per approach to available sir here. This tion. 152 provides. Comparison of this modified approach with the current metho— dology is an area of possible further research. The function 6(5) provides an important link in the proposed meth— odology by identifying the cost of information quality. This chapter discusses the relationships among system alternatives, costs, and infor- mation quality parameters; it also describes needed characteristics of the 6 function. Several examples are given of the development of cost function components. As discussed in Chapter IV, the only “cost" considered here is the monetary constraint on information quality. Equipment and personnel requirements are converted to monetary units. It may be that the equip- ment and personnel limitations require their own “cost” functions. An approach to generating personnel and equipment functions should be available similar to the monetary cost function development described here. This whole constraint and costs area deserves much more atten- tion. the s ing a pose ' of th to be infor provi The w polic Drese t0 pr dgeme This nutri cesse CHAPTER VI INFORMATION FILTERS FOR SYSTEM MANAGEMENT This chapter examines the famine relief information system from the systems' manager's perspective. Chapter V describes a data gather- ing and transmission process as it might occur in Bangladesh. The pur- pose there is to identify the costs involved in surveillance. The role of the decision maker is avoided because management expenses are felt to be a part of the overall relief effort rather than assignable to the information system. In Chapter III a sampling component is modeled, providing information of set precision levels to the system managers. The work of these decision makers is simulated by a series of fixed policy rules. The rules assume a constancy of reaction that is not present in real situations. So the purpose of the current chapter is to provide a more realistic view of the use of information by the man- agement group. A recent symposium on famine relief operations recommends that: ...a headquarters analysis group should be organized in- cluding experts in management, health, nutrition, agricul— ture, and social sciences to collate, interpret the signifi- cance and relationships of all information, determine trends, develop priorities, and predict future developments (7, Re- commendations). This broad charge is echoed by a World Health Organization monograph on nutritional surveillance, which states that system managers need pro- cessed data enabling them to describe contemporary conditions, 153 identi the 51 M curren and go on wat also t as nun f storag crease vary 1 pfipy: and S‘ mine. SPOOST sions mon u Polio P0lic model devis forma used Scrih 154 identify trends, predict changes, and elucidate underlying causes of the situation (25). Many bits and pieces of information will be used by managers. The current model requires data on nutritional level, consumption, private and government food stores, and population levels. Additional reports on water and disease levels, transportation availability, etc., will also be needed. Sample surveys will likely include narrative as well as numerical portions. 5_ppippi knowledge will enter into decision making. For example, storage levels should decrease until the harvest and then should in- crease dramatically. Some variables, such as consumption, are known to vary more rapidly than others. It was mentioned in Chapter V that p ppippi harvest information can be used along with estimates of sales and storage to approximate average consumption levels. The urgency of decision making changes during the course of a fa- mine. Reports of new instances of dire shortages call for quick re- sponse. Unexpected occurrences can alter plans and vary timing deci— sions. War, natural disaster, or additional international aid are com— mon unexpected occurrences. Thus, the decision process involves much more than a series of policy rules. The survival model of this thesis employs the general policy rules for three reasons. First, the hypothetical country being modeled does not have an eXplicit policy structure; each country must devise its own. Second, this model represents the first stages of in— formation system development. It is hoped that this approach can be used to step beyond the current model. Finally, because the model de- scribes processes at a macro level, the policies are constructed as aver gent $11100 5U99 vary the woul numb the out comp incr Chap the sire is d esti whil 155 average expected decisions. It is assumed that the fluctuation in ur— gent data needs, available reports, and unexpected occurrences will smooth out over the several months' duration of the crisis. The variety of actual information sources and timing requirements suggest two additions needed in a more complete survival model: time- varying parameters and information filters and predictors. Allowing the model policy and information quality parameters to vary with time would provide the flexibility needed to simulate response to a great number of scenarios. The disaster type could be better tailored to the particular region of application. But this capability is not with- out a price. Strategy construction and Optimization work are greatly complicated as the number of parameters mushrooms. The parameter total increases multiplicatively with the number of changes allowed (27, Chapter 3). Filters and predictors can be easily added to the model. Recall the sampling component of Chapter III. The ”true“ time series for de— sired variables is estimated at specified survey times. This estimate is delayed and then used in the policy rules. Between surveys, the estimate remains constant; it is a sample-and—hold, or zero-order, de— lay. A filter would affect the estimation process at the survey times, while a predictor would allow changed estimates between surveys. These changes are easily implemented, both in the model and in the real world The basic question to be answered is whether such techniques can per— form better than the simple sample-and-hold estimator. That is, can a filter or predictor sufficiently augment information quality so that total deaths and total nutritional debt are lowered? The rest of this chapter is a step toward the answer. The Kalman filter and the S0-I add mat str are frc 1‘95 prc ini cha cu) sa: dl‘l bu th 156 so-called alpha-beta tracker are briefly described, then the tracker is added to the survival model and performance tests are conducted. Filters and Predictors Any estimator represents an attempt to get the most possible infor mation from a set of captured data. The data processing, population stratification, and sample size determination mentioned in Chapter V are all part of a sample methodology aimed at extracting maximum worth from surveillance work. The inputs to sample estimators would be the results from one survey. Filters and predictors add a dynamic dimension to the estimation problem. The process under study is changing with time, and desired information includes not only absolute levels, but the nature of the changes. A filter commonly uses all previously known data as well as current survey results to make an estimate. This is distinct from the sample-and—hold technique of Chapter III, where current survey results are used exclusively. The predictor also employs past and current data but projects the trends to estimate future results. The hope is that these tools can increase information quality without additional surveiT lance or transmission costs. Testing a filter also provides clues on the system performance effects of auto-correlated information. In this section we examine two filters and their associated pre— dictors. The alpha—beta (0"B ) tracker is commonly used in radar ap- plications to track positions and direction of aircraft. Alpha and beta refer to parameters of the filter. The tracker is added to the sampling component and tested in the next section. The second filter 1discussed is the so—called Kalman filter. This appears to be an exce‘ here piec pred data wher 157 excellent filter alternative in real applications. It is not tested here because its structure is not practical in the current context. The implementation of an o-B tracker is quite simple. Each new piece of information serves as an input to a set of three equations. A predicted function value is computed based on past information. The new data and the predicted value are combined to form a "smoothed” estimate of the current situation. The rate of change, or velocity, of the function is also estimated. The set of equations is presented here (11, Chapter 8.11). Yp(T) = Y (T-SAMP) + SAMP * Yd(T—SAMP) (6.1) Y (T) = YplT) + a *(U(T) - YPIT)) (6 2) vd(1) = Yd(T-SAMP) + B * u(T) — Yp(T) / SAMP (6.3) where: Yp = value predicted from past information Y = smoothed value used as estimate Yd = function velocity estimate u = survey result SAMP = sampling interval (years) T = current time “:5 = parameters of filter. Note how this tracker compares to the sample-and-hold scheme of Chapter III. HOLD(T) equal to u(T) is the output of routine SAMPL in Chapter III and HOLD(T) is sent to the delay VDTDLI at each simulation cycle DT for one complete sampling interval (DT< 164 ,avoided if the number of observations (number of simulation replica- r—l "tions) is the same for each sample. Thus, all testing is done with equal replications for each different 8 value, and the t—statistics are _-—‘C ecomputed as in Equation 6.11. t = (T1 - T2) //_Tr_]_(s§ + $5) (6.11) where: t = t-statistic V5,Té = sample means sample standard deviations n = number of replications A third evaluation of tracker performance is used, based on the in- lformation desired by decision makers. Planners and managers will be more interested in improvements in system outputs than in statistical error reduction. For each replication in the Monte Carlo runs, total death and total nutritional debt are recorded. Then, each replicate in the filter alternative (8 <1.0) is compared to the average figure for the basic sample-and-hold component (8 =1.0). The fraction of improved replicates to total replicates provides an estimate of the probability that the tracker will improve performance. This is, each replicate is considered a possible outcome, and reduction in deaths or nutritional debt a success. Note that separate probabilities will be recorded for deaths and for nutritional debt. Agging the Tracker to the Model The a-B tracker is very easily added to the sampling component of Chapter III. Recall that the term EST in Equations 3.4 and 3.5 repre is t) ceive rout beco tor, so 1 off Tes rol COT ter dll tr 165 represents the sampled variable value before delay is introduced. ESTk is then an input to the routine VDTDLI, whose output is the estimate re- ceived by decision makers. The filter does not at all change the delay routine. An additional stage is added between sampling and delay. ESTk becomes the input to the filter (u in Equation 6.2). The filter output (Y) becomes the new input to VDTDLI. In the case of the linear predic- tor, Y is the input to VDTDLI. Equation 6.5 is included in the model P so that B is the only parameter to be specified. The tracker is turned off by setting 8 equal to one, as discussed earlier. Testing by Sampled Variable A series of tests is now described whose goal is to determine the role of the 9‘5 tracker in the current study. The tests do not provide conclusive evidence about the worth of the tracker in information sys- tem work, but they do indicate the path to follow here. The primary questions to be addressed are which variables to filter and which filter parameters to include in later optimization. The tradeoff is common. Including too many parameters in the optimization will complicate the process and the solution. But the exclusion of needed parameters can obscure model or information system structure. There are nine variables that are candidates for filtering. Four per- capita nutritional debt and four per-capita consumption variables are needed to describe the population groups. And one rural private stor- age figure completes the total. These are the variables covered by the modeling sampling routine, as discussed in Chapter IV. Thus, the maxi- mum number of parameters that could be added to the optimization would be nine. The minimum would be zero. for ( ple ‘ ence dist shou 8 va deaf tat" ure: gio the by Uh fi to El” 166 The first sensitivity test involves the use of identical 8 values for each of the nine filters. The predictor is not employed. This sim- ple test is aimed at discovering whether the tracker makes any differ— ence in measurement error or system performance. Identical 8 values can distort performance effects, but error reduction with tracker usage should beclear.- Five Monte Carlo replications are done at each of four 8 values and the results (absolute error, mean squared error, total deaths, total nutritional debt) are presented in Table 6.1. A represen- tative class has been chosen for nutritional debt and consumption fig- ures. The urban poor class with no rural relatives is listed because it is the one most affected by the relief policy. Note that the 8 values in Table 6.1 cover the (0,1) stability re- gion. As discussed earlier, sample means and standard deviations for the Monte Carlo replications are given. Randomness has been introduced by a fixed ”good” information vector 5, Low error means, low death totals, and small nutritional debt fig- ures are regarded as good in reading the table. So nutritional debt is filtered best for 8 equal 0.7 or 0.1, according to the error measures. Consumption filtering is best at the end points. Note that absolute error and mean squared error do not correspond exactly for all changes but do agree on relative sizes for large error differences. The dis- agreements for close values are probably caused by random fluctuations. The significance of the changed error measures with changing 8 for nutritional debt and consumption filters is examined in Table 6.2. Storage is not included, as the filter provides worse performance. A t—statistic, as computed in Equation 6.11, is presented. The hypothesis is that the sample means for 8 equal 0.1 are improved over the means at UG..—.F\r C 1..1.l ..... . u Am.m_v Aomm.v Ao_MNem.v Am-momm.v m.om em.m N_meuz. “-mme_. AN._MV Amom.v A__mwmm.v Am-mmwe.v mm o.me me.m Nfim_m_. N-mmem. . Am.opv Amkm.v Ao_mmwm.v AN-mNNN.V “A.4m mm.m __mmo_. N-mmam. Am.s_v zoom.v Ao_mo_m.v AN-mme_.v am.ae me.m ,_mmmm. N16Nom. AH: ooo_v “6:0w___2v ameaopw coprEsmeoo peas page?“ wepaao -_aosz _aoop A=Owumw>mm upmucwumv wocmegoeemm Am-mmsm.v m-meke. Am-mwm_.v m-w_mm. Am-mre_.v m-mmmm. Am-mome.v mvmmme. pawn _ecoppatpsz Acowpmw>oa osmocmpmv w.c coppescm Loxcm nogczam 2mm: Akmmom.v A¢N.mV Awmm.v muses. mo.s_ emo., hemeNN.v A4®.NV Ame_.v mmep_. Fm.mm mmm._ Amma_m.v Aam.mv Am__.v wages. oo.mm mmo._ flammhm.v Amm.mv Ammom.v womemm. mm.om maz._ wmwgopm scepaazmcou pawn _meoaowepsz Aco~p8~>mo ugwucmpmv m.m cowpmaom Locgm mp:_oma< .mw:_m> u mzowcm> pm mcowpmungwm o_Lmu opzoz m>pd Low Loxomcp are mgu cpvz mcowpmw>ma chucwpm use mcmmz Locgm ._.w mpnme o._nm St est ter ity dii fi‘ 5‘) dC wry 168 Table 6.2. T—Statistics and Acceptance Levels for Hypothesis Tests on Means of Table 6.1, 8=l.0 versus 8:0.1. Absolute Error Mean Sguared Error Nutritional Nutritional Debt Consumption Debt Consumption t Statistic .473 2.459 1.105 2.219 Significance Level (V=4) .25 .025 .25 .05 8 equal 1.0. The 0.1 8 level was chosen as generally giving the small- est mean, and, of course, the 1.0 level represents the case of no fil— ter. The significance level in the table is the approximate probabil— ity that an error will be made in assuming the compared means to be different. A one-tailed test is used with four degrees of freedom. Statistically, the per—capita consumption filter is much more like— ly to cause error reduction than is the per-capita nutritional debt filter. Table 6.2 shows that both filters may reduce absolute or mean squared error. But performance, as measured by total deaths in Table 6.1, is unaffected. The mean total nutritional debt figures vary widely across 8 values. It should be noted, however, that nutritional debt also has large standard errors for a given 8 . Total deaths is a more reliable performance figure and shows little change with B The inconsistency of reduced error and static performance bears further attention. A second test with distinct 3 values by variable and by class will be conducted. First, however, the case of the rural private storage filter in Table 6.1 will be examined. It is clear from the RE the d: consu: can b the esti addi Equz cha whe th 169 the RSTOR columns that error increases as 8 decreases. It may be that the degrading storage information has offset the improved nutrition and consumption data and left the performance statistics unchanged. This can be checked with distinct 8 values in the upcoming test. It appears that the a-B tracker does not estimate the storage var- iable well. One further filter modification was explored, making use of p_ppippi_knowledge of the expected behavior of the private storage time series. The rural private storage level should decrease monotoni- cally until the harvest. Afterwards, stores oscillate as the new crop is added and then removed for consumption and sales purposes. This is true in the model and would also hold in the real world case where no international aid is forthcoming. The filter modification involves the long downward slope before the harvest. Equations 6.1-6.3 indicate a predicted value Yp and the estimate employed, Y. At each sampling point before the harvest, an additional filter step is added to magnify storage estimate decreases. Equation 6.12 is the simple minimization used. The tracker was un— changed for the period after initial harvesting. Ym(T) = minimum(Y(T), thT)) (6.12) where: Ym = modified tracker estimate Y = original tracker estimate Yp = predicted value from past information T = time. No performance change was noted for the modified filters, even when the storage Biwas uncoupled from E3's for other variables. There was a "x... - slight decreas these i is alsc result: later Igggjp h variat param: and g sepan ple-a tion this beyor debt And: the curs the Squa This fem l70 slight improvement in the error terms, but error still worsened as 8 decreased. It is possible that the policy parameters B being used in these tests do not allow the storage filter to operate efficiently. It is also possible that the tracker does not work well here. Based on the results in Table 6.l, the storage 5 parameters will not be included in later optimization work; the sample-and-hold estimator will be used. Testing by Population Class We now turn to tests involving distinct filters for the separate variables and population classes. From Table 6.l, the most promising parameter values aretg equal 0.7 or O.l for the nutritional debt filters andgg equal O.l for consumption. These three cases were simulated separately, and the results are presented in Table 6.3. The base sam: ple-and-hold case is also given, copied from Table 6.1. Note the frac— tion included in table "performance“ entries. As discussed earlier, this is a probability that the given filter causes improved performance beyond the base case. The two rows in Table 6.3 that represent per-capita nutritional debt filters (ggNUT) show no significant change in system performance. And the measured errors are unchanged forf3NUT equal 0.7 compared to the base case. The only significant nutritional debt filter change oc- curs for error terms when BNUT equals O.l. But the t-statistics, using the five Monte Carlo replications and comparing nutritional debt mean squared error for the base case versus BNUT equal 0.1, is only l.25. This is significant at the .25 level, similar to results in Table 6.2. The consumption filter greatly affects system performance. The reduction in total deaths for BCON equal O.l is statistically very .mcowpmowramm OerU quOZ uywu LOk mmzpm> m #UCrhUTC £+w3 U+Fu -l\f\c ‘Ituu' 'I. m\o m\m Ao.m_v ANN.V AN-MN©_.V Aeo.mv _.oumzoum mo.mm ¢m~.N N-momm. _m.mm o._ n szm m\N m\w Ac mmv Amm v Am-m0NN V Amo_.v o._nmzoum we Re Re m m-mkmm Nam. _.o u szm m\m m\_ Ao va Aem V Am-mkmm v AFNm_.V o._nmzoom mm mm.~¢ mm.m m-mo~¢. mN.F N.cu szm Aw.__v Aom.v Am-mm¢F.V Am-mome.v Amm.mv Ammom.v o._um200m em.N¢ me.m N-mwom. m-mmma. mm.om m~_.F o.Fu FDZm AH: ooo_v ~m=0w___zv cowpmasmcoo pnao cowpmeammmm mmmm paws mgpaao _mcotpvep:z _acowpmep=z _a:owppcp=z _wp0H _mpop Acowpmv>me Ucmucwumv Acowpmp>mo ucmvcmpmv Acowpm?>mo vgmucmpmv mocmELowme w.m cowpmzum m.o cowpmscm Loccm vmcmscm :moz Locxm msz0mn< .mcowpmoquwm opgmu wuzoz w>wm Low mmz—m> m pucvpmwm spwz mu_:mwm waowLH mic .m.© mpnwk sign' at 3| lota rela ror exalt pute ble! umn fig det ex< eve til 172 significant (t=3.5). Just as importantly, each Monte Carlo replication at BCON equal O.l produced a lower death total than the base average * Total nutritional debt increases, as would be expected by its inverse relationship to total deaths. An anomaly is present, however. The er- ror increases when 8 equal O.l. Additional insight is provided by CON examining each class separately. Table 6.4 contains selected filter data by class for the same com— puter runs presented in Table 6.3. Note the agreement between the ta-. bles for the Total Death, Total Nutritional Debt, and the Urban1 col— umns. Only mean squared error terms are given, as the absolute error figures show similar results. Two items are of interest in Table 6.4. Per—capita nutritional debt error is reduced with the use of the a“8 tracker for each class except the urban rich. The differences are not highly significant, how- ever. And performance does not change. Conversely, per-capita consump- tion class filters show little change in error terms but provide a large performance difference. Neither variable type provides conclusive evidence on the worth of the a'3 tracker. The fixed policy parameters E and information quality vector 5_may exert an unseen but powerful force on the test results. Or it may be that the model is, indeed, highly sensitive to changes in measured consumption and not sensitive to varying nutrition measure- ments. Previous work with the model would indicate that the first sug- gestion is more probably correct than the second. M *This is the meaning of the 5/5 fraction in the total death column entry for BCON = 0.]. .mmmro :prmps 0Q XE mpFammm waUNLF «I! _\u (Fal- ltl-I I _u- fl“ ‘ i l73 Ao.wpv ©0.N© Am.__v am.N¢ Ao.mmv e©.~¢ Aw._FV em.he ANN.V mn.m Aom.v me.m Amm.v n¢.m Aom.v me.m AH: ooo_v ammo _acovp_ep=z _mpoc chocp_vzv wepamo _apoe Acowuww>wo ccmucmpmv mocmELomLma N-mmkm. Am-mee_.v AN-MN0_.V Am-mme_.v N-m¢mr. mimomm. mlmoom. N-m~—N. Am-m_m_.v Am-mkkn.v Am-mmep.v Am-men_.v m-moom. NummoP. N-mmom. N-momm. Am-mmmm.v Ao-m~mo.v Am-mmmm.v Am-momp.v wimmmm. m-mwmm. m-m~m©. msmvwm. Am-mmmm.v Am-mP_N.V Am-mowe.v Am-mFNN. qumONP. m-mpom. m-mmmm. mumpmm. mcmnca Nemnc: Pcmnc: chzm Acompmw>wo ucmncwpmv m.m cowpmsvm Loccm umcmzcm :mmz .mmmpo :ovuw_:mom x3 mp_:mmm waomcp mic .w.© mpnm» _.o o.~ _.o c.— mzoum mzoom Haze Pszm ment more rela haV" pre< mon tra par fec so th ra di CE pl l74 One additional test was conducted. The predictor of Equation 6.4 was added to the filter, and each of the simultations covered in Tables 6.l-6.4 was repeated. The predictor produced consistently worse results .for every test. All error terms increased, for each variable and class. fAnd total deaths increased significantly each time. The only improve- jment was provided by a small decrease in total nutritional debt, caused Emore by the fatality increase than predictor benefits. Evidently, the irelatively long periods between sampling points and the oscillatory be- havior of the sampled variables combine to thwart the use of a linear predictor. Perhaps a nonlinear polynomial smoothing function would be ~more appropriate as a predictor. Test results are inconclusive about the real worth of the tracker. It was decided to include the per-capita consumption filter parameter in later optimization work, because BOON had the greatest ef— fect on system performance. The population class results are similar, so one filter parameter will be used for all four classes. It appears that BCON may be able to influence performance, but results do not war- rant additional cluttering of the optimization process. The linear pre— dictor will not be used. Summary The information filter is a tool for extracting maximum value from captured data. It is used in conjunction with sample survey design, program and transportation data, and other information inputs to help system managers gain a picture of the problem to be solved. The “'8 tracker tested here is probably not an ideal filter for in» formation system work. One parameter for a per~capita consumption tra' res ing per fil dC l75 tracker will be added to the optimization work of Part 11. Additional research should be conducted on the Kalman filter and polynomial smooth- ing to determine their usefulness. It may be that the relatively long periods between samplings negate the positive effects of programmed filters. Human intuition and wisdom are likely to be good filters in a crisis. by mo< fo‘ wh CHAPTER VII MODEL VALIDATION The worth of any decision making tool depends on its accpetance =by the peOple who would use it. This applies to computer simulation models as well as statistical formUlasscharts, graphs, and economic forecasts. A broad definition of validation includes the processes where a tool is shown to reflect real world considitions, to be useful in problem solving, and to be acceptable to users. In general each of these conditions must be met before the model or other tool can help produce practical results. The purpose of this chapter is a validation of the survival, in~ formation component, and cost function models of the preceeding chap- ters. Certainly, much of the overall validation procedure described above is beyond the scope of this "approach” thesis. Accordingly, the focus here will be on methods for determining whether the model behaves in a sensible fashion. It is hoped that the usefulness of the modeling will be seen along with the validity and usefulness of the en- tire methodology. The models are not intended to apply in detail to any country. Thus, the desired result here is not to precisely mirror real world magnitudes, but to present a consistent structure with sa- tisfactory outputs, a model suitable for the optimization work of later chapters. 