ungAmss remove this checkout from ”- your record. FINES wiH ——f be charged if book is ‘ returned after the date stamped be10w. 1 M804 RETURNING MATERIALS: P1ace in book drop to E SE???) "‘3 :‘5‘ [FEB o 7 199;; SIMULATION AND CONTROL OF A LARGE-SCALE LOGISTICS SYSTEM HITH APPLICATION TO ,FOOD CRISIS MANAGEMENT by Aliakbar Arabmazar A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering and Systems Science. 1983 ABSTRACT SIMULATION AND CONTROL OF A LARGE-SCALE LOGISTICS SYSTEM WITH APPLICATION TO FOOD CRISIS MANAGEMENT by Aliakbar Arabmazar Logistics has always been a part of relief operations. But balanced distribution, meaning the need to keep supply and demand in balance for the entire domain of operations and optimal allocation and use of existing resources are not usually considered. Unbalanced distribution of food and a waste of resources have always been the cause of more fatalities than the scarcity of aid. These problems could be greatly alleviated by efficient planning and development of strategies for rational management and optimal allocation of available resources. In this dissertation, a simulation model of a logistics system is presented as one approach to the above planning and control probl ems . The design of the logistics system in this study has been based more on temporal structure and economics than spatial. The model is composed of six major parts. The port, regional warehouses and roads, supply and demand, information and data acquisition, capital devel0pment process, and the cost function. The model is equipped to simulate various ship arrival patterns, population movements and road breakdowns with possible transshipments. Ship arrivals, docking, and the informa- tion acquisition process are modeled in discrete time, where the rest of the system is continuous time. The information sampling component enables the model '5 "true" variable values to be disturbed with specific Aliakbar Arabmazar measurement error statistics. Sampling frequency, sampling error and processing delays are applied to model variables, thereby simulating surveillance sampling results received by system managers. Available information plays a vital role in the successful imple- mentation of the designed policies. Due to a general lack of data on famine, there is an inmense need to extract maximum benefit from the gathered information. Two estimation methods resulted from an extensive search in the literature, keeping in mind the characteristics of the process generating the data. These were the Extended Kalman filter (parameter identification via state augmentation) and the adaptive :w-B tracker (time-varying B parameter). When high uncertainty exists regarding the initial values of the demand model's state variables or its trajectories are partially known (common conditions in famine relief efforts), the adaptive a-B tracker performs much better than the Extended Kalman filter. Logistical policies are composed of two different but highly inter- connected decision rules, these being food allocation and capital acqui- sition. The model has been used for the design and experimentation of various policies. There are several performance measures based on the level of service and total cost, which are used for policy evaluation. Several general principles for relief logistics emerged from the study. "Nell" stoCked regional ‘warehouSes speed up grain shipments out of the port, thus reduéing ship waiting time and providing better service at the regional level by compensating for errors in information. A more uniform arrival of aid reduces port congestion hence lowering the total cost. The expected rate of food arrival and the level of the port's silos are important variables in capital acquisition Aliakbar Arabmazar policies. The existence of several conflicting objectives poses new difficulties in the search for Pareto Optimum control strategy. By systematically investigating policy alternatives and the range of choice of important state variables, grounds have been laid for further Opti- mization work. The dissertation concludes by indicating major results, areas for further research and possible extensions. To my parents, who have always made decisions as if their children were their only objective ii ACKNOHLEDGMENTS I wish to eXpress my gratitude to Professor Thomas Manetsch for his guidance, encouragement, and timely comments throughout my doctoral program and research. I also thank members of my thesis comittee, Professors: Frank Mossman, John Kreer, Gerald Park, and Robert Barr for their help and teaching. I am thankful to Judith Ghosin for her editorial assistance and to Rebecca Mather for typing this dissertation. I 111' TABLE OF CONTENTS LIST OF TABLES ........................... vii LIST OF FIGURES ........................... 1X CHAPTER I. INTRODUCTION AND PROBLEM DEFINITION ............ 1 Structure of Logistics System ................... 9 Design of Logistics Support System ............... 27 The Approach .......................... 30 Summary ............................. 31 CHAPTER II. THE LOGISTICS MODEL .................. 32 The Port Model ......................... 32 Regional Warehouses and Roads .................. 4g Roads and Delays ...................... 50 Road Breakdowns ....................... 53 Supply and Demand ........................ 55 Modeling an Information System ................. 70 Sampling Components: SAMPL and VDTDLI ........... 72 Capital Acquisition Model .................... 77 The Cost Function ........................ 33 Additional Model Features .................... 92 Summary ............................. 94 CHAPTER III. STOCHASTIC ADAPATIVE ESTIMATION WITHIN THE FAMINE INFORMATION SYSTEM ......... 95 The Demand Model ........................ 97 Filters and Predictors ..................... 98 General Concepts ...................... 99 iv V Classification and Analysis of Estimation Approaches . . . . TOO Stochastic Methods ..................... l0l Deterministic Techniques .................. lOS Information Characteristics ................. l08 Nhat Method to Choose ...................... llO The Selected Models 5 . . .................. llZ Alpha-Beta Tracker ..................... ll3 The Kalman Filter ...................... ll6 Description of the Demand Model ................. ll8 State Space Representation ................. l20 Two Probability Distribution Functions ........... l22 Modifications of the Estimation Models ............. 123 Extended Kalman Filter ................... l24 Adaptive Tracking ...................... l28 Evaluation Tool ....................... l3l Testing the Estimation Models .................. T32 Sampling Method ....................... l33 Sample Size Determination .................. l34 First Phase of Sampling . . . _ ................ 137 Second Phase of Sampling .................. l4O Analysis of the Tracker Results ............... l43 Analysis of the Kalman's Results .............. l45 General Comments and an Example ............... l47 Partially Known Trajectories ................ l48 Transient Initial Conditions ................ 154 Adding the Filter to the Model ................. 165 Summary ............................. l65 CHAPTER IV. MODEL VALIDATION .................... l68 Consistency Tests ........................ l69 Conservation of Flow .................... l7O Sensitivity Tests ...................... T72 Model Structure Change ................... T79 Simulation Interval DT ....................... l85 Sumary ........................ ' ....... 188 vi CHAPTER V. CONTROL AND POLICY DESIGN ................ T90 Scope and Nature of the Control Problem ............. 191 Performance Indices ....................... 195 Control and Decision Making Model ................ 202 Policy Structure ........................ 203 Two Main Decisions ..................... 206 Food Allocation Policies .................... 207 Capital Acquisition Policies .................. 2T3 Conversion Factor ...................... 2l5 Initial Capital Development Stage .............. 216 Capital Development During the Crisis ............ 2l9 Main Acquisition Policies .................. 224 General Logistical Policies ................... 233 Policy Results Analysis ..................... 239 The "Pareto Better" Policy ................... 245 Testing the Policy Robustness . . . . . . ; ......... 249 Summary . . .' ........... . ............... 259 CHAPTER VI. SUMMARY AND CONCLUSIONS ................ 26l Sumary . ............................ 26l Major Results and Conclusions . . . . . . . . . . . . . . . . . . 265 Further Analysis of the Model .................. 269 Improvements and Extensions ................... 272 Concluding Remarks ....................... 278 APPENDIX A. Numerical Cost Coefficients .............. 280 APPENDIX B. FORTRAN Computer Program ................ 284 BIBLIOGRAPHY ............................ 33) 3.1 3.2 3.3 3.4 4.1 4.2 4.3 5.1 5.2 5.3 5.4 5.5 5.6 LIST OF TABLES Expected Values of Mean Squared Error and Its Variance by Various Estimation Schemes in the First Stage of Sampling ................ l39 Expected Value of Mean Squared Error with 95% Confidence Limit in the Second Stage of Sampling by Various Adaptive Schemes ............ l42 AMSE Value by the o- B Tracker and the Kalman Filter for the Case of Partially Known Trajectories ...................... l54 Expected Value of Mean Squared Error for Transient Initial Conditions ............. -. . . . l60 The Conservation of Flow Test on the Numbers of Trucks and Drivers in Various Times ............ T73 Effects of Varius Ship Offloading Capacities on the System Performance Indices ............... l76 Error Percentages in the Total Number of Trucks as a Function of the Time Increment, DT ............ l87 Policy Parameter List ..................... 234 Averages and Standard Deviations of Overall Performance Measures for Selected General Policies (ten Monte Carlo replications) ............ 236 Averages and Standard Deviations of Regional Performance Indices for Selected General Policies (ten Monte Carlo replications) ............ 237 Means and Standard Deviations of the Overall Performance Criteria for the "Pareto Better" Policy (ten Monte Carlo replications) ............. 247 Means and Standard Deviations of the Regional Performance Measures for the "Pareto Better" Policy (ten Monte Carlo replications) ............. 248 Results of the Robustness Test Due to New Demand and Supply Functions . . . . . . . .- .......... 252 vii 5.7 5.8a 5.8b viii Results of Policy Robustness Test with Population Movement Scenario ....................... 255 Mean and Standard Deviation of Overall Performance Indices Resulted from the Road Breakdown Robustness Test ................ 257 Regional Performance Measures Resulted from the Road Breakdown Robustment Test ............ 258 1.1 1.2 2.1 2.2 2.3 2.4 2.5 2.6 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 LIST OF FIGURES Major Sub-systems and Linkages in Famine Relief Logistics System .................... ll Logistical System Identification ............... 25 Model of the Port and Its Facilities ............. 34 Histogram of Grain Heights by Actual Ship Arrivals (Bangladesh) .................. 37 Probability Distribution Approximating the Actual Tonnage ........................ 39 Model of a Regional Warehouse and Its Connection to the Rest of the System ............. 50 The Demand and Supply Functions ................ 68 Capital Development Process .................. 79 The o-B Tracker's Estimate of a Chosen Trajectory (SAMPT = 2) .................... 149 The Extended Kalman's Estimate of a Chosen Trajectory (SAMPT = 2) ................ 150 The 6-6 Tracker's Estimate of a Chosen Trajectory (SAMPT = l) .................... 151 The Extended Kalman's Estimate of a Chosen Trajectory (SAMPT = l) .................... 152 The 0-8 Tracker's Estimate of a Partially Known Trajectory (SAMPT = 2) .................... 155 The Extended Kalman's Estimate of a Partially Known Trajectory (SAMPT = 2) ................. 156 The 0-8 Tracker's Estimate of a Partially Known Trajectory (SAMPT = l) .................... 157 The Extended Kalman's Estimate of a Partially Known Trajectory (SAMPT = 1) ................. 158 ix 3.9 3.10 3.11 3.12 4.1 4.2 4.3 4.4 5.1 5.2 5.3 X The 6-8 Tracker's Performance when High Initial Uncertainty Exists (SAMPT = 2) ................ 161 The Extended Kalman's Performance when High Initial Uncertainty Exists (SAMPT = 2) ............ 162 The 0-8 Tracker's Performance when High Initial Uncertainty Exists (SAMPT = 1) ............ 163 The Extended Kalman's Performance When High Initial Uncertainty Exists (SAMPT = 1) ......... 164 Estimate of the Demand for the First Region .......... 180 Estimate of the Second Region's Demand ............ 181 Third Region's Demand Estimate ................ 182 Estimate of the Demand for the Fourth Region ............................ 183 Multilevel Hierarchy of Control ................ 193 General Description of the Decision Making Component ....................... 204 New Supply and Demand Functions for the Robustness Test of the "Pareto Better" Policy ......... 250 CHAPTER I INTRODUCTION AND PROBLEM DEFINITION When food is abundant, it is wasted or treated as a commodity. But when food is scarce, it is regarded as the staff of life and its distribution becomes a highly emotional issue. Food production worldwide is increasing faster than the population, but distribution is uneven, reserves are limited, and bad weather conditions could lead to widespread famine (1). While food production may expand 90% (that is optimistic) by the year 2000, the per capita increase will be less than 15%. This global estimate disguises regional disparities; food availability and nutrition levels may scarcely improve in South Asia and the Middle East and may actually decline in the poorer parts of Africa (46). The likelihood of man-made catastrophe is, growing, and even many of the so-called natural disasters such as famine are caused at least in part by people (31). DeSpite all efforts, the history of man is punctuated by frequent famines. There has been a serious famine somewhere practically every year since the end of World War II (78). Except perhaps for nuclear war, nothing in our time so threatens a majority of the world's peOple as does the specter of hunger and starvation. In spite of all the devel- 0pment programs, the technology transfer, and the "miracle seeds" of the so-called Green Revolution, the prospects for eating a reasonably 1 2 nutritious diet seem increasingly dim for hundreds of millions in the 1980's and beyond (44). Catastrophic results of a famine can be seen in the recent Cam- bodian one. At least two million pe0ple were believed to be on the verge of death by starvation or disease. Many had been reduced to eating the leaves off .trees peeling the bark and boiling it, and digging for tubers and roots. Malaria was comonplace, as was a severe form of bleeding dysentery (4). One of the worst famines in modern history struck Honan province in 1943, and as many as five million Chinese perished (126). Famine usually comes with widespread crop failure; but the factors which cause this failure are different and diverse. Natural disasters such as floods, earthquakes, droughts, crop diseases or pests form one group and another is formed by the impact of wars and civil disturbances on both crops and farmers. Some examples of famine and its causes are: successive crop failure due to drought and flood in India, Sahelian drought as desert advances, earthquakes in Latin America and Asia like Iran, civil war in Africa, locusts in Middle East, and a conflict of superpowers in Cambodia. Food crisis can be thought of as a consequence of ecological crisis. In the poorer countries of the world, hunger is often directly connected to the deterioration or the destruction of ecological systems that could provide a harvest of plenty instead of continuing food short- ages (44). One of the major factors contributing to the Sahelian drought is the disruption in the ecological system caused by centuries of impro- per land use and ever-increasing pressures of’ both human and animal p0pulations on available land resources (38). In most of the famine prone countries, ecological deteriorations which have caused the 3 evolution of periodical droughts, have been direct consequences of years of colonialism and international capitalism (19), (44). French politics in Sahel resulted in chronic hunger. Production of cash crops meant a reduced production of food. When less was grown, there was less to store as a reserve in case of a natural or economic disaster (44). The ecological destruction has been widened by desertifi- cation, deforestation and woodcutting which have been a much more serious threat to the ecosystem, (38), (93), (124). Drought causes at the same time crop and income failure for those populations whose main source of income is subsistence agriculture or grazing. Assuming that there is food for purchase outside the affected area, income failure prevents the affected populations from acquiring it (21). The following problems can be discerned in a drought-stricken state:. great suffering, damage to the local economy, widespread migra- tions of people and animals, and cities dangerously overcrowded with thousands of helpless imigrants, bent on finding jobs that will allow them and their families to survive (36). The relationship between ecological destruction and food production is thus direct and close. Whenever an environment is degraded, deprived of its basic resources, or often of even one of the key resources, that environment becomes a part of the world food crisis, and the people ‘ who live there become its victims. These observations show that if famine is to be understood and controlled, there must be an understanding of it's ecology (95‘). It is apparent, however, that famine has major ecological roots and impacts. We must therefore examine these, and seek ecologically sound short-term responses to alleviate occurring famines, and long-term programs to prevent future famines (25). A food crisis is not only a matter of food shortages, inadequate 4 nutrition, economic conditions, and population policies. It is also a matter of politics, both national and international. Indeed, in many ways politics is one of the underlying causes of the current food crisis ('69). Politics have also been an obstacle to relief operation in one way or another. The classic example is the case of famine in EthiOpia between 1973 to 1975. Two coverups took place. The first by the govern- ment of Haile Selassie and the second by the international relief agen- cies and donor nations. The latter group remained silent as the Selassie government requested, despite what its members knew was happening to the Ethiopian people (105). The literature is filled with examples of influences of internal or national policies on relief operations. Refusal of aid by host governments (45), their hesitation to ask for aid (39), (125), and inter- nal corruption (37), (42), (71), (89), (119). As prices rose, at one point the Ethiopian government offered to sell 4000 metric tons of grain it had in storage to the United States, which could then donate it back for relief inside Ethiopia (105). It is important to recognize that internal policies and politics contribute to shortage. Poverty is caused by uneven distribution of resources which in part is an offspring of internal corruption of governments. "Famine is a vogue word, the problem is poverty (123)". Poverty has been an contributing element in famine (130). The real problem faced by the Sahelian countries is not the possibility of a recurrence of the drought but their overall poverty year in and year out (124). Despite a growing population and increasing demands of that popula- tion for improved diets, it appears that the world is not close to universal famine. That people are malnourished or starving is a question of distribution, delivery, and economics, and not agricultural limits. 5 The problem is putting the food where the people are and providing an income so that they can buy it (128). Famine affects both individuals and the society as a whole. It has sociological, psychological and physiological effects (62), (130). Large-scale starvation, increase in death rate of both human beings and large farm animals, social disruption, spread. of’ epidemics, and destruction of seeds for future crops have been devastating consequences of famines. It has uncureable and permanent physiological effects on individuals. The physiological response of the human body, in its broad- est nature, is one which reflects adaptation to the patterns of food availability and shortage that characterizes man's evolutionary history (25). DenHartog describes different kinds of adjustments in detail (29). The psychological state of people deteriorates rapidly causing an increase in mental restlessness and crimes. Obsession with food and apathy and despair become widespread (130). In some cases cannibalism also happens (1%). The stress of the destruction of the familiar environment causes perceptual abnormalities, the illusion of centrality, a reduced sphere of awareness, etc. Sections of society most vulnerable to famine depend very much on the circumstances of the famine, rural or urban setting, cultural factors, physical work requirements, etc. It has also long-lasting influences on culture and social behavior of the maple of stricken regions. In extreme cases of starvation, the breakdown of family units occur and food taboos spread (130). The drought and subsequent famine caused serious long-term damage to Ethiopia. Traditional patterns of society have been broken; in some areas there was little for the Ethiopian peasant to return to; whole villages dead, a way of life shattered. A vast population of abandoned 6 mothers with children roam the land (.105). Unfortunately, the threat of famine is still with us and its pri- mary causes are operative. A series of crop shortfalls in the U.S.S.R., South Asia, and North America in early 1970's and the failure of the major producing and consuming countries to prepare for the event shows how much susceptible the nations are to famine (.100). The Global 2000 Report (46) offers a gloomy view of the world 20 years from now if governments fail to act. The result of three years' analysis of probable changes in world population, resources and environment through the end of the century, the report warns that unless nations do something now to alter the trends, the earth's capacity to support life will decrease while p0pulation growth continues to climb; there will be a steady loss of croplands, fisheries, forests, and plant and animal species; and there will be degradation of the earth's water and atmosphere, all in the next 20 years. It suggests that sufficient resources of basic food should be available for prompt response to a major shortage. Prediction is that population - food collision is inevitable, and iminent famines in Latin America, Africa and Asia are expected (23), (28), (44), (45). Famine in the Horn of Africa is not an event of the past, but of the future; it is cyclical (105). If rainfall in the Sahel is regarded as a stationary random variable, normally distri- Abuted, then a further drought with four or five consecutive years with below-normal rainfall can be expected by the turn of the century (129). Already the news about the drought is coming from Sahel countries. Reports from Senegal, Mali and Mauritania show that rainfall is already delayed in the region (32), (90), (98). There is little doubt that regions in these countries are seriously short of food and that unless supplies are expedited, there is the danger that as the hungry season 7 continues, later seeds and other stocks in villages will have been com- plete1y consumed by people and livestock scratching around for anything on which to subsist (75). "Conditions now are worse than those of the early seventies in several western Sahelian nations, which face a crisis of critical proportions ( 97)". Both the potential of famine and the capacity of human society to avoid it are greater today than ever before. So whatever the primary cause of famine, we must be able to offset it. Because of the urgency for action following a disaster there is little time available for plan- ning, assessment and coordination, personnel may be inefficiently utilized and scarce resources misdirected. It is, however, possible to provide a constructive approach to effective relief planning and administration for future disasters in developing regions of the world (23). Food shortages may have different origins but famine differs from most other disasters in that it is usually predictable well in advance and is often, theoretically, preventable. The disaster could be greatly alleviated by efficient pre-planning by a government agency (75). The basis for relief is to obtain and make available sufficient food to stop the developing famine, maintain the population in body'*weight balance, and eventually rehabilitate the population (78). Planning and development of strategies for rational management and Optimal alloca- tion of existing resources play an important role in reducing catastro- phic results of famine. Indeed, having a better strategy to make better use of available food can lead to significantly higher survival rates in the afflicted papulation (73). It is obvious that the whole process of disaster relief is carried on in totally unconventional and emergency circumstances which in modern 8 times, at least, has tended to infiltrate the total life of the nation. There is a wide range of problems encountered in planning and implement- ing the relief operations depending on size and duration of disaster and the region in which it is happening. With much of the structure of society broken down, lack of informa- tion and data, different political obstacles, it becomes very hard to have a clear picture of the most pressing needs and the scale of them. The poor transportation system of less developed countries and breakdown of main bridges due to earthquakes or floods which also wash away the roads and rails, make distribution of available foods and communication with stricken regions difficult (82). The desperation of the people and the deteriorating situation throughout the Sahel zone made it clear that even the largest of relief operations undertaken by the national governments could not meet more than a small part of the growing require- ments. Not only did the governments lack food, feed and other supplies, as well as funds, but they also lacked the infrastructure and distribu- tion facilities for massive relief operations (33). Frequent occurance of famine in less developed countries and longer duration of crisis, relative to the other forms of disaster such as floods and earthquakes, allow more lead time for better prediction and preparation in order to reduce the impact and results of famine. Yet the problems encountered, the assumptions, techniques and forms of organization required vary, depending upon country and the type of crisis. In general, disaster relief activities are characterized by a lack of understanding of the under development context, by lack of planning and by an obsession with emergency. Some donors are self- interested, disregard national sovereignty, ignore the villager's need for self-determination, and are incapable of using local resources. 9 Disaster relief operations can have numerous objectives. Minimiza- tion of the total number of deaths has been cited as the ultimate goal (25), ('78). Equitable and timely distribution of food, optimal use of existing resources, improvement of nutritional status of peOple while disrupting cultural patterns as little as possible, adjustment to the nature of the local crisis (25), higher survival rates, safe keeping of the food, and preventing the spread of epidemics are other desirable ends. Attainment of these objectives is constrained by limited aid, time, money, equipment and personnel. The basic problem in food shortage is the optimal allocation and distribution of existing food to those who need it and in times when it is needed with minimum cost. Different systems are necessary to fulfill this task. Goals of relief operations set the priorities and clear the way in which these systems should interact. Major support systems are information and resource acquisition, logistics, and communi- cation. Education‘ and training programs at field levels are also required. The effectiveness of operations is in direct proportion to the degree of integration and coordination achieved among the various support systems. Support which is disjointed obstructs existing capabilities. Interdependency cfl’ support systems requires recognition and application at all levels of relief operations by personnel involved. By keeping in mind the other support systems, the emphasis in this dissertation will be on logistics systems. Structure of Logistics System The USAID Report to Congress on Famine in Sub-Sahara Africa sum- marized the enormous problems of transport and communication in the .0 10 following terms: "In 1973 there were times when ships were hard to obtain because of massive world-wide grain movements. Ports in West Africa are poorly equipped to handle huge shipments and there have been port congestion problems, particularly this year. Railroads were often inadequate to move food inland on a timely basis. There are few paved roads. Ferries are slow and inefficient. River transport is important but capacity has been inadequate for the amounts involved. Roads leading to many outlying distribution points where nomads are congregated are difficult at best, impassable when the rains come. Few trucks, and problems of their maintenance, have often caused difficulties. Lack of storage has been a problem. The complexity of managing relief opera- tions of this nature, involving six recipient governments and a number of donors under extremely difficult physical conditions, is without precedent (41)". The significance of logistics in disaster relief operations is clear. Economics limits the available food and resources for relief, logistics limits the mobilization and use of resources which are avail- able. Modern logistics is defined as the process of strategically managing the movement and storage of comodities from point of supply, through facilities involved, to the point of consumption (11). Logisti- cal activities consist of transportation, inventory, facility location, communication, handling and storage. . Figure 1.1. illustrates the general structure of famine relief logistics system. Blocks show the major sub-systems involved. Three important linkages are recognizable. Necessary information such as storage levels, demand for fOOd and other commodities, movement of the population, orders of shipments and transshipments flow 'through 'the comunication link. Transportation link contains air, railroads, river . _. __..