176 \h- ' oftel volv eith figu data here stat tior ass qui exp sta va te' pa l I '2‘ ( V I l77 In testing whether a model behaves as it should, validation most often means either correspondence or coherence. Correspondence in- volves matching model outputs to real world data. This can be done :either by tracking past historical data or comparing future real world figures with model projections as time passes. The lack of real world data for hypothetical countries precludes the use of correspondence here. Even in an actual application, the dearth of famine-related statistics will present problems in the use of this particular valida- tiongform. Coherenece, or consistency, refers to observing model outputs and ; assessing whether they behave in a desired fashion. This method is quite initutive and judgmental; it is imperative that persons highly experienced with the real world system Operation be involved at this stage. Many common sense observations are possible. The next section describes several of the tests made on the current survival model. The importance of reliable data sources becomes apparent in any validation process. The three main data needs in modeling are for sys— tem parameters, initial conditions, and technical coefficients. System parameters in the survival model include CGP, the price control para- meter from Equation 2.8, and the policy control parameters (C636, C632, etc.) in Equations 2.l3-2.l5, Initial conditions and technical coefficients link the model to the particular country's being studied and to real world natural processes. Necesaary initial conditions in a survival model are pOpulation, storage and nutritional levels, and the starting price level. Examples of technical coefficients are the ex— pected harvest yield per acre, YLD, and the nutritional requirement coefficients, UK4 and UK5, found in Equation 2.2. 178 System parameter levels can be estimated through observation, ex- : periment, or experience. Once the model structure, initial conditions, and technical coefficients are set, system parameter changes are help- = ful in "tuning” model behavior to parallel real world performance. Much of the data needed in the current study is not readily avail— able. Where possible, information was gleaned from secondary sources: books, periodicals, private correspondence. The initial conditions and many of the technical coefficients in the survival model followed from Manetsch (38). System parameter feasible levels were derived from es- ! timation and model performance. The component where the data lack is most acute is the cost func- tion. The coefficients chosen represent educated guesstimates based on the assumed information system form. This is discussed in Chapter V. Because of the unreliable input data, it will be much more significant to analyze relative policy and information quality consequences rather than absolute levels. An additional word is in order here on the limitations of this model as a realistic simulation of a real world information system. Because the approach is stressed here, the modeling is done on a macro level, so none of the model components is constructed in great detail. Information system alternatives, policy structure, transportation, re- lief programs, and demographic disaggregations must all be tailored to actual circumstances in the country of application. The lack of com- plexity is an advantage in that it allows examination of the methodol- Ogy without many of the details needed in a real case. Two very important information items that the current model does not cover are health and water data. A lack of water can be more dead fort dati VDTI in 1 the wit ide the ini FIlOC th ch ar 0f l79 deadly than a food shortage. And disease statistics provide needed in- formation for control of famine-related illness and death. After the section on general model coherence, three specific vali- dation tests are discussed in this chapter. These involve the SAMPL and VDTDLI subroutines of the;sampling component, the effect of changes in the level of crisis, and the simulation cycle OT. Coherence Tests The goal of coherence or consistency tests is to determine whether the model behaves in a sensible fashion. One compares model output with expected output and identifies inconsistencies. The comparison identifies the problem area; the next step is to explain or eliminate the problem. Perhaps a coefficient, model structure, parameter, or initial condition change is required. The goal should be a consistent model that is true to the problem being studied. Five types of consistency checks are possible: variable magnitude; time series interactions; and performance variation with parameter change, policy change, or model structure change. The first two methods are common sense observations involving feasible limits on variable size or expected variable interactions. The performance variations are a form of sensitivity test. The direction of performance change is often a more informative indicator than the magnitude change. Several exam- ples of each consistency check follow. Testing for sensible variable magnitudes is relatively simple. Real world conditions dictate limitations that computer models must observe. In the early stages of model development it often happens that calculations produce impossible situations, such as negative l80 population or storage totals. Other examples of variable magnitude in— consistencies include the following: -- negative or astronomical costs -- astronomical market price, PFD -— inappropriately timed emergency trigger, EDPC -- inordinately large error in population estimates Price Level The price level deserves special consideration. In a free market :model, price can theoretically expand endlessly, as long as demand greatly exceeds supply. It is likely that the government will take steps to prevent such gall0ping inflation, to protect the country's economy, and to deal equitably with the food distribution problem. In- flation acts as a screening process for distribution as those with lower incomes are excluded from market participation. In the current model, the natural place to control price is to fix a ceiling on the rate at which the government sells its grain. In a completely controlled market, the price for private sales would also be fixed and black market operations a common result. If the private sales level is not fixed, a two-tiered rate structure will exist. The government sales ceiling will tend to hold prices down as demand for government grain exceeds demand for private. The effect of a price ceiling on model behavior is to increase the number of deaths in the urban poor classes. This is in keeping with theoretical economic behavior. A price ceiling increases demand, as reflected in model output. But the lower price also reduces the desire for the rural class to sell; supply is decreased. The critical time l8l \period occurs immediately after the harvest start. Without price con- ltrol, the rurals place enough grain on the market to meet the demands 30f the rich and sell some to the poor. But the decreased supply caused iby decreased price goes only to the rich. Thus, the urban poor suffer; ithe rurals and urban rich are relatively untouched. Figure 7.l indicates the changed rural sales time series due to a l jprice ceiling. Curve A represents the case of market—determined price, iwhile curve B shows the effect of setting a price ceiling at five times :the initial price level. The two curves are identical through the pre— 1harvest period. Thereafter, the price ceiling curve consistently falls below the free market curve. The peaks in each curve occur as the har- vests near their conclusions. Setting a price limit is an important government decision. It af- fects food distribution and, ultimately, the distribution of fatalities in the country. Price level will be an important piece of information for decision makers to observe; it is a possible early warning signal of food shortages. The current model assumes no government price setting. The rea- soning behind this assumption is that any chosen ceiling would be pure— ly arbitrary. Different countries and different circumstances will cause varying criteria to be used for price setting. The result of not controlling price explicitly in the model is very high prices. At the crisis peak, the grain price is more than fifteen times the initial level. This runaway inflation produced by the model was initially a cause for concern. Consistency demanded an explanation, which has been provided in the previous paragraphs. I82 Rural Sales Rate (100,000 M T/YR) 18 r 16 . 14 r ‘ Curce A 12 L No Price Ceiling L 10 e I‘\ }\ I I\ I \ ,l \ ’l \‘ 8 L ’ \ r ‘ _ I \ I \ \ I \ 6 . Curve B - \ I \ Price Ceiling I \ I \ i I \I \ 4 ’ ’ l u- I \ I \ I \ 2 r I . ,1 ==/J\I L 1/ L I I 1— L Time (Years) .l .2 .3 .4 .5 .65 .7 .8 .9 l.0 Harvest Start Figure 7.l. Effect of Price Ceiling on Rural Sales Rate 183 One result of high prices is attractive, the possibility of gener- ating revenue by selling government grain only to the very rich. The receipts could then be used to finance emergency aid and acquisitions programs. Conservation of Flow The second type of coherency test is an examination of two or more variable time series that are intuitively related. In general, conser- vation of flow must be preserved. For example, the harvest rate should be reflected in storage levels. As the harvest proceeds, rural private storage should increase. The end of the harvest should signal an end to storage increases; consumption should cause storage to decline. By examining model outputs one can observe the behavior and compare it to the assumed desirable performance. The dynamic nature of the simulation allows convenient generation of appropriate time series. If model behavior is not as expected, an explanation must be found. For the harvest and storage example, weather factors may have been set to significantly reduce crop yield, causing consumption to outstrip pro- duction. Government acquisitions may be extremely heavy, depleting pri— ‘vate stores. Either case would cause an apparent model inconsistency. ‘ Other time series checks conducted on the current model include 1the following, each of which the model handled well. —~ increased private storage effect on consumption —— increased total storage effect on average available nu~ trition rate, ARNUT -- decreased price level effect on private sales -- relationship between nutritional level and death rate —— relationship between storage and transportation 184 —— effects of government sales, acquisitions, and emergency aid on consumption Sensitivity Tests The change in system performance as parameters are varied is an im- portant sensitivity test. The direction of system performance change is a good indicator of model consistency. An excellent example of this type of test was presented in Chapter IV. It was assumed that better information quality, represented by decreased values of the vector 5, should produce fewer deaths or a lower total nutritional debt. Much of Chapter IV is devoted to policy structure and modeling changes initiated because the information quality assumption was violated. These changes are summarized shortly. A system parameter sensitivity test is easy to conduct. The simu— lation is conducted twice, each time with a distinct value for the para- meter under study. A defined system output is measured at the end of each run. The output change should follow an assumed pattern. For example, decreasing the sampling interval or the delay time (informa- tion quality parameters) should cause total deaths to decrease. Three system performance outputs were used in parameter sensitiv- ity tests. Two are the members of the F_performance vector of Equation 4.2: total deaths and total nutritional debt. The third output is the percentage of famine-related deaths by class, as computed in Equation 7.l. These PERCD figures provide a measure of policy and parameter effects on the different demographic groups. PERCDJ.(t) = TDETHCJ-(t) / POPJ-(O) (7.1) where: l85 PERCD = class percentage deaths TDETHC = class deaths (persons) POP(O) = initial population (persons) j = index on population classes. Certain parameter sensitivity tests are discussed in some detail in Chapter VIII. The goal there is to identify policy parameters whose effect on system performance is sensitive to changes in information quality or crisis level. Many sensitivity tests were conducted on pol— icy and information quality parameters. A major result of these tests is a policy parameter vector P? that is very nearly "optimal.” Opti- mality is defined with total deaths as a primary criterion and minimum total nutritional debt secondary. g? was found with a fixed perfect information vector k, The following parameter tests were also satisfactorily concluded: -— the effect of relatives' emergency aid parameters RKl and RK2 on fatality percentages -- the effect of information quality changes on costs -— the effect of population estimation on system performance Policy and model structure modifications will generally have a large impact on system performance. The modification should be made with a specific purpose in mind. Chapter IV describes several such changes. In many ways that chapter serves as a model consistency dis- cussion. The modifications addressed there include the following: -— policy changes for more efficient relief operation -- early acquisitions to force rural Population to conserve -- deletion of urban private storage as a useful deci— sion variable l86 -- provision of possible increased transport rates to meet distribution problem -- limited acquisitions immediately preceeding harvest to avoid impractical and inefficient activity -- model changes to more accurately represent real world -- rural consumption pattern -- hand-to-mouth urban consumption at crisis peak -- rural sales pattern -- government desired storage levels -- minimal sales provision The full range of issues and decisions facing decision makers can- not be addressed in the relatively crude model used here. Based on numerous tests and checks, it appears that the model does consistently cover the effect of an information system on famine relief operation. Sampling Component Validation The sampling component described in Chapter III is intended to mo- del the complex data collection, processing, and transmission processes of an information system. Information quality parameters for measure- ment error, sampling frequency, and lag time are used to represent (and avoid) the details of the actual system. The input to the sampling component is a series of ”true" values generated by survival model sim- ulation. Output is a time series representing the lagged, sampled, and stochastic estimates that system managers would receive. Varying the Quality parameters allows generation of a wide range of estimates. In this section, the ability of the sampling component to track a given input series is examined. The test signal is the function h(t) = 25in(2t), whose oscillatory behavior will allow the estimation '187 properties of the routine to be seen. Function h(t) is fed to the FORTRAN subroutines SAMPL and VDTDLI and outputs are observed. The discrete simulation interval OT is set at .05 and the run duration is 4.0 units to allow completion of one sinusoidal cycle. Two distinct information quality vectors are used in the subrou- :tines, one consistently "better" than the other. The vectors are pre- sented in Table 7.l, with values for sampling inteval (SAMPT), time lag :(DEL), and measurement standard error (SD). Table 7.l. Information Quality Vectors Used in Sampling Component Tracking Test. Good Vector Poor Vector SAMPT .2 .3 DEL .l .3 SD .2 .4 Figure 7.2 pictures the resulting true function and sampling com- ponent estimates. The smooth curve A is the true function while curves B and C represent the good and poor information quality vectors, re— spectively. There are four indicators in Figure 7.2 that the sampling component is behaving as desired. The fact that output values for a given curve are in small horizontally equal groups represents the sample-and-hold estimation property. The output is actually a step function. The different group length between curves B and C indicates the changed sampling interval; the group length and sampling interval for curve C are one and one-half times those of curve B. l88 x pmwp mcwxoach pcmcoaeoo mcwpasmm .N.m wcszd x . o.m... , .x :owpmeLomcw voow . 1 mcvuzoc m:w_aswm m F- 9.. m m>c=o x .x 0;; . . . Apmvewmm n Ape; x x o . o . < m>c=u x x moOIl 00 .0. o.¢ m. o.m m.m o.m m._ 0.0. ml 0 .f Jpl 00 000 covuwscomcw Loom x m.o s x.sx mcmpzog mcw_a5mm u m>c=u o.~ . 00 k. X 00. 6. m; . .2. .. o.N o.N a o.F n m.o r 189 Curves B and C are drawn through the midpoints of the output steps to provide a feeling for the shape of the estimated curve. Note that curve C is generally to the right of curve B, reflecting the difference in delay parameters. And curve C is a more distorted version of the true function than is B, tending to flatten out the true oscillations. This is caused by the larger measurement error at each step. This graphical test has shown that the sampling component repre- sented by routines SAMPL and VDTDLI behaves as desired. Crisis Level Variation The crisis level and the extent of outside aid are probably the two most important exogenous factors impinging on a famine relief sys- tem. The outside aid problem has been examined elsewhere (38). The current model assumes that no international aid is available. The cri- sis level can be measured as the expected shortfall of food. Crisis level affects the size and often the structure of the relief system. It will also determine the magnitude of many information quality policy parameters, the rates at which relief operations take place. Thus, the expected crisis level must be accounted for in later Optimization work. The survival model provides a simple means of determining crisis level. Events before the start of simulation are ignored; the initial conditions describe the setting. In particular, the initial value of rural private storage (RSTOR(0)) corresponds to crisis level. It is assumed that an emergency has not been declared before the simulation start. The market, the government, and the citizens are operating nor- mally until that time. The rural class is the largest single holder of grain stocks, and it is this storage amount that is critical. Initial 190 government storage levels are also very important,'but are left con- stant in this study. All of the previous model results and testing have been done with an initial RSTOR equal to 2.0 million metric tons of grain, a medium level crisis for the hypothetical country. The purpose of this section is to show that initial rural private storage can be used as a proxy for crisis level. This is done by con- ducting survival model simulations with several different initial RSTOR values and observing the results. Figure 7.3 contains graphs of total deaths (TDETH) as functions of initial RSTOR level. Information quality is assumed to be perfect. The price control curve A indicates expected fatality totals with little government intervention beyond normal price control policies. The curve B shows the results of active government acquisitions, sales, and emergency aid programs. The graphs indicate that deaths increase dra- matically as the level of available food decreases. Note also that the equalization programs consistently perform better than the price con- trol policy. A second validation test is available for the use of initial RSTOR as crisis level proxy. It was mentioned earlier that crisis level will have a substantial impact on policy parameters. The equalization poli- cies are designed to minimize deaths and nutritional debt by spreading food equally across the demographic classes. Each of the simulation runs made to produce curve B of Figure 7.3 employed a policy parameter set 32.0 that has been found to be very good for runs with RSTOR(O) at the 2.0 million level. Percentage deaths by class (PERCDJ) indicate Deaths (million) 191 d—l—l—l—l—lNNN #mmeLOO—‘N _l (A) Curve A 1(15/7 Price control policy —l—l—J kOO-AN Curve B Nutritional equalization policy #Nw-hmO‘DNOO 1.0 l.5 2.0 2.5 3.0 Rural Storage RSTOR (0) (Million MT) Figure 7.3. Total Deaths as a Function of Initial Rural Private Storage ...d 192 that changing the initial RSTOR value greatly affects the ability of 32.0 to fairly distribute grain. Figure 7.4 charts percentage deaths versus initial RSTOR for three of the four population groups. Note that the percentages are closest to equality at the initial storage level where 32.0 was derived. Increased RSTOR(O) causes deaths to fall dramatically, with the urban poor classes suffering slightly higher fatalities. The rural class is most affected when RSTOR(O) falls. The rich class is always relatively well off. The curves in Figure 7.4 reveal two interesting facts about the model. First, RSTOR(O) influences the "Optimal” magnitude of policy parameters. A needed assumption here is that policy parameters can af- fect the equalization of percentage deaths by class. The second obser- vation is that class differences are as expected over a wide range of initial conditions. The rich are least affected by the food crisis. The rural group and poor urbans are most dependent on the size of gov- ernment policy parameters. It appears that the large death total in the rural class for RSTOR(O) = l.O million is a result of acquisition rates intended for use at the 2.0 million level of RSTOR(O). The para- meters used are too stiff for the case of decreased food availability. Varying RSTOR(O) affects total deaths and the class fatality dis— tribution in a manner expected of a crisis level. Thus, initial rural private storage is used in later work as a proxy for crisis level. Simulation Interval DT The last item to be discussed in this chapter is the mathematical approximation process of a discrete, dynamic simulation. Each of the equations used in the model is only an approximation of a real world 193 Class Fatality Percentages .50 . .40 . .30 . 20 Urban Rural Class ' Poor :2 \. \ \ .10 - Urban ~77“\ Rich // 1.0 1.5 2.0 2.5 3.0 RSTOR (0) (million MT) Figure 7.4. Class Fatality Percentages as Functions of Initial Rural Private Storage 194 'ocess. Further error is introduced when numerical solutions to the leoretical equations, most of which involve continuous non-linear Inctions, are calculated in a discrete computer model. A common computation in the model is numerical integration using he Euler technique. The theoretical integration form given in Equation .2 has been used many times in earlier chapters. The Euler numerical zolution for Equation 7.2 consists of the approximation in Equation 7.3 vhich calculates successive values as the simulation advances through time. LEVEL(t) = )3 RATE(s) ds (7.2) LEVEL(T+DT) = LEVEL(T) + DT * RATE(T) (7.3) Where: LEVEL = variable resulting from integration RATE = integrand variable O,t = limits of integration 5 = dummy integrand variable T = time in computer simulation DT = discrete time interval. Theoretically, the integration in Equation 7.2 is the limiting cal- culation of Equation 7.3 as DT approaches zero. This would imply that the numerical approximation error in simulating integrations should de- crease with DT. The distributed delay described in Equation 2.l8 is another numerical calculation whose error decreases with DT. So all else being equal, model outputs should approach limiting values as the model is run with smaller and smaller DT. This is, in fact, the case 195 ;h the current model, as outputs approach limits for DT near .00025 ears). For numerical accuracy, a small DT value is desired. But smaller intervals also cause increased computer time and increased costs. a tradeoff must be made. Generally, the solution is to choose the .rgest DT that provides acceptable accuracy. The cost consideration ; quite important in the current methodology since many model runs ill be required later for sensitivity tests and optimization work. .The numerical results of simulations with DT equal .00025 and 002 are compared in Figures 7.5 and 7.6. Total death (TDETH) calcula- ions are graphed in Figure 7.5 and total nutritional debt (TNUTD) is raphed in Figure 7.6. These two variables reflect the numerical fluc- ;uations of most other model variables and are the variables by which system performance will be judged. The curve shapes are essentially the same for both DT values. ote that the error in Figure 7.5 using DT = .002 increases as time dvances. This is typical of numerical integration results, since arlier errors are compounded. The curves for total nutritional debt re quite close throughout the simulation. An increase of DT to .004 causes some unacceptable numerical prob— lems, particularly with the relationship between nutritional level and death rate. Thus, DT equal to .002 has been used for all simulation work. Summary The validation process described in this chapter is a set of tests to determine whether the current computer model behaves sensibly. The ' 196 Total Deaths (millions) 2-0 ~ DT = .002 years\ DT = .0025 years 1 l l .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 Time (Years) Figure 7.5. Total Deaths Simulated with Varying DT Values 197 Nutritional Debt (1000 MT) 3.0 ~ 2.4 DT = .002 years .5 2.0 ~ 1.6 » / DT = 1.2 . ‘r,r'.00025 years 0.8 0.4 - / .