__._.._..__| Regional 0 Warehouse 91 .— 11 System Managers and / or Decision Makers and/or Country e—e—o—O—O—OTO 0—0—0—0 —O——e-—o—r—O O -P-‘“'_l. o . i Regional Regional ' Warehouse Harehouse ! A 2 9 3 l r ""“ . . l , I I : 1 l 1 i 1 I ' | L \ I L 1 . 1 \ I | l ' 1 ,’ I 1 1 ‘ I ' ° 1 I 1 1 1 1 ' ' 1 l 1 1 1 1 Regional 1. 1 Warehouse ‘ 1 1 1 f 1 I 1 1 I 1 1 l 1 I 1 1 I I 1 I 1 1 1 '1 ' : 1 i 1 l L‘.. ‘ ---- -- - - - - A 1 Port and its __ __ Facilities u-o- (Io-limitation Link . O '—9 (Data , Order) a? ----- Transportation Link 0 Ships ( Trucks , Drivers ) oe“. <3 Goods Link 0 ._~‘_. _ £1 ( Grain.Fuel.Spare Parts 1 ‘T“' Rest of the Horld CH Local Goods Link (:)-) Goods Link to Sub-regional We: .Figure 1.1.Major Sub-systems and Linkages in Famine Relief Logistics System. 12 transport, trucks and drivers. Movement of food, fuel, spare parts, and maintenance personnel form the goods link. Arrows show the direction of flow movement, either unidirectional or bidirectional. The local goods link symbolizes the help from the region itself which is mostly local food reserves and production. The goods link to sub-regional warehouses is the connection with field offices and final destination, which is affected people. Design of logistics support systems can be considered as an aid for system managers and decision makers who are responsible for total relief system. The process of movement of supplies from ship to affected people entails a series of highly synchronized functions, the failure of any one of which could have a resonant effect, reverberating along the entire line of conmunications. At no time are all the components of the structure in perfect balance. Indeed, the elimination of one limiting factor sometimes creates another at a different point. The elimination of the deficiency in one of the transportation links, for example, makes the forward storages one of the main strictures, for they are unable to receive the large tonnages which the link has become capable of forwarding. "For the donor countries, the major problem has been to select the best means of transporting huge quantities of relief supplies (40)". The history of logistics operations seem characterized by a succes- sion of alarms over one critical deficiency or another, and the theater has been occupied at all times with efforts to eliminate some bottleneck and to bring the system into balance. As already stated, the inadequacy or the breakdown of the delivery system is one of the main problems. Whatever the food commitment on the part of the international community and whatever consignments have reached the points of entry of the 13 affected country, the food deficit has usually reached such a degree that existing intra-country delivery systems are in most instances, inadequate to deliver on time sufficient food to families and individuals in the affected areas (2), (21), (44), (71). "August 6th, 1973. Report from the Field: 10,000 in Bati, and 15 per day dying of starvation at the relief center Farmers eating seeds in Werababu 50 Danakils in the province of Tiger are dying daily of famine. They have grain, but no means of getting it to the Danakil region (105)." Total disruption of comunication and transport system following a disaster always hampers the relief operations (92), (94). Logistical difficulties are often the major limitation of a relief operation (3), (48), (.84). Existence of adquate transportation infra- structure is a key factor to prevention of famine (25). "The material development of Africa may be sumed up in one word - transport (124)." In his classification of different types of famine, Dando (28) identifies “transportation famine" as one of the basic ones. The earth is ringed with a disaster belt south of the equator, Dr. Rudolf Frey of the Club of Mainz points out (31). Within this disaster prone region are many undeveloped countries which lack the financial resources, expertise, and equipment to respond to emergencies. Sahel countries are the best example. The territory is vast and sparsely settled, distant from seaports and lacking in railroads and adequate highways; it has been exceedingly difficult to get food, medicine, and other emergency supplies to the places where they are most needed (35). Transport generally - road, rail, river and by other means - is the biggest bottleneck (27), (33). (41). Selection of the best means of transportation is another important issue. Air transport has some advantages. Relief supplies can be l4 delivered quickly when speed is critical. Aircraft: can transport food, medicine and other conmodities to the interior where it is urgently needed. But air transportation has high operating costs (per unit of cargo) and limited capacity. The aircraft also requires elaborate sup- port facilities for optimum service: airports and landing strips; tech- nical personnel able to handle tower control and ground' directions; and, above all, quantities of fuel readily accessible. In order to appreciate the logistical problems, it is important to remember that of the six Sahelian states only two have direct access to the sea. Others have to rely on the port and transit facilities of neighboring countries (40). Although ships carry far more cargo per voyage and at cheaper rates, they also pose different problems. One of the main problems is congestion. Underdeveloped countries have ports with a very limited handling capacity. Congestion causes another problem, meaning the shortage of suitable storage facilities. Perish- ability of bulk of supply items intensifies this problem (33), (40), (91). (105). When regular warehouse storages are full of grain, relief supplies are stacked in the open where they start to rot. "The rats feed well at Dakar," cabled a reporter to the Guardian on July 24. "Some of those stocks will still be on the wharves in November," he wrote of the trans- port tie-up, "if the rats - the only fat animals I saw in West Africa - leave any at all (104)." “The estimated 1985 production of 450 million tons of cereals will, at 2000 calories a day, give us 45 billion person- days of food. At least it would if it all got into people's mouths. Unfortunately much of it goes to insects, rodents, and microorganisms (51)." Security of food is another task. There is need for adequate protection to prevent excessive losses from moisture, insects and theft. 15 Railroads offer by far the cheapest means to transport commodities inland. It is estimated that shipping by rail costs 25-30 percent less, on the average, than trucking, the next cheapest means of transport (40). Ability to haul bulk comodities, all weather functioning are other advantages. Yet there are problems here too. The railroads are fairly antiquated, single-track systems, with different gauges, and any malfunctioning seriously disrupts traffic. This happened in July 1973 when a derailment prevented trains from reaching Mali, depriving that country of one-half of its normal supplies at a particularly criti- cal time (40). River transport should be considered in the design of relief opera- tions. Although it is a viable alternative in some parts of the world like north-eastern India and Bangladesh, it has not been an important mode in relief logistics in Africa. In a drought situation, the rivers are usually below normal levels. Also, owing to the river's shallow channel, it takes only light barges. Road transport has played an important role in the effort to deliver relief supplies. Although the road quality varies from country to country they usually connect the capital cities with administrative centers and major coastal ports and many remote towns and villages. Usually underdeveloped countries have trucks and other types of vehicles which can be utilized. Since they are driven by local drivers which are familiar with the region and roads, it has the advantage of creating jobs for a substantial number of people. Also, trucks critically comple- ment the railway systems. "In the long run, the most effective way of getting relief to the Sahel's interior is by road (40)." Road transport has its own bottlenecks. Bad and incomplete infra- structures of road networks, weather dependability, long distances 16 between cities, lack of suffiCient number of trucks and maintenance are some of the problems encountered. No two disaster relief operations will necessarily be faced with identical requirements (25), (45). While their logistics problems will contain many similar aspects, there will always be important differences. In all cases the logistics will have certain critical items, certain important issues, and a vast amount of subsidiary detail which 'may easily obscure the critical and important factors. Almost never will all logistic requirements be satisfied in an exact balance, and as long as that is true some phase of logistics is bound to be the limiting factor. In all operations, transportation, fuel, technical spare parts, and technical repair personnel will be critical (17), (33), (40). "There is no point in sending lorries without supplies of spare parts and per- haps without directly ensuring their fuel supplies in Chad, for example, twelve lorries were meant to be distributing relief food but were immobilized by a shortage of fuel (41)." There will be a con- flict between demand for transportation to carry food and the spare parts. Mayer suggests that "maintenance personnel are as critical as logisticians and drivers; spare parts may have to take priority over food (78 ." System managers should have prior knowledge of the logistics limitations. Every logistics endeavor must be guided by a clearly stated objec- tives. The objective to the greatest extent possible, must be so speci- fied as to permit continuous measurement of the degree of accomplishment of the endeavor toward the objective. The logistics objective is valid only in so far as it supports the overall objectives. Therefore, the propriety of the logistics objective must constantly be reappraised 17 in the light of the intentions of total relief operation. There must be a flexibility of logistics support. Responsiveness to the needs is most readily assured through adaptability of logistics which is the basic measure of flexibility. The capability to react rapidly and reliably to changing situations, is a mark of effective logistics. One of the chief problems which usually follows disaster is a lack of organization and coordination of the relief efforts made by the various agencies involved. To improve the efficiency of relief operations, it is essential that every country should prepare a national disaster relief plan (8),. (88), (111). Many difficulties stem from lack of coordination among individual efforts undertaken by various national and international groups, and by failure of these groups to work effectively with local governments (25). "The difficultlogistical problems involved in supplying the more remote areas of Mali with food, medicine, and other essential comodities are further complicated by the inefficient use that is made of existing transport facilities (34)." Weak administrative organization and management in the rural areas of India is one of the causes for creating problems in devising and imple- menting effective food policies (43). Coordination is one of the main stumbling blocks. Referring to relief operations in Biafra, Western (125) found an extreme lack of coordination between agencies and haphazard distribution methods such that some areas were receiving aid regularly from several agencies and others were not receiving any. It is not enough merely to have the right resources; rather the right resources must be at the right place at the right time. This is a foremost objective of logistics flexi- bility. It is an objective to be attained through responsiveness, a 18 condition of flexibility. Control of the performance of logistics involves a management effort. A measurement of logistics to assess its efficiency in terms of economy and effectiveness must be made internally and externally. Although internal measurement of the logistical activity may give con- siderable emphasis to cost minimization, external measurement must empha- size effectiveness. Of these, the latter is the only reason for logis- tics. The essence of successful logistics is to do more with less through an economy of resources. Economy of resources seeks to avoid depletion while assuring that needed resources are readily available. It is achieved not only through an exchange of quality for quantity but is predicated on a continual striving for the most effective management of resources. Pe0ple, supplies, and facilities may be designated as basic resources. Services, transportation, and comunication constitute func- tional resources. The virtue of accomplishing a logistics task with the least quantity seems obvious. Yet there is danger in interchanging the words "economy" and "least". The latter may be too little while the former suggests providing no more than the minimum amount and degree of support needed to do the job effectively. "Least" implies, primarily, quantity, "economy", on the other hand, involves a combination of quality and quantity. The nature of "economical logistics" is not necessarily that of least quantity but involves an input of quality so that mission accomplishment is in fact enhanced rather than jeopardized. Money, time, and technology are to be thought of as "determinant resources" in that they determine to a large extent the quantity and quality and proportions of basic functional resources which will be 19 available for different support systems. Timing of relief is a very important factor. Often priorities are inadequately' worked out and by the time supplies have reached the area, needs have changed (44), (105). The transport problem was largely due to the fact that aid was not provided quickly enough and at the pr0per times of year to ensure distribution before the rains struck (97 ). -Experience during the recent famines in arid areas of Africa has shown that the main limiting factor has been the lack of funds for the intra-country transportation, storage and distribution of supplies. The foods made available at the points of entry of the affected countries have been in excess of the funds available for transportation, storage and distribution. Donors have been more generous with foods than with funds. Voluntary agencies have been unable to locate sufficient funds for the intra-country delivery of their planned food aid programs. Some local governments in fact were unable to allocate funds for the distribution of relief foods and large quantities of supplies were left at the ports of entry or in the warehouses, undistributed (31). So, acceptable operating cost, low capital cost, and minimum per unit cost of delivering to final destination are desired characteristics of logis- tics system. Of course, there exists the trade-off between mentioned attributes and speed and consistency of operations which are also desired. I Logistics systems should be designed such that it minimizes the deterioration of normal activities at main port and transportation network. Since the fundamental purpose underlying the very existance of relief operations is to provide adequate food for the people in need, safeguarding of food is a very important issue. Contamination, humidity, insects and animals such as rats, and corruption are some of the problems 20 which can be encountered. System managers decisions are based on available data. The impor- tance of an information support system is easily realizable. Existence of it is essential for keeping the total operation in balance and making distribution and allocation decisions. Knapp (64) demonstrates that optimal policy implementation varies with information quality and quan- tity. He discusses the importance and crucial effects of consumption patterns on relief policy and prediction of famine duration. There is usually inadequate and unreliable data regarding the crisis (49). In times of disaster due to disruption of comunication it is difficult to obtain information (27). Acquisition and assessment of information have been advocated for a long time, but have not been applied (2), (91). The most conspicuous failure of the relief efforts from 1968 through 1973 was the failure to gather, retrieve, and use information. At every stage of disaster every piece of information missing added up to yet a larger void. The absense of information para- lyzes planning (104). Some of the causes for general lack of information in less devel- oped countries are: meager budgets for statistical research; lack of trained personnel; vast distances and critical lack of infrastructure; limited internal comunications system; poor record-keeping in outlying districts; and, above all, a population to a large extent illiterate and often profoundly distrustful of anyone seeking information (39). In disaster we are in need of knowing all about different support systems. Appropriate and relevant information will lead to effective management and balance distribution of resources. Of course, we should keep in mind the trade-off between the cost and quality of data. The design of an early warning system is an effective device for famine 21 prevention. If we recognize the signs of disaster early, a whole range of preventive and protective measures can be applied (52). There is a need for early warning indicators that can provide substantial advance warning of food crisis with low probability of false alarms (72)." The United Nations (2) prescribes continuous monitoring of informa- tion on the following four aspects, along with the evaluation and inter- pretation of information. First, is that "geographical zones" where disasters occur should be mapped. Secondly, "meteorological data," that means climate and rainfall, on different regions, in order to iden- tify various conditions and anticipate trends. Third is to report on "the agricultural situation and food supplies, crop conditions, factors responsible for not planting, harvest, bottlenecks in crop movements, food imports/exports, food security, and food relief stocks." The fourth consists of "monitoring political events, wars, civil disorders, and anticipation of probable effects." Capone (21) and Currey (26) also give a list of early warning indicators. During an emergency, the relief foods are scarce and should be given to the people in the greatest need. So we need rapid and objective measurement of nutritional status. Also surveillance of communicable disease must be carried out as part of nutritional surveillance (48). Information on size and trends of demand, population movements, storage levels at different regions, back-logs, transportation network, condi- tions of roads and vehicles, fuel and spare parts provide better manage- ment of logistics system and Optimum use of resources. Not having enough knowledge of the situation leads to catastrOphic results. In short, an information system is the "nerve system" of overall Operation. Field Offices are in direct connection with affected peOple. Here is where the effects of a relief system can be seen. They are , 22 in charge of distribution of food, operation of health clinics and food kitchens. The results of their efforts and the data which is collected by them are used by system managers for ever improving the balance of the total system. For operational efficiency the field unit should be kept small, generally with no more than five or ten persons. Depend- ing on the task and size of the population served, multiple units should be used to provide the services (2). Camps must be prOperly admini- stered. Auxiliary personnel should be from the local peOple and receive fixed and clearly defined monetary or non-monetary salaries. Key per- sonnel should not be from the population affected (48). Field offices are responsible for gathering information and trans- mitting it to the system managers. So data feed back by them is very important for the stability of the total operation. The followings are typical field reports. These are from the 1973 famine in Ethiopia (105). June 20th, "Merca, 30 kms south of Weldiya. The situation is 'very serious. PeOple were seen dying of starvation cattle, sheep, and goats have almost all died." July 2nd, "Medical situation: Bati health center has 100 patients suffering from Amoebic Dysentery, and eight per day die from it." The goal of the logistical mission is to achieve a predetermined level of support at the lowest possible cost expenditure. Clearly ser- vice performance policy and logistical cost have a direct relationship. The attributes of high availability, fast and consistent capability, and high quality have associated costs. The higher each of these aspects of total performance, the greater the cost of logistical Operations. Reasonable balance between performance levels and total cost expenditure is typically the best. Rarely will either the highest ser- vice performance system or the least total cost constitute the best 9. 23 logistical goal. Measurements of cost performance trade-offs are good aids in comparison of different logistics system designs. The estimates of expenditures are needed for alternative levels of system performance. In turn, alternative levels of system performance are meaningless unless viewed in terms of overall relief goals and objectives. Logistical performance is, in fact, a question of priority and cost. With respect to total performance, almost any level of logistical service can be obtained if we are able to pay the price. For example, a fleet of trucks could be held in a constant state of delivery readi- ness. Logistical performance is measured with respect to availability, capability, and quality. Availability involves the system's capacity to consistently satisfy material or goods requirements (11). Availability deals with inventory level. It can be measured by either the total stock-out time or percent- age of stock-out time. We should remember that the consequence of any stock-out is the possible increase in the total number of deaths, and reduction of it is the prime goal of total relief Operations. ,The capability Of-logistical performance.refers to the elapsed time from receipt of an order to inventory delivery (11). Performance capa- bility consists of the speed of delivery and its consistency over time. Here, the following measurements may be identified. Delivery time, or accessibility, which reflects the time required, on the average, for the goods to reach the affected peOple through the logistical system once the order has been received. Variance in delivery time and accessibility is another measurement which may be more critical that the average time. Idle times of trucks, drivers and different facilities are good measurements in reflecting where design could be made more efficient. Waiting time for ships to 24 unload is a good indicator of efficiency and stability of the system. Performance quality relates to how well the overall logistical task is completed with respect to damage, correct quantity of goods (i.e. low error rates), and resolution of unexpected problems (11). There is no use in speedy and consistent delivery of wrong orders. Total amount of goods transshipped, excluding_those transshipments which are due to break down in the tranSportation link, is a good index for quality of logistical performance. Regional equilibrium and balance distribution is another important performance criterion for logistics support systems. Unparallel supply _ and demand will increase the possibility of stock-outs and idle times of trucks, drivers and different facilities. Increase in the variance of delivery time and waiting time for ships are other consequences of unbalanced distribution. Sum of the squares of the differences between supply and demand, integrated over the period of operations is an index which should be minimized to achieve optimum balance. Figure 1.2 shows the logistical system identification. It tries to clarify the relationship between goals and the obstacles which must be removed in order to reach these goals. Logistical performance provides time and place utility. Such utility represents an important aspect of operations. The basic purpose is to assure that the quality and quantity of food and other necessities are in desired locations, in the time and condition needed to success- fully fulfill the relief task. The responsibility here is to design a logistics system to control the flow and strategic storage of food, spare parts and other commodities to the maximum benefit of the entire relief system. 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As the country becomes less developed and poorer the implementation of it becomes harder. Most of the time the major hauler in. rural and in many urban areas is the animal cart. Man himself is a major carrier of food, fuel, and other comodities in rural areas, crowded city lanes, and roadless mountain sections. For example, the International Red Cross in Wollo (Ethiopia) used camels to haul grain as far as 150 kilometers from storage points along the Addis-Asmara highway (105). FAO/OSRO (Office for the Sahelian Relief Operations) financed and organized camel caravans to areas that had become impassable to vehicles. Some 5000 camels were used in this Operation, each carrying a load of 250 Kg. They were sent out in trains of 50 to l00, accompanied by two soldiers of the Niger Camel Corps and the number of drivers required to keep the line under control and moving. Another expedient adopted to ensure deliverence of supplies was to have teams of porters carry bags of grain across flooded points where truck transport was dislocated (33). Political, social and cultural obstacles must be taken into con- sideration. As relief grain arrived at port, red tape delayed shipment inland. The Ethiopian government refused permission to use storage facilities, and relief grain rotted in the rain (l05). Cultural and religious factors often exacerbates the problems. Food taboos and dietary habits are very important. Officials of USAID were surprised by a Washington Post report from Timbuktu that nomads were unable to digest American-donated sorghum and diarrhea is rampant (104). There are more factors in the real world than what appears in Figure 1.1. For examMe, warehouse location patterns. Locational deci- sion in a logistical system design usually centers on warehousing. 27 Determination of the number and geographic locations of them is deter- mined by port location and distribution of affected population. The warehouse location is justified only if it increases the capability of reaching more people or reduces total cost. Locational impact on inventory is worth mentioning. More locations reduces the uncertainty of stock-outs as a result of a shorter replenishment-cycle. Much more thought is needed for richer appreciation of the complexities involved in design of support systems. Design of Logistics Support System The relationships within a logistical system can be classified as spatial or temporal. The spatial structure relates to the combination of facilities and linkages. The temporal structure of the logistical network relates to inventory levels and flow rate (ll). Logistical system design could be based on either spatial or temporal economics but the interaction of spatial and temporal factors should be evaluated on a simultaneous basis. In this dissertation the design is more on temporal structure and economics. It is assumed that the population of the stricken country or pro- vince is about sixty million, which is divided into four regions. The bulk of the aid from different agencies and donors around the world comes in the form of grain by ships to the closest port. System managers and decision makers analyze the information received from different regions, the amount of promised aid from foreign donors, and available logistical capability and then decide about appropriate allocation of aid to each region. Assigned aid then will be carried by trucks to corresponding regional warehouses. Transshipments allow for needed flexibility in the case of breakdown of transportation links between 28 two points, or unexpected demand in one region. Available food in regional warehouses is then carried by different means to sub-regional silos and field offices. The affected people will receive food from field offices which in turn provide reports of necessary data to the system managers. Three echelon inventories exist in the system. Port sub-system consists of incoming ships and dock, ship unloading facilities, grain silos and storages, truck and driver’ pools, truck loading facilities, maintenance and repair shops. Each regional ware- house is composed of truck unloading and loading equipment. silos and storages, repair shops, and information surveillance units. The design of logistical support systems involves two policy con- siderations: (a) service performance, and (b) total cost expenditure (ll). The challenge is to establish a balance between performance and cost that results in attainment of the desired return on specified goals. This balance is the logistical policy which in turn provides the manager- ial mandate for guiding system design. Logistics has always been part of relief operations. But balance distribution which means the need to keep supply and demand in balance, and optimal allocation and use of existing resources have not usually been considered. "Application of the latest knowledge and tools for the monitoring and control of relief operations will help to facilitate the most efficient deployment of available resources as well as the effective distribution of relief aid (2).“ Having a good control sub- system not only increases theh performance levels but also decreases the cost. Minimizing the transshipments reduces the cost and minimizing the total time of stock-outs leads to higher survival rates which mean lower total number of death which was prime goal of disaster relief system. 29 One of the factors contributing to the relative inefficiency of disaster relief work is low cost effectiveness due to logistical diffi- culties and the necessity for speed in operations. Forty percent of the value of the relief supplies may be spend on their transport (3). In an interview in LeMonde in mid—l973, Niger's then president said that the cost of transporting 20,000 tons of cereals to the relief areas came to three to four times the cost of the grain (35). DuBois (40) gives a good cost-benefit analysis in using aircraft or trucks in Sahel drought. "Trucks at normal comission rates would have cost roughly l/l4 of what it cost to ship by air." Fuel, manpower, spare parts and maintenance constitute the most important elements of total cost. Fuel is very critical considering the world wide energy crisis and that the high prices of fertilizers and energy have made the poor countries more vunerable to famine. "Rising fuel costs added to the road transport problems (62)." Efficiency, effectiveness, and economy are not forever synonymous. They co-exist where related activities are meshed, where duplication is avoided, and where the process flow from one activity to another and through the entire system approaches a simple pattern. Minimum requirements, limitations and undesired outcomes of each design should be well considered in selection of logistics system. Monitoring relief supplies is a key operation. "Any interruption of supplies to the remote areas would have inmediately affected thou- sands of people who depended for their daily food ration on emergency deliveries. This necessitated the internal monitoring of food movements from the ports to the ultimate points of destination by rail, road and desert tracks, to ensure a continuous flow (33)." Logistics design with a better control system is highly preferred. Unbalanced 30 distribution of food has usually been the cause for more fatality and death than the scarcity of aid. The Approach The discussions in previous sections should have shed some light on famine relief efforts in general, and the logistics system in parti- cular. In coming chapters, an attempt has been made to model a logistics system for which various strategies for managing available resources can be experimented with. The generation of different control alter- natives is a standard part 'of cost-benefit analysis. It leads to an understanding of the choices available. The conmon cost-benefit form 'converts all Constraints and benefits to a monetary base for comparison purposes. Here, however, constraints and benefits could be measured in units of the linfiting resources: man-hours, time, equipment units, etc. Computer simulation has been used to represent the logistics system, its environment, and to evaluate the overall relief system's performance. It should be noted that a comwter model has definite limitations. All the important factors influencing the system under study cannot be included. Different relationships and interactions can be modeled to the extent that they can be converted to numerical relationships. Another important factor limiting the scope of the model is cost. If every detail and element affecting the system is included, the cost of such a model is going to increase. The most complex model is not necessarily the best one. After all, the simulation is one of the analyst's tools in design. Models should be simple enough to dis- close the inevitable design errors and sufficiently flexible to allow for corrections and evaluation. 31 The organization of this dissertation consists of the following chapters roughly leading to the development of the logistics system components represented by Figure l.l. An application of the approach to a hypothetical country' is ‘followed ‘through the individual steps, including major findings, pitfalls, and areas for ‘further research. Chapter II covers the generation and simulation of the logistics system and its various components. A cost function and several performance measures have been developed which are used to evaluate different policy structures. To make effective use of gathered data, a detailed discus- sion on various information filters and estimation methods has been conducted in Chatper III. The chosen technique of this chapter comple- ments the information system model of Chapter II. Testing and validation procedures and results are discussed in Chapter IV. Experimentation with various logistical policies, their' results and analysis has been reported in Chapter V. Experiments include several control policies and investigation of the sensitivity of policy results to changes in certain parameter values. This chapter, in essence, des- cribes the decision making process and managerial aspects of logistics system. Finally, Chapter VI presents a sumnary and conclusions, and outlines areas for further work in refining, improving and extending the model. Summary The approach and design presented in this dissertation is by no means complete and can only be considered an initial attempt to address the logistics of relief operations. No specific country has been intended and the model is in general form. More work is needed to im- prove the model and to connect it to an overall famine relief model. CHAPTER II THE LOGISTICS MODEL A computer simulation is an excellent tool for the systematic study of complex problems which are composed of several large, inter- connected, dynamic systems, A famine relief system is of this type. Different management strategies can be tested in a relatively short period of time without the need of experimentation in the real world. This chapter is a description of the famine logistics model. Various building blocks and their relationships have been described. These blocks are models of different functions and activities which form the logistics operations or influence these operations directly. Each of the components of the logistics model is discussed in some detail in the next sections. A copy of the computer program displaying all equations, parameter values and initial conditions used in these com- ponents and their related subroutines is shown in Appendix B. Ship arrivals, docking, ship unloading facilities and information surveillance processes have been modeled as discrete time systems. The rest of the model is continuous time. The Port Model The basic port model addressed in this section was originally developed by Dr. A.G. Knapp (65). A detailed description of that model with its extensions and modifications is provided here. These changes 32 33 enable the port to interact with the rest of the logistics system and add new important features that were not discussed or assumed given in the basic model. The port system is defined to include ships from the time they enter the harbor, the ship offloading service facilities, grain silos~ and storage areas, and truck loading facilities. Truck and driver pools, and maintenance and repair sh0ps are new additions. Subroutines EXGEN, FACPORT, DOCKY, ARAIVAL, and CHOICE of the simulation model are related to different functions at the port which will be discussed in the next few pages. One of the most important indications of a port's ability to handle grain shipments is the relationship between thruput and input in grain tonnage. Hence the model is constructed to follow the flow of grain through the port. The block diagram in Figure 2.l depicts the form of the model. Ships are assumed to arrive with a Poisson distribution, thus the interarrival times will be exponentially distributed. The capacity of the ships is assumed to have a two level uniform distribution, based on data obtained for Bangladesh. The service time needed to offload a ship's cargo is based on docking time, machinery rates for offloading, and the capacity of the ship. The availability of trucks and drivers to carry the grain into the country's interior is an important part of the overall transportation picture. Truck loading rate depends on the number of trucks and drivers available at port, rate of machinery for loading, available grain in silos, and regional demand for food. Integration of the difference between the ship offloading rate and the truck loading rate gives the net input to storage, and integration of the truck loading rate results 34 33:38 a: 3. t2. .5 an 3.2. ...~ .932 so“. . $38... o>¢on :0 32.3. co .2. 3.5.: 9.3-»723 anal—3:09 «33:0 =22. _ ":34 nozua $329 . xoafir A385 :85 3388 3038 030.5 ”5.3.303: gun—3.— Pg 388 «8.— 9.? «be amino O O O 0 $38: O 2335-: mnzm 0-: 1:309: :58 38 Quasi-c no» I. . . _ Pu Pascal—av scab. .338 3- 8.3.3 «a 6- Aavua .. 33 9.33m :35... 3% «.335 u .580 in“. 2.35 "28.5 253.: no.5... 35 in the amount of grain passed through the port into the country. Two factors which affect the overall port capacity are availability of stor- age and frequency of "down-times" at the port when no work' is done. Too little grain in storage causes trucks and drivers to be idle, while too much in storage implies that ships no longer unload, thus the ship service center is idle. During a "down-time" period neither the ships nor the trucks are serviced. Even though the model can handle "down- times", it has been assumed that due to the emergency circumstances, there will be no "down-time" at any component of the logistics system. The interarrival times for ships has been assumed to be exponen- tially distributed. The time varying mean of the distribution is calcu- lated from a system parameter and one state variable. In Knapp's model this mean was assumed to be constant. EAT(t) = AVTONS / YRTONS(t) (2.1) where: EAT = expected value of interarrival time (years) AVTONS = mean tons of grain per ship (tons/ship) YRTONS = tons of grain arriving (tons/year) t = time index. To reduce the error caused by different patterns of grain arrival, EAT is recalculated at (t + EAT(t)/2) and is used in this form which can handle a cyclical arrival rate. Then the interarrival time is computed stochastically as AT(t) = -EAT ( t + EAT(t)/2) * LOG(R) (2.2) where: AT = length of time before next arrival (years) 36 R random number uniformly distributed in range (0,l) LOG Natural logarithm. AT(t) is calculated in subroutine EXGEN each time a ship arrives. A simple counter is incremented by AT(t) to note the time at which the next ship arrives. YRTONS is computed using a supply model which is discussed in later sections. The cargo weight and service time requirements of a given ship were used to be calculated in the basic model, by separate subroutine at the time the ship enters the offloading facility. In the current model, the cargo weight is modeled in the EXGEN subroutine and is com- puted when the ship enters the harbor. This modification is necessary for calculating the cost of ship waiting time. The service time require- ments are modeled in the FACPORT subroutine and is calculated as the ship enters the offloading facility. Calculations for cargo weight are based on Specific data from Bangladesh.* Figure 2.2 illustrates the histogram of cargo weights. These tonnage figures approximated a two stage uniform distribution, with 86% of the weights falling in the interval 4000-27000 tons, and the remainder distributed in the 27000-55000 ton range. Using the above data, the dividing percentage, Pl, for Bangladesh was calculated as fol lows . Expected tonnage = 19000 = (4000+ 23000/2) * Pl + (27000+ 28000/2) * (l-P'l) P1 = .86 Thus, to generalize the Bangladesh case, two equations are * From "World Food ProgranIne - Bangladesh, Foodgrain Digest," l2 May, l976. 37 Engaging can: 2..» 732 .3 3:3... :38 «a 8333: .«.~ 933.. Anna» cadlaosav nacho owmou .masu\d:oa ouduo>< mm .nmanu mo .03 A233 88“? :53 go... hoaosaohh o>uadnos 38 available, and the choice on which to use is based on comparison of a random number, R, with system parameter Pl as a dividing line, for 'R,: Pl TONSHi = A2 + (l - R) * (A3 - A2) (2.3) (l - Pl) and for R.g Pl TONSHi = Al + R * (A2 - Al)/Pl (2.4) where: TONSH = amount of grain on ith ship (tons) Al, A2, A3 = smallest, middle, and largest tonnages in distribution (tons) R = randon number uniformly distributed in range (0,l) Pl perCentage of ships that have cargo weight in interval (Al, A2) i = ship index. Figure 2.3 shows the probability distribution used in the model to approximate the actual tonnage. Service time required for offloading is based on a constant docking time plus the time needed to empty the ship, which is based on the off- loading rate of the equipment available: ST(t) = C] + TONSH/RMS (2.5) where: ST = service time remaining for ship in service center (years) Cl = docking time required (years) RMS = offloading rate of port equipments (tons/year) 39 Amaopv ooomm mganm «o m< ages H.393. on... magaafionmfi 533053 3:32on .m..~ magma , ooomm N4 coo: H< 230: A. 5.30 3233on A 40 TONSH = amount of grain on ship (tons). As the ship is unloaded, ST(t) is decreased by the time increment, DT, once each time iteration. Note that AT(t), the interarrival time of ships, is an exogenous variable; it can thus be calculated at times set by a single counter. But ST(t) is affected by several factors within the model (e.g. storage capacity, "down" times) and is defined as a time remaining, to allow for time periods during which no offloading occurs. ST(t) = 0 is the key used to indicate that the current ship is empty, a new ship can enter the service center, and a new ST(t) needs to be calculated. The ship service facility modeled in subroutine FACPORT keeps track of two main items; the waiting line of ships and the offloading rate of grain, which is calculated each period and is defined as the average rate (tons/year) of grain movement in the time period (t, t + 0T). Some parts of the offloading rate are computed by the subroutine DOCKY. Observing the waiting line over time gives an indication of the stability of the port system and whether it can handle the tonnage that is arriving without tremendous backups. Note that the length of the waiting line (INL(t)) changes only when AT(t) and ST(t) are calculated. AT(t) indicates arrivals, so IwL(t) is then increased by one. ST(t).=.0 indicates a departure from the service center and availability for the next ship, so if a ship is waiting (IWL(t) > 0), IWL(t) is decreased by one. If no ship is waiting, the service center will be idle and the performance statistic, TIDT(t), is increased by [H1 Thus TIDT(t) gives the total idle time (years) of the service center during the period (0,t). The total waiting time of ships in the harbor can be calculated as 4l TWT(t + DT) = THT(t) + DT * INL(t) (2.6) where: TNT = total ship waiting time in period (0,t), (years) INL = length of waiting line at time t 0T = length of time increment (years). And by keeping track of the number of ships that arrive, another useful performance measure is reached. AVTNT(t) = TWT(t) / INTOT(t) (2.7) where: AVTNT = average waiting time for ships in period (0,t), (years/ship) TNT = total waiting time in period (0,t) INTOT = number of ships arriving in period (0,t)- Generally when a ship is in the service center, the average off- loading rate for period (t, t + 0T) is equal to the rate of the equip- ment, meaning Rl(t) = RMS (2.8) where: Rl = average offloading rate for period (t, t + DT), (tons/years) RMS = offloading rate of port equipment (tons/year)- A utilization measure of the unloading facility, TIDRMS, is incremented by DT. There are three exceptions to this. First, if the storage silos at the port are full, no unloading can be done. A check is made by comparing STOG(t), the storage in the silos at time t, with CAPWH, the 42 capacity of the silos. If STOG(t) _>_ CAPNH, then no offloading is done (Rl(t) DT. TIDCAP(t) is the idle time (years) in period (0,t) of the offloading 0) and the performance variable TIDCAP(t) is incremented by equipment due to storage limitations. The second case in which Rl(t) does not equal RMS occurs when the ship is not in port for the full DT time increment; that is, when ST(t) < DT. For this case Rl(t) is equal to a portion of RMS. Rl(t) = (ST(t)/0T) * RMS (2.9) where: Rl, RMS = as in Equation 2.8 ST = service time remaining (years) 0T = length of time increment (years). Note that the occurrence of this second case is the appropriate time to signal that a ship has left port, the service center is now empty, and a new ST(t) should be calculated if a ship is waiting. The last case for modification of Rl(t) corresponds to the time allowed for docking manuevers, Cl. A counter, TEMPCl(t) is defined to be the remaining docking time at t. TEMPCl(t) is set to Cl when a ship enters the service facilities and is decreased by DT each time 'loop. So if TEMPCl(t) 3 0T, all of the period (t, t + 0T) is spent in docking, no unloading is done and Rl(t) = 0. But if TEMPCl(t) < DT, partial unloading can take place, and again the rate equals a portion of RMS: T - TEMPCl(t) 0T Rl(t) = D * RMS (2.10) where: Rl, RMS, DT = as in Equation 2.9 43 TEMPCl = remaining docking time at time t (years). After being in the country's interior, the returning trucks and drivers enter their pools at the port and form the queue for loading. From the total number of trucks and drivers coming back to the port, ALPHA% and BETA% respectively, will go out of the system temporarily. Trucks go to the repair shop and drivers take a leave. Subroutine ARAIVAL handles the above processes and computes net input to the truck and driver pools. These are new additions to the basic port model. The choice of ALPHA and BETA parameters and the length of delay in which the trucks and drivers are out of the system are important design questions. Significant factors affecting ALPHA are the general conditions of trucks and roads in the country under study. If trucks are old and roads are out of shape, as is the case in most of the third world countries, ALPHA increases accordingly. There is not much the decision makers can do about ALPHA other than to try to assign a value for it. But they can have some flexibility in the choice of BETA, mean- ing that, by some means, asking the drivers to stay on the job longer. Of course there is some limit that BETA can not be lower than. Tired and unhappy drivers can interrupt the delivery system by either accidents or slow work. The decision about the length of the delays involved more or less resembles and to some extend depends on the ALPHA and BETA selection and their values. If the trucks are new and in good shape, fewer numbers of them need repair and the frequencies of major and minor repairs are lower than when not too many good trucks exist in the system. The length of time for which a truck is out of work depends on the extend of the repairs it needs. Also, the drivers can have different delay 44 times depending on the distances they have travelled and other human factors such as age, sickness, etc. In the current model, it has been assumed that constant percentages of trucks and drivers leave the system and there exists an average delay for the repair shop and the length of the time in which a driver is out of the system. The following are the prime reasons for such a deci- sion. As mentioned earlier, these parts of the system have been modeled in continuous time form, thus it is difficult, if not impossible, to single out each truck and driver. Secondly, this model is just a general representation of the real world and does not belong to any specific country, but the choice of the above parameters and delays is determined case by case and is country dependent. At last, these assumptions eliminate the need for detailed modeling of the above processes, .and it is believed that the model preserves its integrity and generality. The above delays have been modeled using a Kth order distributed (con- tinuous) delay process DELVF (74) which will be explained later in a more appr0priate place. No constraints have been assumed on fuel, spare parts, and maintenance. The average rate of change of the truck pool in the port for period (t, t + DT) is R3(t) = TRUCKAR(t) + TRUCKRD(t) - TRUCKRN(t) - TDR(t) (2.ll) where: R3 = average rate of change of the truck pool in period (t, t + DT), (#/years) TRUCKAR = total rate at which trucks enter the port, (#/years) TRUCKRD = rate at which trucks leave the repair shop, (#/years) TRUCKRN = ALPHA percentage of TRUCKAR which enter the repair shop, (#lyears) 45' TRD total rate at which full trucks leave the port (#/years) ff ll time index (years). Then the total number of trucks at the port ready to be utilized, TPOL, is obtained by integrating R3. By integrating TRUCKRD, total trucks which have used the repair shop can be calculated. The average rate of change of the driver pool in the port for period (t, t + 0T) is R4(t) = DRIVEAR(t) + DRIVERD(t) - DRIVEIN(t) - 00R (t) (2.l2) where: . R4 = average rate of change of the driver pool in period (t, t + DT), (#/years) DRIVEAR = total rate at which drivers come back to the port (#[years) DRIVERD = rate at which drivers come back to the system (#/years) DRIVEIN = rate at which drivers take a leave (BETA percent of DRIVERD), (#/years) DDR = total rate at which the drivers leave the port with full trucks, (#/years) t = time index (years). Here, again, the total number of drivers in the pool, DPOL, can be obtained by integrating R4. ' The truck loading rate from the storage silos is limited by RMT, the rate of the loading equipment, by the quantities of grain in storage, STOG(t), drivers at pool DPOL(t), and trucks available to be utilized, TPOL(t). When adequate supplies of grain are in storage, trucks and drivers exist to carry them, the average loading rate is given by Equation 2.l3. In the basic model, a steady supply of vehicles and ,- 46 drivers were assumed. R2(t) = RMT (2.l3) where: R2 = average truck loading rate in period (t, t + DT) (tons/year) RMT = loading rate of silo equipment (tons/years). A utilization measure for the loading facility, TIDRMT, is incremented by DT. If any of the above supplies, i.e. grain, truck, or driver, is not available the loading rate will be zero and an appropriate per- formance statistic is incremented by 0T. These measures are: TIDGR for shortage of grain, TIDTR for shortage of trucks, and TIDDR for drivers. If enough _supplies do not exist, then R2(t) must be a fraction of RMT corresponding to 'the amount of supplies available at ‘time ‘t divided by the time over which it is loaded. But first, an inventory check should be made to see which one of the supplies is least available. Then R2(t) is calculated based on that type of supply and an apprOpriate performance measure is incremented. If grain is the limiting factor, then, R2(t) = STOG(t)/DT (2.l4) where: R2 = average loading rate in period (t, t + DT) (tons/years) STOG = storage in silo at time t (tons) 0T = length of time increment (years). and TIDGR (t), the idle time of trucks, drivers and loading equipment 47 due to shortage of- storage, is increased by DT. When trucks are the least available, the loading rate becomes R2(t) = TGRC * TPOL(t)/DT (2.l5) where: TPOL = total number of trucks in the pool at time t (#) TGRC = grain capacity of one truck (tons) = as in Equation 2.l4. R2, OT and TIDTR which is the idle time of drivers, loading equipment due to unavailability of trucks, is incremented by 0T. For the time when drivers are not available, the loading rate becomes, R2(t) = TGRC * DPOL(t)/(TDRC * DT) ' (2.15) where: DPOL = total number of drivers available at time t (#) TDRC = number of drivers required to Operate a truck (#) R2, TRGC, DT as in Equation 2.l5. Here TIDDR, the idle time of trucks and loading equipment caused by shortage of drivers, is incremented by' 0T. R2(t) computations are carried out by the subroutine CHOICE. Once the ship offloading rate Rl(t) and the truck loading rate R2(t) are computed, the amount of storage and thruputs of grain, truck, and driver are derived by simple integrations. A lost factor models loss of grain due to animals, moisture, etc. The following equations explain all these relationships: THRUPUT (t + DT) = THRUPUT(t) + DT * R2(t) (2.17) TTRUPUT(t + DT) = TTRUPUT(t) + DT * R2(t)/TGRC (2.18) 48 DTRUPUT(t + DT) = 0TRUPUT(t) + DT * TDRC * R2(t)/TGRC (2.l9) STOG(t + 0T) = DT * (Rl(t) - R2(t) - STGLST * STOG(t)) (2.20) where: THRUPUT = amount of grain thruput in period (0,t) (tons) TTRUPUT = number of trucks which have been utilized in period (0,t) (#) DTRUPUT = number of drivers which have been utilized in period (0,t) (#) STGLST = grain loss factor due to insects, moisture, etc. R1 = average ship offloading rate in period (0,t) (#) STOG = storage at time t (tons) R2, TGRC, TDRC, 0T as in Equation 2.16. Several idle times which have already been mentioned, are a result of random endogenous events (e.g. TIDT(t), TIDCAP(t), TIDTR(t), etc.). The port model also contains the capability to include planned, regular "down" times. This would correspond to those periods of the day when no work is done (e.g. night, delays, between work shifts, etc.). Counter NSP is incremented by 1 for each iteration of the time loop, and all work activities are skipped when NSP = NDTSKIP, a positive integer constant. NSP is then reset to 0. Note that ship arrivals and waiting lines will be unaffected. The effect on the model of this feature is 1 NDTSKIP tioned earlier, this feature of the model meaning the "down" times, to cause a "down" time equal to of the total run time. As men- is not activited in the current study. Hence it is assumed that every- thing works around the clock. Regional Warehouses and Roads Grain from the port is taken by truck into the country's interior and to the prespecified regional warehouses. Figure 2.4 shows the model of a regional warehouse (RWH) and its connections to the rest of the system. Each RWH consists of truck unloading and loading facilities, silos and storages, and an information surveillance unit. The model handles four RWH as it was assumed, but by some small changes in array sizes can handle any number of them. Subroutines SILOS, DELAY, and TRNSHIP simulate the total activities related to each RWH. Demand is the chjving force for grain flow through each RWH and actually the total system. It has been assumed that loading and unload- ing rates are functions of demand and accomplished by manpower. This assumption is based on rational that at famine time and in an under- developed country, there will usually be enough labour to unload any number of trucks which are coming. In many cases manpower is the only mean even in normal conditions. In spite of this fact it has been assumed that there exists a maximum limit for unloading rate. By the above assumptions the service time at RWH's becomes variable, hence the standard queuing theory cannot be used to model truck arrivals. Thus, loading and unloading rates are time-varying. The grain received by each RWH is either distributed to the area which is covered by and is close to that RWH or is carried to smaller sub-regional silos or field offices. The carrying process is done by different means. Small carts, manpower and animals are usual carriers. Thus, it is unnecessary to unload the trucks into storage facilities when they arrive at an RWH. At any time, when food arrives, the trucks are directly unloaded into the other means of transportation for distri- bution throughout the region. The modeling process goes as follows. 49 I3:- 2. .3 an... I: 3 3339-380 .3 v:- goa «1.3:: a be :3: 3." 0.3.: 50 T :8 5. 2:! f3— . .8: a: ha :00... a: i 2 0a.: Adv—Ia... an 32.2 .4 .3 IF— .— uo ~38 no =1: 3.8:: 3.3.: 9.3833 Adair—Fr 3 9-395 so .03 32...: 0.33398 an 30.5 3 .0- n- !- a 98.. an... 38:.- .38 - N h- o . a... our .. noon...- uua ~38 3 on no.8 3.8.8 A Innis... m Advg. ’i: o .0! 8.3 :6. H .3 .25 ll]: . 1.8. _- 3.31-2.33... R V m 8 i l E- 58. 38.— .3883. and... T T . 