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 Time (years) Total Nutritional Debt Simulated With Figure 7.6. Varying DT Values 198 lack of hard data means that a statistical fit with real world experi- ences is not possible. Thus, the judgments made here are based on in— tuition and background knwoledge of the problem. The model is now ready for the Optimization work of Part II. PART II OPTIMIZATION APPLICATION CHAPTER VIII OPTIMIZATION PRELIMINARIES ,One of the biggest problems in simulation and optimization work is having to deal with numerous independent, interacting variables. The number Of variables is an important consideration; normally, the experi- mental load increases at least as the square of the number of variables. The size of the observation space is also crucial. The tighter the limits placed on parameters under study, the more likely it is that one finds an accurate response surface. Not only does Optimization become more difficult as the parameter space increases, but computer costs in- crease and reliability Often decreases. The advantage of including many parameters in Optimization work comes from the use of the most general model available. The mistake Of ignoring important variable interactions is more likely when parameter size is limited. But it is not always possible or wise to use every r and variable in the Optimization phase. A very good decision paramete question to be answered is which variables should be included to cap- ture the most crucial aspects Of the decision process. In other words, 'Which parameters have the most effect on system performance? The tradeoff is obvious. By sacrificing some of the accuracy present in 199 200 the most general model simulations, a more manageable problem is ob— tained. Difficulty, time, and cost savings are traded for generality and accuracy. The mathematical formulation for the Optimization problem is re- peated here as Equation 8.1. In this case minimization of the observa- tion Space would imply two things. First, the dimension of the com- bined vector (NJP) should be as small as possible. And second, the ranges between vectors E4 and E2 and between 94 and 92 should also be minimal. Minimize 503,3) (8.1) subject to G(_)(_) _<_ C 941i XLi 22 < < Ej" Ef‘ £2 where: _[ = system performance vector( =total deaths, TDETH; F2= ~total nutritional Fdebt, TNUTD) G = cost function (monetary units) 1. = information quality vector (sampling fre— quency, measurement error, time lag) E_ = policy parameter vector (rates and triggers) parameter constraints r) 1?” VI kc: rim u—J Iél II II budgetary constraint. One of the objectives of this chapter is to discuss means of mini- mizing the observation space needed in the next chapter. The informa- tion quality vector 5_has been limited and we11~defined in Chapters V and VI. It is given in Table 8.3. Thus, the policy parameter set_P will be the focus here. In exploring methods for identifying sensitive 201 N_and E_parameters, it is hoped that some understanding will follow of the relative overall importance of policies, information quality, and crisis level. These preliminaries should shed some light on difficul- ties and expediencies to be encountered later. The next section gives a more detailed introduction to the para- meter limitation problem. Following that are sections discussing a straightforward "sensitivity test" solution and a computer search al- gorithm. The last section presents a summary and conclusions. From hindsight it is clear that an algorithm is the quickest way to Obtain useful results. The sensitivity test section is included mainly to il- lustrate the complexities that abound when a nice algorithm is unavail« able and to indicate possible alternative analysis tools in such a case. Sensitivity Test Design Let us now turn to the matter of selecting the most ”sensitive” policy parameters. Recall the overall goal of this dissertation: de- sign of an information system for famine relief. Thus, the problem formulation of Equation 8.1 implicitly assumes that the P_vector will contain only parameters related to the information system. The Objective function 5_is sensitive to changes in the policy parameters. This was demonstrated in Chapter IV. It is also true that some policy parameters are "sensitive” to changes in information quali- ty. That is, when working with values ofIN and E that produce ”opti- mal“ F results, a change in the 5_vector Often leads to a corresponding change in the P_vector to restore an “optimal“ condition at the new_§ vector. A concrete example is useful. Suppose that Equation 8.1 has been solved with vectors x? and 39. Then, suppose that information 202 system resources are reduced, causing a general decrease in information quality. Simulation results show that the emergency transportation rate should be increased to partially offset the use of poorer data. Evidently maintaining urban stores at a certain level is very desirable, but faulty reports on the nutritional standing of the urban population can allow storage to fall dangerously. Increased transport volumes serve as an insurance against low grain levels. We are searching for such E_variables, those that change optimal value with information quality 5, Policy Parameters Table 8.1 contains a set of fifteen policy parameters from Chap— ters II, III, and IV. A description, the units of measure, and the specific equation numbers are given to help identify the parameters which were chosen from the policy rules and transport and storage equations. Several of the Table 8.1 variables can be eliminated immediately. Urban private storage was shown in Chapter IV to be an unnecessary data item. Therefore, the control parameter C634 is deleted. The normal transport rate CGl can be ignored since a crisis transport parameter C025 has been included in Table 8.1. Note that 0625 and C01 both ap- pear in Equation 4.5; examination of that equation shows that the for- mer “covers for” the latter. The use of C025 also partially explains the deletion of the de- sired government storage levels GSUD and GSRD. The transport parameter serves as a proxy in the decision rule of Equation 4.5. NAME CG1 C621 C024 0025 C627 C030 CG32 CG34 CG35 CG36 CG45 CG81 GDE GSRD GSUD 203 Table 8.1 Original Policy Parameter List DESCRIPTION Normal transport rate, urban-tO-rural Emergency trigger for declaration of famine Consumption control, emergency food equation Crisis transport increase parameter Nutritional debt control, emergency food equation Rural private storage control, acquisitions equation Nutritional debt control, sales equation Urban private storage control, emergency food equation Consumption control, acquisition equation Nutritional debt control, acquisition equation Rural private storage control, early acquisitions Average nutritional availability control Consumption control, sales equation Desired government rural storage Desired government urban storage IJILIIS. year”1 MT/person year’1 none year"1 year-1 year-1 year—1 year—1 year-1 year-1 none year"l MT MT EQUATION 2.10, 4.5 see 2.11 form in 3.8 4.5 2.15 2.13, 3.8 2.14 2.15 3.8 2.13, 3.8 4.3 4.13 form in 3.8 2.10, 4.5, 5.8 ’ 3 4.5, 5.8 204 A simplified explanation of Equation 4.5 is that no emergency transport is allowed if GSUD is too low or if GSRD is too high. Simu- lation results tend to concur that maximizing GSUD and minimizing GSRD are good choices. Actually, system performance is not appreciably af- fected by wide variation in the value of either storage level setting. The initial rural storage level chosen to represent a medium cri- sis obviates the use of the emergency trigger C021. The famine is se- vere enough that some positive level of nutritional debt is to be ex- pected throughout the one year simulation cycle. The only deviation Occurs when several million peOple die quickly, allowing the remaining food to be spread among fewer survivors. But this is clearly non— optimal according to the primary objective of minimizing deaths. It should be noted that C021 is deleted here because Of the crisis set- ting for thi§_experiment. Normally, a good value of C021 will be of primary interest to planners. The final parameter to be deleted is perhaps the most interesting. C081 was intended as a control on the target nutritional debt level. It was felt that a final control on that complicated calculation may help to compensate for measurement errors. But all preliminary test- ing under varying conditions demonstrated that deviation of C081 from a unit value in either direction could only worsen the results of the famine. It may be that such a control is useful only if it can vary with time or under different crisis conditions. C081 is excluded from consideration here because it showed little inclination toward varying from one under any information quality setting. Further examination of this area is recommended but is not pursued here. 205 Several reasons have been given for parameter elimination. CG34 should actually have never made the initial list, because it no longer is part of the policy structure. Any contribution from C01 or the storage level parameters could be covered by the included variable C025. The storage levels as well as C081 are eliminated because they had little effect on performance. C021 (and the storage levels) are exclud— ed because the simulated famine milieu renders them inconsequential. An understanding of the model and familiarity with simulation results lead to confident conclusions about the worth (or non-worth) Of several variables without rigorous testing. Model testing and simulation results were mentioned as one of the criteria for eliminating six of the original fifteen policy parameters. This testing also serves as a powerful tool for determining reasonable limits on the size or range of the remaining parameters. Note also that assigned units help in setting limits. In general a rate unit (such as year‘1) cannot be negative. A rate's inverse represents the amount of time expected to pass until the estimated and target control values are equal, if all else remains the same. For example, nutritional debt controls 0027, C032, and C036 all have rate units (year'I). This can be interpreted to mean that for a control setting of C, the gap between measured nutritional debt should be closed in l/C years. Thus, a value Of any Of these parameters greater than twenty-five would lose its practical value, because nutri- tional debt changes take longer than one twenty-fifth year (two weeks) to accomplish. Logic dictates an initial range of acceptable parameter values. Numerous simulation runs at varying parameter levels help to further 206 limit known useful ranges. It should be noted that the equations in Chapters II and III, particularly 2.13-2.15, were constructed to pro- duce control parameters with some practical interpretation. This is an excellent modeling practice. By following the above logical and experimental approach, limits were derived for each of the remaining nine policy parameters. These values will be used in the next three sections and are given in Table 8.2. Descriptions and units are repeated from Table 8.1. Test*Methods The methods to be used to determine the sensitivity of the nine policy parameters are similar to those outlined in the first section of Chapter IV. Three information quality vectors are chosen, representing clairvoyant, good, and poor data values. At each fixed 3k, a study is done on the policy parameters E, Study results are compared across the fik's to determine which E_variables change with 5, Those that vary will be included in Chapter IX research. Others will be assigned a value close to their demonstrated ”best” values. The 4k are displayed in Table 8.3. Again, descriptions, units, and equation numbers are provided. Several factors must be included in the test design to allow a fair Observation of each policy parameter's worth. First, the famine crisis level must be accounted for. Recall the discussion in Chapter VII concerning the use of the initial rural private storage level (RSTOR(t=0)) as a proxy for crisis level. Second, the §_vectors as de- fined in Table 8.3 will introduce a stochastic nature to model results. Statistical, Monte Carlo methods will be needed to assess the 1 e e 207 LOWER UPPER mere Dasciueirpu mus LIME. 2.11411 €825 EEZiQESErSEiL’iZ‘ée. 1-0 5-0 C032 2:122tlgflgiigfibt control year-1 0.0 12.0 an; GDE Consumption control, year'] 0.0 0.] sales equation Table 8.2 ‘fiw‘ Policy Parameters to Be Used in Sensitivity Testing 208 +3 8. 8. 8. mo. +o.H Ho. mo. No. No. mo. mo. mooo. meow +3 25. N8. N8. N8. o.o 0.0 0.0 fix Hz<>o>mH >m>e:m\amcmm> >w>c:m\«mcmm> >w>c:m\wmemw> mHHz: mcoz mcoz mcoz mmwu upocivcmim_aamm+ xwmz H u meow» No. mpoza lll zoom memEmcma meumgp mic :o_paE:mcou >d_mu mcwueoame cowpmscomcH wocmFPwm>cam mmmcopm .Fm>cmpcw mCVPaEmm mucmppwm>czm covpaszmcoo .Pm>emu:w mavPaEmm mucmppwm>czm vamp Pmcowpwcpzc .Pm>cmpcw mcwpasmm mmmeoum mpm>wca Fags; .Loccm vgwucmpm acmsmezmmms coppassmcoo .Loxgm vcmncmum pcmEmgzmme “new Pocowuwguac .Logem ucmvcmpm onHmHmumo mm mmcvppmm mewEmcwm quszo cowpwELomcH m.m mFQmH mmwu 94mm mmaZm ummZm Haz AAp [(1.026 (:11) 433) 21.075 (:08) 318) .922 .401) 10) .983 373) 09) 963 337) .09) 976 .309) 08) .958 .290) .290) 092 484) 12) .077 458) .11) VECTOR Total Nutritional 212 The most valid use of standard sensitivity testing would start ith definitions of an appropriate objective function based on F. Then for the information quality vectors XJ, X2, and X3, best policy vectors P?, 33, and 33 would be determined. Differences in the optimal policy vectors would indicate sensitive policy parameters. Unfortunately, finding 33 is a very difficult task when using one—at-a—time sensitivity tests. An alternate approach is suggested. Since the goal is not to find optimal Pfs but, rather, to find sensitive P_parameters, the di- rection of change in system performance will be used as a sensitivity indicator. A note of caution is issued; the following formulation does not always lead to well—defined results. The procedure followed here was a multi—stage analysis using a complicated but limited series of model runs and avoiding the use of an optimization algorithm. Previous testing of the model had produced a set of parameters E_that provided a good system performance when combined with the clairvoyant vector X4. Using this set as a starting point and keeping XJ fixed, a manual gradient search technique was employed to identify a “best“ policy vector PR. (The definition of ”bestIl will be discussed shortly.) The search involved varying each parameter a short distance from its base value and examining the per— formance results. When performance improved, the better parameter value was substituted to create a new base vector. In this manner the base vector produced better and better results and hopefully ap- proached 33. Once a satisfactory E? was determined, a second set of tests were conducted at the different information quality levels and at varying crisis levels. F(X '19 P?) serves as a base performance for the 213 clairvoyant EJ and crisis level RSTOR(O). Each policy parameter Pj was varied a set amount to determine the magnitude and direction of change in system performance. New base performance levels were formed at different X_and RSTOR(O) values. Specifically, E(X2,E$) and F(X_,P§) were calculated at RSTOR(O), representing changed information quality. Also, _F_<_><_1 crisis levels RSTOR(O)+ and RSTOR(O)’ respectively. Once base values , E§)+ and E(X_, Pfi)’ were computed at increased and decreased were established, each Pj was again varied a set amount and perfor- mance changes noted. The rationale for this test is that the direction Of performance 1 change with varying Pj may be significant when viewed across X_and RSTOR(O) values. The magnitude of change may or may not be important, depending upon the objective function used. It should be noted that the sensitivity displayed by the P- is not exactly sensitivity to changes 3 in X, since the base vector P? is used throughout. Performance Function Let us examine the Objective function used in the above calcula- tions. Recall that Equation 8.1 presents a multiple response problem. A method must be devised to determine when a given system performance is better or worse than or equal to a second performance. The results recorded in Table 8.4 indicate that of the two system performance variables being used, the number of deaths (TDETH) is much more reliable than total nutritional debt (TNUTD). Thus, a weighted average performance change will be calculated in order to place more of the decision burden on TDETH. One number is 214 obtained as a measure of system performance. It will be labeled STYNUM. Equations 8.2 define the weighting function to be used. Note that STYNUMjk represents a weighted percentage change in f_caused by a change in Pj, at base vector k. Hence, STYNUM is dimensionless. Here, k represents one of the five base options discussed earlier (£151,331, E(X2,P?), etc.). At each base, an idea of the degree of sensitivity of £_to each of the Pj's is obtained. The order Of calculations is clear. Each base level TDBASk and TNBASk, as well as w] and ”2’ must be deter- mined before any sensitivity tests are made. Then a performance sensi- tivity number is calculated for each parameter and base option. * (TDETij - TDBASk) STYNUM- = w Jk l TDBASk +w2* (8.2a) (TNUTDjk — TNBASk) TNBASk W] + w, = l (8.2b) where: STYNUM = system performance sensitivity number (dimensionless) TDETH = total deaths (persons) TDBAS = base level of deaths (persons) TNUTD = total nutritional debt (MT) TNBAS = base level nutritional debt (MT) j = index on policy parameters k index on base calculations w], w2 = weighting constants. Note that no absolute values are used in Equations 8.2 in order to distinguish positive and negative STYNUM. This is potentially impor— tant when comparing STYNUM across X_vectors. Besides sign changes, the size of STYNUM and the size and variance of TDETH and TNUTD may be im— portant decision factors. One further point should be mentioned. The difference in sizes of the individual Pj's must be taken into account when comparing STYNUMj values. The increment in Pj for sensitivity testing is defined accordingly. Equation 8.3 shows that the range of acceptable values (from Table 8.2) provides the desired standard. Each parameter varies proportionately with its size. Pj,test = Pj,base if ’1 * (Pj,max ' Pj.min) (8'3) where: Pj,test = incremental variation of P Pj,base = member of base vector Pj,max = maximum range limit Pj,min = minimum range limit j = index on E, Initial Optimization Vector The policy parameter values P are the same for each base. j,base They'comprisethe ER vector and are given in Table 8.5. As described above, one-at—a-time sensitivity tests were conducted, starting with a satisfactory E_vector obtained from earlier work. Equations 8.2 pro— vided the performance measure, with TDBAS and TNBAS being recalculated each time E_changed. The weights w1 and w2 were assigned values .75 216 Table 8.5 Policy Parameter Vector £1 and Preliminary Sensitivity Test Results 10% TDETH* TDETH* of PO TNUTDi TNUTDi Name M12. Max_ Range —j STYNUM+ STYNUM + 1.877 1.790 C024 0.0 15.0 1.5 14.0 102.0 98.1 .076 .028 1.795 1.795 C025 1.0 5.0 0.4 3.9 105.4 101.1 .051 .039 1.795 1.80 C027 0.0 25.0 2.5 18.0 95.9 106.0 .025 .052 1.814 1.827 C030 0.0 15.0 1.5 5.5 89.7 99.5 .015 .044 1.82 1.771 C032 0.0 12.0 1.2 5.0 92.2 94.9 .023 .011 1.796 1.794 C035 0.0 0.1 .01 .01 102.0 102.0 .042 .041 1.851 1.810 C036 0.0 8.0 2.0 0.8 79.3 108.0 .0005 .064 1.787 1.804 CG45 0.0 1.0 0.1 .65 93.6 87.6 .014 .004 1.793 1.797 00E 0.0 0.1 .01 .02 96.2 87.2 .024 .0005 Base 0 1.795 1.795 (X4, 31) 87.4 87.4 Figures 0.0 0.0 measured in million deaths + 10% increase in Pj + measured in 1000 MT 10% decrease in P. 217 and .25 respectively. These constants were derived from the results of Table 8.4. The decision to stop the manual search for E3 was based on STYNUM values, using a derivation Of common gradient techniques. Once all performance changes were positive, implying worse results away from the base vector, the process stopped. Table 8.5 includes the results of the final set of sensitivity tests, including TDETH, TNUTD, and STYNUM. The tabulated TDETH and TNUTD values show that the stopping criteria insures no test case will be pareto optimal to the base values. That is, both TDETHj and TNUTDj cannot be lower than TDBAS and TNBAS, for any parameter Pj. Additional Base Vectors E? has been determined. The next step is to compute base values 1 TDBASk and TNBASk for each of the four remaining cases: E(X2,E§), E(X3,E3), F(XJ,PR)+, F(XQ,P§)’. The regularly used value for RSTOR(O) has been two million metric tons. This represents an approximate twenty-two percent shortfall in required foodstuffs, a medium level crisis. Tests were conducted with ten percent and twenty—five percent variances in the initial storage level. Results are recorded in Table 8.6. Note the expected worsened death totals with decreased RSTOR(O) and poorer information quality. Also note that performance improves as food supply increases. Nutritional debt figures always act inverse- ly to death totals. One cannot determine from these figures whether nutritional debt is more influenced by changing X_and RSTOR(O) or by changing death totals. Later tests seem to indicate that allowing Policy parameters to vary can help reduce TNUTD totals. The ten .cowme>wt ucwucmwma o.HNv aHNm.V . 1...: No.H aH H.4N Hoe.e e o N L8a Hoe xv HH.mHv aHma.v . .1 .N: eNm. a m.Hm HNN.N m o N coca Hoe xv ON.H Hm.e meN.m H m.H peaso>eHaHo ++Hmm ..mv a. 4H4. m.mm aHH.m H m.H HeaHo>eeaHu +Hmm .emv 2 o.o 4.NN mmN.H H o.N pcaHo>eHaHu Ham .emv . . . . cm>d>LHw i..Hiq NNH - o NoH Noe H H N N H . H8 -Hoa x . . . . . >. I «Hi mmm - a ma Noam H m N Hem o>eHaHo --Hoa xv MN .HN swam Hp: coeds Hmcoe__sze £3.20: Hp: coPHHeze tosaa> mums .z=z>pm papa wepaao Hapoe HOV mopmm compaeeoeeH HacoHHHepsz HaHOH mpmmh zuv>wpwmcom Low mgmumsmcma mmmm o.m mpnmp ,N 1 I 219 percent change levels (2.2 and 1.8 million MT) were chosen for further work because they produce results in the same vicinity as 2.0 million. The larger band represents too wide a spread; the credibility of the model may become overtaxed. Observations The above approach has several appealing characteristics when no optimization algorithm is available. Only one manual optimization step is needed, inStead of the three suggested earlier. And the single Op- timiZation takes place at the clairvoyant vector X4, where the lack Of randomness allows use of MONRUN equal to one. So stochastic error and the number of simulation runs required are both reduced dramatically. Once the optimization determination is made, the exact number of further required model runs is known. This allows planning for compu- ter expense requirements. The number Of runs needed is computed in Equation 8.4. The ”2" stands for positive and negative parameter in« crements; the rest is self—explanatory. Model use for identifying 33 can be estimated. Each cycle of tests requires two runs for each parameter plus one base run. The base run can be eliminated if the best result from the previous cycle is used. In the current example, seven test sets were required before Table 8.5 was Obtained. Thus, 7 * 18 = 126 model runs were needed. When added to the result from Equation 8.4 (m2 = 3, m3 = 4), the over— all total becomes 288. NRUN=n*2*(m1+m+m+r) (8.4) 2 3 where: 220 NRUN = number Of sensitivity test runs after B? found n = number of P_parameters m] - MONRUN at X4 (1) m2 = MONRUN at X2 m3 = MONRUN at X3 MONRUN at RSTOR(O). 1 II A third appeal here is that the 288 runs should offer plentiful data about the worth of policy parameters in relation to information quality and crisis level. Unfortunately, each Of the above appeals is flawed. It is true that only one optimization is required, but it is nearly impossible to o . . . . get close to a true "best” value 34, Since variable interactions are not taken into account. Further, there is no guarantee that the pro- cess will converge to a global Optimum. It is also true that the num- ber of simulation runs can be estimated fairly closely. But the addi- tional factor of Operator time must be considered. To approach a good E_set quickly, intuition and an understanding of the model are invalu- able assets. This is most easily demonstrated when two separate l3's indicate directions of better performance but their combination greatly worsens objective values. Where does one make the next tests? Opera- tor expereience is crucial. Results These flaws are acceptable, especially if no algorithm is avail— able. But an unacceptable flaw in the approach occurs if results ob— tained are so fuzzy and confusing as to be worthless. Indeed, in this case, the lack of variable interactions, the use of a nonOptimal E_at 221 X2 and X3 and the presence of a fuzzy objective value led to inconsis— tent outcomes. The complete set of STYNUM results is given in Table 8.7, arranged by base option. Note that the clairvoyant 5454’ PR) entries match the STYNUM columns of Table 8.5 and the TDBAS and TNDAS figures tie to those from Table 8.6. What conclusions can be drawn? Several decision criteria can be used. First, examine the direction of the performance change induced by each Pj by studying the positive and negative signs on STYNUMj values. All clairvoyant X~ STYNUMj values are positive. If such a l trend continues across X, conclude that Pj is not sensitive. Look for a trend across X2 and X3 columns: positive-negative, negative-positive switches with plus and minus increments. Such a match accompanied by a definite change in magnitude between X2 and X3 would result from a sen— sitivity to data quality change. Similar tests could be made across RSTOR(O) values. Sensitivity at such points would represent the effect of crisis level on the ability of Pj to influence performance. Unfor- tunately, no parameters meet either set of criteria. 0024, 0032, and C030 are positive at one X_vector but mixed or negative at the other. C036 and 6025 are negative at all values, indicating that any change is an improvement. This would seem to indicate the sensitivity of these two parameters. No parameter is consistent in its positivee negative alignment. For the crisis level sensitivity tests, 0024 and CG45 indicate consistent direction of performance improvement. C036 is positive for reduced RSTOR(O), while 00E is negative for all four quantities, indicating a sensitivity to crisis level change. A second criterion for determining sensitivity would add a magni- tude qualification. Exclude all STYNUM absolute values less than .02 .0H0.- 0N000.- 00000. m0H0.- , awoo. xmoo. . 0000.- 000- 9. m0N0.- 000. 2 2 0000. 000.- *oHo. mmwo.i *moo. mmmo.n mHH0.- 000. s 00H +1000 -000 .5 *Hooo.i mHNo.i *NOO. mHmo.i 0000.- 0000.- mwfio.| momo.i rwfio.i mmvo.i amooo.i *moo. roooo. rfiooo. 0 . . amoo i *oHo m000.- 000. 0 on + 00H H1 0.71 +000 NV 0000. NNN0. 0000.- 0000. *0HH0. N000. 0N000. 00N00.- come.- + xofl 0. 0000 0000 op 00000500 .szmoL quumn 000000 u m 0H00.- 0NH00.- 00N00.- 00000.- «0000.- 00N0.- 0000.- 0NN0.- 00N0.- a00H0.- 00N0.- 0N0H0. 0N000.- N000. 0H00. 