8:18»:- 333 T T i 0.3! _ 51 When assigned trucks to the ith region arrive, they enter the truck pool at that RWH and form a queue, waiting to be unloaded. Multiple servers have been assumed, so a group of trucks are unloaded at the same time. When full trucks arrive the truck pool increase is modeled by Equation 2.21. TRP0L1(t'+ DT) = TRP0L1(t) + or * TRPi(t) (2.21) where: TRPOL = total full trucks available at time t (#) TRP = truck arrival rate at time t (#/years) DT length of time increment (years) i = RWH index. when trucks are unloaded and leave the'regional silo facilities, TRPDL is reduced accordingly. This will be discussed later in Equation (2.41). Thus, the grain ready to be unloaded is equal to GRi(t) = TGRC * TRPOLi/DT (2.22) where: GR = grain in trucks ready to be unloaded at time t (tons/years) TGRC = grain capacity of a truck (tons) TRPDL, DT, i as in Equation (2.21). Now current demand is satisfied, first by using this waiting grain (GR). But before that it should be checked to see how much of this grain can be unloaded without exceeding the maximum unloading rate (RMSS) assumed for that specific RWH. A variable is used to represent the current unloading capacity (TGR). If GR is greater than RMSS then 52 TRGi(t) = RMSS, (2.23) where: TGR = average actual unloading capacity for period (t, t + DT) (tons/year) RMSS = max unloading capacity (tons/year) i = RWH index. Otherwise TGRi = GRi(t) (2.24) where: TGR = average actual offloading capacity for period (t, t + DT) (tons/years) GR = grain in trucks ready to be unloaded at time t (tons/years) i = RWH index. The demand turn comes now. First, it is satisfied using Equation 2.25. RESTi(t) = DEMi(t) - TGRi(t) (2.25) where: REST = variable indicating excess demand or excess grain at time t (tons/years) DEM = actual demand at time t (tons/years) TGR = average actual offloading capacity for period (t, t + DT) (tons/years) i = RWH index. Then it is checked to see whether demand has been completely satisfied 53 or not. This is done by checking the sign of the variable REST. If the sign is positive, there exists unsatisfied demand and ifit:is negative, excess grain exists. From here two separate branches appear. In the second case, the rest of the grain in unloaded into the regional silos, providing the existence of storage. Otherwise the full trucks should wait in the queue in order to be unloaded at a later time. Thus, the storage is checked against the capacity. ACAPi(t) = (RCAPWH.i - RNSTOGi(t))/DT (2.26) where: ACAP = available rate of storage capacity at time t (tons/years) RCAPWH = regional silos capacity (tons) RWSTDG = amount of grain in storage at time t (tons) i RWH index. If ACAP is greater than zero, there is room for more grain to be stored. To decide on how much grain can be unloaded and stored, ACAP is checked against REST (or course, the absolute value of REST, since this is the extra grain after satisfying the demand from Equation 2.25). If ACAP is less than REST. RESTi(t) = ACAPi(t) (2.27) where: REST = excess grain to be unloaded at time t (tons/years) ACAP = available storage capacity at time t (tons/years) RWH index. 1 By this equality, only as much grain will be unloaded as there is a 54 place for it. Otherwise there is enough space to store all of the REST and empty the truck pool. In any case, the following equations will result. SRli(t) = RESTi(t) (2.28) SR21(t) = 0.0 (2.29) SUPi(t) = DEMi(t) (2.30) TDPRi(t) = (DEMi(t) + SRli(t))/TGRC (2.3l) where: SR1 = average input rate to silos for period (t, t + DT) (tons/years) REST = excess grain unloaded in period (t, t + DT) (tons/years) SR2 = average silo output rate for period (t, t + DT) (tons/years) ' DEM = actual demand at time t (tons/years) SUP = actual supply at time t (tons/years) TDPR = average truck unloading rate for period (t, t + DT) (#/years) TGRC = grain capacity of a truck (tons) i = RWH index. Therefore, in the above case supply is equal to demand. The supply has been defined as the amount of grain used to satisfy the demand. It does not mean the amount of grain available i.e. the supply capacity. If demand has not been completely satisfied using all of the full trucks in the pool, the rest should be compensated by the grain in silos, 55 providing there is enough grain in there. Available grain rate is cal- culated by Equation 2.32. ASTOGi(t) = (RNSTOGi(t) - TRSHOLD * RCAPWHi)/0T (2.32) where: ASTOG = available grain for loading in storage at time t (tons/years) RWSTOG = actual amount of grain in storage at time t (tons) RCAPWH = regional silos capacity (tons) TRSHOLD = threshold factor DT length of time increment (years) i = RWH index . If ASTOG is less than zero, it will be equated to zero for further compu— tations. Now, ASTOG is checked against REST. If ASTOG is less than REST, only part of the remaining demand can be satisfied. SR21(t) = ASTOGi(t) (2.33) where: SR2 = average silo output rate for period (t, t + DT) (tons/years) ASTOG, i = as in Equation 2.32. Since the demand has not been satisfied, the stockout performance index will change STKOUTi(t + DT) = STKOUTi(t) + DT (2.34) where: STKOUT = stockout index (years) 56 OT, i = as in Equation 2.32. Thus this measure reflects the total time, when the demand has not been satisfied fully and has nothing to do with the quantity difference of demand and supply. This aSpect of performance will be reflected in other indices which will be discussed later. If demand has been fully satisfied, the output rate becomes SR21(t) = RESTi(t) (2.35) where: SR2 = average silo output rate for period (t, t + DT) (tons/years) REST = satisfied excess demand at time t (tons/years) i = RWH index. In any case, the following equations will be computed. SRli(t) = 0.0 (2.36) SUPi(t) = TGRi(t) + SR2i(t) (2.37) TDPRi(t) = TGRi(t)/TGRC (2.38) where: SRl = average silo input rate for period (t, t + DT) (tons/years) SUP = actual supply at time t (tons/years) TGR = average actual unloading capacity for period (t, t + DT) (tons/years) TDPR = average truck unloading rate for period (t, t + DT) (#/years) 57 TGRC grain capacity of a truck (tons) SR2, i as in Equation 2.35 Thus the output of the RWH and its storage, at any time, are calcu- lated as follows. RTRUPUTi(t + DT) = RTRUPUT1(t) + DT * SUPi(t) (2.39) RWSTOGi(t + 01) = RWSTOGi(t) + DT * (SRli(t) - SR21(t) - (2.40) RSTGLSTi * RWSTOGi(t)) ' where: RTRUPUT = amount of grain thruput in period (0,t) (tons) SUP = supply rate for period (t, t + DT) (tons/years) RWSTOG = storage in regional silo at time t (tons) SR1 = average silo input rate for period (t, t + DT) (tons/years) SR2 = average silo output rate for period (t, t + DT) (tons/years) RSTGLST = grain loss factor due to insects, moisture, etc. DT = length of time increment (years) i RWH index. and the full truck pool is adjusted accordingly. TRPOLi(t + DT) = TRP0L1(t) - DT * TDPRi(t) (2.4l) where: TRPOL = total full trucks available at time t (#) TDPR = average truck unloading rate for period (t, t + DT) (#/years) DT, i = as in Equation 2.40. 58 Two other important performance measures are computed in the SILOS subroutine. One is the ratio of total supply to total demand for each RWH. TSUPPLYi(t + DT) TSUPPLYi(t) + 0T * SUPi(t) (2.42a) TDEMANDi(t + DT) TOEMANOi(t) + DT * DEMi(t) (2.42b) PR00EM1(t + DT) = TSUPPLYi(t + DT)/TDEMANDi(t + DT) (2.42C) where: TSUPPLY = amount of grain supplied in period (0,t) (tons) TDEMAND = total demand in period (0,t) (tons) SUP = actual supply rate for period (t, t + DT) (tons/years) DEM = actual demand rate for period (t, t + DT) (tons/years) PRODEM = ratio of supply to demand in period (0,t) OT, 1 = as in Equation 2.40. Above index along with stock-out index are used to evaluate service performance at RWH's. Another performance measure represents balance distribution. This index is also calculated for each RWH, which, by adding them together, results in the balance performance measure for total logistics operation. sosvsoi(t + DT) = soevsoi(t) + or * DEMESTi(t) * (2-43) MAX((TOTPRO(t) - SUPi(t)/DEM1(t)),0IH where: SDEVSD = balance distribution measure for period (0,t) J 59 DEMEST = estimated rate of demand for period (t, t + DT) (tons/years) TOTPRO = ratio of total regional supply rates (SUPi) to total actual demand rates (DEMi) for period (t, t + DT) MAX = maximum SUP, DEM, DT, i as in Equation 2.42. and the total balance performance index (BALANCE) becomes, BALANCE(t) = "Mk SDEVSDi(t) (2.44) i 1 There are a few important considerations regarding the RWH opera- tions. It has been assumed that no backlog is being kept for demand. It goes without saying that the famine situation is different from what one might see in business. In a food crisis, if, for any reason, the opportunity to feed the people is lost, it cannot be recovered. Its effect is probably a loss of lives. For example, if lunch meal is missed, there is not going to be two meals for dinner. Current demand is only accounted for and no track of past demand is kept. Even though the backlog has not been explicitly modeled, the effects of unsatisfied demand are reflected in the aforementioned performance measures. It was said that the queuing theory cannot be used to model trucks at RWH's due to the assumptions made. But queuing delay has been impli- citly modeled. All the trucks coming to a RWH enter the truck queue and will be there until unloaded. Thus the model implicitly keeps track of queuing delay. This delay is used in the capital development process which will be explained in Chapter V. The storage capacity is a design question. In a famine situation, the trucks which carry grain to RWH's should not be kept loaded for 60 extended periods of time. Apart from the cost consideration, there is always a shortage of trucks and drivers in an underdeveloped country. There is no need to emphasis the importance of trucks and drivers for total performance of operations. Thus when the silos are full and there is not enough demand at that time, the sacks of grain are piled in a protected area and covered with plastic for protection. This type of second class storage can also be modeled with a higher storage loss factor, than the first class silos. It should be said that the above situation is a rare event in a famine case and may be caused by a wrong control policy and imbalance distribution. In the current model, it .was seen unnecessary to model this type of storage. A minimum storage is kept at all ~silos, port and regional, for emergency situations and the corresponding parameter in the model is TRSHOLD. This threshold is calculated with respect to the storage capa- city. The RWH model, SILOS, also handles "down" times but it is not used. Data surveillance unit and demand and supply will be discussed later. It has been assumed that the empty trucks will stay “overnight" at RWH's before they come back to the port. Regardless of their time of arrival, each truck and driver gets a specified length of time to rest and get ready to return to port. Modeling this delay and the delays between port and RWH's are discussed next. Roads and Delays In transporting large quantities of grain, the arrival of the cargo at its destination will be distributed in time around some mean value. This elapsed time for trucks and drivers to travel among port and RWH's and also the "over night" stay at RWH's have been modeled using a Kth order time varying distributed (continuous) delay process DELVE (74, 61 Chapter 10). In other words, the roads in the logistics model has been represented by DELVF which is a set of K first order time varying dif- ferential equations (2.45). d’1(t) + l * “D(t) r](t) = X‘t) ' '1‘t) (2.45a) dt D(t) dt D(t) dr2(t) + 1 * dD(t) r2(t) = r](t) - r2(t) (2.45b) dt D(t) dt D(t) drK(t) + 1 * dD(t) rK(t) = rK'](t) ' rK(t) (2.45k) dt D(t) dt D(t) D(t) = DEL(t)/K (2.451) where: X = output of the delay rK = input to the delay r1, r2, ..., rK-] = intermediate state variables of the distributed delay DEL = length of delay at time t K = order of delay, parameter which is used to "tune" the model to approximate real-world behavior d = derivative operator t = time index. 'R) compute the total storage in the above delay process, the following equation is used K Q(t) = D(t) 21ri(t) (2.46) 1: 62 where: Q = total storage at time t D, K, r = as in Equations-2.45 intermediate state variable index. do N In the current mmde1,-storage refers to the total number of trucks or drivers on each specific delay process. The DELVF subroutine represents the simulation of the above set of equations (Equations 2.45, 2.46). By assigning an array of the intermediate state variables and DEL and K parameters to each road and delay process in the model, the subroutine DELVF can be used over and over. Thus each road is identified by its delay specifications. Delays on Figure 2.4 are modeled by DELVF sub- routines unless a different delay has been specified. Also, drivers time-off and truck repair shop delays in Figure 2.1 are represented by DELVF in the current model. The distances between port and various RWH's are» different and the trucks travel at different speeds. Thus, the travel delay is given by the following formula. DELAY(t) = DISTANCE/SPEED(t) (2.47) where: DELAY = elapsed time between two points (years) DISTANCE = distance between two points (km) SPEED = speed at time t (km/years) t time index. Distances are constant most of the time unless a breakdown in one of the roads forces the trucks to use alternate roads, causing distance changes. In the current model different but constant speeds have been 63 assumed for trucks depending on whether they are full or empty. Full trucks move slower. This makes the delay on each side of each road constant. The subroutine DELAY which takes care of travel delay compu- tation is capable of handling different distances and speeds. Road Breakdowns It is quite possible that one of the main roads connecting the port to a RWH becomes unusable due to different reasons. Flood can wash away some parts of the road and make it impassable; or one of the main bridges may break down due to structural failure or natural dis- aster. No matter what the source of the problem, the decision makers should be ready to deal with it and the model should be equipped to handle it. Thus, the planners should consider the second shortest pos- sible routes from the port to each RWH. Different settings are possible for the above event and hence dif- ferent ways to model it. Sometimes, the breakdown is such that a local route can be used to connect two different parts of the main road. Other times, one has to use absolutely different connections. The second case has been assumed in the current model. The ability of a model to handle breakdowns gives an excellent opportunity to managers and potential users to test different control policies by creating different scenarios. Different routes can have breakdowns at random times. An optimal policy is one which does well on the average under different scenarios, in comparison with different policies. This is why the question of where in the road the breakdown has happened loses its importance. As a result, an arbitrary point can be chosen as the breakdown point. Even though a random breakdown point modeling is also possible, it is an unnecessary complication. 64 In the current study, the following assumption has been made. The breakdown point is the middle point of the road. This slightly simplifies the modeling process. In the current model, when the break- down happens, a binary variable, XGT, changes its value and by this means, the occurrence of the event is transmitted to different parts of the model. The trucks at the port start using the second shortest route to reach the specific RWH, and the empty trucks at the RWH also use the new road to return t0‘the port. Thus, the same SILOS subroutine can be utilized. The only difference is the use of a new distance be- tween port and RWH instead of the old one used for delay calculations. Also, new arrays for intermediate state variables of the distributed delay are used. Back on the old. road, the trucks, full or empty, which have passed the breakdown point, continue their way to their destination. But the full trucks that have not passed the breakdown point should turn around and go back to the port. It has been assumed that these returning trucks are reassigned to the same RWH and are dispatched using the new road. The empty trucks, stuck on the other side of the road, must go back to the RWH and use the new road to return to the port. It has been assumed that these trucks would not stay again overnight at the RWH. The structure of the delay model simplifies the modeling of the problem. To keep track of the trucks still on the old road, two new auxiliary arrays are introduced (AUXRM, AUXRF) to handle the intermediate state or rate variables of the distributed delay belonging to the old road. It was said that each road has its own arrays, one for full trucks and one for empty ones. When the breakdown happens, the values of the intermediate rates corresponding to the stuck full and empty trucks are transferred to the above auxiliary arrays and zeros fill their place 65 in the old arrays. By knowing the breakdown point, it is easy to find out the number of intermediate rates in different sides of the road. Care should be taken in the above transfer. By looking at the EquatiOns 2.45, one can see that the rates leave the delay process sooner if their lower subscript numbers are smaller; ‘Thus, in tranferring the ‘rate values into the auxiliary arrays, the value in the last intermediate rate (i.e. with the largest lower subscript) should go to the first intermediate rate (i.e., with lowest lower subscript) and so on. This is the modeling of the fact that the trucks which left their origin last, should come back to their initial place first. Knowing two other parameters, DEL and K in Equations 2.45, complete- ly identifies the delays for stuck trucks. The number of intermediate rates in different sides of the breakdown point is parameter K. Since the distances from the breakdown point to either destinations are known, the DELAY subroutine computes the DEL parameter. Checking the delay storages is a good way to see whether there are any trucks left on the old road. In this model, a variable, BRFLG, signals the end of the trucks on that road. The above process which is modeled in the TRNSHIP subroutine, is accomplished simultaneously with other’ activities and movements in the model. Supply and Demand Demand and supply are the forces behind all movements and flows in a logistic system. Nothing is going to move if there is no supply. If the supply exists, the demand identifies the direction of the move- ments and forces the supply to move. Information about supply and demand is essential for planners and decision makers. Almost all of their decisions are based on this information. 66 In a famine situation, the data on supply is more available than data on demand. The accuracy of the supply data is usually of a greater degree than that of demand. The fact is that, the central government of the involved country usually knows about its main silos' storage levels. Also, when a foreign country makes a donation, it sends a mes- sage to the decision makers managing the crisis. Then the donated grain is usually loaded into ships which normally takes somewhere between fifteen and forty-five days to reach their destination. This information and lead time give the managers a good basis for their policy makings. But the situation on the demand side is not so bright. Poor data, if any at all, exists in third world countries. Problems with informa- tion gathering and availability of data were discussed in the first chapter. Famine also creates other problems. Populations start moving on the basis of any rumor that food exists in some location. This makes planning and. allOcation decisions very difficult. Another difference between supply and demand is the degree of accuracy of data. Information on supply is usually more certain than of demand because demand must be estimated through data which has been gathered and sent to decision makers by surveillance units in each region. Different supply and demand patterns generate different food crisis scenarios. Here also, in comparison with other control policies, a pareto optimal control should be able to do well regardless of supply or demand patterns. And the total logistics model itself should handle any type of food arrival and movements. The current model indeed, can work with any pattern of supply and demand. More on this issue will be seen in the next sections and chapters. Although different patterns of supply and demand could exist, some forms are most likely to happen. Bell shape curves with right or left 67 skewness are typical. Then the area under the curve is the total amount of aid or demand. In the current model subroutine FOODAR simulates the supply. It is a table look-up function which contains the following desired features. It has been assumed that the maximum rate of food arrival is approximately equal to 1.1 percent of port capacity. It is left-skewed and its maximum is attained after the demand function's maximum point. These are the benefits of simulation. Figure 2.5 iHus- trates the supply function along with the total demand function which will be discussed next. Remember that subroutine EXGEN uses the sub- routine FOODAR to generate stochastic: exponential interarrival times for ships. That is why the non-zero initial value has been assumed. The area under the curves, representing total amountof demand and supply, can be assigned by the user. The table look-up function is one way to approximate a function by linear interpolation. In this case the supply function is approxi- mated by a series of straight line segments. This approach is easy to use and its accuracy depends upon the number of approximating line segments. These line segments could be of varying sizes. At a given time T, the subroutine calculates the value of the independent variable (food arrival rate) by first finding which interval (line segment) T belongs to. It then uses Equation 2.48 to get the desired linear func- tional approximation of the food arrival rate: Y(T) = (T - XTAB(I - l)) * (YTAB(I)- YTAB(I - l))’(XTAB(I) - XTAB(I - l)) + YTAB(I - l) (2.48) where: Y = desired linear functional approximation of the independent variable 68 Rate (tons/years) O O! p YIIO' ’1 Time (Years) Figure 2.5. The demand and supply functions 69 T = dependent variable YTAB = array of the independent variables' values XTAB = array of the dependent variables' values I = interval that desired value lies in. Subroutine DEMAND simulates the following assumed function for total demand. D(t) = TDEF * (l - COSZIlt) (2.49) where: D = demand rate for the country at time t (matric tons/years) TDEF = total demand for the country for the entire operations (metric tons) t = time index. The area under this curve is equal to TDEF and the function attains its maximum at 2 * TDEF. It has been assumed that the demand rate is initially 20% of the maximum rate. Thus, up to some point in time, TDEM, the demand function is constant and after that it uses Equation 2.49. TDEM can be calculated using Equation 2.49 for different values of TDEF. Total demand is the sum of four regional demands which are calcu- lated using the following equations. 01(t) = ai(t) * D(t) (2.50) ant) = .4 +s](t) . -.2 581:.2 012(12) = .4 + 82(12) , -.2 $8.2 5.2 63H): .l+B3H),-.li83§J 3 04(t) =1 ‘1: 01(t) a 04(t): O l 70 where: Di = ith region's demand rate at time t (metric tons/years) a = partition coefficient at time t B = population movement coefficient at time t D, t = as in Equation 2.49. So the demand function takes into consideration seasonality and popula- tion movements in each RWH. This allows generation of different patterns of demand. Notice that the above demand function represents the real world in the model. The decision makers do not know this function. That is why there is a need for data surveillance units. At known ,sam- pling intervals, the demand functions are sampled. This process contains errors. Then, these results are used to project the total regional demand. The second stage-has its own errors. In order to get rid of these errors and provide better information for decision makers, these observations must be processed. But what kind of estimation procedure should be used and if so, does this help to increase the quality of information tn“ not? These questions are answered in detail in Chapter III. There, different methods have been used to estimate a spectrum of different families of functions which Equation 2.50 is one member of them. After all Equation 2.50 is one of the forms the demand function can take in the real world. Next is the process of modeling the sampling Drocedure. Modelinggan Information System To allow evaluation of the effects of information quality on the performance of logistics efforts, apprOpriate additions to the logistic model are necessary; A sampling component modeled by Dr. A. G. Knapp (64, Chapter III) has been used here. This section is aui outline 71 extracted from his work. This 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. Here the emphasis is on surveil- lance, data processing and comnunication. The problem becomes one of estimation, since many dynamic variables can never be known perfectly. The evaluation of an information system includes learning how precise the data must be for efficient relief work, together with the cost of obtaining the desired data quality. The evaluation is largely a sensi- tivity analysis. ENerything else fixed, observations are made of the relationships between system performance and changes in information quality. 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 delay parameter is decreased; no mention is made of the cause. This approach is taken in the interests of generality because specific com- munication devices, sampling techniques and statistical methods *will differ in cost and applicability from country to country. 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 4' 72 compensate for long lags in another. The use of a sampling frequency parameter 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 dis- organization, machinery errors, or corruption. This parameter is not used in studying the current model. Random measurement error is produced by the standard deviation parameter; error distributions are assumed to be normal with a mean equal to the true value. Normalcy is assumed because the variables estimated are averages derived from many samples. Although 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. 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 responsible for the introduction of errors and delay. The sampling component des- cribed next provides for error, delay, and the sampling frequency. Sampling Components: SAMPL and VDTDLI A simple method is needed to introduce data quality parameters into a simulation. Simplicity is desirable, since one of the reasons for approaching information system evaluation through the use of para- - meters is to avoid the detail of describing particular surveillance and communication methods. At the same time, the method must approximate the real delays, measurement error and sampling frequency in the system. The routines, SAMPL and VDTDLI, are quite easily implemented. A sampling frequency is given and, at the Specified intervals, random measurement 73 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 computer as the model advances through a given delay period, after which the sample serves as theestimated 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. Chapter III is allocated for the discussion of different filtering methods and the choice of the "best" information filter for the problem under study. The discrete model SAMPL translates the sampling interval into a specified number of simulation cycles, using Equation 2.51. A simple counter (NCNT) is set to zero each time the sampling procedure occurs. The counter NCNT is incremented by one each cycle OT 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 (2.51) where: NSAMP = number of simulation cycles in sampling interval SAMPT = sampling interval (years) DT' simulation cycle increment (years) x ll index on variables. The measurement of a desired variable, corresponding to data collec- tion, is simulated in SAMPL with the introduction of bias and a random standard error parameter. Then, the estimation method computes an error term proportional to the true value. 74 ESTk(TS) = VALk(TS) * (l. + SDk * Y) + BIASk (2.52) where: EST = estimated value of variable VAL = true value of variable BIAS = measurement bias TS = sampling time Y = standard normal random variable k = index on variables. Straightforwardcalculations show that the expected value of the estimate is the true value plus the bias term and the estimate variance is equal to VALE * sofi (Recall E(Y) = 0.0, Var (Y) = 1.). The produced error is normally distributed. The form of Equation 2.52 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 Equation 2.52 depends on the size of the variable, the implication would be that measurement techniques get better as the variable decreases. To overcome the problem, the following method should be used. ESTk(TS) = VAL + SD * Y + BIASk (2.53) k k where: all as defined in Equation 2.52, The variance of this method is equal to 50: and the standard deviation of the error is fixed. The choice of error estimators is based on examination of time series data for true variable values. In the current 75 model Equation 2.52 has been used to estimate regional demands. Subroutine SAMPL produces estimated values for sampled variables. These estimates are then used as inputs to a discrete, variable delay routine, VDTDLI. The form of the delay follows that of familiar discrete boxcar routines (70). 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 parti- cular 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 with the latest supplies (or information) joins the train's tail. And each car moves forward one position. Equations 2.54 describe this process. The equations must be solved in the order presented. OUT = CAR] (2.54a) CAR, _ 1 = CARi, for i = 2, 3, ..., N (2.54b) CARN = IN (2.54c) where: OUT = output of the routine CAR, = ith car in the array IN = input to the routine i = index on cars N = number of cars. The delay parameter of information quality is related to N, the 76 number of array positions, by the simulation increment DT. The calcula- tion is simply done in Equation 2.55. Nk = DELAYk/DT + .5 (2.55) where: N = size of delay array DELAY = delay involved in the process (years) DT = simulation increment (years) k = index on variables. Note that the relationships of Equations 2.54 and 2.55 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; and the newest data values are affected. An increased delay causes the newest data to be held for the extra period. Equations 2.54a and 2.54b are retained, but Equation 2.56 replaces Equation 2.54c. CARJ = IN, for j = N, N + l, N + 2, ..., NNEW (2.56) where: j = index on new cars in array NNEW = 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. This implies that implementation of the new methods 77 cannot force the old information through the system any faster. The only modification to Equations 2.54 is that N is recalculated to fit the new, shorter delay. Note that conservation of flow is not a cri- terion in modeling information transfer. The output of VDTDLI is a lagged, randomly measured estimate to be used by decision makers. 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 interval, so additional inputs to VDTDLI are necessary. The simplest scheme is to retain a samMed value from SAMPL as a constant input in VDTDLI throughout the sampling interval, or using some filtering techniques to include the results of previous measurements of the variable in the estimation process. -As was mentioned earlier, discussion on this subject will be made in detail in the next chapter. In the current study, the above information system has been used to estimate the regional demands and constant and identical transmission delay has been assumed for all regions. Capital Acquisition Model Availability of transportation means for carrying the grain into the country's interior is an important factor in the overall logistics picture. System planners should first decide about the type of transpor- tation mode they are going to use. Then, comes the question of that particular mode's availability which means how much and .at what rate it can be acquired. A detailed discussion on these questions was made in the first chapter. The first question has not been answered in this study because the choice of transportation mode must be answered in the context of a particular country. It is very probable that different 78 modes are used simultaneously. Also, .it has been tried to keep the model as general as possible. The second question was felt to be the most important one to be addressed. In fact, the answer to this question will clarify many points for the first question. The second question arises in any logistical efforts, thus it does not belong to any specific case. How much "carry- ing" capacity and at what rate is available. How efficient are the available transportation modes in terms of speed and reliability? In the current study, modeling these aspects of the real world has been tried. Thus, trucks have been chosen to be the mode of transportation.- Important concepts of capital acquisition delay and limits on the rate of acquisition have been modeled. Average capacity and equal numbers of operators for each truck have been assumed. In the current model, the truck's capacity is ten tons and one driver is operating it. Dif- ferent values can be assigned if necessary. I The capital acquisition process has been shown in Figure~ 2.6. Managers of the system should decide about the desired amount of capital needed (YD). The word' "capital" in this dissertation, has been used primarily in the context of rented trucks and hired drivers. This decision making process will be discussed in Chapter V along with other decision rules and controls. Then, the managers try to ac- quire the desired capital from the market.) This process and the question of whether they can obtain the needed capital should be answered with‘regardctO‘the‘case involved.< Many factors influence this process. For example, the severity of the disaster; if famine is wide- spread the central government could announce that the country is in an emergency' situation and by some legislation obtain any’ amount of capital possible. To keep the model as general as possible, the above 79 «309$ «co-nodgon guano .w.~ a: mg: .39. aaa SEHmHan: (80) processes have not been modeled. But the delay involved has been implicitly modeled with the other delays in the acquisition process. No matter how the managers get the desired amount of capital, there are two factors which prevent their decisions to be fully materialized. One is the rate at which they could acquire the capital. There is a maximum limit (TRLIMIT) beyond which they can not go. TRLIMIT is a design parameter. It is specified either by the managers of the system or the model can be used to see what TRLIMIT is needed in order to achieve a desired total system performance. This is one of the advan- tages of using models as tools in decision making. Decision makers can use the model to find out about different values of TRLIMIT for various performance levels. This can help them to plan ahead and decide whether it is needed to use extra measures in order to get the desired amount of capital. , The other important factor is the acquisition delay. Part of this delay was discussed earlier. The other part involves the time it takes for the capital to arrive at port. For example, trucks and drivers are Spread all over the country. They should be brought to the port, and this process requires time. Figure 2.6 configuration goes as follows. Decision makers decide about the desired amount of capital (YD). This number is compared with the actual amount of capital existing in the system (Y). If more capital is needed, the extra amount will be ordered (YEE). After passing the test on capital acquisition rate, this amount or its modified one will be given as an input (W) to the acquisition process delay. The Kth order distributed delay (Equations 2.45) modeled by subroutine DELVF has been used to represent the above delay. ' If the desired amount of capital is less than what exists in the 81 system, the rest (YN) should be discharged. There is no delay in this process, because the trucks and drivers will leave the system at the port and their connection with the model will end. A lost factor (TRLOST) has been modeled to account for the amount of capital which after acquisition does not make it to the port due to various reasons. Thus, the actual amount of capital is obtained by the following equation. Yi(t + DT) = Yi(t) + DT * (Ui(t) + YNi(t) - TRLOST * Yi(t)) (2.57) where: (Y = actual total amount of ith capital in the system (#) U = rate at which new capital is added to the system (#/years) YN = rate at which capital leaves the system (#/years) TRLOST = capital lost coefficient i = index on capital DT = length of time increment (years). As shown in Figure 2.6, the capital acquisition process contains feedback and a controller (GC). The prime purpose of this controller is to keep Y in line with YD. Other objectives of the above feedback control are: stability of the acquisition system, steady-state error performance (i.e. the difference between steady-state desired and actual capital), and the dynamic performance, meaning how fast the actual capital can adjust itself to the changes in the desired amount of capital. An off-line analysis of the capital acquisition process resulted in the conclusion that proportional control is good enough for current model purposes. The question of TRLIMIT was also analysed in off-line fashion. The above model was operated with no limit on capital acquisition rate. A 82 A simple variable kept track of the maximum amount of the rate (W in Figure 2.6). Different controls also were applied. The maximum rate obtained in this fashion is just an indication of capital need. It does not mean that this rate is needed throughout the logistic Opera- tions. After observations of different values for TRLIMIT, a fraction of it ( 80%) was used as TRLIMIT in the current model. After all, dif— ferent control policies, and conclusions derived from them, are affected equally by the choice of TRLIMIT. This decision can also be reached on an on-line fashion. More on this subject will be said in Chapters IV and V. Subroutine CAPITAL simulates the capital acquisition process. This model follows the same process of acquisition explained above. Trucks and drivers are the capitals which are modeled. Equal average delay time, TRLOST coefficient, and TRLIMIT have been assumed for both types of capital. It is assumed that the acquired capitals enter and leave the system at port. Thus, changes in capital are reflected in, TPOL and DPOL, the truck and driver pools in the port (See Figure 2.1). This follows closely the events happening in the real world. Notice that when capital is added to the system, TPOL and DPOL are increased accordingly. But there must be enough trucks and drivers in the pools allowing their discharge when there is no need for them any more. For. this reason two variables, TRLACK and DRLACK, are introduced in the model which keep track of the number of trucks and drivers which should be discharged upon their return from various RWH's. Y(t) and YD(t) represent the actual number of trucks and drivers in the system at time t, respectively. It is believed that more details on this component fit. better when control policies are discussed in Chapter V- Thus, 83 the above explanation of the capital acquisition process will be com— pleted in that chapter. The Cost Function The preceding sections described a mathematical formulation and modeling of the logistics system. This section describes a process for generation of the cost function. This is a crucial task because the cost function links real world system designs to the simulation of the previous sections in this chapter and control policies of Chapter V. A detailed discussion and modeling of the cost function has not been intended here. It is mainly an accounting job. A single-valued monetary cost function is calculated which gives the total cost of logistic operations. The total cost is the sum of the costs of the major components in the system; e.g. capital, fuel, inventory, loading and unloading, ship waiting cost, and information. The above decision is based on different factors. First, there is a severe shortage of data in this area. Second, further disaggregation would not lead to significant results about the nature of famine relief resource alloca- tion. At last, the cost coefficients are different in each case. Some resources which are more readily available in one country may not abound in another one. ' In this study, only those costs which have been generated exclu- sively by the famine logistics effort, have been considered in total cost calculations. Thus the costs of equipment which already exists has not been included. For example, loading and unloading machinery at the port. These machines usually exist, regardless of the existence 84 of famine in the country. The cost for such itmes acts as a fixed cost, pushing the total cost upward. For comparison of different control strategies, variable cost should be used as a criterion. Subroutines CALCULT and COSTS are used to compute the total cost and its breakdown to various categories of costs. Subroutine CALCULT is called every simulation cycle and it keeps track of variables necessary for cost calculations. Then at any desired time, the total cost can be computed by calling the subroutine COSTS. In this way, model efficiency increases and computer costs decrease by omitting many unnecessary computations. Transportation costs are calculated by the following equations. CDRWAGE(t) = CDWAGE * DT * TRDIOP(t) (2.58) CRNTR(t) = CRENT * 0T * TTRIOP(t) (2.59) where: CRDWAGE = drivers' wage cost in period (0,t) (5) CDWAGE = unit wage cost per driver (#/years) TDRIOP = incremental sum of total number of drivers in the ;.* system in period (0,t) (#) CRNTR = truck rental cost in period (0,t) (S) CRENT = unit truck rental cost (S/years) TTRIOP = incremental sum of the total number of trucks in the system in period (0,t) (#) 0T simulation cycle increment (years). TDRIOP and TTRIOP are modeled in the subroutine CALCULT. At every Simu- lation cycle, the total number of trucks in the system is computed by Equation 2.60. 85 4 TRIOP(t) = 2 (TRPOLi(t) + PTSTRGi(t) + FTSTRGi(t) + RTSTRGi(t) (2.60) 13) + TTSTRGi(t) + TTSTRG, + 4(t) + TTSTRG (t) i + 8 + TTSTRGi + 12(t)) where: TRIOP = total number of trucks in the system excluding port at time t (#) TRPOL = number of trucks waiting to be unloaded at ith RWH at time t (#) PTSTRG = number of trucks on the road to ith RWH at time t (#) FTSTRG = number of trucks staying "overnight" in ith RWH at time t (#) RTSTRG = number of trucks on the road to port from ith RWH at time t (#) TTSTRG = number of trucks on different sides of a broken road t6 ith RWH at time t (#). Notice that TTSTRG'S will be zero if there are no breakdowns in the road or after the broken road has been cleared. Now TTRIOP is calculated using the following equation. TTRIOP(t + or) = TTRIOP(t) + TPOL(t) + TTIRS(t) + TRIOP(t) (2'51) where: TTRIOP incremental sum of the total number of trucks in the system in period (0, t + DT) (#) TPOL number of trucks in the port's pool at time t (#) TTIRS total truck in repair shop at time t (#) 86 TRIOP = number of trucks in the system excluding the port facilities at time t (#). But TDRIOP is computed using Equation 2.62. TDRIOP(t + DT) = TDRIOP(t) + DPOL(t) + TDRC * TRIOP(t) (2.62) where: TDRIOP = incremental sum of total number of drivers in the system in period (0, t + DT) (#) DPOL = number of drivers in the port's pool at time t (#) TDRC = number of drivers required to operate a truck (#) TRIOP = as in Equation 2.61. Note that TDRIOP is different from TTRIOP in the sense that the drivers "on leave" are not paid but the trucks rent cost should be paid regard- less of whether it is in operation or in the repair Shop. It has been assumed that any changes in the number of trucks and drivers take place at the end of the DT interval. Generally speaking, the lower limit on truck cost is its deprecia- tion value and its upper limit is the opportunity cost. But in a famine situation, by government intervention it is very unlikely that the opportunity cost is paid for trucks or any other item. An average repair cost has been assumed for trucks. CRPAIR(t) = CRPIR * TTBS(t) (2.63) where: CRPAIR = total variable truck repair cost in period (0,t) (S) CRPIR = average unit truck repair cost (S/truck) TTBS = total trucks being serviced in period (0,t) (#). 87 Remember that TTBS is computed by integrating the output of truck repair delay in subroutine ARAIVAL. There is yearly fixed cost for a truck repair shop which is the only assumed transportation fixed cost. CFTRNS(t) = t * CFRPIR (2.64) where: CFTRNS = fixed cost of transportation in period (0, t) (3) CFRPIR = fixed cost of truck repair shop (S/year). The last item on the list of transportation costs in fuel cost. This cost is a function of different variables including distance, speed, and load. Here it is calculated based on the total distance travelled by each truck. Thus the cost of fuel used by trucks other than travel- ling is assumed to be zero. Also, equality of fuel consumption by full and empty trucks has been assumed. The logic behind this is that a truck that is empty goes faster, causing increased fuel consumption. When a truck is full it goes slower, but the heavier weight now increases fuel use. Fuel cost is calculated by the following equation. CFUELS(t) = CFUEL * TROUTE(t) (2.65) where: CFUELS = total fuel cost in period (0, t) (S) CFUEL = average unit fuel cost per truck (S/KM) TROUTE = total distance travelled by all trucks in period (0, t) (KM). TROUTE is calculated in subroutines SILOS and TRNSHIP. It is computed by integrating the outputs of truck delays (Figure 2.4) over time and 88 multiplying them by appropriate distances. Total variable cost of trans- portation is obtained by Equation 2.66. CVTRNS(t) = CDRNAGE(t) + CRPAIR (t) + CRNTR(t) + CFUELS(t) (2°55) where: CVTRNS = total variable cost of transportation in period (0, t) ($) CDRNAGE = drivers wage cost in period (0, t) ($) CRPAIR = total variable truck repair cost in period (0, t) ($) CRNTR = truck rental cost in period (0, t) (5) CFUELS = total fuel cost in period (0, t) ($). Total cost of transportation, TCTRNS, is the sum of fixed and variable costs of transportation. Other logistical functions have their own costs. Inventory cost is calculated as CVAINV(t + DT) = CVAINV(t) + CSTRG * DT * (STOG(t) +121RNST061(£§)67) where: CVAINV = variable inventory cost for period (0, t + DT) ($) CSTRG = average unit inventory cost ($/ton/year) STOG = port storage at time t (tons) RNSTOG = regional storage at time t (tons) i = regional warehouse index DT simulation cycle increment (years). Loading and unloading operations are highly labor intensive in most underdeveloped countries and most of the time takes place by man- power. Another important consideration is the abnormal situation of 89 famine. This means that there is a high probability of the food-for-work program in such circumstances, covering part of the manpower cost. The above two points should be kept in mind when calculating the unit cost of loading and unloading facilities. Note that, as it was men- tioned, the costs of loading and unloading equipment, at port is not included in the calculations. Loading and unloading costs are computed by the following equations. CVLOAD (t + DT) = CVLOAD(t) + CLOAD * DT * (iglRLOADi(t)) (2.68) . 4 (2.69) CVULOAD(t + DT) = CVULOAD(t) + CULOAD * DT * (iiiRUNLOADi(t)) where: CVLOAD = variable cost of loading in period (0, t + DT) (S) CLOAD = unit cost of loading ($/MT) CVULOAD = variable cost of unloading in period (0, t + DT) (S) CULOAD = unit cost of unloading ($/MT) RLOAD = grain loading rate for period (t, t + DT) (tons/years) RUNLOAD = grain unloading rate for period (t, t + DT) (tons/years) i = regional warehouse index DT = simulation cycle increment (years). RLOAD and RUNLOAD are modeled in the subroutine SILOS. Information cost is based on the frequency of sampling. An average per sample cost has been assumed equal for all regions. This directly reflects the tradeoff between the quality of information and its cost. The informa- tion cost for one region is multiplied by four to get total cost. 90 CVSMPL(t) = 4. * (t/SAMPT) * CSMPL (2.70) where: CVSMPL = total variable cost of information in period (0, t) ($) CSMPL = unit cost of sampling ($/survey) SAMPT = sampling interval (years) Another important contributor to total cost is the cost associated with the ships waiting to be unloaded. Most of the aid is carried by comercial shipping companies and have to be paid as long as the ship has not been unloaded. The cost here includes only the time from when the ship enters the harbor until it is unloaded. Note that the total grain waiting on ships to be unloaded, QGRAP, increases discretely when- ever a ship arrives but decreases continuously as the ships are unloaded. Hence QGRAP is increased by TONSH in subroutine EXGEN whenever a ship arrives and it is reduced as follows in subroutine CALCULT. QGRAP(t + DT) = QGRAP(t) - DT * Rl(t) (2.7)) where: QGRAP total amount of grain at harbor in period (t. t + DT) (tons) R1 = average offloading rate for period (t, t + DT) (tons/years) DT = simulation cycle increment (years). Then, the ship waiting time cost is obtained by Equation 2.72. This cost is proportional to the ship's load, assuming everything else to be the same. 9l TCSHIP(t + DT) = TCSHIP(t) + CSHIPN * DT * QGRAP(t) (2.72) where: TCSHIP = ship waiting time cost in period (0, t + DT) ($) CSHIPW = unit cost of ship waiting time (S/ton/year) QGRAP, DT = as in Equation 2.71. The above equation gives an exact amount of cost, because, in a real world situation the exact number of ships waiting and their weights are known. There are some other ways to calculate an approximate waiting cost. One way is to use IwL, number of ships in queue, and multiply it by AVTONS, the average ship capacity. This gives the amount of grain waiting to be unloaded for period DT, i.e. QGRAP. Bias in this method becomes obvious when different patterns of arrival for ships are taken into consideration. It overestimates the cost if the number of small ships is greater than large ships and vice versa. _ Some fixed costs have been assumed for different logistical func- tions. These, together with the fixed cost of transportation, add up to the total fixed cost of logistic operations. (2.73) TFCOST(t) = CFTRNS(t) + t * (CFSTRG + CFLOAD + CFULOAD + 4. * CFSMPL) where: TFCOST = fixed cost of operations in period (0, t) ($) CFTRNS = fixed cost of transportation in period (0, t) ($) CFSTRG = fixed cost of silos ($/year) CFLOAD = fixed cost of loading facilities ($/year) CFULOAD = offloading facilities fixed cost ($/year) CFSMPL = fixed cost of information gathering (S/year/RWH) t = time index. 92 Total cost of operation is the sum of fixed and variable costs of opera- tion. (2.74) TOTCOST(t) = TFCOST(t) + CVTRNS(t) + CVAINV(t) + CVLOAD(t) + CVULOADH’.) + CVSMPL(t) + TCSHIP(t) where: TOTCOST total cost of operations in period (0, t) (S) TFCOST = total fixed cost of operations in period (0, t) (S) CVTRNS = variable cost of transportation in period (0, t) (S) CVAINV = variable inventory cost in period (0, t) (S) CVLOAD = variable cost of loading in period (0, t) (S) CVULOAD = variable cost of unloading in period (0, t) (S) CVSMPL = total variable cost of information in period (0, t) (S) ship waiting time cost in period (0, t) (S). TCSHI P TOTCOST is one of the overall performance measures. and it will be used for comparison of different control strategies. Appendix A represents and summarizes the numerical cost coefficients used in the current study. Additional Model Features Several general features and assumptions of the total model are discussed in this section. The first feature concerns computer use rather than modeling. The stochastic results of simulation runs involv- ing 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 a Monte Carlo simulation. A para- meter set is fixed and several separate model runs are made using 93 different random values (63). As was explained in previous sections, random variables enter the model at different points. Thus, the current model is equipped for Monte Carlo experiments. Each run of the model produces one sample from the distribution of a given variable. The desired statistics are then calculated from the samples, using well known formulas. Computer storage requirements are reduced considerably by calculating the mean and variance recursively, according to Equations 2.75. Note that only two stored values, Y" and Sn’ are required for each variable. Another advantage of the recursive calculation is that current statistics are available after each run, providing a convenient structure for cbnducting hypothesis testing with a minimum number of computer runs. 'Y] = x1 , Sl = 0.0 (2.75a) 7n =%(("'1)Yn-l + "n’ 3 "32 (2.75M - - _ 2. Sn-n 2*Sn_]+l()(n l X") , n32 (2.75c) n - l n where: n = number of samples xn = nth sample 'Yh = sample mean of n samples n = sample variance of n samples. Since the shape of the distribution of the desired variables and performance measures are of interest in this study, samples generated from different variables at the end of each run are stored in array TT(J, K) in the main program. "J" refers to the number of variables for which the various statistics are desired, so it changes according 94 to the need for statistics. “K" is equal to MONRUN, the number of Monte Carlo l00ps. Subroutine AVERAGE keeps track of the means, and variances are calculated in subroutine MONPRNT. In the current study, no internal food flow has been assumed, except the initial amount of grains in the silos. This feature can easily be added to the model. The decision making body has been modeled by subroutine CONTROL. There exists an initial control policy which the logistics model has been tested with. It is thought that a more appro- priate place for the discussion on this subroutine is in Chapter V, where the control question is addressed. Sumary The logistics model described here was constructed as an aid for decision makers in ‘evaluating various strategies for famine relief logistics. The mmdel describes and simulates different components of a logistics system. It is aggregated and does not adequately detail a specific country, but it sheds light on important issues to be faced by any relief operation. CHAPTER III STOCHASTIC ADAPTIVE ESTIMATION HITHIN THE FAMINE INFORMATION SYSTEM Accurate information is needed to achieve overall system objectives. As mentioned earlier, one of the major support systems for relief opera- tions is the information system. Management* decisions on resource allocation and food distribution are based on available information and an assessment as to its accuracy. Although different kinds of data are needed to run the total system, data on food deficit is the most important. To get existing food stocks to those who need it when it is needed and at minimum cost, estimates of food demand should be available. The information system links the real world to the model and the demand for food is the force behind movement of all flows in the system. World Health Organization's monograph on nutritional surveillance states that system managers need processed data enabling them to describe contemporary conditions, predict changes, identify trends, and elucidate underlying causes of the situa— tion (58). The purpose of this chapter is to examine the problem of information estimation iri detail. Then different estimation methods are compared in the context of a famine relife system. A few selected filters are tested under various assumptions. At the end, one technique is chosen for use in the logistics model's information component. 95 96 To control a system, one uses available data to find out what the system is actually doing; i.e., to estimate its state. If the system's state can be estimated within some reasonable accuracy, the desired control is often obvious (lOl, Chapter 2). Hence estimation of the state or some function of the state from the observations is the first step in solving the control problem. Estimation has been defined as the problem of using observed data which is contaminated by noise in order to estimate properties of the actual system (56), (85), (lOl). It is comon to distinguish (between a number of different types of state estimation problems. For example, the estimation of the system's state X(T) based on obser- vations Y(t) where to g t _<_ T, is called filtering or causal filtering and is the most conInonly considered problem. The estimation of X(T + r) from Y(t) where to _<_ t _<_ T and 1 >0, is called prediction. The estimation of X(r) relative to Y(t), where o _<_t _<_ T and r varies between to and T, is called smoothing or interpolation. A detailed mathematical description of the above concepts, and their breakdown into continuous, discrete, and mixed continuous-discrete estimation is in Reference (56, Chapter 5). In our sampling component of the overall model, the "true" time series for the desired variable is estimated at specified survey times. This estimate is delayed and then used by policy makers. Between surveys the estimate remains constant; it is a sample-and-hold, or zero-order delay. A filter would affect the estimation process at the survey times, while a predictor would allow changed estimates between surveys. Before changing the sampling model, the following basic questions must be answered. Which of the existing estimation methods fits the problem 97 stated and is "acceptable", and will such a technique perform better than the simple sample-and-hold estimator? The rest of this chapter is a step toward answering these questions. The Demand Model To decide on a filter which is suitable, an outline of the char- acteristics of the process that is going to be filtered and the type of assumptions going to be made is necessary. The overall relief system and exogenous circumstances should also be taken into consideration. A priori knowledge plays an important role here. The characteristics and assumptions of this process are as follows. l. Discrete observations of a continuous process imply a sampled-data estimation problem. These random observations are assumed to be independent but are generated by one process. 2. Incomplete knowledge about state structure of the process. The equations of motion of the process can be narrowed to a family of functions and even this information is not certain. 3. The demand function of the process, is nonlinear (variable rate of change) and stochastic. Population movements add to this non- linearity and randomness. 4. There is no data (observations) at the beginning. The observations are generated by surveys as we go ahead in time. There exists a relative lack of information. Sample surveys can provide data weekly, at best. Remember that there is a tradeoff between cost and more information. 5. The stochastic processes involved are assumed to be Gaussian. No 98 other information on error structure has been assumed. Specific descriptions about the demand model will be presented later. Filters and Predictors The problem of state estimation in a dynamical system, given noisy observations of the output variable, is of fundamental importance in control theory. When the models for signal and noise are completely specified, it is possible, at least theoretically, to obtain Optimal solutions to the state estimation problem under various optimality cri- teria (56). (80). The problem is considerably more difficult when uncer- tainty exists regarding the system parameters, the system model, or the noise statistics; especially if the uncertain quantities are time- varying. The derivations and applications of modern estimators and estimation algorithms are buried, so to speak, in the technical literature on com- munication theory, statistics, control theory, and others. Thus, ‘it is difficult to get a comprehensive summary of useful results. In this section, first, a brief explanation of several general estimation con- cepts and a few coments regarding the comparison of different methods is given. Some important techniques will also be discussed to try and clarify the assumptions and limitations of them. Various estimators are also compared, keeping in Inind the~ different characteristics of the process which was explained earlier, and a narrowing of options. The next stage is the selection of the "desired" estimator. 