00NH. 0000.- *0HH0. 0000.- 00N0.- 0000. 0H0H0.- 0000.- 00000.- NN00.- 0000. 00N0. Himmw Miwmm .Hiwmw .mmv 00m..NmV No. 0020 000H 00H0> u a *mooo. vao. mow rfi¢oo. ¥H¢Ho. mvwo ¢wmo. *mooo. wmwu 0H00. H000. 0000 *vaao. vmmo. wau fivwo. rmeo. omwu ommo. m¢mo. Ammo 0000. 0H00. 0N00 ¢wNo. Nome. ¢Nwo .lemw .Hiwmw 0w0050000 00m .000 0000 0000000 aw0>0pwmcmm 0500-0-00-000 we mqumwm Azzz>pmv Lwnsszlxuw>wpwmcwm 0.0 0H000 (representing less than a two percent change in system performance). Then once again examine the columns for patterns. Such a decision rule would say that very small values indicate very little sensitivity Of performance to the particular Pj' The STYNUM entries less than .02 in Table 8.7 are marked with a ”*” in the upper right corner of the entry. For information quality variation, 0045 is seen to qualify for sensitivity if its insignificant value is excluded. 0032 has only pos— itive values remaining, indicating insensitivity. These judgments are tempered by the fact that both parameters‘ changes are insignifi- cant in half the tests. Crisis level variation is more revealing when magnitude is con- sidered. Using the two percent qualification level, parameters 0025, 0045, 0030, 0036, 00E, and 0027 are significant at least half the time. This may indicate that these parameters are not highly influenced by crisis level. 0024 would be judged insensitive, based on significant values. Pareto criteria can be applied as a secondary consideration. By examining TDETH and TNUTD figures from which STYNUM was calculated, those Pj which produce clearly better results compared to the corres- ponding base are discovered. These are marked ”B“ in the lower right corner of the table. Parameter GDE presents a paradox in that movement in either direction improves performance when X2 is used. The case for 0045 sensitivity discussed above is strengthened by the identification of pareto better movement. One clearly noticeable item is that policy parameter changes are more likely to cause pareto improvement when crie sis level varies than when information quality varies. 0f the Pj 224 variants listed in Table 8.7, 14/36 produced pareto better results for RSTOR(O) changes, as opposed to only 4/36 for X2 and X3 changes. Still other rules were considered. The STYNUM figure presents an average evaluation of parameter sensitivity over a set of runs. A possibly more telling piece of information would be the percentage of runs that produced similar positive or negative STYNUM results. Here, again, very few parameters produced solid performances. Most STYNUM averages were indications of majority rule. The last rule tried was complete elimination of TNUTD from objec- tive calculations. This was done on the grounds that TNUTD varies widely and TDETH would provide a more reliable value. But the data was no more useful than previous work. The problem here is that we know what STYNUM picture would result for a particular "nice" type Of sensitivity. We do not know what sen— sitivity type is represented by the “unanice" STYNUM pictures in Table 8.7. Does a positive-negative (or reverse) combination in a column represent a clear case for sensitivity? The available information is not sufficient for accurate prediction. Any decision criteria would have to include outside data sources or qualification judgments. Parameter Choice Given all the above reservations on the quality of results here, no solid decisions will be made on the P_parameters to be used in further optimization work. If absolutely necessary, I would choose the following: 0036, 0025, 0045, 00E, 0024, 0030. My reasoning would be that 0045, 0036, and 0025 appear to be most promising, and 0032 appears to be least significant. 0024 and 0030 are included to insure 225 representation of one variable of each type and equation in the final list. The problem of confidently reducing the number of parameters and their size limitations has not been solved here. A set of parameters can be guessed at, but the choosing is unreliable and affords little real comparison. No allowance is made at all for reducing the size of the observation space. But a few positive results still Obtain from the sensitivity testing exercise. The objective surface f_is seen to be very fuzzy, especially where TNUTD is concerned. Planning will have to be done to insure that me— thods used can handle variability. Because TNUTD varies widely, it is worth examining multiple response methods that reduce to a single Ob— jective value. The worth of a good optimization algorithm is clear. Reliable knowledge of the vectors 3?, fig, and B; would settle the sensitivity question without the drudgery and uncertainty of numerous sensitivity tests. The routine must be able to handle parameter interactions and crisis level changes in addition to the variability problem mentioned above. An interesting side problem is also presented. Results in Table 8.6 show that a 500,000 MT difference in initial storage RSTOR(O) is roughly comparable to the change in going from best to worst informa- tion quality. This tonnage represents a twentyefive percent change in the defined crisis level or approximately eleven percent of the total food requirement. So prediction of the extent of a famine is an im- portant matter. Preliminary results in Table 8.7 indicate that policy parameters may be more able to improve on a poor crisis level than on 226 apoor information quality. A more thorough study of such points would greatly aid planners in resource allocation decisions and the use of apolicy decisions to influence a famine's effects. The Complex Algorithm This section describes the use of a computer algorithm to solve :Equation 8.1. Again the test design calls for three fixed information quality vectors Xk, an estimated "best" 3: for each vector, and a study rof differences among Pfi‘s. It was noted in previous sections that varying one Pj variable at la time is a slow, cumbersome and contradictory process. Thus, we are looking for a method that allows all policy parameters Pj to vary at the same time, allows for constrained parameters, is cheap but accur— ate, can be interfaced with a computer simulation, can handle at least nine independent variables, can handle randomness, and can handle the problems of multiple responses and crisis level. An algorithm has been chosen for use in this chapter that should be able to quickly and easily produce desired results. The Complex algorithm was developed by Box (8). A discussion and FORTRAN coding of the routine are presented by Kuester and Mize (33, Chapter 10). The Complex method was chosen because it has been used previously by the author, is readily available, and is easily adOpted to interface with simulation models. It has the further desirable quality that it com- monly converges quickly to an optimum area although it is slower to pinpoint exact solutions. This fits the expected stochastic nature of the response surface in this problem. Monte Carlo techniques can be used to help eliminate random errors, and crisis level variation fits 227 nicely into the Monte Carlo methods. A quick, fairly accurate solution is desired, to determine sensitive parameters and gain an understanding of the performance surface. The solution "best” parameter levels are not as important as the determination of sensitivities. A quick description of Complex follows. REferences to the current problem are interspersed in the commentary. In the Complex method, a vector of N independent variables con- tains the E_parameters and forms one point in the Observation Space. A total of K points are selected and form a polyhedral complex in N0 space. K must be greater than N. One starting point is specified by the user; the rest are randomly selected within the limited defined ~space. This random selection normally helps assure convergence to a global Optimum, if one exists. The specified starting point must satisfy all implicit and expliw cit constraints. The explicit constraints are the upper and lower limits for the N parameters. Implicit constraints are algebraic com~ binations of the parameters that must satisfy predetermined conditions. M is defined as the total number of constraint sets (upper and lower values). Note that in the current case, M equals nine. Since X_is fixed, there are no explcit constraints on X and no implicit con- straints on 0(X). Thus, M also equals nine. K is chosen equal to twelve for all test cases here. Although a larger K implies more com- putation time, it also lessens the chance that the algorithm will be— come trapped on a ridge or valley of the response contour. The value of the Objective function is calculated at each starting point. This is the interface with the simulation; the model uses the starting point's parameters as inputs and produces the Objective 228 function value. The algorithm proceeds with the deletion of the worst point. It is replaced by a new point c: times as far from the centroid of the remaining points as the distance of the rejected point from said centroid. The direction of travel is on the line between the replaced point and the centroid. The centroid calculation is given in Equation 8.5, while Equation 8.6 contains the computation of the new point. A value of 1.3 is used for d., as suggested by Kuester and Mize (33). K ”P“. = 1 * P. . '=l,2,..., 8.5 J TCT 1:21 1,J J N ( ) ifl P. e = *P.—P. ld +17. 8.6 J(0 W) a (‘J J(0 )1 J ( ) where P3 = jth member of centroid of remaining points Pi j = jth member of point i Pj(old) = jth member of rejected point Pj(new) = jth member of prospective replacement point k = number of points N = size of vector P i,j = indeces on vector E‘ or _ - reflection factor. The single—valued Objective function for the new point is computed by the model. If this is still the worst value, the new point is moved back one-half the distance to the centroid and tested again. This con— tinues until the objective function for the new point is better than one of the other values, and the cycle repeats. One iteration is com- pleted. Checks are made at each stage. Each new point must satisfy all implicit and explicit constraints. For explicit constraint violations, the new point is moved a small distance, 6 , inside the violated limit. In the case of implicit encroachment, the point is moved one—half the distance to the centroid and tested again. Note that the centroid it- self will always obey all constraints as long as all original pointsdo. Covergence is achieved if the objective function at each point falls within Bunits for a consecutive interactions. 8 and a are important parameters for indicating the degree of reliability of the algorithm's outputs: X and E_parameter settings and the objective value they produce. Recall that randomness is introduced in the model, and the model computes the performance level (objective value). The simulation is run in a Monte Carlo mode, producing an average objective function value. The parameter MONRUN determines the number of model runs used to compute averaged function values. All of the Complex method parameters (and their employed values) are presented in Table 8.8. Design Criteria Several design matters are now discussed before presenting test results. These matters include the objective function used, the inclu- sion of crisis level in the Optimization, and the selection process for starting points. Performance Function Substitute-—PERTOT Work in the previous section suggested that both E relief goals TDETH and TNUTD vary with poor information quality and that TNUTD produces especially unreliable objective results. To combat this, an 230 Table 8.8 Complex Method Parameters and Levels Used For Preliminary Testing PARAMETER 0- Monrun DESCRIPTION Reflection factor Convergence parameter Convergence parameter Constraint violation correction Number of points in complex Total number Of constraint sets (upper and lower limit) Number of explicit independent variables Number of Monte Carlo runs for each complex point VALUE USED IN CHAPTER 8 1.3 .001 5 .0001 12 231 objective proxy has been devised, making use of the theoretical basis of nutritional equalization across population classes. Recall from earlier chapters that four distinct groups are present in the model. The goal of the policy strategy is to spread foodstuffs as evenly as possible across the groups, thereby spreading nutritional losses. Up to a point, weight loss means lowered food requirements, allowing available food to go further. The proposed objective function builds on this, trying to equalize deaths across all classes. Since popula- tion totals within groups are unequal, percentage death within a class will be the key statistic. It is desired to keep total percentage death low and to equalize percentages across classes. Equations 8.7 present the calculations. PERAVG = h * ’gl PERCDi (8.7a) 1: 4 l PERTOT = w3*PERAV0 + W4 * 1:](PERCDi—PERAV012 (8.7b) ‘ where: PERCDi = percentage death in class i (after one year) PERAVG = average percentage death PERTOT = Objective function value (dimensionless) W3,w4 = weights. Equation 8.7b provides a weighted sum of the average percentage deaths for all groups and the sum of squared deviations from the av— erage. The average is included to keep total deaths low and the devi— ations calculation is to provide equality among classes. The only weight settings used here were with both W3 and w4 equal one. 232 PERTOT was used at this stage for two reasons. First, some sort of single-valued function was needed by the Complex algorithm. TDETH is a logical choice, but minimizing TDETH causes an unacceptable result TNUTD skyrockets. The equalization theory provides a possible alter— native. The second reason is that this preliminary optimization phase provides an excellent testing ground for compromise Objective functions such as PERTOT. By examining intermediate algorithm results, one can determine whether minimization of PERTOT will lead to decreased TDETH with a reasonable TNUTD level. Thus, Complex results (Table 8.9) will include PERTOT, TDETH, and TNUTD values. Recall that the goal here is not to minimize F, but rather to identify sensitive P_para— meters. This goal can be reached with PERTOT. A bonus is possible if the sutstitute Objective can serve in Chapter IX as well. Crisis Level Variability A second design feature is the inclusion Of crisis level varia- bility. To insure a spread in thesstarting values of RSTOR(O), an ex— plicit calculation is made that ties RSTOR(O) to a set range of values and to the number of simulation runs, MONRUN. For MONRUN equal one, the standard value of RSTOR(O) equal two million metric tons is used. For MONRUN greater than one, iterative calculations increment RSTOR(OL so that initial values range from 1.9 to 2.1 million metric tons. Equations 8.8 were used. DIFF = 2 * 105/ (MONRUN-l) (8.8a) RSTOR(O)O = 2 * 106 — DIFF * (MONRUN+1) (8.8b) ———'—2 “— RSTOR(0)N = RSTOR(O)N_1 + DIFF N=1,2,...MONRUN (8.8C) .233 where: DIFF increment between run values (MT) MONRUN = number of model runs to be averaged RSTOR(O) = crisis level proxy = initial rural private storage (MT) N index on model runs. Simple calculations show that for MONRUN equal two, the RSTOR(O) values will be 1.9 and 2.1 million. And for MONRUN equal three, the RSTOR(O) will be 1.9, 2.0, and 2.1 million for N=l,2,3. Thus, vari— N ability of crisis level is built into the simulation averages. Re- sults can now be expressed as expected outcomes for a given information quality and a food shortfall in the range of twenty to twenty—four per- cent. Algorithm Starting Points The final design feature to be discussed in the use of starting points for the algorithm. Table 8.2 describes the upper and lower lim— its imposed on the nine 3 parameters examined in these sensitivity tests. For each of the three X vectors, a starting E_point for Com- plex was picked by taking the midpoint of the allowable range for each parameter. The tests with clairvoyant and good X converged quickly. Second tests were run with Off—center starting points. These were chosen by alternately selecting values half—way from the center to the Upper and lower limits of the variables. Convergence was achieved close to the first results. for the fixed poor vaector, convergence did not occur on the first Complex run. A second run was made by constricting fl limits and using the new midpoint as a start. The intent Of the further 234 constraint was to limit the space over which optimization was conducted. The new limits were based on results of the first run. Again, conver— gence was not obtained. In both cases, the algorithm bogged down near a centroid that produced consistently bad results. Evidently, the randomness in the model produced a few inaccurate points which unduly influenced the centroid. The problem was only minor, though, since the range of values from the best ending vectors is reasonably narrow. Optimization Results Table 8.9 presents the results from the above experiments. The l algorithm provides details at each iteration. Thus, the figures in Table 8.9 are averages of the best E_vectors over the course of two runs at each X_vector. Best refers to minimum PERTOT. In the clair- voyant X cases, convergence was so good that only an average Of the two best Pfs and the centroid is given. For good and poor X, the range of the best values is listed along with the average. The cen— troti is not included in poor nyigures. The intent is to provide as broad a picture of the true results as possible, so that decisions reached on policy sensitivity are well—informed. Policy parameter settings and objective results are given in Table 8.9. Following them is a set of optimization runvtime parame~ ters. Iterations refers to algorithm iterations. MONRUN is the fa- miliar number of Monte Carlo simulation runs averaged for each Objec- tive function calculation. Model runs refers to the total number of model simulation cycles made. It is affected by MONRUN and by the need for calculation Of repeated prospective better points at each al- gorithm iteration. Time refers to CPU seconds on a Control Data 6500. And the convergence entry repeats the results discussed above. OUTPUT C024 0025 C027 C030 C032 CG35 CG36 CG45 GDE PERTOT TDETH (Millions) TNUTD (100 MT) Number of Model runs CPU Time (SEC) Convergence Table 8.9 Optimization Algorithm Results at Three Different Information Quality Vectors PARAMETER/ CLAIRVOYANT 41 4.75 2.69 6.58 6.97 3.33 .057 1.26 .82 2.69 .053 1.76 102.5 87 525 Yes 235 0000* X -2 0.5-1.65 1.15 2.23-4.13 3.01 8.17-11.77 10.03 16.85-23.47 19.84 2.93-4.56 3.57 .024-.049 .039 1.47—1.77 1.65 .46—.835 .69 2.23-4.13 3.01 .053 (.016) 1.92 (.65) 93.5 (22.6) 222 1150 Yes * = Spread and average of runs given PO0R* 43 1.46-2.59 1.92 3.08-3.83 3.41 2.95-5.68 3.97 9.96-17.06 12.80 5.32-7.95 7.04 .057—.074 .061 .87-l.50 1.21 .482-.602 .52 3.08-3.83 3.41 .074 (.016) 2.76 (.64) 92.1 (32.0) 224 1200 No 236 Table 8.9 reveals several interesting facts about famine relief policy parameters. Four parameters vary little with information qual— ity: consumption controls GDE and 0035, nutritional debt control 0036, and rural private storage control 0045. The first three are quite evi— dent; their spreads either overlap or are consistently close to a starting value. 0045 was excluded from further work because the spread of values does not indicate a large change, and parameter 0030 is to be included. Note however, that the average figures indicate a pattern; CG45 decreases with information quality. In retrospect, it would have been a good idea to look further at this variable because the pattern has a practical interpretation. The early acquisition rate (see Equa— tion 4.3) should be decreased if information quality degrades. This would imply that a looser control is needed when only poor data are available. Two parameters provide clear indications of good relief policy. Crisis—transport-increase parameter 0025 and nutritional debt control 0032 show a consistent pattern for dealing with changes in information quality. 0025 increases as data quality erodes. This would mean that the emergency transport between rural and urban storage should be stepped up when information quality is poor. Nunerically, the rate should be increased from three times normal with good data to 3.5 with poor data. Evidently such an increase would help to insure enough urban storage when the actual situation is not well known. As information quality decreases, parameter 0032 increases. 0032 represents the nutritional debt control in the government sales equa— tion. It is intended to help provide equality between the rich and poor urban classes. The Complex results indicate that control should be tightened as nutritional status data are less reliable. In earlier model work, such control tightening with poor information often led to large oscillations in urban class nutritional debt. Poor decisions made from poor data had poor results. A looser control helped avoid such cases by decreasing the impact of any data. Somethinghas occurred to alter earlier results. Perhaps the other parameters contributing to government sales decisions (see Equations 2.14 and minimum sales pro— portion discussion in Chapter 3) have softened the effect of a tight 0032. This is left as an area of further exploration. The remaining three variables are nutrition control 0027, consump- tion control 0024, and storage control 0030. Each of these varies widely with X_and so is included according to the sensitivity defini— tion explained earlier. No explainable pattern is discernable in the numerical results noted. In each case the preferred value increases then decreases with information quality or vice—versa. Such a rela- tionship would be strange, but possible. It is also possible that the objective function is insensitive to changes in these parameters, and they vary for some unknown reason. Another possibility is that MONRUN is too small, resulting in large error terms. 0027 and 0030 have especially large spreads. But they cannot be ruled insensitive at this point and will be included in further work. Table 8.10 has been constructed from the above remarks and Table 8.9. Four policy parameters are ruled insensitive; their fixed values for further work are given. The remaining five are to be included in Chapter IX studies. Note a pleasant result of this optimization ap- proach. The limits on parameter values can be reduced from their ori— ginal status in Table 8.2. The new constraints follow from the best PARAMETER 0024 C025 C027 C030 C032 PARAMETER 238 Table 8.10A Policy Parameters to Be Carried to Final Optimization Stage DESCRIPTION MINIMUM Consumption control, emer- 0.0 gency food equation Crisis transport rate- 2.0 increase parameter Nutritional debt control, 0.0 emergency food equation Rural private storage, 5.0 acquisitions equation Nutritional debt control, 2.0 sales equation Table 8.108 Fixed Poligy Parameter Values C035 C036 C045 GDE DESCRIPTION Consumption control, acquisition equation Nutritional debt control, acquisitions equation Rural private storage control, early acquisitions equation Consumption control, sales equation MAXIMUM 6.0 5.0 12.0 25.0 10.0 VALUE .05 1.5 .65 .08 value spreads contained in Table 8.9. Since the three X_vectors cover the range of possible information quality, the spreads plus small in~ surance margins should span the likely optimal observation space. This reduction of the search space should speed further Optimizations. One note of caution does come from the Complex process. An extremely fuzzy surface places limits on the ability of the algorithm to converge. In such cases, constraint reductions will not make estimated results any more reliable. One additional aid provided by Complex that was not extensively used here is the ability to follow the course Of the polyhedron formed by the K—point ”complex.’I Quantitative data are available at each iteration, including new point choice, variability of the Objective value and rejected new points. Study of such data will be used in the next chapter to determine reliability of results and help pinpoint ”best” parameter values. Conclusion and Summary Several helpful results can be drawn concerning the use of opti- mization algorithms, results of fuzziness in the model, relative impor- tance of policy choice and Optimization, and particular policy para- meter settings. The worth of a computer algorithm is evident. Results and choices are much clearer than with one-at-at-time sensitivity testing. The amount of work required is less when a "canned” algorithm is available, and the amount of computer time required may be smaller also. Here, the algorithm approach required roughly four times as many model runs, if preliminary work necessary for the standard sensitivity testing is 240 excluded. Preliminaries in the standard case would include setting tight parameter limits and obtaining a good starting P_vector. Addi- tional runs would be needed if P_sensitivity questions and observation space reduction were to be resolved through the one—at-a-time varia- bility process. Note that guesstimates at the end of the standard sen- sitivity testing section agree with Table 8.10 on only four of nine parameters. The Complex algorithm has several desirable features. It is easy to use, allows for randomness and constraints, interfaces with the model, and converges to a general area rather quickly. It also pro- vides data for possible reduction of the range of each tested parameter. When faced with the problem of no available algorithm, it may be worthwhile in the long run to develop the necessary code rather than rely on manual searches. Some form of regression or factorial design would also probably be better than the technique outlined in this chap- ter. The only real advantage of using the approach here is that one becomes very familiar with the intricacies of the model's being used. The nature of the performance function surface for F_is fairly clear. The two objective values TDETH and TNUTD are fuzzy, especially nutritional debt, TNUTD. Contributing to the variability in the sur- faces is the inverse relationship present between the two objectives. This also leads to the conclusion thatTDETH cannot be used as a single goal, since minimization of total deaths leads to huge, unacceptable levels of nutritional debt. The use of substitute objective function PERTOT worked well here. PERTOT was defined to take advantage of the policy strategy‘s