99 General Concepts Stochastic estimation is the operation of assigning a value to an unknown system state or parameter based on noise corrupted observa- tions involving some function of the state or the parameter. Any func- tion which assigns an estimate to each observation is an estimator regardless of whether the resulting estimate is close to or far from the "correct" value‘(85). The estimation Operation is termed optimal if the assignment of an estimate is in accordance with the optimization of some estimation criterion, or "cost function." This criterion is usually a function of the estimation error. An optimal estimate is a function of the received observations and chosen so as to minimize the expected value of the cost function. One of the most important categorizations in estimation is the distinction between linear and nonlinear estimators. A linear estimator yields a linear function of observation data as the estimate (85, Chapter 4). Nonlinear estimators give a nonlinear function as the estimate of the state. The problem of estimating the parameters or states of a nonlinear system, whether the nonlinearity is introduced by the model generating the stochastic process or by the observation mechanism, is a very complicated one and by no means is solved in a usable form in the general case (56, Chapter 5). (85, Chapter 7). The practical need for solutions to such problems has resulted in a large number of ideas and methods, but few procedures attack a specific problem and result in useful estimators. Generally, analytical solutions in closed form are not available and computational algorithms have been sought in their place. Thus, it appears that ingenuity as well as discretion is required in obtaining practical solutions to lOO meaningful nonlinear estimation problems (86). Another distinction is between probabilistic and deterministic models. Some techniques place the estimation problem in a probabilistic framework, meaning stochastic processes involved are modeled by sto- chastic differential and difference equatiOns. In the deterministic case the problem is looked upon as a deterministic problem of minimizing errors. In this form, very little statistical assumptions are required concerning the nature of the input disturbances or of the measurement errors. The absence of these assumptions corresponds closely to the physical situation in many practical problems, as the determination Of valid statistical data concerning disturbances is in itself a diffi- cult theoretical and practical problem. Classification and Analysis of Estimation Approaches One may distinguish two approaches which have been employed in developing modern state estimation theory. I. An approach in which the basic problem is taken to be Optimum linear filtering and prediction (59), (61). II. An approach in which the results are developed as elaborations of the classical method of Least Squares (95), (llQ), (l16). In this approach, the resulting estimates may be linear or optimum under certain conditions, but in general may be neither linear nor optimum. In fact, in most practical applications they are neither, because the necessary Conditions generally do not apply in practice. Most workers in the field have started from the "linear optimum filter" viewpoint, even though the papers developing the subject from the method of Least Squares viewpoint appeared lOl earlier. The discussion now turns to first stochastic, then deter- ministic approaches. Stochastic Methods The general linear (nonstationery) filtering prediction problem is essentially completely solved in the pioneering work of Kalman (59). and (60) and Kalman and Bucy (61). The parallel work of Stratonovich (112). (113) and Kushner (67), (68) provides the bases for subsequent developments in nonlinear filtering and prediction theory. These authors adopt the probabilistic approach in modeling of their problem. A host of papers and reports have appeared, following the funda- mental work of Kalman and Bucy, formally deriving their linear filtering algorithm via "Least Squares," "Maximum Likelihood," and other classical concepts. Statistical methods have also been formally applied to the nonlinear estimation problem. Due to a maze of problems encountered in nonlinear estimation and the relative success in linear estimation, many have attempted to apply related linear procedures to a class of nonlinear systems whose behavior is close to that of linear systems. Clearly, one can at best expect to derive an estimator which is approximately optimal. Using lineariza- tion of one sort or another, Kalman-like filtering algorithms were developed and applied to nonlinear problems. "Everyone derived his own Kalman filter, perhaps partly because of lack of understanding of Kalman's original work (56, Chapter 1)." Note that linearization of' the process generating the observations is not an easy task, even if the process model is accurately known. The Kalman-Bucy formulation of thefiltering problem assumes com- plete a priori knowledge of the process and measurement noise statistics. 102 So, any kind of extended Kalman-type algorithms is based on this assump- tion. But in the most practical situations, as our case, these statis- tics are either unknown or inexactly known. The use of wrong a priori statistics in the design of a Kalman filter can lead to large estimation errors or even to a divergence of errors (81). This technique is diffi- cult to use with respect to the problem being discussed due to incomplete knowledge of the process and measurement noise. To reduce or bound errors and shortcomings many have tried adaptive estimation to modify the Kalman filter to actual data. Extensive litera- ture exists on Kalman-type adaptive or extended filtering (81), (127) and is discussed later in this chapter. There exists a large class of estimators which are based on state space structure with uncertainties modeled by white processes. This .is due to the fact that the vast majority of real world problems can be expressed in the state space - white process form (101, Chapter 3). The use ‘of this model form simplifies the mathematical manipulation and provides a good basis for implementation. The general description of a white process is that it, has no time structure, meaning that know- ledge of the white process's value at one instant of time provides no information of what its value will be (or was) at any other time point (lOl, Chapter 3). Bayesian, Fisher, and Unknown-but-Bounded are three models which fit in the above definition. These three models are fundamentally different, both in terms of physical assumptions and interpretations and in terms of the type of mathematical concepts required. Any other estimator with a state space - white process form is a special case of the above models. Schweppe (101) bases his book on- this type of classi- fication of estimation theory. See Chapter 3 in (101) for a detailed 103 description and definition of the above models. The problem with the above estimators, considering the situation of discussion, is that they assume knowledge of state structure of the process and some information about different disturbances. As was men- tioned earlier, there is incomplete data regarding the model of the process generating the observations and the characteristics of its dis- turbances. It is good to know that many common estimators fall in the above class, including Autoregressive models, Moving-average models, and Maximum likelihood estimatorsto name a few. Note that the basic difference equations for the Baysian model estimator are the same as the Kalman-Bucy filter (101, Chapter 6). There exists another broad class of, estimators known as tracking algorithms or recursive filters which have been used extensively in military, civilian, and aerOSpace industries. This filter, which utilizes the engineering concept of feedback, tracks a maneuvering target by means of estimating its position, velocity, and sometimes accelera- tion using observations of the target. Most of the problems addressed. by this type of estimator are sampled-data estimation problems. These estimation procedures can generally be separated into two parts. One, the extrapolation (prediction), is a generation of the estimate of the state at time K + 1 based on the first K observations. The second part is the processing of the new observation to update the state estimation, i.e. to generate the estimate of the state at time K + 1 based on the first K i- 1 observations. In other words, the tracker uses the model output to predict what the next Observation will be and then it uses the difference between model prediction and the actual observation to "correct" the model. 104 Tracking problems have been looked upon from different angles, and various types of estimates have been designed. Polynomial-type filters and various kinds of extended Kalman are of this form. Kalman based tracking schemes constitute a large part of the literature (23). (107). (127). Most of the tracking techniques make different assumptions about state model for the target and rely on a statistical description of the maneuver as a random process. Considerable attention has been directed toward the synthesis of Optimal target tracking filters for real-time surveillance systems (7). (87), (108). As it was said earlier, some modifications have been necessary 'hi most situations, 'hi order to apply different techniques to the real world problems. This is due to the fact that many assumptions such as complete a priori knowledge of the process structure and measurement noise statistics can not be met in practical cases. These modifications are somehow' particular to each situation and usually' cannot be used for other cases. Different authors have designed their own estimator, based on their special interest, by modifying one basic estimation tech- nique. These changes can come under the title of adaptive estimators, whiCh adjust themselves to unknown or varying operating conditions. These adjustments could be caused by modifications of either external signals or the internal structure of the filter alone. Adaptation is accomplished by a variation of filter parameters (or if it is necessary, even by modifying the structure of the filter) so that a certain cri- terion of optimality which characterizes the operation of the filter is minimized (122, Chapter 6). See (22). (50). (79). (81). (107), (118), (120), (127) as a few examples of the vast literature on adaptive esti- mation theory. 105 An approach to tracking a maneuvering target has been developed by Bar-Shalom and Birmiwal (6) which does not rely on a statistical description of the maneuver as a random process. Instead, the state model for the target is changed by introducing extra state components when a maneuver is detected (adaptivity). Deterministic Techniques The need for probablistic assumptions, concerning the nature of the unknown inputs or the measurement errors, have been removed by deter- ministic approaches. It is important to know that many of the substan- tive results, including the fundamental theorems of recursive state estimation, do not require any statistical concepts or assumptions either in their formulation or in their proof. Even when the problem is formu- lated statistically, there is no essential difference in the treatment of problems where the state is stochastic and of problems where the state is nonstochastic or deterministic. Every problem in which the state is a stochastic process can easily be reformulated as a problem of estimating a vector of nonstochastic parameters, yielding identical solutions (115). For the purpose of deriving optimum recursive solutions to linear filtering and prediction problems, it is unnecessary to make several assumptions regarding the state equation, which have been thought (61) to be necessary. Swerling (115). (116) shows that every problem in optimum linear filtering or prediction ofrandom processes can be formu- lated as an equivalent problem of estimating a vector of constant para- meters by the method of least squares. The estimation procedures satis- fying the above requirements are Least Squares, Maximum Likelihood 106 (deterministic), and the method of Moments. In dealing with the method of Least Squares, it is necessary to distinguish a terminology distinction. the "method of Least Squares" is a class of computational procedures for deriving estimates from data while "mean square error" is an accuracy measure and “minimum mean-square error" is an Optimality criterion. In the ordinary least square problem, we simply choose the least square estimate such that the expected obser- vation comes as close as possible to the actual observation while mini- mizing the expected sum of squares of the errors (85, Chapter 8). A minimum mean square error estimate, on the other hand, is one for which the statistical mean square error is minimum among all estimates of a given parameter within some specified class of estimates, e.g., linear estimates, regular estimates, or arbitrary estimates (115). The usual classical approach to least square estimation leads to nonsequential (nonrecursive) estimation schemes. The basic objection to a nonrecursive scheme, when applied to a dynamical system, is that each time additional output observations are to be included, the entire least square calculation must be repeated. In general, the time required to perform this calculation increases with the number of measurements. However, for some cases, a recursive procedure has been developed which enables one to estimate the parameter value based only on the last esti- mate and the last additional Observation (30), (85, Chapter 8). Many authors have developed optimum linear recursive estimation procedures when the observation noise is correlated (9). (10). (18). The method of Least Squares is not only the oldest method in estimation theory but it has also been used, explicitly or implicity, in many other tech- niques. Detchmendy and Sridhar (30) have used the classical Least lO7 Squares method as the criterion for estimation. But they only have assumed the dynamical behavior of'the process to be described by an ordinary differential equation. A reasonable estimate of a parameter is that value which will make a given observation most likely, i.e., the parameter value which causes the conditional probability density induced on the observations to have its greatest maximum at the given Observation. This estimate is called the Maximum Likelihood estimate (122, Chapter 3). It has been shown (85, Chapter 8) that the methods of Maximum Likelihood and Least Square yield the same result in the special case of additive white Gaussian noise. Nahi (85, Chapter 8) treats the Maximum Likelihood estimation as a deterministic problem. He reaches the following two conclusions. First, that the results of Least Square estimation (a purely determinis- tic operation) with a probabilistic interpretation (via maximum likeli- hood) agrees in form with the Kalman linear estimator minimizing average quadratic cost. Second, the solution to the Kalman estimation equations requires knowledge of initial value of covariance matrix. This is the same as requiring a priori density function for the parameter to be estimated. Maximum Likelihood estimation does not require such data, and conse- quently the initial'conditions are not given a priori. Instead we wait until n Observations are received (since there are n parameters involved) in order to establish a probability density function. The method of moments is another procedure for providing an estimate of a parameter without requiring a priori knowledge of its probability density function, although, as in the case of Maximum Likelihood esti- mation, a conditional probability density on the observations is required 108 (85, Chapter 8). This method yields an estimate which is not necessarily optimal in any sense. Yet, like Least Squares method, it is intuitively appealing due to its simplicity. In many cases, the estimate approaches the true value of the parameter as the interval of observation becomes infinite, or as the amount of observed data becomes large. Information Characteristics There are two other problems related to estimation theory which would be discussed here. They are the notion of observation dependency and the question of the total number of observations. Since the problem in question is a sampled data one, it is appropriate to address the above concepts within this type of estimation problem. The ideas and notions of how to handle sampled data systems are very important, as a very wide range of practical problemS‘are of this form. Economic problems are the best examles of this type of system. Observations Of some economic variable, for example demand, are taken at discrete times even though demand itself is a continuous function of time. Some of the estimation techniques are concerned with models in which observations are assumed to vary independently. However, a great deal of data in business, economics, engineering and the natural sciences occurs in the form of time series, where observations are dependent and where the nature of this dependence is Of interest in itself. The body of techniques available for the analysis of such a series of depend- ent observations is called time series analysis (13). A time series may be considered to be composed of several components, including trend (progressive changes over a long period of time), seasonal cycles (regular periodic variation), irregular undulating variations (for 109 example, business cycles), and a random component whose effect may be transitory or permanent (5). Time series is a sampled data system, but since it has been assumed that random observations in question are independent, it is not necessary to explain time series analysis further. One should be careful about the question of the total number of observations and existing data. Of course, this is a problem more closely related to discrete-time and sampled data systems than to the continuous one. How many observations are needed from the process before being able to implement a specific method is a point to consider. And after starting the estimation procedure, how frequently is a new data point needed in order for the estimator to work properly? Some tech- niques may sound very well in theory, but when it is time to apply them, unless there exists enough data, one will see that the technique needs a period for "take-off". The length of this transient period is dif- ferent for various methods. For Least Squares based techniques and deterministic Maximum Likeli- hood estimator, we need to have enough information at the beginning. Econometric methods are also in this category. For a finite number of Observations, the Bayesian methods provide the optimum estimate by minimizing a certain loss function (122, Chapter 3). This is accom- plished by using the complete a priori information about the probability density functions, and unfortunately, by very tedious computations. The next section discusses the model selection process and the connection of our problem with the question of the number of observations. What Method to Choose As it was discussed, a number of different approaches and viewpoints have been applied to the estimation problem. However, almost all of the approaches assume some a priori knowledge of the system generating the Observations, ranging from complete description of the system's state equations and error structure down to incomplete knowledge of the mathe- matical model of the system and errors. The algorithms work well (at least theoretically) within the context of their underlying assumptions. If the observations are assumed to be random in nature, some a priori statistical description must be given to the maneuver process. This requires more knowledge about the system [than is normally available '(6). In addition, if the assumptions made do not correspond to the actual nature of the system, the techniques performance may be degraded. In choosing an estimation method, a distinction should be made of the difference between theory and practice. The term practical does not really have a viable definition. Practicality of a procedure changes at each situation. Schweppe (101, Chapter 8) suggests that one approach is to define the "most practical " filter to be the "simplest" one that performs the necessary job satisfactorily. The fact is that in many cases none of the estimates can be calculated exactly and the general tOEORy. is merely a guide to the choice of "reasonable" estimation tech- nique. Thus, the question of complexity and degrees of accuracy of a method should be decided case by case. In this situation, considering a third world country with problems such as a lack of trained personnel and high speed calculating machines which will pose to the job of infor- mation surveillance, the degree of complexity and accuracy is different 110 111 from the case Of, for example, a chemical experiment. Or in the case of a missile much of the control is based on the tracking method's ability, but for relief operation, the refined data on food deficit is one of the instruments in the possession of decision makers. Another important factor in selecting an estimation procedure is the problem of nonlinearities. The develOpment of successful estimators for nonlinear models is more of an art than a science (101, Chapter 13). Most of the work in nonlinear filtering is very theoretical, involving such hitherto obscure and (difficult subjects as stochastic differential equations and the ItO calculus, which require a fair know- ledge of measure theory for understanding (56, Chapter 2). The basic idea of handling nonlinear models by combining linearization with the linear model theory has been discussed in an almost uncountable number of papers. But this extension, most of the time, has been with regard to a particular problem the author has had in mind. No attempt has been made here to discuss all these possibilities. When a good mathematical model for the real world is available, Schweppe (101, Chapter 8 ) gives a list of steps to consider in answering the question of the selection of an estimation method. Having considered all the characteristics of the process in current study, it was concluded that there is no single technique that can do the job by itself. Non- linearities, incomplete information about state structure and noise model, lack of Observations at the beginning: and in the period that estimation takes place, are just some» of 'the problems being faced. In addition, there are some expectations that an estimator should be able to fulfil. Even though the accuracy of a technique is a very important factor, in a famine situation, efficiency and cost play major 112 roles. Few monetary resources exist in a third world country struggling with a wide Spread food crisis. Techniques which need a considerable number of professional personnel and computers, cannot feasibly be con- sidered, even if their performances are extraordinary. Also, due to lack of the data and costs involved in information surveillance, the method should have good transient and noise reduction capabilities. .The Selected Models After sunning up all the facts and important elements, together with the list of different methods available, it was concluded that it is better to choose a technique more suited to this problem than the others under the assumed conditions. Then, using the knowledge about the family of functions representing the process, some kind of adaptive design can be added to the basic estimation model in order to improve its performance. The technique which satisfies the previously stated conditions, is the Alpha-Beta (a-a) tracker. This method is conInonly used in radar applications to track positions and directions of an aircraft. Alpha and Beta refers to parameters of the filter. In order to expand the scape of the study for the sake of comparison of different estimation models under different conditions, two other scenarios have been assumed. One is when complete information about the process model and its noise statistics is available and the other when the process model is partially known. The Kalman filter was chosen, in addition to them - B tracker, for testing these scenarios. 113 Alpha - Beta Tracker This model is a very simple but highly effective form of data processing. It is a means of estimating the value and time rate of change of an input observed by measurement errors. There are no assump- tions regarding the state equations or the error structure of the model generating the Observations and no constraints exist on data correlation. In actuality, in a study which was conducted on time series analysis (5), this technique proved to be the "best" in comparison with other methods considered. The 0-8 tracker also has important minimum error properties. It is optimum for both the value and time rate of change tracking with-in the given performance measures (noise reduction and transient response). in the class of all fixed parameters, linear tracking equations, given) the following relationship (7) a2 (3.1) 2-a The tracker gives the minimum mean square error. The problem at hand is similar to radar tracking. There, the target can move in any direction and we have no clear idea about the model of motion or its noise. But we knOw other information regarding its velocity and movement capabilities. Also, no observations exist until the target comes into the domain of the radar. This tracker has also been used by Knapp (64, Chapter 6) to estimate per capita nutritional debt and consumption and grain storage levels in a famine situation. The governing set of equations for this samled data tracker is as follows (20, Chapter 8): 114 Yp(t) = Y(t - SAMPT) + SAMPT * Yd(t - SAMPT) (3.2) Y(t) = Yp(t) + a * (U(t) - Yp(t)) (3.3) Yd(t) = Yd(t - SAMPT) + B * (U(t) - YD(t))/SAMPT (3.4) where: Yp = value predicted from past information Y = smoothed value used as estimate Yd = function velocity estimate U = survey result SAMPT = sampling interval (years) t = current time a, B = parameters of the filter. Implementation of this tracker is quite simple. Each new piece of information enters as an input to the above set of equations. A predicted value is computed based on past information. The new data and the predicted value are combined to form a "smoothed" estimate of the present situation. The rate of change, or velocity, of the process is also estimated, which affects the next predicted value. So, the above filter gives a new estimate at each sampling point. A modification of Equation 3.2 can be used as a predictor between surveys. Replacing SAMPT with the differences between current time and the time of the past survey (t - T') produces the following equation, which is a comnon linear extrapolation equation. The function is pre- dicted to be moving in the direction indicated by. the rate of change Yd. Yp(t) = Y(T') + (t - T') * Yd(t) (3.5) 115 where: t = current time T' = time of last sampling point Yp, Y, Yd = as in Equations 3.2 - 3.4. An analysis of 0-3 tracker characteristics is presented by Cadzow (20, Chapter 8) and Benedict and Bordner (7). Selection of a and 8 plays an important role in filtering design. There are three consider- ations with this regard. First, to satisfy the stability requirement of the model, a critically damped response will require that a and B satisfy Equations 3.6 and 3.7. a = 2%: -8 (critical damping) (3.6) O: 8 :4 (system stability) ' (3.7) Two other parameter considerations stem from the necessary compromise between the conflicting requirements of good noiser smoothing (heavy filtering, sluggish system) and good transient capability (light filter- ling, fast system) of the tracker. Values of 8 close to one cause fast response to new information, for when 8 equals one, a is also one, according to Equation 3.6. Then Y(t) equals U(t) by Equation 3.3, no matter what the outcomes of Equations 3.2 and 3.4 are. This is interest- ing from a different point of view. If either a or B is chosen equal to one, the tracker transforms into the simple sample-and-hold scheme which was discussed before. This gives a good basis for comparison of the performances of different designs. For noise reduction, a value of 8 near zero is needed. Thus, the normal parameter selection processlimits 8 to the interval between zero and one. The value of a can be obtained from Equation 3.6 when 8 is 116 known. a is the free parameter which is left for construction of a tracker that gives the "best" compromise between noise reduction and transient capability or maneuver tracking characteristics of the system. The Kalman Filter Some of the characteristics of the Kalman filter have been mentioned and discussed earlier. As it is known, in order to use this method, state space structure and noise statistics of the process should be available. This filter has been used extensively in various fields .of science, especially in aerospace industries and orbit determinations where discrete observations are received from a continuous process (56, Chapter 8). This resembles closely the problem addressed here. The Kalman filter is the "best" linear filter in the sense that it yields the minimum error covariance matrix of any linear estimator (101, Chapter 6). Even though the filter is applicable to both continuous and discrete systems, it is more appropriate to present the continuous-discrete version of it, i.e. continuous process, discrete Observations. Given the continuous-time system model and discrete observations to be Sign) = 5n) 33(0) + §(t) gut), t 3 0 (3.0) dt ‘ y_(k) = M(k) _)((k) +_\_/_(k). k = 1, 2, (3.9) E [35(0) 39(0)] = _‘i: (3.10) 5 [gm 5%)] = gm (3.1)) E 121(k) you] = an) (3.12) 117 where: y_= Observation vector '5 = state vector _V = white observation noise vector .! = white system noise vector .§(0) = initial condition, which may be uncertain t = continous time index k = discrete time index E = statistical expectation d = derivative operator. The matrices f_, G, and _M are all assumed to be known. _)_(_(O). !(t). ‘V(k) are uncorrelated. An estimator to process the observations should be determined so as to yield an estimate of the state. The Optimal (nfinimum variance) Kalman filter for the above system consists of the equations of evolution for the state fit) and covariance matrix £(t). .Between observations, these satisfy the differential equations (56, Chapter 7) -g-—_)$(t) = fi(t) 33(0) . (3.13) dt d ‘ I o (3014) ——yu=5nLHU+gu)§n)+guon)cnrk3t_ CCTRL.i * RCAPWH]. where: GNEED = regional "need" based on the desired storage level at time t (tons/years) RWSTOG = available grain in regional storage at time t (tons) RCAPWH = capacity of regional silos (tons) CCTRL = control parameter DEMEST = regional estimated demand at time t (tons/years) i RWH index. Then REST is allocated as follows. llM-h TOTNEED(t) = . GNEEDi(t) (5.15a) 1 1 RGNEEDi = (GNEEDi(t)/TOTNEED(t))* REST(t) (5.150) 212 where: TOTNEED = total regional "need" based on desired storage level at time t (tons/years) RGNEED = allocated extra food based on the estimated regional demand at time t (tons/years) REST = extra available food at time t (tons/years) = as in Equation 5.14. GNEED, 1 Hence the total allocated food for each regional warehouse is ob- tained by the following equation. This equation is comparable to Equation 5.13. GRWHi(t) = RGNEEDi(t) + DEMEST1(t) (5.16) where: GRWH = allocated food to the ith RWH at time t (tons/years) RGNEED = extra allocated food based on the estimated regional demand at time t (tons/years) DEMEST = regional estimated demand at time t (tons/years) i RWH index. No matter which one of the policies has been used, the following equation calculates the total assigned grain to various RWH's. 4 TGRWH(t) = ifl GRWHi(t) (5.17) where: TGRWH = total food assigned to various RWH'S at time t (tons/years) 213 GRWH, i = as in Equation 5.11 or 5.13 or 5.16. Capital Acquisition Policies The capital development model was described in Chapter II. The pur-- pose of this section is to find the desired amount of capital (trucks and drivers) needed (YD in Figure 2.6). In order to carry the available grain assigned by previous policies into the country's interior and to be able to reduce the ship waiting line thus reducing the corresponding cost, "enough" capital is needed. Results of seaport operations (65) indicate that to avoid excessive buildups, the output rate from port's silo to land transport must be considerably larger than the expected input rate of grain in ships. The implication is that adequate transpor- tation is essential for the operation of any allocation policies. There is an important concept underlying the logistics operations and capital acquisition policies. It is the fact that capital is needed to deliver goods, not to satisfy the demand. Thus, the data which is available and usable for managers in their decisions for capital are: expected grain arrival (YRTONS), ship waiting line in the harbor (IWL). and available grain in the port's storages (STOG), the "supply" sources. The use of expected grain arrival rates as the base for capital _ development policies needs some explanation. In the real world and at the time of crisis, the managers are usually notified by the donors of the aid. Then, it takes some time for the aid to reach its destina- tion, meaning the port in this model. This gives the managers a buffer time to make the appropriate decision about the needed capital. Thus, the expected grain arrival becomes almost an exact information (taking into consideration the probable inconsistencies and events) and does 214 not need sampling and estimation. This lead time knowledge is a very important factor in the overall picture of famine logistical decisions as will be seen later. It depends on many factors, including Ship load- ing time at the origin, the distance between the origin and destination of aid, Ships characteristics, weather conditions, etc. For example, assuming a ship speed of 15 miles per hour, the approximate 8000 mile distance between the United States and India results in a 22 day lead time. There are, also, various constraints on capital acquisition deci- sions. As discussed in Chapter II, the foremost constraint is the limit- ing rate of capital acquisition, TRLIMIT. The effect of capital acquisi- tion delay (see Figure 2.6) can practically be removed by the lead time information on the food arrival rate. TRLIMIT computation varies country by country and in each case the system planners should decide how they are going to cope with capital shortages. Using this model, they can foresee the severity of the problem and design a policy for its solution, for example, trying to acquire capital with lower possible rate and stock pile it. Of course, this higher capital inventory will increase the cost, but it reduces the risk of running short of needed capital. The TRLIMIT computation, in the current model was explained in Chapter II. It was mentioned in Chapter I that famine has some early warning indicators and by recognizing and using them, the consequences of the disaster will be far less than what they could be. Usually, a central decision-making unit is set up by the country's authorities to handle the crisis. One of the first actions taken by this unit is acquisition of capital. The data on aid lead time comes into play here. The 215 decision makers, knowing when the first shipments of food are arriving, try to have enough capital to handle these arrivals. Thus, the capital decision-making process starts here and ends when the crisis is con- sidered to be over. This makes capital acquisition policies different from food distribution ones. Later policies become effective after food arrival. Capital development policies in the current study are modeled in two stages; one for the initial phase, i.e., before the food arrival and the other, for after the food arrival and up to the end of the crisis. This stems from the fact that different circumstances and infor- mation exist in the above stages. But before analyzing various policies in two stages, an important question should be answered. How will the information on the food arrival rate be transformed into the desired number of trucks and drivers? This question will be answered in the next section, followed by capital acquisition policies 'hi different stages. Conversion Factor To find a conversion factor which transforms data on expected food arrival into the desired amount of capital, one should start with the fact that all of the received aid is going to be sent to various regions, thus forming the food flows on different roads. Dividing these flow rates by the capacity of each truck (TGRC) results in full truck flows. In a steady-state, the number of trucks needed to keep these flows going is obtained by the product of full truck flows by the total delay time, related to capital flows, in the logistics system. The sum of all food flows is equal to the amount of available food 216 for distribution which itself is equal to the expected food arrival rate (YRTONS) in a steady-state. Thus, instead of multiplying each flow rate with its delay time, the sum of all full truck flows, obtained from YRTONS is multiplied with a weighted average of all delays in four existing cycles. A cycle is defined as the route which one truck travels when it is going from the port to a RWH and back. This weighted average of the delays, called SUMDEL, is time-varying and different procedures are used for its computation depending on which stage of capital development process it is concerned with. Thus it seems more appropriate that each procedure is explained together with its corre- sponding capital acquisition stage. NO matter which method is used, Equation 5.18 gives the conversion factor needed to obtain a desired number of trucks from the expected food arrival rate. CONVFAC(t) = SUMDEL(t)/TGRC (5.18) where: CONVFAC = conversion factor at time t (years/tons) SUMDEL = weighted average of all delays in four cycles at time t (years) TGRC capacity of a truck (tons). Note that TGRC in Equation 5.18 is needed to obtain the full truck flow from grain flow. The conversion factor and SUMDEL computations are modeled in subroutine CONVDEL in Appendix 8. Initial Capital Development Stage The purpose of this stage is to have "enough" capital ready for the start of operations when the first shipments of aid begin to arrive. 217 This capital accumulation process should take place such that minimum cost is attained. The duration of this stage varies case by case, but three important factors are the main determinants of it. One is the buffer time between the receiving of the food promise by a donor and actual arrival of the food at the port. The second factor is TRLIMIT, the limiting rate of capital acquisition. The third is the capital acquisition delay. After the decision making unit is set up, the managers, based on the food buffer time and TRLIMIT will decide on an appropriate control strategy such that the needed amount of capital is ready on time and the cost is minimal. This makes the duration of this stage of capital development time-varying. Now, if TRLIMIT is low, managers start stock- ing the capital sooner and vise versa. In the current study, this initial stage has been modeled (in the subroutine CAPITAL) such that the desired amount of capital is available for the start of operations. Thus, the effect of changes in TRLIMIT, capital acquisition delay, and food arrival lead time, is to change the duration of this stage of capi- tal development; hence, the cost of acquired capital. The initial process of capital acquisition goes as follows. First the initial food arrival rate (t = 0.0) is computed from the supply function (subroutine FOODAR). This rate, times the appropriate conver- sion factor, gives the initial desired number of trucks (TYD). This desired amount of capital becomes the input to the capital acquisition model developed in Chapter II. TYD remains constant during this stage, making the control problem a regulator one, in which an attempt to make the output of the capital development model equal to its input is made (see Figure 2.6). Except for the process of determining desired amounts of capital, two stages of capital acquisition are similar, because both 218 use the capital model of Chapter II. More on this subject will be dis- cussed in the next section. But the question of a conversion factor for this stage still remains to be answered. The end of this stage in the current logistics model, signals the start of Operations. The conversion factor for this stage is constant. The total delay on each cycle consists of the sum of the travel delays from port to a RWH and back to port, plus the expected service time at RWH and delay due to an "overnight" stay of trucks and drivers. Travel delay iS computed given the appropriate speed and distance by using the sub- routine DELAY (Equation 2.47). .Expected service time at a RWH is given by Equation 5.19. ESTIMEi = 1./(RMSSi/TGRC) (5.19) where: ESTIME = expected service time (years/truck) RMSS = maximum offloading rate at RWH (tons/years) TGRC = truck capacity i cycle index. Then each cycle's total delay is computed as follows. DELi = ESTIMEi + DISDELi + DELFi (5.20) where: DEL = total delay of a cycle (years) DISDEL = sum of the travel delays in a cycle (years) DELF = delay due to overnight staying of trucks and drivers at RWH's (years) A ESTIME, i = as in Equation (5.19). 219 Since in this stage the only available information about. different regions is their approximate populations, each region's population has been used as its weight in the SUMDEL computation, given by following equation. 4 SUMDEL = (l/TPOP) * iil POPi * DELi (5.21) where: SUMDEL = weighted average of all delays in four cycles (years) TPOP = total pOpulation of the country (#) POP = regional population (#) DEL, i = as in Equation (5.20). Now using Equation 5.18, the conversion factor is obtained. Remember that the desired number of trucks and drivers are equal in this stage. The capital pools at port (TPOL and DPOL) are incremented as new capital is acquired. Capital DevelOpment During the Crisis In this stage different information becomes available to the deci- sion makers. The food arrival rate and the delay on each cycle become time-varying. All of these make the desired amount of capital a function of time. This stage starts, as the initial stage ends, and it lasts to the end of the crisis. Availability of other information makes possible the generation of various policies for' determining (desired amounts of capital. These policies form the core of capital acquisition processes which will be combined with food allocation decisions in order to give the overall logistical policy structure. Due to their impor- tance, they will be discussed separately. The effect of each of these 220 general capital policies will be the same on the number of trucks and drivers. The purpose of this section is to clarify the existing dif- ferences in calculating the desired amounts of different capitals. Assume that the desired amount of capital (YD) has been given by one of the capital acquisition policies in the second stage. This number will be given as an input to the subroutine CAPITAL, which is used as the basis for calculating the desired numbers of trucks and drivers. Various modifications become necessary at this time. A new element appears in the cycle of each truck and driver, which was not present in the first stage. AS it was discussed in Chapter 11, certain percent- ages of trucks and drivers leave the system temporarily upon arrival from different RWH's. Trucks go to repair shops and drivers take a leave. The total number of trucks currently in repair and the total number of drivers on leave should be accounted for in capital acquisition decisions. Another important factor is truck attrition. Some percentage of the total trucks in the system goes out of work due to various reasons. No attrition for drivers has been assumed. This factor should be taken into consideration by the decision makers when they are computing the desired amount of capital. The following equations are the final form of the desired numbers of trucks and drivers, which will be used as inputs to the capital acquisition model developed in Chapter II. TYD(t) = (.l + DT * TATTC) * (YD(t) + TTIRS(t)) (5.22) DYD(t) = YD(t) + TDOL(t) (5.23) where: TYD = desired number of trucks at time t (#) 221 YD = desired amount of capital derived from one of the capital acquisition policies at time t (#) TTIRS = number of trucks in the repair shop at time t (#) DYD = desired number of drivers at time t (#) TDOL = number of drivers on leave at time t (#) TATTC = attrition coefficient OT 3 length of time increment‘ (years). Note that the conversion factor, which will be explained for this stage, has been used in deriving the YD. After computing the desired amount of capital, two stages of the capital development process use the same set of equations, in order to obtain the output of the capital acquisition model of Chapter II, which is the actual number of trucks in the system given by Equation 2.57. Of course, this equation is modi- fied for trucks in order to take into account the attrition rate, as explained by the following equations. ATTRATE(t) = TATTC * Y(t) . (5.24a) (5.24b) Y(t + DT) = Y(t) + DT * (U(t) + YN(t) - ATTRATE(t) - TRLOST * Y(t)) where: ATTRATE attrition rate at time t (#/years) TATTC attrition coefficient Y actual number of trucks in the logistics system at specified time (#) U = rate at which new trucks are added to the system at time t (#/years) YN rate at which trucks are discharged from the system 222 at time t (#/years) TRLOST capital lost coefficient OT length of time increment (years) The same Equation 2.57 is used for drivers DY(t + DT) = DY(t) + OT * (DU(t) + DYN(t) - TRLOST * DY(t)) (5.25) where: DY = actual number of drivers in the logistics system at specified time (#) DU = rate at which new drivers enter the system at time t. (#/years) DYN = rate at which drivers are discharged from the system at time t (#/years) ' TRLOST, DT = as in Equations 5.24. Note that Y and DY are the end results of the capital acquisition model in Chapter II, with TYD and DYD (Equations 5.22 and 5.23) as its inputs. At every simulation cycle (DT). the actual amount of capital is checked against its past value. There are two possibilities. Either the result is positive, meaning more capital Should be acquired, or nega- tive, meaning that a lower amount of capital is needed and the; excess capital should be released. When capital is increased, corresponding pools at port are also increased, but there must be enough capital in the pools permitting the discharge decision to be fulfilled. As it was said in Chapter II, two variables, TRLACK and DRLACK are introduced to keep track of the numbers of trucks and drivers which should be 223 discharged upon their return from RWH's. The following equations des- cribe the above processes. CHANGE (t + DT) = Y(t + DT) - Y(t) (5.26a) TPOL(t + D1) = TPOL(t) + CHANGE(t + DT) + TRLACK(t) (5.26b) DCHANGE(t + DT) = DY(t + DT) -DY(t) (5 27a) DPOL(t + DT) = DPOL(t) + DCHANGE(t + DT) + DRLACK(t) (5.27b) where: CHANGE = difference between current and past values Of actual number of trucks in the logistics system (#) ' Y = actual number of trucks in the logistics system at specified time (#) TPOL = number of trucks in the port's pool (#) TRLACK = number of trucks whose discharge has been delayed at time t (#) DCHANGE = number of drivers which are either acquired or will be discharged in period (t, t + DT) (#) DY = actual number of drivers in the logistics system at specified time (#) DPOL = number of drivers in the port's pool (#) DRLACK = number of drivers whose discharge has been delayed at time t (#). Now, TPOL and DPOL are checked. If they are positive, TRLACK and DRLACK will become zero. But if they are negative, that means the deci- sion is to discharge more capital. Note that one or both of them (TPOL ,0 224 and DPOL) can be negative. In this case the corresponding variable (TRLACK or DRLACK) will be equated with the negative amount of capital in the pool (trucks or drivers) and TPOL or DPOL or both will become ZEY‘O . Main Acquisition Policies The conversion factor for this stage of the capital development process is time-varying. It basically consists of the same elements of the first stage's conversion factor. The time-varying element is in- troduced into it by the delay of the trucks waiting to be unloaded at RWH's. Also, different and time-varying weights are used here for SUMDEL computation. In order to compute the delay of waiting trucks at RWH's, the following fundamental principle of queuing theory (steady- state condition) has been used. Lq = AWq (5.28) where: Lq = expected queue length Wq = expected waiting time in queue (excluding service time) for each individual entity A = mean arrival rate (expected number of arrivals per unit time). For the delay computation, Wq is needed. Approximate Lq and A are obtained from the model, using the following equations which have been modeled in the subroutine SILOS. (21051 (t + DT) = CIQS1-(t) + TRPOLi(t) (5.29) 225 TARi(t + DT) = TARi(t) + TRPi(t) (5.30) where: CIQS = incremental sum of the number of trucks waiting to be unloaded at RWH in period (0, t + DT) (#) . TRPOL = number of full trucks waiting to be unloaded at RWH at time t (#) TAR = incremental sum of the total truck arrivals in period (0. t + DT) (#) TRP = number of trucks arrived at time t (#) i : RWH index. Then, waiting time delay is given by Equation 5.31 (modeled in subroutine CONVDEL). Xi(t) = CIQSi(t)/TARi(t) (5.31) where: X = expected waiting time in the queue at time t (years/truck) CIQS, TAR, i = as in Equations 5.29 and 5.30. Now, using Equations 5.20 and 5.31, each cycle's total delay for the second stage of the capital acquisition process is calculated as follows. DELi(t) = Xi(t) + ESTIMEi + DISDELi + DELFi (5.32) where: DEL = total delay of a cycle at time t (years) X = expected waiting time in queue at time t per truck (years) ESTIME = expected service time per truck (years) 226 DISDEL sum of the travel delays in a cycle (years) DELF delay due to overnight stop of trucks and drivers at RWH's (years) RWH index. do II There is more information available at this stage than the first one. Hence, different weights can be used in order to compute SUMDEL. In the current model, total number of trucks in each cycle has been used as given by the following equation. (5.33) Wi(t) = TRPOLi(t) + PTSTRGi(t) + FTSTRGi(t) + RTSTRGi(t) where: W = ith cycle delay weight at time t TRPOL = number of trucks in regional offloading facilities at time t (#) PTSTRG = number of trucks on the way to a RWH at time t (#) RTSTRG = number of trucks on the wav back to the port at time t (#) FTSTRG = number of trucks stopping for overnight at a RWH at time t (#)" i = cycle index. Then, Eduati‘on 5.34 gives the SUMDEL for this stage of the capital acquisition process. SUMDEL(t) = (l/TW(t)) * iil Wi(t) * DELi(t) (5.34) where: SUMDEL = weighted average of all delays in four cycles at time t (years) TW = sum of four cycle weights at time t W = cycle delay weight at time t DEL = total delay of a cycle at time t (years) 227 i = cycle index. Again, using Equation 5.18, the conversion factor is obtained. In the case of road breakdown and transshipment the above formulas are modified. These modifications affect the total delay of each cycle by changing DISDEL, the sum of the travel delays in a cycle such that Old distances are replaced by new ones. Delays on the old road are added to the corre- sponding cycle, as long as there are trucks left on that road. Also, the number of trucks on the broken road is added to the corresponding cycle's weight. Other weight candidates usable in the above formulas are regional estimated demands. The model was tested using each regional estimated demand (DEMEST) as a corresponding cycle delay weight (W). Better system performances were achieved using a regional flow of trucks (Equation 5.33). but the differences were not Significant. In computation of the sum of the delays in a cycle, the delays at port pools and port loading facilities were not included due to the following reasons. First, considering the port loading capacity, loading time delay for a truck is negligible. Second, in an efficient system, delay at pools Should approach zero as was discussed in the performance indices section. A bigger SUMDEL means more capital. Thus, if the pool delays are in- cluded irI the conversion factor, more capital is going to be acquired, adding to the inefficiency of the System. Finally, note that the repair ShOp delay and the delay of drivers on leave, are not part of a cycle, Since just a fraction of the total flow passes through them. But the desired amount of capital is compensated for in these delays, as seen in Equations 5;22 and 5.23. Having had the conversion factor, various capital development 228 policies are now discussed. There are six such policies in this stage (modeled is subroutine CONTROL) which provide a good control action range for the decision makers. Each one of these policies will be an input (YD) to the CAPITAL subroutine which then is used to compute the . desired amount of capital (Equations 5.22 and 5.23). These policies will now be described. 1. To begin with, one naturally chooses to continue the first stage policy. In fact this control rule is the basis of all other policies of the second stage. This policy provides the major part of the needed capital. Other policies are used to cover the shortcomings of this policy. Equation 5.35 explains it. CAPNEED(t) = CPEFA * (n(t) * CONVFAC(t) (5.35) where: CAPNEED = the amount of capital needed at time t (#) YM = expected rate of food arrival at time t (tons/years) CONVFAC = conversion factor at time t (years/tons) CPEFA = control parameter. The same formula excluding CPEFA was used for the first stage of the capital acquisition process with a constant CONVFAC and YM evaluated at zero (initial value). This policy should be enough if everything goes as planned, but random events, the stochastic nature of the control problem, restrictions on different resources, and imperfect information change the picture. Even though excess capital is not desired (increase in total cost), in a famine Situation the shortage of capital has 229 a greater impact than an excess of it. If there are more trucks or drivers than needed, the extra can be discharged easily, but what Should be done if there was a shortage of them? Thus there should be some information that decision makers can use in conjunc- tion with the expected rate of food arrival in order to achieve a policy on capital acquisition. There are three pieces of data which will be used in the current study to construct the other policies. They are: ship waiting queue length (IWL), quantity of grain in the port storage (STOG), and quantity of grain waiting to be unloaded in the harbor (QGRAP). These state variables are chosen on the basis of the fact that the capital is needed to deliver goods, not to satisfy demand. Note that the above information was not available in the‘first stage of the capital acquisition process. This policy, like others which will be discussed later, is a combina- tion of the first policy with one of the above pieces of information. Here, the ship waiting line, IWL, is going to be used as the follow- ing equation explains, QUE(t) = IWL(t) - QUEFLAG (5.36) where: QUE = Ship queue length which is going to be used in decision-making at time t (#) IWL = actual ship queue length at time t (#) QUEFLAG = desired ship queue length. (#) If QUE is greater than zero, there is indication of a probable need for extra capital in order to clear the harbor. In that case 230 QUE becomes active, and is added to Equation 5.35 to give the follow- ing equation. (5.37) CAPNEED(t) = CPEFA * YM(t)""CONVFAC(t)‘+ CPQUE * QUE(t) * AVTONS/TGRC where: CAPNEED = the amount of capital needed at time t (#) CPQUE = control parameter AVTONS = average tons per Ship (tons/ship) TGRC = capacity of a truck (tons/truck) QUE = as in Equation 5.36 CPEFA, YM = as in Equation 5.35 CONVFAC = conversion factor at time t (years/tons). This policy is simply the previous one with the exception that the exact amount of waiting grain is used in the policy formulation. The use of AVTONS makes the above decision rule biased toward smaller ships. The exact amount of waiting grain is calculated from equation 2.71 and modeled ‘in subroutine CALCULT. There, it is used for cost calculation purposes. With this option, the basic capital acquisition policy (Equation 5.35) becomes, (5.38) CAPNEED(t) = CPEFA * CONVFAC(t) * YN(t) + CPQUE * QGRAP(t) where: CAPNEED the needed capital at time t (#) QGRAP total quantity of waiting grain at harbor at time t (tons) CPEFA, CPQUE control parameters CONVFAC conversion factor at time t (years/tons) 231 YM = expected rate of food arrival at time t (tons/years). The storage at port is an important indicator of the smoothness of the port's Operations. High storage levels Show that the grain is not leaving the port fast enough, forcing the offloading equipment to be underused and the ship queue to grow. This can happen either from a low demand or a Shortage of capital. In any case this infor- mation should be utilized in policy construction. The fourth policy uses the port's storage along with Equation 5.35 as follows. First the threshold amount of grain is reduced from the current level, and then the remainder is used, ASTOG(t) = (STOG(t) - TRSHOLD * CAPWH) / TGRC (5.39) (5.40) CAPNEED(t) = CPEFA * CONVFAC(t) * YN(t) + CPTND * ASTOG(t) where: ASTOG = available storage at time t (tons) STOG = total storage at time t (tons) TRSHOLD = threshold parameter of the port's storage CAPWH = port's silos capacity (tons) TGRC grain capacity of a truck (tons) CAPNEED needed capital at time t (#) CPEFA, CPTND control parameters YM expected rate of grain arrival at time t (tons/years) CONVFAC = conversion factor at time t (years/tons). 232 The last two policies are combinations of the previous four ones. Combining the basic capital acquisition policy given by Equation 5.35 with the second and fourth policies results in the fifth deci- Sion rule given by Equation 5.41. (5.41) CAPNEED(t) = CPEFA * CONVFAC(t) * YN(t) + CPQUE * QUE(t) * AVTONS/TGRC + CPTND * ASTOG(t) where: CAPNEED needed capital at time t (#) YM, CONVFAC as in Equation 5.35 QUE, AVTONS, TGRC ASTOG as in Equation 5.36 as in Equation 5.39 CPEFA, CPQUE, CPTND = control parameters. This policy was used in all the sensitivity and validity tests in Chapter IV. The Sixth policy is the combination of the first, third, and fourth policies which is given by the following equation. CAPNEED(t) = CPEFA * CONVFAC(t) * YM(t) + CPQUE (5.42) * QGRAP(t) + CPTND * ASTOG(t) where: CAPNEED. needed capital by sixth policy at time t (#) YM, CONVFAC as in Equation 5.35 QGRAP as in Equation 5.38 ASTOG as in Equation 5.39 CPEFA, CPQUE, CPTND control parameters. 