being used and succeeded in keeping both TDETH and TNUTD at low levels. Table 241 8.9 presents average values for PERTOT, TDETH, and TNUTD over the best policy points at each Of the fixed X vectors. The results displayed in Table 8.9 and 8.10 offer several inter- esting conclusions about the relationship of policy parameters and in- formation quality in the current model. Optimal consumption policy parameters are quite insensitive to information quality change. Only 0024, the parameter in the emergency food aid equationashows variance with X, This could indicate that consumption policies do not greatly affect system performance, or it may be that the effect was oversha- dowed in these tests by the predominance of nutritional debt and stor- age policies and data measurement. Three particular situations are candidates for further study. Re- sults indicate that as information quality is reduced, the following policy adjustments are helpful: increase the emergency rural-to-urban transport rate, increase the nutritional debt decision control in gov- ernment sales, and decrease the early government acquisitions rate. It was mentioned in the chapter introduction that policy parame- ters were to be the focus here. This was done because information quality parameters had been set previously, in Chapters V and VI. In general, an approach similar to the algorithm method in the previous section could be used to reduce the number of information quality para- meters to be used in final optimization work. The problem would be to determine the sensitivity of the Objective function f.to the individual X_parameters. The insensitive X members could be identified by the following process. Fix policy parameters F and use Complex, with st varying at two or three different cost constraint levels. Recall that G(X) must be used, necessitating implicit constraints in Complex. At 242 each solution, simple one—at-a-time sensitivity tests will indicate the _X parameters with little effect on performance, as long as a factor is included to Offset the difference in parameter sizes. Summary The reduction of the observation space is a good practical goal in any optimization problem, especially when the number of variables is quite large. A general approach is discussed here, where an examina- tion Of desired optimization results leads to the identification of the particular sensitivities that certain variables should possess if they are to be included in the optimization. Sensitivity tests can then be designed to uncover the desired traits. In the current problem, sensi- tivity to information quality changes told which policy parameters to use. Objective function sensitivity to information quality changes would tell which information parameters to use. The advantage of a computer algorithm is clearly seen, as results and choices are much more reliable than under a one-at-a-time sensiti- vity test pattern. The Complex algorithm with a substitute objective based on nutrition equalization proved to be a useful optimization tool. A discussion of a possible approach in the event of no available com- puter algorithm showed that results in such a case are largely unsatis~ factory. CHAPTER IX SIMULATION OPTIMIZATION Much ground has been covered in Chapter VIII. Parameter limita- tion preliminaries have been completed and the factor vectors X_and P_ are chosen. The form and type of the objective response surface have been examined. The optimization problem definition has been narrowed. The simulation computer model is ready. The remaining task is to pick a routine and optimize. Let us first reexamine the purposes of the planned optimization since they will determine the direction of research. Clearly, one of the main goals is to identify ”best" parameter levels for X_and P_at several different cost constraints. Not only must the parameters be determined, but the associated chosen information system alternatives must be described. And, for each set of "best” parameters, the ex- pected performance level and the degree of confidence in results must be noted. As the optimization proceeds, it is hoped that some understanding can be gained of the relative importance of the individual information quality parameters and the system components that the parameters repre- sent. Such knowledge would be extremely useful in assigning priori- ties to resource expenditure when the allocation for the information system is limited. Similarly, the relative importance of‘E policy parameters should be studied, as well as the relationships between X and.fi. 243 244 One final goal is the generalization of results from this study. For actual famine relief planning, a list of real-world variables with suggested monitoring statistics would be invaluable. Chapter I has out- lined a perspective on the use of information and data collection. The chapter follows the development of the optimization research. The first section finalizes the criteria for selection of an algorithm, both from a standard Optimization point of view and from the perspective of the current study. Then, the actual selection process is discussed. The third section outlines the experimental design to be used, followed by results and analyses. The final section serves as a summary and con- clusion. The Optimization Problem and Solution Considerations The problem to be solved is stated in Equation 9.1. In attacking this problem, the tools to use depend a great deal on the nature Of f, 0, X, E) and the constraints 0, 91’ 92’ Ed and E2. Many factors influ- ence the choice Of an Optimization algorithm. These factors are grouped here into three categories based on their relationship to the overall problem. Minimize __F_(_x,_P_) (9.1) subject to: 0(X) < C 1 LC) [A |>< 1A 1L? [m _._l [A |'U [A ]m N where: 245 E_ = system performance vector (F]=total deaths, TDETH; F2 = total nutritional debt, TNUTD) 0 = cost function (monetary unit) X_ = information quality vector (sampling frequency, measurement error, time lag) E- = policy parameter vector (rates and triggers) QJ’QZ’EJ’E = parameter constraints 0 = budgetary constraints The first group of criteria consists of common theoretical Optimi- zation difficulties present in Equation 9.1. The description of each item in this group will center on optimal approaches to solving the difficulty and will identify the course deemed most suitable for the current simulation and hypothetical country. The second group deals with considerations introduced by the nature Of famine relief informa— tion system design and by the current approach. Most of these have been mentioned in previous chapters and are included here to help tie the theorietical Optimization technique to this study. The third and final group is a set of specific decision criteria normally used when choosing a particular algorithm. Lists of such criteria are available for application of algorithms to simulation models (59). The set pre- sented here results from an adaptation of such lists to the current problem. Theoretical Optimization Difficulties The presence of constraints on X, E, and 0 favors a constrained Optimization routine. The only contrary situation occurs when the search is guaranteed to stay within limits by the nature of the 246 solution. But given the fuzzy flat response surface deduced in the previous chapter, such a case is unlikely. Two types of constraints are evident. First there are limits on individual parameter values. Recall from Chapter VIII that definitions of some X_and E parameters lead to Obvious limitations, and preliminary work with the simulation model helps to sharpen and reduce these limits. A comparison of Tables 8.2 and 8.10 reveals the parameters and limits used here. The constraint on 0 represents a functional constraint on combinations of X_and P_parameters. As in most areas where a cost con- straint holds, when one splurges on X], one has to reduce expenditures on X2. A second theoretical problem to be faced is that the response 5 is generated by a stochastic model, implying there exists variability in F, A non-exact solution implies that statistical methods are needed to handle the problem. The so-called Monte Carlo techniques are com— monly used. Mentioned in Chapters IV and VII, these involve multiple simulation runs for fixed X_and E_vectors in order to obtain average output values. The Obvious reason for use of ”average” results is that uncommon occurrences can lead to improper conclusions. To be relevant, results must be couched in terms of expected or likely outcomes. The goal of any statistical design is to extract as much information as possible from the experiments done (29). Each model run's results can also be extracted in order to construct histogram displays of model re— sults. This would be important in avoiding skewed performance results whose importance may be masked by the average. The problem where the least amount of research has been done is that of how to deal with an objective or goal vector of more than one 247 variable. Many routines and algorithms exist for problems of only one response, but more than one presents special difficulties. The fact that E has more than one objective leads to the classical problem Of trying to improve one Objective without harming another. This type of condition is commonly called a pareto Optimality problem after the economist who suggested Criteria for "pareto” Optimality. Multiple responses lead to multiple (in fact, infinite) solutions where no mu- tually advantageous objective improvement is possible. VNote that a computer algorithm cannot make judgments. It can only proceed along well-defined, albeit complicated, paths. Thus, multiple response systems need to have an explicit tie defined between values and algorithm processing. Some approaches deal specifically with individual values and Opinions (16). One general solution method is to form a single objective by at» taching weights to the distinct responses Of the original problem. The weights correspond to value attached through questionnaires, Opin- ion polls, discussions with decision makers, etc. A wide range of . solutions is possible by varying weight structures to allow inspection of relative value implications. Recall that a weighting function is used to define the sensitivity number of Chapter VIII (see Equations 8.2). A second common approach is to designate one response as the most important and relegate others to a constraint role. The problem is changed from optimizing f_= (F1, F2) to optimizing F1 provided F2 stays within acceptable limits. There are several extant papers on multiple response solution a1- gorithms, with such varied method titles as Sensitivity Function (51), Proper Equality Constraints (34), and Goal Attainment Method (19). 248 These papers all present theoretical mathematical formulations and do not discuss application to simulation models. Montgomery and Betten— court (47) have prOposed an algorithm for handling multiple Objectives in simulations. Their test case used only two input variables and in— volved considerable on-line input from decision makers. This is clear« 1y an area where further research is needed. Famine Relief and Approach Difficulties A very important factor to be included in any analysis of famine relief will be the expected crisis level. There is a natural tie-in to the current approach, although it is not directly stated in the problem formulation. It has been noted that Statistical methods are needed to handle the built-in stochastic nature of information quality. Crisis level is another unknown quantity that can be handled by a Monte Carlo scheme. Recall from Chapter VII that the variable RSTOR(O), the ini— tial rural private storage level, is functioning as a proxy for crisis level. By varying RSTOR(O) according to a regular distribution, model outputs can be interpreted as likely results for a given range of crisis. This scheme was applied in Chapter VIII (see Equations 8.8). The overall approach of this study places heavy emphasis on the use of a computer simulation. It should be noted that model intrica- cies can be easily obscured in an Optimization process keyed on one or a few objectives. That is, the optimum (optima) chosen may occur be- cause of some unacceptable modeling quirk. Examination of several out- put variables in the region of the optimum should indicate possible need for further model development. A TF-k'_ ) 12‘— 249 Care must be taken to explicitly state value judgments being used in evaluation and interpretation of results. The Objectives to be used must be humanitarian; famine relief is a humanitarian activity. Model outputs cannot be taken as absolute because of human factors; the prob- lem is different from minimizing water leakage or other mechanical and physical systems. By "solving" Equation 9.1, it is very likely that a * value is implicitly assigned to human life. It projectnmnagement issue that must be faced is the importance of X_and P, information quality and policy parameters, compared to over- all strategy choices. Earlier model results show that a policy of , ”equalization” reduces the death total resulting from price control policy by more than two-thirds. It is unlikely that any optimization routine will lead to such marked improvement. Note that to pursue a high-powered Optimization course on a poorly constructed policy base would be unwise. It is hoped that the results of this chapter's work will reveal the relative worth Of the optimization stage compared to the strategy design phase. A The cost vector 0(X) requires substantial off-line analysis, as explained in Chapter V. A unique information system definition for each X_yectpr_is required beforehand to insure results that make real- world sense. The solution set for Equation 9.1 will be particular X and P_vectors. The chosen vectors should be such that constraints 94 and Ej are satisfied and the information quality X automatically de- termines information system characteristics and choice. Thus, the need for a unique system for each X, It is unclear which is likely to be more difficult, determining the 0 function (off-line) or completing the optimization process. Certainly both will contribute considerable E—ill 250 insight to information system development. Real—world data and experi- ence would be most helpful. Algorithm Choice Criteria The following items are mentioned as aids in comparing specific optimization methods. Two major considerations exist: the type of problem and the nature Of the algorithm. In examining the type of problem, the number and range of the independent variables is important In the current study, this would be the size and parameter limits on_X and E, Smith (59) tests cases of thirty and 120 controllable factors, so there is some hope of solution for very large models. The nature of the response surface or objective function to be encountered affects algorithm choice. Concave or convex surfaces are easy to work with. The presence of variability, ridges, multiple peaks or plateaus requires more sophisticated handling. A very important criterion involves the information desired from the Optimization and the likelihood that a given algorithm will supply such data. It may be desirable to "build" a picture Of the response surface by creating a function to estimate the simulation model. Such a function would be useful for regression analysis. On the other hand, the goal of opti- mization may be to obtain best value solutions, which only require one or a few function values. The accuracy of solution is also important, whether an exact point is required or whether a solution "region“ is desired. The nature of the algorithm should cover the above items; it must handle parameter size, variability, and output requirements as needed by the problem. Other factors are also important. The ease of use of 251 the model should be considered: the availability of programs, adaptabil— ity to a particular machine and model, and costs involved. Costs include not only straight monetary costs for purchases and salaries, but also the time costs for planning, programming, computer operations, model run requirements, and results anslysis. Other resources necessary to pre— pare reports and communicate results may vary by algorithm, the entire system should be examined to determine the crucial interfaces for al- gorithm choice. Alternative Solution Methods The intent Of this section is to explore Optimization routines that were examined for use in the current study. Let us first describe the state Of research at the end of Chapter VIII, as it relates to the optimization process. A single—valued weighting function has been tested that captures the flavor of both Objective responses and relates to policy structure. A set of X and 3 parameters has been defined, as has the function 0(X). All that remains is to settle upon the form of objective F_to use, values for cost constraint 0, and the algorithm. Constraint 0 values can be easily calculated from data in the model. The algorithm choice is the subject of this section. But, first, a decision must be made on the nature of f, Single Response Optimization Only single-response Optimization techniques will be examined here. As mentioned in the previous section, little work has been done with multiple response in large models; a substantial effort would be re— quired to adapt and test such techniques on the current model. Also, work in the last chapter showed the sizeable variability of total death (TDETH) and total nutritional debt (TNUTD) objectives. Thus, a —;_ ,, 252 concerted effort at this point to work with multiple response techni— ques would be misplaced and beyond the scope of the current study. The weighted average PERTOT, defined in Equations 8.7 (and repeated in Equations 9.2) will be used as the objective function in this chapter. It combines TDETH and TNUTD into one value and approximates a multiple optimization. The weights w3 and w4 can be used to alter the mix be— tween TDETH and TNUTD; only values w3 = w4 = 1 will be used here. The revised form of optimization is given here as Equation 9.3. One fur— ther note on Optimization work, a numerical solution technique is needed. The classical problem involving a vanishing first derivative is important only as it is used by an algorithm to determine a stopping point. 4 PERAVO(X,E) = 1/4 * .2 PERCD; (535) (9.2a) 3:1 4 PERTOT(X,P) = w3 * PERAVO(X,E) + W4 * .2 (PERCDi(X,E) -PERAV0(X,P_))2 1:] (Mb) minimize PERTOT(X,E) (9.3) subject to: 0(X) 5_0 21 .<. 1 5. 92 _E_ .<. .P_ 5. £2 where: PERCD = percentage deaths by class (after one year) X_ = information quality vector P_ = policy parameter vector PERAVG = average percentage deaths PERTOT = Objective function value (dimensionless) w3,w4 = weighting values __— ___ 253 G,C,P_‘| ,92,£'| ,2 as 11] Equation 9.1 1 index on population classes. Two generaloptimization techniques are discernable. The differ— ence lies in the function that the algorithm searches. The first method would construct a function S(X,E) covering the entire space on X and E, S(X,P) would be the resulting equation from a regression utilizing X_and E_as input variables and model outputs PERTOT or TDETH or TNUTD as the output variable. Then an Optimization process would be run On the function S. The second method deals with the simulation directly, searching over model—generated points on the response surface. Regression Surface Running a regression algorithm on the whole vector space has sevu eral appealing features. The resulting equation, or metamodel, would allow considerable testing without further model runs (28). (Con- straints on X and E_can be handled by careful selection of data points. Using selected points and model results as inputs, a regression has much built—in statistical analysis. The S function develOped allows a look at the variability and significance of parameters and parameter interactions, plus the sensitivity of the surface to individual para- meters. Further, a separate function can be generated for each objec- tive value or combination of values. Other factors weigh against the use of a regression analysis. The function is a further step removed from the real world. Just as real- world intricacies are missed by the model, so are model intricacies missed by the function. This is especially true when a fuzzy, flat 254 surface exists, such as PERTOT(X,E), TDETH(X,E) or TNUTD(X,E). A re- gression involves a two-step process. On developing function 5, para- meter sensitivities and function relibility are deduced. But an additional optimization step is required to minimize values over the space Of X and E, It is true that this optimization should be easier over the function S than when using the model. But two sepa- rate algorithms are still required, in a situation where highly de- veloped programs may be hard to find. Search Algorithms Three examples Of search algorithms using the model itself are presented next: the Complex algorithm discussed in Chapter VIII, the Powell algorithm (33, Chapter 10) and a response-surface methodology adaptation developed by Smith (60). Recall that the Complex method oper- ates with a set or "complex" of points in the factor space. The worst point, in terms of Objective value, is rejected and replaced by a better factor set on the far side of the centroid of remaining complex points. Only one point is replaced at each iteration. The Powell and Smithnmth— ods identify a small subspace and do calculations within the subspace at each iteration. The purpose of the calculations in each case is maiden— tify the direction of most improved movement on the surface. Powell de— velops a quadratic surface at each stage and moves in the direction Of the gradient. Smith has a more sophisticated technique whereby a first- Order equation is initially computed using experimental design methods. A test is run to determine the adequacy Of the equation; a second-order approximation is develOped if the first-order is not satisfactory. The search continues in the projected direction of steepest descent. 255 Complex and Powell are often used in tandem because of their complimentary convergence properties. Complex tends to move quickly to an optimal area, but bogs down in final stages. Powell converges quickly near the optimum. So using Complex,tfimn1Powell is a reason- able approach. Unfortunately the Powell algorithm cannot handle con- straints, so its usefulness may be negligible. The Smith routine appears to be quite powerful but its availablity is limited. Smith has done research comparing algorithms very similar to the Complex and Smith methods discussed above, as well as a one-point-at— a-time technique (59). In comparing the use of a Complex-like routine to Smith's response surface method, the conclusions are drawn that each performs well and is much better than any single factor search. A slight advantage is given to the response surface.technique because the direction of search is more direct. However, it was generally true that the Complex algorithm required fewer total model runs. Both routines are for single-valued objectives and can handle the optimi- zation requirements discussed above. Convenience was a major factor in the final choice of a computer algorithm. The Complex program is readily available. It was able to handle the nine variables, with constraints, in Chapter VIII tests, and its nature is well-suited to the fuzzy surface PERTOT(X,_). Add- itionally, the results required at this point must be generally accu- rate, not pinpointed. Note that hypothetical data permits a study of parameter trends only. Exact answers with inexact inputs are illogical. Complex will suffice to provide the desirable pieces of information discussed in the introduction to this chapter. The 256 algorithm generates enough data to compute a cost versus performance graph, reasonable "best" alternatives at different cost levels, and, when run in a Monte Carlo mode, degrees of confidence in results. Increased accuracy expected from the response surface method- 1ogy of Smith is somewhat nullified in the current problem by the extremely variable surface. Also, the importance of policy strategy makes extremely accurate optimization a secondary priority. The Powell method is rejected because it does not handle constraints. With the narrowed limits provided by Chapter VIII research, an uncon- strained routine is undesirable. The main advantage Of Powell is its quick convergence near an optimum. Again, superior accuracy is not needed here. Optimization Plan The ground work for this section has been laid in the previous chapter. Since the Complex algorithm will be used and the problem is largely the same, much of the discussion of optimization problems and model peculiarities from Chapter 8 also applies here. Optimization Constraints Equation 9.3 presents the problem to be solved. The objective PERTOT is defined in Equations 9.2. The independent variables X and .3 have been defined and limited. Table 9.1 presents each factor along with the constraint vectors 94,92,§4 and E2. Note that Tables 8.3 and 8.10a have been combined to form Table 9.1. Cost formula G(X) in the problem statement has been developed in Chapter 5. One item will be included in the optimization that is not 257 Table 9.1 Independent Variable Vectors X and_g With Associated Constraint Vectors 91, 92, El, g2 X VARIABLE DESCRIPTION MIN (01) MAX (D2) SDND Standard error, nutritional .0005 .002 debt SDRC Standard error, consumption .05 .2 SDRS .Standard error, rural private .05 .2 storage SAMPT Sampling interval, nutritional .02 .08 debt SMPRC Sampling interval, consumption .02 .08 SMPRS Sampling interval, rural .02 .08 private storage DELD Information reporting delay .01 .04 0029 B parameter, consumption 0.0 1.0 0-8 tracker E_VARIABLE DESCRIPTION MIN (E1) MAX (E2) 0024 Consumption control, emergency 0.0 6.0 food equation C625 Crisis transpor+increase 2.0 5.0 parameter 0027 Nutritional debt control, 0.0 12.0 emergency food 0030 Rural private storage control, 5.0 25.0 early acquisition 0032 Nutritional debt control, 2.0 10.0 sales equation 258 expressly stated in Equation 9.3. A varying crisis level will be in- cluded to simulate the uncertainty in evaluating the extent of a fam- ine. As in Chapter VIII, the variable RSTOR(O) will be assigned staggered starting values at each call to the model by the Complex routine. The details are presented in Equations 8.8. Complex has been chosen as the algorithm to proceed with. Given the above definitions, the experimental design problem has only two remaining issues: the values to be used for the budget constraint 0 and_the run parameters, including number of cycles through the Com- plex method. The objective in setting the 0 levels is to obtain a distinguishable range of performance versus cost results. Two factors were most helpful in deciding On the cost constraint levels to employ. The first was the establishment of "benchmark" cases marking upper and lower limits on expected costs. The second was simply the use of several experimental computer runs. Given the limit vectors 24 and 22’ maximum and minimum costs can be determined by applying the equations of Chapter V. There are several constants and parameter values which must be defined, and Appendix A provides a discussion Of the translation of the cost chap- ter's theoretical formulas to an acceptable numerical model. A few calculations using the formulas of Appendix A show that 0(X) can vary between 120 million and 960 million won. (The model conversion rate is four hundred won equal one dollar.) Model runs showed that C=155 million won would be a good lower limit on the budget. An upper limit will be provided by putting no explicit constraint on 0. Of course, 0 is uniquely determined by .X, so the constraint vector_D_2 sets an explicit limitation on costs. 259 Additional model runs showed very little difference in performance for 0 values above 500 million won. Thus three intermediate budget levels were chosen, in addition to the two limiting cases: 400 million, 300 million and 200 million won. A third cost benchmark was also available. The price control policy mentioned in Chapter 11 provides an additional upper limit. A Complex algorithm optimization was made, using several price control variables as the independent factors and PERTOT as the Objective:* Thebest result Saw over nine million deaths (TDETH) and negative nutritional debt (TNUTD). TNUTD was low because many people died quickly in the simulation, leaving fewer citizens to share the avail- able food. The price control results will be used only as benchmarks, indicators of a worst possible case. A note on the use of the price control benchmark is in order here. A fairer test would have incorporated two modeling changes. First, the objective should have been some other combination of total deaths (TDETH) and nutritional debt (TNUTD). Recall that PERTOT was designed specifically to take advantage of the equalization policy. Given the negative final value for TNUTD in the price control test, a logical objective would be a single variable, TDETH. A second modeling change would involve the variables being sampled. Price control policy decisions would not be based on nutritional or con- sumption variables. Rather, market prices, storage information and price change data would be the desired indicators. Of course, such a change would mean a different information system from that described *The price control variables used were 006, CGP, 003, C65, TRUNDO, TPUNDI. See Chapter II and Appendix B for detailed equations. 260 in Chapter VI and would require substantial additional effort. The estimate derived here is meant only as a gross upper bound and is very likely overstated. A combined view of the equalization policy and price control policy benchmarks provides a validation point for the computer model. The range of crisis levels used in the current experiments accounts for a percentage shortfall of food between eighteen and twenty—six percent. Based on previous tests of the model, percentage survival should be greater under the equalization policy than under price control, for the tested range of percentage shortfall (39). This result is affirmed in the relative performances of the benchmarks in Table 10.1 Complex Algoritim Parameters Many of the parameters needed by the Complex algorithm have already been implicitly chosen. The number of variables in.X and E and standard practice algorithm values account for all but the con— vergence factors and the number of Monte Carlo runs at each Complex point. A definition for each Complex parameter and the value used in the final optimization stage is given in Table 9.2. (A more thorough description of the parameters is given in the discussion of Table 8.8.) Note that parameters 8, a and MONRUN are multi-valued, since they vary with the cost constraint employed. A general pattern was followed in conducting optimization runs at the various budget constraints. A non—stochastic trial optimization was made with MONRUN equal one, 8 equal .005 and 0 equal 8. The starting point was picked at a point known to be within the implicit 261 Table 9.2 Cgmplex Algorithm Parameters for Final Optimization VALUE IN PARAMETER DESCRIPTION CHAPTER 9 0 Reflection factor 1.3. 8 Convergence parameter Trial - .005 Later - .001 y Convergence parameter 8 or 12 6 Constraint violation correction .0001 K Points in complex 16 N Number explicit independent variables 13 M Total number constraint sets 14 Monrun Monte Carlo runs per point Trial — 1 Later - 3 0 Budget constraint 155 million 200 II N 300 II II 400 II II Unconstrained 262 cost constraint. For the largest three values Of 0, this point was the centroid of <01, E1> and <02, E2>. The main purpose of the MONRUN equals one test was to identify 3 starting values. A second Optimization was done, using the best overall point re— sulting from the trial and increasing MONRUN to three to allow a more detailed statistical study. Data from the first two runs were used to supply a third stage with restricted bounds on X_and E, This limiting of the search space allowed quicker convergence. MONRUN was again set to three. The convergence criteria 8 and a were also strengthened. It should be noted that better convergence properties would be expected at higher budget levels, since the sampling error decreases with increased fiscal support. And, in fact, for the largest two con- straints, step two was bypassed since convergence came so quickly on the first trial. A fixed computer time cost limit was used to deter- mine convergence; the algorithm was alloted a specific amount of time in which to complete its processing. The standard technique Of in- suring global optimization by employing multiple starting points was ignored here because of Chapter VIII results. The "piggyback" approach of building on a previous best result was helpful, especially for small cost constraints. The approach re— duced the area of search and led to somewhat better convergence. The results of these runs are presented and analyzed in the next section. OptimiZation Results and Analysis This section has two emphases. First, the numerical results of the Complex routine are examined for consistency with real world ex— pectations. And the ability of these results to answer the several 263 analytic questions posed in Chapter I and the introduction to this chapter is discussed. As described in the previous section, two or three runs were made at each constraint level. The two Abest? points in the factor space were identified at each constraint as those with the lowest PERTOT value. To help prevent adverse effects of random noise on results, the "best” points were chosen from the second half of the algorithm's iter— ations. That is, stray low values of PERTOT early in the Optimization process were ignored. In particular, for the constraint 400 million won, the second iteration produced the second-best PERTOT level. But the X and P_parameters for this point were far from convergence values, and the results could not be repeated. The conclusion was drawn that this point was a fluke, a result of random error. In future studies, a higher MONRUN would be prudent. The average Of the "best" points is presented, parameter by para- meter, in Table 9.3. An average value is used because the flat sur- face encountered lends itself to area, rather than pinpoint, optimiza— tion. X and P_parameters are easily identified in Table 9.3. Average performance values PERTOT, TDETH and TNUTD are given, along with aver- age percent standard deviation figures. System cost COSTGX is uniquely determined by X and so is not a random variable. Four algorithm usage variables are presented as indicators of the ease of convergence for each constraint level. The number of iterations refers to the number of times a new superior point was found in the complex; the number Of model runs indicates the number of times the algorithm requested a point value from the model, multiplied by MONRUN runs to give the ac- tual number of one year simulation cycles. And CPU time refers to 264 Table 9.3 Optimization Results Budget Level 1X "U mmW>TJ§ 265 computation on a 000 6500. Convergence was based on meeting the B and 0 requirements within a given time-cost limit. MOdel Validity Let us first examine the aspects of Table 9.3 that confirm or cast doubts on the model’s validity. Some conclusions are apparent from a first glance at the table. The final cost, COSTGX, stays sig— nificantly below its boundary, especially for the 400 million won case. This is a technical success, but the magnitude of the difference be- tween boundary and result is disconcerting. There may be a way to im— prove convergence by allowing a closer approach to boundaries. Para~ meter 6 should be studied in any future use of Complex; this parameter stipulates how far inside the boundary an Offending factor value will be moved. Several trends across budget levels are easily detected and follow expected patterns. A larger budget leads to better information quality as indicated by decreased Optimal X values. This in turn leads to decreased death (TDETH) and PERTOT values; better information im- plies a better system, implying fewer deaths. Model computer time re— quirements also decrease with increased budget, reflecting the easier convergence path of reduced introduced error. Conversely, the likeli— hood of convergence increases with budget. Other reflections on the computer model from Table 9.3 require a bit more study. The idea of quicker convergence with higher budget recieves support when examining the ratio of model cycles to the num- ber of Complex iterations. For the five budget levels studied, the cycle-tO—iterations ratios are 12.8, 8.6, 5.0, 7,0 and 5.6, 266 respectively, for the budget figures in increasing order. The trend indicates an increased instance of a predicted better point failing, probably because variance of estimates increases with smaller budgets. To combat loss Of reliability, an increase in MONRUN should help. Other algorithms may also prove more successful in dealing with higher levels of introduced error. The budget level of 300 million Won is seen to be somewhat out of step with the other results. The objective values are very close to those of 400 million Won, but several of the X_parameters are incon- sistent, particularly DELD, 0029, SAMPT, and SMPRS. This appears to be a problem of the fuzzy, flat surface. In a larger scale project, it would be well to increase the number of model cycles (MONRUN) con- siderably. Recall that an inverse relationship is expected between the two performance criteria TDETH and TNUTD. Figure 9.1 pictures TDETH ver- sus TNUTD at the five budget levels of Table 9.3. Note that there is a slight but definite inverse relationship between the two variables. The 300 million, 400 million and unconstrained cases are clearly ”Pareto-better” than the 200 million constraint. The 155 million Won case has a lower nutritional debt but "costs" one million additional lives. Figure 9.1 also provides a vote of confidence for the use of min- imum PERTOT as the optimization objective value. From earlier model runs it is known that the use of minimizing TDETH as the objective would make the TDETH-TNUTD inverse relationship much more pronounced. PERTOT makes clear the model's ability to improve performance with a larger budget (synonomous with better information, from Table 9.3). IIIIIIIIIIIIIIIIIIIIIIIIIIllll--:::;____________ 267 Deaths (million) 4.0 . 155 milliOn 3.0 r 400 million . 300 million ' Z 200 million 2-0 unconstrained 1.0 h 60 70 80 90 100 Nutritional Debt (thousand MT) Figure 9.1. Nutritional Debt Versus Deaths at Varying Budget Levels 268 That is, the higher budget levels of Figure 9.1 are bunched in a po- sition that is close to a Pareto improvement over the lower budget levels; PERTOT reduces deaths while keeping nutritional debt at ac- ceptable levels. One quirk is evident in Figure 9.1. Note that the increased budget from 300 million to 400 million won results in a worsened per- formance. This may be attributable to the fuzzy flat response sur— face. The fact that after a point, increased expenditure does not im- prove performance will be examined later. Note the cyclical nature of solution to this overall problem. The results of the Optimization are used as an additional check on the model's validity. The Complex Algorithm Table 9.3 also provides information about the worth of the Com— plex algorithm. A convergence pattern for the algorithm can be easily visualized by graphing performance versus iteration number in the Com- plex process. Two such graphs are presented in Figures 9.2, for the boundary budget cases. Four curves are actually given, two each for budget constraints 155 million won (A+B) and the unconstrained case (0+0). Curves A and 0 contain data from the first algorithm trial with MONRUN equal one, while B and 0 represent the final optimization. Note that "stray" points on the curves are more prevalent in the early stages of the algorithm and for the MONRUN-equal-one trial. Such results are expected, as is the fact that the unconstrained curves are clearly below the constrained case. By continuing the comparison of constrained versus unconstrained, one sees that curve 269 D has a much narrower band of final values than does curve B, con- firming the convergence of D and not B as stated in Table 9.3. The conparative ease of convergence for curve 0 is also indicated in the figures. Note that with less error, curve 0 had more algorithm itera- tions in less time than did curve B. Based on graphical indications, the conclusion is reached that the Complex algorithm does converge to a satisfactory area of the fac- tor space. Clearly, the degree of convergence is better for the more relaxed constraint cases, but the PERTOT performance achieved are near minimal at each budget level. The flat fuzzy surface and the nature of Complex values are used in Table 9.3. A more comprehensive study might present a range of parameter levels as indicated by multiple algorithm runs and would provide expected range estimates. Figures 9.2 examine the convergence pattern of the objective value PERTOT. Another useful exercise would be to similarly study the behavior of X_and 3 parameters as the algorithm proceeds. Conver— gence graphs, combined with the range-Of-values study suggested above, would provide a clear picture of the confidence one can place in Table 9.3 values. A further study of the algorithm‘s effectiveness would be to examine the M-1 dimensional volume represented by the M points Of the Complex. This volume should decrease with convergence, and a simple volume-versus-iteration graph similar to Figure 9.2 would be useful. In light of the earlier discussion on the relative ease of con- vergence, it is interesting to study the actual and percent standard deviation figures for the three Objective values, as presented in Table 9.3. Particularly for PERTOT, actual standard deviation 270 003 eowHHHz 00H H0>00 000000 -- 000000000 Ecuwgomp< £000 pm #00000 0H00000> 00:050o0000 H0002 .0N.0 000000 000822 awassz :00000000 cowpmc0uH om om 0H 0H 2 00. o... o no JOP. m n zzmzoz . m 0>czo - NH. 000000 00205000000 o0 om om op .1 H n zsmzoz < 0>000 .H s 00. .0. .... .o 1 or. . ... NF. behmma 00005000000 27] 000000000000: p0>00 000000 nu 000000000 500000050 comm 00 000000 0P00000> 00005000000 p000: .nm.m 000000 000502 000502 cowpm0mpHom cm or 000000000 o0 om om op - - a 4r «I 11 - In! — 0a “0 coo... to... 0 o o o L on. o 0 0 o o .000. m u 200202 . 0 00. _ ... 200202 . 1 00. 0 0>000 o 0>0=u . . . 0.0 mo. 0 L mo. 0 mo 0 mo. 505000 505000 00005000000 00005000000 272 increases with decreased budget; a larger input error leads to more variance in outputs. No clear trend is apparent for the percentage figures, although the PERTOT and TDETH values increase slightly with budget. It appears that within the range of values employed in the current experiments, model performance is consistent and not seriously distorted by increased input error. One further test would solidify this conclusion. Model calculated outputs, such as population, prices and production should be examined at the computed optimal points, to insure that the "best” values are not the result of some modeling quirk with no real world analog. Comparison of performance figures in Tables 8.9 and 9.3 lead to the preliminary result that Chapter VIII optimizations were "better” than those in Chapter IX. But a closer look at the experimental guidelines show that the Chapter VIII figures are actually limiting cases of the Chapter IX studies. The purpose in Chapter VIII was to select a set of policy parameters for further optimization work. Ac- cordingly, the information quality szas stationed at three different levels. The Table 8.9 "good" 52 corresponds to the limiting Table 9.3 "unconstrained” case, while the Vpoor" 53 roughly corresponds to the 200 to 300 won case (See Table 8.3). Thus the seemingly better per- formance in Chapter VIII should be expected. A weakness in the chosen Complex method parameters shows itself in the comparison between the tables; the convergence criteria are too loose, allowing the algorithm to st0p short of a possible Optimal point. But besides this weakness, the two tables support the model‘s validity, because the objective values are close, the five policy parameters are close, and the run statistics are very similar. 273 A study Of Table 9.3 has revealed no glaring model or algorithm inconsistencies. Only the ability of the algorithm to combat model randomness is suspect. Let us now move on to an examination Of the factor space, the information quality and policy parameters. Translation to Information Quality Terms The optimal 5 values of Table 9.3 can be translated tO more famil- iar terms. Recall that one of the prime considerations Of Chapter V was that the cost function had to be computed in such a manner that once an Optimal 5? point was found, a unique information system would be identified. By using the component descriptions in Chapter V and the calculations outlined in Appendix A, the Optimal system at each budget level can be defined in terms of three information system types. First, the data transmission delay, in days. This is available from the delay parameter DELD. Second, the sampling interval, in days. Each sampled variable has its own interval, represented bylg parameters SAMPT, SMPRC and SMPRS. Finally, standard deviation parameters SDND, SDRC and SDRS can be translated to provide the sample size, the number of persons or households. The delay and sampling interval are computed easily by converting years to days. The sample size can be computed using the formulas de- rived in Appendix A, repeated here as Equations 9.4. The statistical method explained in Chapter V (see Equation 5.22) also provides a sur- vey cost, based on allowable error and frequency. The aggregate cost formulae are also repeated from Appendix A as Equations 9.5. The six equations indicate the relationship between error and sample size and among error, sample frequency and cost. 274 N = 0059 / SDN02 (9 4,) nutrition ' ' _ 2 Nconsumption - l0.6 / SDRC (9.4b) _ 2 Nstorage — 9.2 / SDRS (9.4c) 2 CSUR . . = 875,000 + (5000 + l.297 / SDND ) / nutrition SAMPT (9.5a) 2 . = l,312,5 0 + 5000 + l4 58 D CSURconsumption SMPRCO ( O / 5 RC ) / (9.5b) _ 2 CSURstorage — 875,000 + (5000 + 7086 / SDRS ) / SMPRS (9.5c) where: N = sample size (persons for nutrition, house— holds otherwise) CSUR = survey costs for one year (won) SDND,SDRC,SDRS = allowable error parameters SAMPT,SMPRC,SMPRS - sample frequency parameters. Table 9.4 presents the translated information quality parameters, sorted by system component. The cost for each Optimal component at each budget level is given, along with the component cost as a percen- tage Of the overall system. Transmission delays and sampling inter- vals, as well as sample size, are noted. In addition, the type Of transmission system as described in Chapter V (see Figure 5.l) is given. Before examining the feasibility Of the items Of Table 9.4, let us take a look at the overall picture. Each column gives best infor- mation system parameters to be followed at that column's budget level. For example, the most inexpensive system in the table calls for QUAC stick measurement Of 2221 children and consumption surveys of 44l households every twenty-four days. Personal storage supplies would CATEGORY Transmission Delay Nutritional Sampling Consumption Sampling Storage Sampling Total Won Total Won 2275 Table 9.4 Information Quality Parameters Translated to Sampling Terminology Data (Units) DELD (Days) Non (Million) % Type SDND SAMPT (Days) Won (Million) % n (Persons) SDRC SMPRC (Days) A n (Households) SDRS SMPRS (Days) Won (Million) 0/ n (Households) From Appendix Equations Model Results - Table 9.3 Non (Million) BUDGET CONSTRAINT LEVEL (Million won) 152 12.7 126.9 85 Two—Nay Transceivers .00163 24.2 8.1 5 2221 .155 24.4 9.9 7 441 .173 26.2 4.2 3 307 149.1 149.1 2.92 6.3 145.0 80 Minicomp .00131 18.0 15.9 9 3438 .160 19.3 11.6 6 414 .168 12.3 8.3 5 326 180.8 182.9 102 4.4 180.3 70 Renovation .000131 24.4 12.0 5 3438 .091 16.6 37.7 15 1272 .118 7.4 25.5 10 661 255.5 276.5 929 5.1 159.3 59 Renovation .000685 18.5 54.1 20 12574 .100 12.3 42.3 26 1066 .149 9.6 13.0 5 414 268.7 280.6 Unconst 3.8 233.3 44 Renovation .000679 10.1 100.5 19 12797 .066 10.0 116.8 22 2433 .066 7.5 78.3 15 2106 528.9 654.2 276 be sampled for 307 households every twenty-four days. The result of each survey would reach decision makers some twelve days later. The cost for this service for one year would be appfoximately l50 million won. With the given policies and systems for distribution and alloca- tion, the projected death total is 3.32 million and the overall nutri- tional deficit is 77,000 metric tons 0f grain at the end of the year. Similar descriptions can easily be generated from Tables 9.3 and 9.4 for each budget level. These descriptions are one of the prime results of the current work. This is no mean accomplishment. Let us now examine the details of Table 9.4. Two different total cost figures are reported in the table. The first is a sum of the component costs calculated from Equations 9.5 and Figure 5.1. The second is the COSTGX figure reported in Table 9.3. The reason that the two totals differ is that all values reported in Table 9.3 are the averages of two model simulation runs; comparison of single model runs would tie exactly. It is interesting that the totals diverge with in- creased budget. Based on convergence criteria, the averages would be expected to coincide more closely with the more relaxed constraints. But the opposite happens here. TWO reasons can be cited for the apparent discrepancy, both indi- cating that convergence of PERTOT is not the most important factor in determining system cost. The first reason derives from Equation 9.5. Cost increases as the squared standard deviation decreases. That is, cost becomes more sensitive to a change in allowable error as that error drops. Any difference in the standard deviation between the two "best" simulation runs is magnified at higher budget levels. 277 Second, the close match of cost calculations at the low budget levels is caused by high fixed costs. Recall that the minimum system expenditure is 140 million won. The lower budget levels effectively restrict the X_factor space. Since cost is a non-stochastic function of 5, it is restricted also. But the range of 5_includes large error parameters so that the objective value PERTOT does not converge. To combat the divergence of the two total cost figures, the con- vergence criteria must be tightened for higher budget levels. This would force the average_§ vector closer to actual simulation results. Policy_Results Let us now examine the individual X_and E_variables as reported in Tables 9.3 and 9.4. The five policy parameters appear only in the first table, as they do not directly affect the information system design. 0f the five parameters, three show possible meaningful trends. The parameter for nutritional debt control in the emergency feed- ing equation (Equation 2.15) is CG27, which increases with the budget level. That is, control is tightened with better information, causing quicker response in moving food from rurals to urbans. 0n the other hand, nutritional debt control 0632 in the sales equation (Equation 2.l4) decreases with budget. Control is relaxed here with better data meaning thatiflwarich are not as burdened. The effect of the C032 trend is an advantage of good information; better data allows decision makers to tax the rich less heavily. That is, the equalization policy may be hard to implement, but better information makes it easier. A second instance of the model showing the advantages of good information is found in the performance of C625, the crisis transport 278 increase parameter (Equation 4.5). C625 decreases slightly at higher budget levels, implying that the better data allow the normal Operating system to work more efficiently. Thereis less of a dramatic increase at the crunch. Both 6625 and C632 respond consistently with Chapter VIII performance (see Table 8.9). The two remaining E_variables are fairly consistent across the budget levels. C624 and C630, the consumption control on emergency food distribution (Equation 3.8) and the rural private storage control on the acquisitions equation (Equation 2.l3), respectively, give indi— cations that they do not belong in the final optimization. Recall that both parameters were included in the final tests because they varied widely in earlier runs (Table 8.9). If only C625, C627 and C630 were to be factors in an Optimization, the consumption and rural storage influence on policy would be fixed. This raises the question of how well the system would perform if these policy variables were excluded entirely. A modification of the model eliminating consumption and storage sampling and their respective influence on allocation decisions would allow such a check. This sug- gests a user-oriented enhancement of the model, providing a choice of combinations of sampled variables and control equations to be perfor- mance tested. This would be in addition to the current capability of changing and Optimizing on control equation paramters. Tracker Results The a-B tracker variable C629 (Equation 6.6) is the only X_para- meter that does not lend itself to a common usage translation, al- though it is tied to the 5_consumption parameters. It is clear that 279 C629 decreases with increased spending, paralleling the decrease in consumption sample interval (SMPRC) and standard deviation (SDRC). The rule being stated here is that with more frequent sampling and in- creased accuracy, a smaller 8 value should be used. How does this rule relate to the tracker? Recall the tracker design discussion of. Chapter VI. The choice Of B is based on desired response characteris- tics. 5 close to one is desirable for quick response to new data, and 8 close to zero helps to suppress error. i The Optimization results show that less frequent sampling with more error has 8 close to one, while more frequent, less noisy sampl- ing has 8 close to zero. As is Often the case, sample frequency and allowable error are at Odds here. Evidently C629 is affected more by interval than accuracy. If error were the only question, then the B should be closer to zero for low budget. But the opposite is true. The determining factor is that as the sampling interval increases, 8 approaches one so as to weigh more heavily the new (and infrequent) data. Information System Results Several interesting concepts result from a study of the 5_infor- mation quality parameters of Table 9.4. The sampling intervals are nearly the same for nutritional and consumption surveys, especially at the boundary budget cases. This suggests that some efficiencies could be achieved by having teams sample both variables at the same time, subject to statistical constraints and the affordability of multi- talented personnel. "280 The sampling interval for storage is generally less than for the other two variables. There are two possible explanations for such a relationship. First, it may be that storage needs closer monitoring to provide data that affects performance. The other option is that the storage sampling cost does not prohibit more frequent samplings as the consumption or nutritional measurement costs do. The second ex- planation is the more feasible, based on Unapercentage cost figures of Table 9.4. Note that the cost of storage surveillance is the smallest portion Of the overall system at four Of the five budget levels. It is good to examine the sample size figures of Table 9.4 to determine if they fit the real world situation. The crucial aspects of sample size are that the number fits the actual population and that the planned number Of teams can reasonably be expected to perform their tasks in a short amount of time. Increased staff would alter the cost function while increased measurement time would invalidate transmis— sion times and possibly the statistical Optimization routine. Let us examine the feasibility of the sample surveys defined at the highest budget levels of Table 9.4. The nutrition surveys call for examination of l2797 persons, or about .04 percent of the total initial population. This is reasonable, but recall that the chosen QUAC stick method can only be used on children. Also, the model as- sumes that a survey of the whole country is needed, whereas a true famine would concentrate by region. The number of samples is high, but the QUAC stick method may accomplish the task. Given that a team of two observers can sample two hundred children per hour (36), the l2797 measurements can be Obtained in sixty-four team-hours, or about three hours for each of the twenty—four projected teams. IIIIIIIIIIIIIIIIIIIIIIllllll--:::;___________ 28l However, the two hundred per hour figure does not include the time con- suming tasks of sample selection and travel. TOO much time spent will affect the assumption on delay costs, while too much travel jeopardizes the sample size function of Chapter V. Consumption and storage surveys do not appear to be as feasible as the nutritional, mainly because the time allotment per survey is much higher. Given one-half hour per household (42), the 2433 con- sumption samples would necessitate twenty-six hours for each Of forty— eight individuals. The fact that the time between surveys is only ten days implies that almost continuous sampling would be necessary. Simi- larly, the storage measurement of 2l06 households would require eleven hours per Observer, given a sampling rate of four per hour. Note that these sampling rates do not include travel time, so that the survey in- terval of 7.5 days would be quickly reached for storage sampling also. There are at least three possible cures for these lengthy survey times. The real-world situation can be aided if unit sample times are reduced, as has been suggested elsehwere (64). Two model particulars should be carefully examined. The population standard error parameters Sh for Equation 5.23 may not be estimated correctly. And the equations themselves may not be valid, especially since travel time becomes a very large consideration. Also, delay as a function of measurement may have to be added to the cost function formulation (see Chapter V). The most reasonable selection, from a real-world perspective, may be to drop consumption and storage as measured variables. The usefulness of a computer model cannot be overemphasized at this point. A set of model runs at varying levels of Sh can indicate answers to the tough questions of estimating a proper size for the population variance. IIIIIIIIIIIIIIIIIIIIIIIlll-ll--::;___________ 282 InformatiOn SyStem Priorities The 5 variables do behave in an expected fashion. The higher bud- gets lead to better (lower) X_values and better system performance. A question remains. Given a budget cut, which X_variables are the most crucial? Or, with limited resources, which parts Of the information system should have priority? One figure that provides a comparison is the percentage of total expenditure from Table 9.4. Note that the transmission cost is consis- tently the largest expenditure of the four components. But the percen- tage cost is affected by the fixed costs and does not account for the difference in component units. That is, component costs are related to X_variables which have varied allowable values and varied cost struc— tures. To combat the problem of non-comparable variance, one could com- pare the X_values as percentages of their respective allowable ranges, as stated in Table 9.l. But fixed costs are still not accounted for, and the ranges of Table 9.l are subjective. How then do we compare X_variable worth? Two concepts are impor- tant. The first is that of a percentage change in the cost of the com- ponent. The percent change smooths out the effects of fixed costs. The second concept is that the change in cost (or variable value) must be tied to a change in system performance. Recall that the use of sensitivity tests, as conducted in Chapter VIII, is one method for mea- suring the change in performance due to an input variable change. But a less time-consuming method presents itself here. Another way of wording the current question is which extra invest- ment in information system components will have the greatest positive 283 results? To put this into a numerical setting, let us examine perfor- mance variables versus cost. Figure 9.3 presents performance values PERTOT and TDETH as functions of cost COSTGX. The values are taken from Table 9.3 and represent all five budget levels. Note first that the shapes of the two curves are very similar. This is another confirmation that PERTOT is an acceptable optimization proxy for TDETH. A second, and more important, consideration is that curves show marked performance improvement for low budget levels but then reach a plateau where extra expenditures contribute only minimal system improvements. Marginal performance increases are negligible for investment greater than three hundred million won. At that point system improvements must come from other sources: more food, better policies, or more efficient transportation and distribution operations. This plateau is reflected in Figure 9.l where the three hundred million four hundred million, and unconstrained budget levels produce similar results that are a marked improvement over the l55 million won case. The implications for studying the X_variables Of Table 9.3 and 9,4am13Cléar. The changes in §_value and resulting expenditures be- tween l55 million and three hundred million won are likely to be more productive than the changes from three hundred million won to the un- constrained budget level. A means Of measuring and comparing the stated changes is needed. The measurement must account for fixed costs, dif- ferences in variable units, and effects on performance. Equation 9.6 defines a measure which meets the required criteria. The function H is a ratio with the change in performance between the minimal budget case and higher cost levels as numerator and a 5.0 4.0 3.0 2.0 l.0 284 Deaths (Millions) PERTOT l l .l .0, .09 .08 - .07 . .06 » .05 b .04 .03 r .02 - .Ol PERTOT (C) Deaths (C) J.— _J_ 4 _4__ I _L lOO 200 300 400 500 600 700 Budget l55 200 300 400 Unconstrained C Cost (million won) Figure 9.3. Performance Versus Cost .285 denominator comprised of the range of the X_variable. The ratio of differences allows a comparison across X_variables. Xi (l55) - Xi (C) ”1“” = (9.6) R1 where: H = comparative performance measure on information quality parameters (dimensionless) C = budget level (won) X(C) = optimum information quality parameter at given budget level R = defined boundary on range of Xi (from Table 9.l) index on quality parameters. —Jo II The numerator of H serves to smooth the fixed costs problem and compare performance differences. Note that costs are a direct function of 5_so that studying X_changes is the same as studying cost differ- ences. The ratio of Xi differences eliminates the variable unit and cost structure problems with one proviso. The range definitions of Table 9.1 must be equitable. That is, each range must reflect a standard likelihood that the Optimum Xi falls within the range. Re- call from Chapter VIII that the ranges of Table 9.l were subjectively selected after a multitude of model sensitivity tests. A more pre- cise range calculation method would increase the validity Of measure H. Figure 9.4 presents H values for X variables at each budget leveL Calculations were performed using Equation 9.6 and Tables 9.l and 9.3. A large Hi(C) value in Figure 9.4 indicates a large change in Xi be- tween budget level C and thelSS million won level. The difference Hi(C1) - H1(C2) shows the magnitude Of change in Xi between budgets — “UV: mczmmmz bmou mzmcm> mucmseowcmm .v.m mesmwd Aces coa_Pasv pmou o pmmvzm eacwmzpmeoucz cow com com mm_ capawuomm< com gem ooe com com co, IIKI q a 1 « fil . < < a “x, mmom . z / umom I F. _. ,, c. ~ / _ z \ DZQW . . a ‘ 1 N ,Y\ ..lgl. omazm . \\ x 28L... \ \ E23 . m. \\\\ - \x 6 \\ «w. 95% \ \ \ \ \ umOm . 1 m omazmnnqul..l\.l\. - ~ . \ lll ll... 4 O ozom.\\x . . N osmo.nu Ill / \ L m. maazm . g m ADV: — --—‘—.—_rv i, C] and C2. The discussion of Figure 9.3 implied thatta desirable pat- tern would be to have Hi(200) and Hi(300) large. A secondary consid- eration would be that the differences Hi(400) - Hi(300) and Hi(500) - H1(300) be small. The most striking feature Of Figure 9.4 is that the delay para- meter DELD and the storage sampling frequency SMPRS are dramatically "better” than the other five X_variables. Both DELD and SMPRS have large H at low cost. At the two hundred million won budget level, three second-priority parameters are identifiable: SAMPT, SMPRC and SDND. And the remain- ing two variables, SDRC and SDRS, show minimal change at the two hun- dred level. But both SDRC and SDRS rebound to have high H at three hundred million won, while SAMPT declines sharply. Such large fluc- tuations may indicate that these variables are not reliable predictors of system performance. Based on the previous observations, there appear to be three priority levels among the individual information quality parameters. First, DELD and SMPRS are superior. Expenditure for reduction of transmission delay and increased storage sampling should be of primary concern. Additional expenditures would go toward increased consump— tion sampling and reduction Of nutritional measurement error since SMPRC and SDND show steady improvement in Figure 9.4. Finally, SAMPT, SDRC, and SDRS should be supported only at a level necessary to keep the information system in balance. Let us now examine Figure 9.4 with reference to groupings by type of parameters. It is clear that the delay variable is superior to either frequency or error parameters. And, at the two hundred million 288 level, frequency parameters score consistently higher than their error counterparts. The situation is clouded at the three hundred million level since oscillations make the superiority of frequency over error less evident. But based on this one graph's evidence, it is possible to rank information quality by component type: delay, frequency, error. Note that it is somewhat inaccurate to make these priority state- ments since the optimum points shown in Table 9.3 are combined effects of all X_variables. The measure H provides an indicator, not a defini- tive statement. Also, the generality of these rankings cannot be dis- cerned here. It would be necessary to examine many model variations before making general statements. Real-world experience must provide the final test. Conclusions and'Summagy The model seems to perform well based on the reliability and ex- pectedness of outputs. The issues of model variance; algorithm con- vergence; the use of a single variable performance function; and the cost-change trends of information quality'(§), policy parameters (3) and system performance have all been faced. More importantly, the approach provides quantitative answers to . the several questions posed in Chapter I and the introduction to this chapter. Optimum information system alternatives at several budget levels are derivedanuipresented in Tables 9.3 and 9.4. The expected performance level is also given in Table 9.3 and is pictured in Fig- ures 9T and 9.3. A standard deviation is given in Table 9.3 for each 289 variable and performance, so that ranges of likely values can be com- puted. Table 9.4 provides suggested monitoring statistics for the real— world variables included in the model. As mentioned previously, a fuller explanation of the problem would greatly expand the decision- making portion of the model to include such variables as water and medical supplies, incidence of illness, and transport availability. The results of the approach touch not only on information quality, but on operating levels for policies. The E_portion of Table 9.3 ties operations to information quality. The relative importance of X_components is examined. The cost breakdown in Table 9.4 allows a comparison of absolute expenses across information quality components. And the measure H of Equation 9.6, along with its related graph in Figure 9.4, lead to a prioritized spending list for information: timeliness, frequency, accuracy. It should be noted here that in this complex system, the numerical results of this chapter depend a great deal on the situation set in previous chapters: the cost function, the raw data, the model assump- tions. The model validation work of Chapter VII must be done prior to Optimization, but its real worth is not evident until the optimization results are scrutinized. Once again, many valid research projects have only been touched in passing. A great amount of wisdom is needed to anticipate the most crucial areas for work, since extended research is not possible in a famine or in famine—related work. The following items are mentioned as means of improving on the present optimization framework. 290 The single performance criterion of Equation 9.2 allows for dif- ferent weighting patterns. A study of several disparate weightings would be useful in relating the numerical optimization package to the real—world results of lives saved, nutritional debt, and available grain. A deeper look at the results of a price control policy should be made, as well as exploration of other policy alternatives. It is like- ly that the criteria of Equation 9.2 will need to be significantly al- tered to fit a different policy structure. Further convergence tests on Complex and its boundary parameter would help to delineate the causes of output fuzziness. Error para- meters, the optimization algorithm and the model itself contribute to the flat, fuzzy surface encountered. It would be very useful to make more precise statements about the causes of output variability. The effects of cost function changes on optimization results should be studied. Such an examination would provide great insights into the relative worth of X_parameters and information system com- ponents. PART III CONCLUSIONS CHAPTER x~ RESULTS AND SUMMARY A systems approach to nutrition in general and famine relief in particular is a large project. This dissertation has not been an ex- ception. The goal of this Chapter is to attempt to tie the package together. The major results Of the study are presented first. Follow- ing sections are devoted to general Observations about concepts likely to be encountered during application of the approach, advantages and disadvantages of the method, and a presentation of areas for further related research. Major Results The simulation approach outlined in Figure l.2 and described in this dissertation is a viable Option for the study of information sys- tems. Computer simulations are excellent tools for the study Of com- plex, quantifiable processes, and the sampling component developed here allows macro simulation of an information system. An example problem has been followed through the approach to a successful con- clusion. The computer simulation model has shown that it can be an inval- uable asset. A model can definitely serve as a design tool. The 291 292 model can be used as an educational tool for decision makers, an aid in discerning the relevant outputs to be aware of when plotting relief strategy. And a refined model could serve as an on-line predictor during an actual famine. In each application, the computer simulation would provide a deeper insight intO the problems to be faced. Many questions about relief work are answered and many more relevant ques- tions are unearthed as a result of simulation analysis. Information quality has a great potential as a model validation tool. The assumption that better information should lead to better system performance leads to a thorough study of model and policy struc- ture as well as model and policy parameters. Similarly, the sampling routine described in Chapter III is a useful general modeling tool. It can shnulate many data quality sets as part of a large simulation or can be used to test the efficacy of filters and predictors. It has been demonstrated that optimal policy implementation varies with information quality. This requires the current problem formula- tion to include a performance function dependent on both policy and information quality (E(§;E))- An alternative to multi—variate Optimization was found to be both useful and accurate. The single variable PERTOT served as a proxy for the defined optimization variables Of nutritional debt (TNUTD) and total deaths (TDETH). PERTOT was defined in Chapter VIII as a weighted measure of the percentage death figure in the four population classes (see Equations 8.7). Such a weight was picked to complement the stated policy of equalizing nutritional debt across the classes. In optimization runs, minimizing PERTOT led to a minimization of TDETH with TNUTD at acceptable levels. The key finding is that the policy 293 and goals of the real world system can lead to a useful measurement and objective value in the model. Three items emerge as important issues for relief efforts to address. Study of the simulation model in Chapter IV shows the crucial effect of consumption patterns on relief policy. An addi- tional aspect of this problem is the long-term education implications of poor consumption habits. Secondly, there is a harsh question to be answered when outside aid is not enough to meet a food shortage. Will short term (two—three months) or long term (one year) solutions be implemented? The long term solution requires the unpopular im— position of immediate rationing, but has significantly better results when the crisis peaks. Finally, the ability to predict famine extent is important. In Chapter VIII, a twenty-five percent change in crisis level produced a change in model results approximately equal to shifting from the best to the worst information system. When the goal is minimization of deaths, poor estimation of this one variable can undo the finest design work. A cOmparison of the relative importance of policy choice and optimization can be made, based on five model benchmarks. The original price control and equalization strategies of Chapter II, the modified policy without Optimization of Chapter IV and the optimized results of Chapters VIII and IX provide the basis for comparison. Each output was generated at a mean crisis level of two million metric tons and optimal information quality. Table 10.1 contains the relevant data. Note the continued inverse relationship between total deaths (TDETH) and total nutritional debt (TNUTD). Also note the tremendous 294 Table 10.1 Comparative Performance at Five Points in Study_ Benchmark Description and TDETH TNUTD Chapter of Occurrence (million) (1000 MT) Price Control Policy 10.5 0 Chapter 2 Original Equalization Policy Chapter 2 5 50 Revised Equalization Policy 3.5 80 Chapter 4 Manual Optimization 1.76 102 Chapter 8 Complex Algorithm Optimization 2.19 87 Chapter 9 295 improvement Of equalization policy over price control. As mention- ed in Chapter VIII, further model work should improve the price con- trol results, probably reducing TDETH to nine million. It appears that the complex algorithm does not lead to a sub- stantial improvement in system performance. But the system descrip- tion resulting from the manual Optimization in Chapter VIII is poorly defined. The success Of the manual Optimization is due more to the flatness of the response surface than to the method itself. On such a flat, fuzzy surface, no algorithm is likely to pro- duce exact quantifiable results. But an algorithmsnuflias Complex has the valuable feature of simultaneous variance of all input variables, allowing a study of interactions. And the results Of Complex are well-defined according to performance. As mentioned in Chapter IX, another reason for the seemingly worsened performance of the Complex method is the fact that infor- mation error is introduced. Each of the other four benchmarks was run at "Clairvoyant" information levels, with no random error cn~delayin information. Improved policy reduces deaths by 1.5 million. Optimization led to an improvement of some 1.3 million. 50 policy modifications and optimization are similar in their ability to improve the model- ed relief system. The choice of policy appears to be more important. In any large scale project, the wisdom to know what to look for is vital. Several stages of this dissertation, particularly Chapters IV and VIII,demonstrate the overwhelming truth of this 296 statement. Such wisdom is not guaranteed by expert help or hard work; it is a gift. Observations on the Approach and the Current Problem The numerical outcomes of this study are meant as indicators Of the nature of expected results, not as actual recommendations, mainly because the model has not been adequately validated against real famine data. In fact, the model backgroundissa hypothetical mixture of two countries. Thus, more important than numerical results 15 the type 0f outcomes encountered. Chapter 1X produces the numerical data mentioned in Chapter I as aids to planners: optimal system descriptions at several budget levels, likely levels Of performance for each alternative and priorities on system components, variables to be monitored and surveillance parameters. Study of the model alone results in a broader under- standing of system processes, as described in Chapter IV and VII. In following the current example through the methodology Of Figure 1.2, several items became clear on the structure of the approach and its relation to the example. The cyclical nature of simulation work carries over to the approach itself. An exam— ple appears in Chapter IX. The use of sampling Equation 5.21 and the assigned value of parameter Sh within the equation may be invalid for consumption surveillance because of time and transportation constraints. This was discovered in the Optimi- zation phase and could result in a restructuring of the cost function. Note that this leads to an observation about the 297 validation process. Validation should extend to the modeled func- tion 6(X), insuring that modeled alternatives actually do pro— vide the cited information quality. Relief system performance is likely to be a fuzzy, flat surface. Thus, the goal of the optimization stage should not be to pinpoint parameters. Rather, the discovery Of a cost value where a performance plateau begins would be most helpful (see Figure 9.3). Too high powered an algorithm will be wasteful in this context. The Complex algorithm is easily programmed and operated, and it converges satisfactorily. It is a good optimi- zation alternative here. On the other hand, manual sensitivity tests are unreliable as an optimization tool because the results are very poorly defined. I would recommend that the final optimization stage of Figure 1.2 be avoided unless an algorithm package is available. Based on tasks performed for this dissertation, the areas where most research and analysis effort can be expected are: -- development of 6(X) -— construction and testing Of the model -- development of experimental scheme/design The actual experimentation and interpretations go quickly once the above items are in place. There exists a great tendency to want a more and more detailed model. But, detail leads to disaggregation (by class, region, variable type, time, etc.). This makes it harder to analyze 298 outputs because of the volume of data, and the large number of parameters makes Optimization more difficult. At several points the concern has been voiced over the imple- mentability of this systems approach. The usefulness of this or any other planning methodology depends more on the level Of com- “. “'\\.' \7 ' mitment of the government than on the worth of the methodology. Advantages and Disadvantages of the Approach Most importantly the current approach provides a frame work . for future research on famine relief information systems. As seen in Figure 1.2, performance is tied to cost and to informa- tion quality variables. The final output is a set of criteria 1 for information system design: optimal system descriptions, likely performance levels and priorities for resource allocation between sampling error, delay and frequency. The approach com- bines the tools of management information systems (MIS), computer simulation, optimization, and cost-benefit analysis. Several segments pictured in Figure 1.2 can be used indivi- dually to provide rich rewards. The validation stage and construc- tion of the simulation model are powerful learning tools, as discussed shortly. The cost analysis used in generating function 6(X) must sort through policy information needs while constructing alternative mechanisms for Obtaining data. It must also evaluate restrictions on money, manpower, equipment and time; much useless evaluation can be eliminated by limiting the scope to feasible alternatives immediately. 299 A sampling component added to the simulation model allows study of results of given information quality without specifying the details of surveillance and processing. SO criteria sets are evaluated which can cover a multitude Of alternatives. And the sampling component allows evaluation of information filters even without the remaining simulation components. A simulation is a powerful tool. Use of the computer allows comparison of a multitude of situations quickly, examining results Of varying initial conditions, data collection parameters, data collec— tion variables and MIS—policy combinations. Sensitivity analysis can help indicate further work priorities. The numerical comparisons in simulation work are useful. Ex- ploration of satisfactory answers to the repeated question "why?" is even more helpful, as related in Chapters III and IV. Knowledge of trends and cause and effect relationships as well as the recommended parameter and performance levels results from this excellent learning tool. Understanding component linkages and the relationship between policy structure (the equations) and implementation (the parameters) can help identify problems to be met in implementation. The simulation can be useful in different forms to several governmental units. By removing the sampling component, one can examine results of varying crop failure levels. Optimal timing for imports and foreign aid distribution has already been studied (38). Identification of the important links to transport and distribution systems is possible, as well as management and training requirements. And policy making is enhanced as the model helps set criteria for information quality. 300 Finally, the feedback equations and cutoff levels used in the modeling of policy structure lead directly to MIS rules in the imple- mentation stage. The learning process of studying the model can bear fruit when examining specific operating procedures for field programs and the transport system. There are two main disadvantages to the current approach. It requires a high degree of systems sophistication which may make it difficult to implement in a third world setting. And some issues are outside the scope of the analysis portion of the approach. A fairly high degree of computer technology and software power will be needed which may not be readily available. Possibly more limiting than the need for computer power is the need for a sophis- ticated level of data for the model. A real-world data base is not available for much of the performance and cost data that would allow comprehensive model validation. The approach, in its full scope, is a time-consuming process in a field where time is a major constraint. In addition, the cost function 6(X) is defined in a form not normally developed, making it harder than usual to Obtain. Uniform goals and Objectives are central to a ”systems" approach, but these are generally not available in the sectored government commonly found in the third world (17). Although this approach is a framework for design, it does little to explain how to set up alternatives or implement a designed system. Expertise in these areas would be logical components of a systems team. 301 Tgpics for Further Research The tremendous number of tasks to accomplish in any relief effort is staggering. Even with limiting the scope Of the current study to the role of an information system, many complex components have been noted. The purpose of this section is to draw together some of the tOpics touched on in previous chapters, to provide a guide to areas that deserve additional study. Due to the methodology orientation of the dissertation, many items are mentioned. The main subjects include information system ties to other relief components, including impor- tant background factors to consider' in implementation planning; topics in simulation and modeling research, and deeper probes into subjects covered in this dissertation. A well-planned relief study should examine many facets of relief before choosing those areas that seem to promise the greatest rewards for continued effort. This is a common sense approach; knowledge of the overall picture is invaluable when reaching more detailed levels. Ijes to Other Relief Components It was mentioned in Chapter V that there is a natural overlap between ongoing nutritional surveillance and emergency sampling. A link between the two would be early warning signals of an approaching crisis. Some study has been done on the most useful variables to measure (25). Possible signals include crop forecasts, migrations, food prices and hoarding. The transportation system will be vital in any plan that requires distribution of available foodstuffs. The transport rate proved to be an important policy item in Chapter IV (see Equations 4.5 and 4.6). 302 The expected transportation and storage capabilities have a great effect on the amount of foreign aid or imports that can be made available for relief (30). Using obtained surveillance results for relief field program , planning presents an excellent opportunity to link system components. Apparently a well-defined and coordinated survey can provide a "topo- graphical map of malnutrition" for a region (36). Standardized results plotted on a map indicate villages where program efforts need to be concentrated. Additionally, information and program ties with world organization efforts Should be explored. The World Health Organization (WHO), United Nations Diseaster Relief Organization (UNDRO), and others are actively pursuing research on relief activities. Actual implementation of an information system design deserves a much harder look. Corruption, hoarding, a "black market," and the reaction of the people to surveillance techniques are all influences on the information and food allocation systems. Certainly the power concentration in the government will affect the degree of organization and cooperation between relief components. And the degree to which responsibility for the nation's nutrition is handled by varying gov- ernmental units will affect implementation feasibility (l7). The amount of cooperation from the affected peOpleS will depend on their faith in the government and on cultural attitudes toward strangers and outsiders. Strife and prejudice will be enemies of relief. Struggles be— tween rich and poor, between politicians, between races, religions or regions have long been causes of the unequal distribution of food in 303 the world. These conflicts must be taken into account when planning programs and when designing an information system. Simulation and Modeling The computer simulation discussed in Part I is a cornerstone of the current approach. Many modifications are possible to make the model conform more closely to real-world behavior; such modifications deserve further study. Many variablesin the current model are aggregations or averages. For example, the urban population is split into three classes, but all rurals are included in one group. A more accurate portrayal would result by identifying the distinct rural groups: landless poor, small and large landowners, etc. (2l). Similarly, a breakdown by regions would be useful, especially in the case of only one region of a coun- try struck by famine. Food types, nutrition and crop patterns are all related when con— sidering variable aggregation. The current model uses One grain equivalent figure and one average nutritional requirement and has no crop breakdowns. This was done in the interest of simplicity, and an effort was made to discern the most important relationships between crops, nutrition and food types. Once one of the above variables is disaggregated, logic generally dictates that others be handled similar- ly. Suppose that a study of the effects of differing diets was de- sired. Several food type variables would be required. Production and storage variables might then need to be disaggregated to portray the availability of each food type. And the nutritional calculations would need to be reworked so that the total nutrition picture affected nutritional debt and deaths. 304 One type of disaggregation that stands out in a famine setting is an age and sex distribution. Children and pregnant women are most susceptible to malnutrition. Food requirements differ with age and body size. A breakdown by sex and three or four age categories would provide added insights to the study of age-dependent surveillance techniques such as the QUAC stick. One positive result Of disaggregation is evident in the use of the substitute objective PERTOT (Equations 8.7). The varying effect of policies on social classes can be studied. It would be very useful to know which policies favor which Classes or groups. It would also be very useful to Observe several highly aggregated variables; macroeconomics indicators of the country's stability. Trade balance, food and other prices and the extent of indebtedness acquired to purchase equipment and food are all affected by the management of the relief effort. Addition of a suitable set Of equations to the model, as briefly stated in Chapter VII, would allow decision makers to study limiting outside factors on system operations. A simulation can evaluate alternative allocation strategies but it cannot design them. It has been demonstrated that a strategy Of equalizing nutritional debt across an entire population performs better than a price control policy. But neither of these may be fea- sible in a specific country. Thus there is a great need to devise strategies that are tied to actual situations. Strategy frameworks must be constructed apart from the computer. Computer models can then aid in testing alternative strategies. Related to strategy design is the modeling problem Of decision rules. Nutritional debt, consumption and storage variables are used 305 in the current model as decision variables. Additional factors that could be added would include water level and disease incidence. These would be needed especially if a more detailed model of field programs was desired. It may also be that such factors are best handled out- side the model. Possible equations for the use of crop level and harvest time estimate are included in the Appendix computer programs listing. These equations were constructed as an aid in the calcula- tion of average required nutrition (ARNUT) in Chapter IV. . Decision making has been modeled here as a continuous process with constant control parameters in policy equations. The possibility of varying controls with time was discussed briefly in Chapter VI. Allowing control parameters to change at specified intervals leads naturally to the use of dynamic programming (27, Chapter III). Con- tinuous decision making refers to the modeling fact that the control values are computed at each discrete model time interval At. As At decreases, decisions are made more and more continuously. Compromise would allow for regular decision times, say at weekly intervals. The negative side of dynamic programming is the tremendous increase in the number of distinct control parameters. It was noted in Chapter VII that a fairly small At has been used in this study. A small At will lead to large computing costs, espe- cially when more disaggregation and complexities are added. It may be possible to reduce computation time through introduction Of a two- step discrete interval process. The model components that require small At values can be cycled through many times for each cycle of the bulk Of the model. Manetsch and Park describe such an application to delay processes (see Equation 2.l8) (40, Chapter l0). For example, 306 the nutrition and death total calculations require small At values, while production, storage and price calculations provide accurate results with coarser time intervals. Another ”time" problem is that of modeling the reversible nutri- tion process, as mentioned in Chapter II. The cumulative normal prob- ability—of-death function (F2) of Equations 2.3 depends on the initial population nutritional level. A country that faces a famine and then recovers will probably not return to the same initial level. This creates a problem when modeling repeated food shortages (as would occur in chronic food-deficit countries). Thus, a modeling technique is needed to adequately portray this reversible process. Deeper Probes into Covered Topics The study of information quality was limited here to delay, fre— quency and error parameters. The introduction of bias in estimations is distinctly possible, as is the effects Of autocorrelated data. The sampling component can easily be altered to model such occurences. In fact, bias is provided for in the original formulation in Chapter III. A more detailed model could examine the sources of information error and delay. The discussion of Chapter V concentrated on the error inherent in data capture and processing. There is also a sig- nificant problem in assuring the reliability of data storage. A simulation model can be used to study many budgeting issues that were touched on in this dissertation. The effect of cost equa- tion changes on optimization results is an additional factor in con- sidering cost versus performance (see Figure 9.3). Since it was shown that optimal policy parameters vary with information quality, 307 a significant topic in the overall relief system is the policy imple- mentation costs 62(3) as a function of X, This was described briefly in Chapter V. 62(3) is computed dynamically, so it would be fitting to study this topic when information costs 6(X) were also figured dynamically, so that the same occurrences in the model cycle affect both. The possibility of computing information system costs related to the model cycle rather than as a direct function Of X_was also mentioned in Chapter V. .Related to dynamic cost function modeling is the larger issue of developing a framework for construction of the cost function 6(X). The example used in the current work conveniently avoids some of the more complex problems. Handling the case of multiple system alterna- tives requires the use of multiple equations to specify E(X). These equations must preserve the uniqueness rule of Chapter V. The approach has the theoretical ability to handle personnel, equipment and time constraints separately from finances. It would be helpful to develop a sub-methodology for such a case, especially when modeling informa- tion system links to transport and distribution systems in more detail. In order to build on previous work, it would be useful to develop a solid connection between standard cost/benefit analysis and computer simulations. Several topics for optimization studies have been suggested in Chapters VIII and IX. Chief among these is an examination of the usefulness of other algorithms, particularly response surface method- ologies (48, 60). Another topic would be the different performance Objectives' effects on model variables such as population, storage, price, crops, etc. This could constitute an in-depth study of the 308 consequences of stated goals and objectives. If no dynamic cost func- tion is used, the complex algorithm should be modified to check that a given input vector X_Satisfies constraints, without going through a complete model cycle. This would save computer time, especially on a fuzzy surface. The facility with which simulation results are produced would be enhanced by the development of several user aids. The framework for the current model is based on a punched-card processing system. Adaptation to a more interactive mode through use of CRT terminals would reduce computer operations time. The program now in use allows for easy changes in certain parameter initial values. An interactive model could prompt for such changes from default values. An additional helpful feature would be to also prompt for the particular policy alternative desired. As mentioned in Chapter V, consumption surveys are not likely to be practical. A model that allows the exclusion of such a variable would be useful. Similarly, it would save time if the program allowed for a sensitivity testing mode, where changes in inputs are specified and the appropriate percentage change in system perform- ance is calculated as one of the program outputs. Such a feature could be helpful in any computer simulation. In particular, the sensitivity tests in Chapters IV, VI, VII and VIII would all have been accomplished much more quickly. Filters and predictors to fit the varied estimation problems in famine relief are needed because variable estimation is a key problem. As mentioned in Chapter VI, the a-B tracker and the use of polynomial smoothing as a predictor are possible starting points. 309 There are many economic and personal factors affecting relief efforts that deserve study. Again, wisdom is needed for productive selection Of topics. Certainly research on consumption habits pre- ceding and during a famine is a top priority. As light is shed on the likelihood of hoarding, the tendency toward self-rationing and the starting point for hand-tO-mouth feeding, the model consumption equa- tions can be further tied to reality. Price level, the rate of in- flation, international grain costs and supply are some of the macro- economic factors that will impinge on relief. A study comparing the effect Of these factors on relief performance would help to design ongoing surveillance. Summary One of the goals of this dissertation was to provide a framework for future study. As this section shows, many items logically connect to the information system design problem; much additional work is needed. Man has a responsibility to study these questions because he must be a wise steward Of what has been given to him. The next steps are logical extenstions of the "proposed methodology" nature Of this dissertation: evaluation of the approach by the intel- lectual community and adaptation of the model and approach to a real- world situation. APPENDICES APPENDIX A NUMERICAL COST COEFFICIENTS NUMERICAL COST COEFFICIENTS There exists a large jump from the theoretical equations of Chap- ter V to the hard numbers presented in Chapter IX. This appendix is intended to fill part of that gap by presenting the numerical coeffi- cients used in the simulation work. The same data is also available in the computer program of Appendix B, but is much less accessible there. Equations will be presented here without complete explanations. The rationale and variable definitions can be found in Chapter V, Equations 5.l8-5.36. The goal of the cost function is to determine information system costs based on information quality parameters X, Equation A.l (5.36) is the final step, stating that total costs will equal the sum of transmission cost, nutritional survey cost, consumption survey cost, and private storage survey cost. COSTGX = CDELF + CSN + CSC + CSS (A.l) The transmission cost is most easily computed. It is an inter- polation problem using the function of Figure 5.l. The four points Of the curve and their corresponding system descriptions are listed in Table A.l. The cost parameters CDEL in Table A.l were derived from Equations A.2, A.3, A.4 (5.33), and A.5 (5.34). The constants used in used in the simulation are given in Table A.2. 310 Point System (1') Component UEQ (#). WEQ(1000 won) MAINT (%) PDEP (%) PUS (%) UPR (#) WPR(1000 won) TPR(IOOO won) PRPUS (%) 311 Table A.l Transmission Interpolation Points System Description Current microwave system Two-way transceivers Base microcomputers Renovation of UHF network New microwave network CDEL DEL (million (Yrs) won) :.038 126.6 .023 128.7 .015 153.3 .011 193.3 <.011 193.3 + (.011-DEL)* 1010 Table A.2 Transmission System Cost Components Fixed Cost (0) 1 5,000,000 .25 .15 .05 20 800 .05 Current Two—way Base UHF Microwave Transceivers Micro- renovation base links computer (1a) (1b) (2) (3) (4) 3O 1 75 3O 1 800 10,000 50 400 500,000 .25 .25 .25 .25 .25 .30 .35 .30 .30 .15 .5 .2 1.0 1.0 .2 6O - 30 - 600 - 600 - ,5 - 1.0 - 312 CDEL0 = CEQO + CPRO (A.2) CDELi = CDEL1._1 + CEQi + CERi , i=l,2,3,4 (A.3) CEQi = UEQ, * WEQ.i * (MAINT, + PDEPi) * PUSi , l=O,l,2,3,4 (A.4) CPRi = UPRi * (NPRi + TPRi) * PRPUSi , l=O,l,2,3,4 (A.5) Survey costs are calculated using the form of Equation A.6 (5.l8), with details as presented in Equations A.7 (5.21) and A.8 (5.22 and 5.26). Note that A.7 provides the needed number of samples, given al- lowable variance, and A.8 calculates the cost of one survey. Recall that CSUR and n are computed with the assumptions that each population class represents a separate survey and the four regions are the statis- tical sampling strata. If the classes and regions are considered to- gether as sixteen separate strata, the formulae A.7 and A.8 would not .flltmvthe Sj's to be taken outside the inner summation signs. CS = CFIX + CSUR / SAMP (A.6) M L L _ 1 Z 2 /'* * / ". ’V*j=lsj*)hlwh/Chj) (hzlwh/ ChJ) (A7) .. 2? 2.. % ff 2 CSUR = C0 + ((SAMP-COST) / V) i=1 Sj ( h_1 ”h Chj) (A 8) Chapter V provides for four divisions of the country (L=4) and four population classes (M=4). Costs (Chj) are figured on two breakdowns, by region and by class, while standard error (Sj) varies only by * u class. The basic core of data is given in Tables A.3. Costs Chj in Table A.3 are relative indices Of cost size by class and region and are multiplied by appropriate per-unit sampling costs to obtain the cost for a particular survey type. Note that some mathematical 313 Table A.3a Relative Costs and Population Percentages for Surveillance Calculations Wh Population Percentages * Class 3 Chj Relative Sampling Costs Urban poor Urban poor Urban Rural Region hl NO relatives With relatives Rich 1 2 3 4 Region 1 1 1 1.2 .9 Region 2 1 1 1.2 .9 Region 3 1.1 1.1 1.32 .99 Region 4 1.2 1.2 1.44 1.08 Table A.3b Standard Error and Per-unit Sampling Costs for Surveillance Calculations Class Sj Standard Error Type Of. Urban poor Urban poor Urban Rural Surveillance No relatives With relatives RlCh 1 2 3 4 Nutrition (SN) .03 .03 .045 .045 Consumption (SC) .3 .3 .35 -35 .2 Storage (SS) - ' ' .233 .301 .198 .268 Sampling Cost (won) 200 1,200 800 314 o I o * 1 economies are pOSSTble 1f the Chj are employed in the body Of the cal- culations and the per—unit costs are multiplied at the end. Two further items must also be computed. Variance V is influenced by Equation A.9 (5.28). And fixed costs are calculated as in Equation A.lO (5.27). The appropriate constants are given in Table A.4. : * 2: SDT.i STP.i VAVG_i (SDTi Vi) (A.9) 2: l CFIXi = TEAMSi* (TRAIN.i + £01 * PMNTi) (A.lO) (SDT V ; SDPi = SDRC or SDRS) Using all of the above values, the following simplified, approximated equations result (A.ll-A.l6). These equations are extremely useful in estimating partial or total costs for given levels of information quality. The figures for Table 9.4 are derived from an application Of these equations to the raw averages of Table 9.3. _ 2 ”nutrition — .0059/SDND (A.ll) _ 2 _ _ “consumption - l0.6/SDRC (A.l2) ' 2 = A.l3 "storage 9.2/SDRS 1.297 ( ) -——2 = + SAMPT A.l4 CSURnutrition 875,000 + (5000 SDND ) / ( ) l4058 ( = , l , + 5000 + 2 SMPRC A.l5 CSURconsumption l 3 2 500 ( 7086 SDRC ) / ) CSUR = 875,000 + (5000 + SDRS2 ) / SMPRS (A.l6) storage 315 Table A.4 Fixed Cost Parameters and Variance for Total Cost Calculations Survey Fixed Cost Parameters Variance Type Teams Train E0 PMNT VAV6 (#) (1900 Won) (1000 Won) % Nutrition 25 10 20 1.25 1.0 Consumption 25 3O 18 1.25 0.2 Storage 25 20 12 1.25 .066 APPENDIX B FORTRAN COMPUTER PROGRAM T ...2u- .UCL Tufvuu .L 95 TD. 9 .\9 GMT Du 991“." (u chVTV CCUn..N T. ONT 9 (:.nSQu) MO 90a... f..7..nh-Cl. OSU 9‘ I..CA\.XH|. A 9? 8N afiUVITX .IRCS 9 PCV 9C) FIBUCO Drunk... ,a.‘ T ’R)!‘ .UGU.....~. TOSTX LECTIV. 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Pu ab...» “LC; LD + CYRSUR = CCE COSTGX TOTLL COSTS CF.C CCSTGY CCSTGP ¢ THU. 0R vIU CLlpJ RU.»‘UH About. 1? DLGES PRINT. 7 12/28/79 0'! ‘U 14:17 BIBLIOGRAPHY (2) (3) BIBLIOGRAPHY Abkin, Michael H., Policy Making for Economic Development: A System Simulation of the Agricultural Economy of Southern Nigeria. Unpfiblished PhD dissertation, Department of Electrical Engineering and Systems Science, Michigan State University, East Lansing, Michigan, 1972. "And now the horror of famine," Time, vol. 114, Ocotber 22, 1979. Anderson, M.A., ”Use of height-arm circumference measurement for nutritional selectiviey in Sri Lanka school feeding," American Journal of Clinical Nutrition, vol. 28, July 1975. Arnold, R., "The QUAC stick: a field measure used by the Quaker Service Team in Nigeria,” Journal of Tropical Pediatrics, vol. 15, December 1969. 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