233 Note that the last two policies blend the second, third and fourth together and give new options to decision makers. General Logistical Policies The combination _of various food allocation (FAP) and capital acquisition (CAP) policies form the general logistical control structure. Twelve different combinations are possible from two FAP and six CAP rules. Of course, the possibilities become infinite if the values of the control parameters are taken into consideration. The purpose of this section is to discuss various results obtained from different general logistical policies in order to choose the "best" policy among them. The "pareto" Optimum principle is the underlying criterion Of selection. A very important point with respect to this selection process is the fact that no optimization method has been.used in this study. But the discussions and results of this chapter form the basis for optimiza- tion work. The variables which have significant influence on model results and the important range of values of each control parameter are identified in this study. Because of the multiobjectivity feature of the current control problem, any optimization work is Significant by itself. But having the results of this section, the only remaining important task is the search for an optimization technique. Note that the Complex algorithm explained in Chapter III can only be used when a single objective function exists. As the number of control parameters and their ranges increase so do the complexities of the control and optimization problems. This has been kept in mind in designing previously mentioned policies. There 234 are twelve control parameters in this study and their descriptions are sumarized in Table 5.1. From these, the first eight are the most important ones. The regional silo level parameters do not influence the model outputs Significantly in the second food allocation policy. They become active whenever supply is higher than demand at the RWH level. But the story is different for the first food policy. Here, there are two parameters (CTRL and CCRS) which can influence the allo- cated food for each RWH and each of them alone or both together can be used. Table 5.1. Policy Parameter List LOWER UPPER NAME DESCRIPTION EQUATION LIMIT LIMIT CPEFA Capital acquisition, 35.35 0.0 none expected food arrival CPTND Port's storage effect 5.40 0.0 none CPQUE ship queue length, . 5.37, 5.38 0.0 none quantity of grain waiting to be unloaded QUEFLAG acceptable number of 5.36 0.0 none ships in queue CCRSi regional food allocation 5.9 0.0 none coefficient i=1, 2, 3, 4 CCTRLi . ith region's storage 5.14, 5.17 0.0 1.0 CTRLi level control, 1 = 1, 2, 3, 4 In the face of different possible policy combinations and the ranges of policy parameters as given in Table 5.1, the tasks of finding a "pareto better" control policy will be easier if policies with higher and better influence on the model are distinguished'and separated from 235 the rest. In this way the search domain becomes smaller and the computer cost decreases substantially. Otherwise, due to continuity of the ranges of control parameters, the number of policy possibilities is infinite. In the current study, various policies'were tested with different values of related parameters. Some of the better results obtained and the corresponding policies are summarized in Tables 5.2 and 5.3. Alpha- betic abbreviations stand for the policy category and the numbers identify the control rule in that class; For example FAP2 stands for the second policy in the food allocation category. The parameter values these results have been achieved at are reported below each policy name. In all policy experiments with the first food distribution policy, CCRS's were equal to one and CTRL's have been equal to .9. After some initial experiments it was found that the determination of numerical values for these parameters are quite impossible without any knowledge of the demand functions. Any arbitrary choice which works and results in better performance for one case does not give the same results when the scenario changes. For example, it is better to keep low the coefficients of the third and fourth regions because their demand is half of the first two regions under the assumed demand functions. But this policy does not work when the population moves. Thus it was concluded that with the above parameter values, on the average, this policy should result in better performance than any other choice of parameter values. But if a priori information exists on the demand function, certainly other choices are preferable. The storage level control parameters for the secOnd food policy, CCTRL's, were kept equal to .95 in all policy experiments. Even though the experiment results are not too sensitive to these parameters, higher 1236 Table 5.2. Averages and Standard Deviations of Overall Performance Measures for Selected General Policies (ten Monte Carlo replications) AVE. PER-SHIP TOTAL cosT SHIP COST WAITING TIME THRUPUT POLICY (3) BALANCE (3) (Years) (tons) FAPI 8 CAPI 190147475 132072 86699401 .0587 2691502 (36365026) (16530) (34989284) (.02317) (92352) FAPI 8 CAP4 184238268 117418 74604860 .0495 2882622 -(CPTND . .06) (33452465) (20160) (31159149) (.0198) (118570) FAPI 8 CAPS 184163963 115612 75055019 .05 2869955 (CPQUE - .01, (34098110) (20924) (31003187) (.01962) (120833) CPTND - .01, QUEFLAG - 5) FAP2 8 CAPl 184368828 85435 86627160 .0587 2694589 (37089807) (7556) (35082032) (.02336) (86394) FAP2 8 CAP2 181428921 73101 77904218 .0522 2820276 (CPQUE - .01, (35827411) (10809) (31120641) (.01998) (107788) QUEFLAG - 4) FAP2 8 CAP3 189339626 71389 72314137 .0483 2918394 (CPQUE . .0085) (38048860) (11638) (29172926) (.0185) (116103) FAP2 8 CAP4 178306164 72055 73460279 .0488 2906493 (CPTND . .06) (33184545) (10235) , (30361543) (.0192) (118238) FAP2 8 CAPS 178547072 70787 73914953 .0492 2895614 (CPQUE . .01, (33564497) (11051) (30686857) (.01946) (113232) CPTND . .04, QUEFLAG . 4) FAP2 8 CAP6 188800762 70852 71784188 .0477 2932647 (CPQUE - .0085, (37846927) (10959) (29187199) (.01852) (117434) CPTND - .03) * Nunbers in parenthesis represent standard deviation. 2377 Table 5.3. Averages and Standard Deviations of Regional Performance Indices for Selected General Policies (ten Monte Carlo replications) ~ srocx—our TIME (years) RATIO OF SUPPLY 10 DEMAND POLICY RHH 1 RHH 2 RHH 3 888 4 RHH 1 Run 2 Run 3 RHH 4 FAPl 8 CAP1 .9599 .9615 0.0 0.0 .7511 .7512 1.0 1.0 (.0038) (.003) (0.0) (0.0) (.0347) (.0346) (0.0) (0.0) FAPl 8 CAP4 .5426 .5459 0.0 0.0 .7761 .7757 1.0 1.0 (CPTND . .06) (.0992) (.0997) (0.0) (0.0) (.0436) (.0438) (0.0) (0.0) FAPl 8 CAPS .6449 .6492 0.0 0.0 .7783 .7776 1.0 1.0 (CP00E - .01, (.0375) (.0369) (0.0) (0.0) (.0438) (.0438) (0.0) (0.0) CPTND - .01, ' ouEELAC - 5) FAP2 8 CAPI .7866 .7742 .5552 .5689 .8118 .8219 .8454 .8323 (.13) (.1) (.098) (.1307) (.0277) (.0337) (.0349) (.0384) FAP2 8 CAP2 .6251 .6043 .3762 .4471 .8214 .8329 .8591 .8446 (CPQUE - .01 (.118) (.074) (.083) (.0665) (.0273) (.0339) (.0358) (.0382) QUEFLAG - 4) FAP2 8 CAP3 .5023 .4897 .3408 .3405 .83 .842 .866 .854 (CPQUE . .0085) (.0569) (.0524) (.0829) (.0573) (.0329) (.0398) (.0407) (.0388) FAP2 8 CAP4 .4508 .4084 .3459 .36096 .8298 .8412 .867 .8525 (CPTND - .06) (.0928) (.0853) (.0968) (.0982) (.036) (.0414) (.0418) (.0405) FAP2 8 CAPS .4431 .4078 .33415 .3523 .8315 .8429 .8664 .8521 (CPQUE . .01, (.0939) (.0936) (.0853) (.0794) (.0364) (.0422) (.0413) (.0395) CPTND - .04 QUEFLAG . 4) FAP2 8 CAP6 .4207 .386 .3246 .3281 .8317 .8442 .8661 .8533 (CPQUE . .0085, (.0905) (.0871) (.0859) (.0731) (.0363) (.0426) (.0416) (.0388) CPTND - .03) *Nulbers in parenthesis represent standard deviations. 238 values are better because this helps the task of clearing the port much easier in periods of high supply. 0n the other hand, these parameters become inactive in periods during which the demand is large. The expected food arrival control parameter CPEFA has also been kept equal to one in all policy tests. One of the underlying ideas of these experiments was to identify the important state variables which have significant impact on model results and can be used by policy makers. From different CAP policy structures, it is obvious that the desired amount of capital can be obtained by just increasing one of the coefficients. For example, CPEFA can be used alone. But in this case, these parameters should be time-varying or the result is either excess capital or a shortage of it. Also, since the magnitude of the expected food arrival is large, a small perturbation in CPEFA will result in a proportionally higher amount of capital. This is not the case when dealing with other state variables.' CPEFA's equality to one also stems from the fact that, at least theoretically, if everything goes well the acquired capital based on the expected food arrival should be enough. Finally, since this coefficient was equal to one in the pre-crisis stage of capital development, it seems better, for the sake of comparison, to keep it the same in the second stage of the process too. The first food allocation policy (FAPl) was tested with few capital policies due to its poor performance. As is shown in Tables 5.2 and 5.3, there is a sharp improvement in various performance criteria as FAPl is replaced by FAP2. It is important to remember that the above search is just a screening process, and is in no way an exhaustive one. The discussion and analysis of the results will be presented in the next section. Policy Results Analysis This section has two emphases. One is on the analysis of the numerical results of various policy experiments shown in Tables 5.2 and 5.3 leading to the choice of one of the policies. The other is drawing some conclusions which are useful for further extensions of this work, especially in the Optimization part. For a better understanding of the results it is good to remember the underlying basis of all designed policies. As was stated in the policy design sections, the concept of "well" stocked regional warehouses should be employed in order to achieve a better system performance. Doing so has two important implications. First, it covers for errors inherent in the estimation process of regional demand in the case of a sudden increase in actual demands, meaning better service from the logistical point of view. Second, it causes the port to clear faster, resulting in a shorter ship waiting line and, hence, reducing the cost. Looking at the results presented in Tables 5.2 and 5.3, the poor performance of FAPl is obvious. Unbalanced food distribution is the result of the fact that no information on demand has been used. In Spite of this, since the concept of "well" stocked regional warehouse has been utilized, there does not exist a large gap between the results of the two food policies. The imbalance in food policy has been re- flected in regional performances. Part of' the) better-than-expected performance of FAPl should be credited to the fact that no delay has been assumed for the availability of information on regional silo levels for the decision makers. Note that the impact of this data is minimum in FAP2 and effective only for the short period when supply is high. 239 240 An interesting point is the effect of regional silo capacity on FAPl policy results. Since the capacity of all RWH's are assumed to be equal, this substantially improves the service level at the regions with lower demands, as can be seen from Table 5.3. This can be modified by changing the values of corresponding control parameters (CTRL) which again brings up the problem of a lack of data needed as a basis for the above alterations. It is clear that the initial capital acquisition policy (CAPl) cannot be continued during the crisis without modifica- tions. Better performances of PAN with other CAP policies are due to the existence of more needed capital generated by the use of these policies. These results point to an important conclusion which is observed throughout other policy experiments, and that lis the impact of a little more capital on policy results. An item of the total lo- gistical cost, one as significant as the ship waiting cost is the cost of fuel. This cost was found to be the main reason behind the increase in transportation cost, and which offsets some of the cost saved by the shorter ship waiting time (the result of the use of other CAP policies with FAPl). The increase in THRUPUT (last column of Table 5.2) also increases the cost of capital acquisition and fuel. By minimizing the effect of regional silo level data (RWSTOG) in the design of the second food allocation policy, two undesired features of this information have been removed. One is the use of unlagged actual RWSTOG figures, which is a departure from a real world situation. Second is the problem caused by the capacity of RWH's. These make FAP2 to be nearly based on estimated regional demands. Of course, if more infor- mation is available for the decision makers, this policy (FAP2) might not be a desirable one. But in the face of the model's underlying 24l assumptions on the available data of supply and demand it proves to be sound. Hence, FAPl is discarded and this reduces the number of important policy parameters to the first four of Table 5.l. The difference between the other general logistical policies, is the question of which capital development policy has been used. Again, it is seen that relying only on the expected food arrival rate is not enough for capital acquisition. A higher balance and ship waiting cost and lower thruput are caused by the shortage of capital. A lower than expected total cost for CAPl is the result of lower capital cost. These problems are solved by going from CAPl to CAP2 as the performances improve, but still there is insufficient capital. These conclusions were reached in theprocess of working with various policies and trying to obtain a "pareto better" policy by changing the control coefficients. Generally, the comparison of idle time due to the shortage of trucks (TIDTR) and the idle time caused by the shortage of grain (TIDGR) is a good indication of the need for extra capital. If the idle time atri- butable to trucks increases faster than grain shortage, more capital can be utilized. This excess capital need is satisfied by increasing the appropriate capital control parameter. This fact was used in the process of arriving at the final results of various policies. The last four general policies' performances are quite close to each other with some exceptions. The use of the quantity of grain wait- ing to be unloaded (,QGRAP) causes the acquisition of useless capital. This is the main reason for an increase in the total costs of CAP3 and CAP6 policies. Of course, this extra capital provides better service as seen from the reduction in balance index. It was said in previous sections that by looking at two state variables over time, capital 242 acquisition decisions can be adjusted in order to Optimize capital effi- ciency. These are capital pools at the port, meaning TPOL (truck pool) and DPOL (driver pool). For policies with QGRAP option, TPOL and DPOL were higher than the other policies. This needs further explanation, since important elements are at work behind these results. It was concluded in Chapter IV that the port offloading capacity is a significant factor in the overall performance of the logistics model. This fact was reiterated by the policy experiments. During the model operation there is a stage at which the port offloading equip- ment is working at its limit capacity. In that case, the cost of ship waiting time is not going to change by changing the policy. Then the extra capital acquired by the ship queue information is going to be useless after the port storage has been depleted. This causes an in- crease in total transportation cost which in turn increases the total cost of logistics. Under the assumed supply and demand functions, this phenomena takes place in the second and third quarter of the year. The better performance of CAPS policy, where ship queue length has been used, is probably due to the use of average ship tonnage, AVTONS, and the use of port storage in the policy structure. An important result obtained from the extra capital discussion is the tradeoff between cost and balance indices. It was observed that as more capital becomes available, along with the increase in cost, the balance performance improves until some peak is reached, after which no significant change happens and only the cost increases. The better performance of the fourth capital acquisition policy, CAP4, is primarily caused by the following fact. When the port's stor- age, STOG, increases, extra capital can be utilized. Exactly at the 243 same time, the appropriate coefficient, CPTND becomes active resulting in the desired decision and vice versa. But this does not happen when ship queue data is used. Actually, when the queue is long and STOG is low, it means that the port is working at its limit offloading capa- city; hence extra acquired capital due to the queue is not usable. This shows that the port's storage level is an important state variable which should be used in the deciSion-making process. The above policy conclusions are also reached with respect to the regional performance indices (Table 5.3). The policies with better overall performance, have lower stockouts and higher ratios of supply to demand. The equality of these indices for different regions signals a good overall balance, which is also desired. This, in fact, shows whether the overall relief operation's goal, which is balanced distribu- tion, has been achieved or not. Of course, optimal policy will result in such a balance. In what follows, an attempt is made to answer the apparent inequalities of these measures in the current study. The differences in the regional performances of two different policies are reflected in their overall performance and thus, does not need further discussion. The two better policies, CAP4 and CAPS have very similar regional performances. The question is the inequalities between various regions for a given policy. The most important factor is the difference between regional demands. It is clear from the results that the regions with similar demands have similar performances. In Chapter II, the error of estimation was modeled proportional to the true value (Equation 2.52). Thus the regions with the greater demands have generally poorer performances. (See Figure 4.] - 4.4 for a better understanding of the above issue). In spite of all of these, the "pareto 244 better" solutions, i.e. CAP4 and CAPS, have very close inner equality of regional performances. Other elements couple with the demand factor to give the results shown in Table 5.3. For example, the stockouts were defined to be the total time that supply is less than demand. In the case of rapid fluc- tuations in demand, this index becomes biased toward the regions with higher demand rates. This follows from the time it takes to raise the supply level to match demand, resulting in an increase of the stockout time. An important element which should be recognized in analyzing all of the results obtained from policy experiments is the number of Monte Carlo replications (MONRUN). In the current study, MONRUN was set equal to ten, but in a large scale project, it would be wise to increase this number considerably. There are some final comments to be made before closing this sec- tion. It is necessary to emphasis the importance of an amount of capital sufficient "enough" in arriving at a better solution. Increasing the cost by acquiring more capital helps to offload the ships faster, thus reducing the total cost by lowering the tremendous cost of ship waiting time. But this should be continued only as long as the tradeoff is of benefit to decreasing the total cost. The sign indicator that this limit has been reached is the ship offloading rate, RMS. Zero idle time due to average storage capacity (TIDCAP) and low storage levels at port explain approaching to that limit. So, if the offloading equip- ment is working at the maximum rate, any increase in capital most proba- bly increases the total cost. Only the policies which reduce the ship queue at port are "cost cutters". The capital pools, TPOL and DPOL, at the port are good indicators 245 of a sound acquisition decision. Everything else being almost "accept- able", low TPOL and DPOL and their numerical equality or closeness show not only the soundness of policy but also the efficient use of capitals. Finally, in comparing different results, the random error should not be overlooked. The "Pareto Better" Policy The multi-objectivity feature of the control problem under study causes the existence of infinitely many noninferior solutions to the optimization problem. One noninferior solution is as good as the other and strictly speaking, one cannot be compared with another (99). The analysis of the results in the previous section suggests the general logistical policy FAP2 and CAP4 as a candidate for the "Pareto better" policy. The following are some explanations for this choice. One of the conclusions drawn from the experiments was the fact that the port storage level (STOG) contains enough, if not all, information regarding the port's activity. It was seen that the use of ship waiting line data will result in complication when the port reaches its offloading limit. Another characteristic of this policy is its simplicity. The number of control parameters is minimum, and one parameter (CPTND), actually should be perturbed for policy experiments. Note that this choice is by no means the "last“ word. It is the result of the assumed framework of this study. The purpose of this section is to study the above policy in more detail. First, various values of the parameter CPTND are examined in order to present different tradeoffs for various performance measures. Then the robustness of the policy is tested in several ways. 246 Providing data on different opportunities possible by a policy is good information for decision makers. For better management of the logistics system, the managers should know about the consequences of change in policy parameters. For this reason the corresponding control parameter, CPTND was changed and the results are presented in Tables 5.4 and 5.5. The case of CPTND equal to zero has been included for comparison purposes. The total cost reaches its minimum at CPTND equal to .04 and its general shape (U form) can be seen from the results. As the value of the control parameter, CPTND, increases, so does the available capital, resulting in the increase of the transportation cost and reduction of ship waiting time cost. This tradeoff is good until the total cost passes through its minimum and starts to increase. As the quantity of capital increases, the port thruput also increases and the balance measure's best value is obtained at CPTND equal to .06. Actually the results for the CPTND values around .06, are very close to each other, but still show the tradeoff between cost and service. Looking at the overall balance index and regional measures for the control parameter values greater than .05, it is seen that as the value of CPTND increases, the balance measure slightly increases as the stockouts start decreasing and ratios of supply to demand stay the same more or less. At first glance, this seems a contradiction, but a closer analysis of the results reveals an interesting policy design fact. As the policy parameter increases, more capital is available in the first quarter of the year. This causes the port storage to deplete faster. when the "crunch" comes, meaning the suden sharp increase in the demand, the well stocked regional silos sustain them- selves for a while. This is the reason for the reduction in the 247 Table 5.4. Means and Standard Deviations of the Overall Performance Criteria for the "Pareto Better“ Policy (ten Monte Carlo replications) AVE./SHIP PORT PORT TOTAL COST SHIP COST WAITING ' INPUT THRUPUT CPTND (S) BALANCE ($1 TIME (YRS. (tons) (tons) 0400‘ 184368828 85435 86627160 .0587 2863985 2694589 (37089807) (7556) (35082032) (.02336) (88915) (86394) .02 178934640 73416 75862475 .0507 3031605 2885178 (33857896) (10434) (31722716) (.02038) (140739) (112184) .04 178065088 73230 74029477 .0492 3038164 2896264 (33249528) (10573) (30823798) (.01953) (143178) (114516) .05 178171745 72535 73751196 .0490 3043079 2901017 (33214855) (10860) (30538240) (.01933) (143429) (118077) .06 178306164 72055 73460279 .0488 3045552 2906493 (33184545) (10235) (30361543) (.01921) (143920) (118238) .07 178501349 72131 73383839 .0488 3045552 2908228 (33201831 ) (9691 ) (30359080) (.01 920) ( 143920) (115755) .08 178691017 72460 73237665 .0487 3047636 2911545 (33214199) (9188) (30311930) (.01918) (144834) (115168) .09 178886008 72844 73070678 .0486 3046226 2915040 (33227797) (8579) (30226593) (. 01914) (143886) (115541) * Numbers in the parenthesis represent the standard deviations. 2423 Table 5.5. Means and Standard Deviations of the Regional Performance Measures for the “Pareto Better” Policy (ten Monte Carlo replications) STOCK-OUT TIMES (years) RATIOS 0F SUPPLY T0 DEMAND CPTND RHH 1 RWH 2 RWH 3 RHH 4 RHH 1 ANN 2 RHH 3 ROM 4 0.0 .7866 .7742 .5552 .5689 . .8118 .8219 .8454 .8323 (.1303) (.0999) (.0981) (.1307) (.0277) (.0337) (.0349) (.0384) .02 .4904 y .4653 , .3895 .4071 .8279 .8391 .8636 .8474 (.0979) (.1019) (.0880) (.0982) (.0343) (.0419) (.0409) (.0406) .04 .4649 .4289 .3632 .3789 .8298 .8410 .8652 .8494 (.0992) (.0982) (.0861) (.0959) (.0364) (.0423) (.0413) (.0407) .05 .4578 .4149 .3531 .3695 .8298 .8412 .8661 .8508 (.0972) (.0911) (.0903) (.0970) (.0364) (.0419) (.0413) (.0402) .06 .4508 .4084 .3459 .3810 .8298 .8412 .8670 .8525 (.0928) (.0853) (.0968) (.0982) (.0360) (.0414) (.0418) (.0405) .07 .4483 .4041 .3413 .3542 .8297 .8412 .8682 .8542 (.0925) (.0841) (.0979) (.0985) (.0356) (.0411) (.0423) (.0411) .08 .4447 .4010 .3362 .3483 .8295 .8412 .8691 .8556 (.0913) (.0817) (.0979) (.0976) (.0353) (.0409) (.0426) (.0416) .09 .4407 .3992 .3312 .3413 .8292 .8412 .8702 .8570 (.0894) (.0808) (.0972) (.0973) (.0349) (.0407) (.0429) (.0421) * Numbers in parenthesis represent the standardrdeviations. 249 stockouts. But, later, the effect of the "crunch" appears in the balance measure, as the low port storage can not supply enough grain. The regions with higher demands contribute more to the balance criterion. Note that the above scenario has been the direct consequence of the shapes of supply and demand curves. It was said that this informa- tion is not usually available for the decision makers. Testingthe Policy Robustness The purpose of these tests is to examine the robustness of the selected policy under different circumstances. It was said that one of the desired characteristics of a good policy is its generality, mean- ing that it can handle various scenarios. This was based on the fact that very little information is available about the famine situation and any famine logistics model should be able to Operate in different conditions. This point has been stressed several times in previous chapters, especially in the policy design section. Several robustness tests have been conducted and will be discussed here. The first robustness test has been done by changing the supply and demand functions. This is the most important test because all the movements, flows and decisions are based on these two functions. This ‘ is also a test for other components of the logistics model, espcially the information subsystem and the estimation technique ( 6-8 tracker). Figure 5.3 illustrates the new form of the supply and demand curves. There are several differences between these curves and the original supply and demand fUnctions (Figure 2.5). The initial values of both supply and demand are higher in this new version. The implications of this change will be discussed when the results of this test are 250~ Demand and Supply Rates (tons/years) <3 .91 SUPPLY YnlO' Time a 6 T— r T 1 r ‘12 (years) Figure 5.3. New Supply and Demand Functions for the Robustness Test of the "Pareto Better" Policy 251 analyzed. The supply is flat at the top, meaning a more uniform arrival of ships and after some point, when the demand becomes equal to the maximum supply, the demand values are computed by multiplying the value of supply by some known constant. In the current study this constant is equal to 1.05. These changes in the supply and demand functions will inCrease the area under both curves. But it is desirable to have the crisis level remain as before. This causes the reduction in the maximum rates of demand and supply. Of course, the total quantities of demand and supply are slightly larger in this new version. The results of this robustness test is summarized in Table 5.6. The number of Monte Carlo replications (MONRUN) is equal to ten. By looking at the results, one can observe a big reduction in the ship waiting cost, but this decrease has not been fully reflected in the total cost. To find out where this extra cost is coming from, a detailed cost analysis was conducted in order to itemize the cost func- tion. First, it is helpful to know that two factors are responsible for the reduction in the ship waiting cost. These are the more uniform arrival of ships and the lower maximum rate of food arrival in comparison with the limit offloading capacity at port (RMS). This new form of the supply function is equivalent to the increase of the offloading capacity, the importance of which has been discussed in previous chapters. Again the fuel cost was found to be the prime cause of the increase in the transportation cost, which offsets some of the cost saved by the shorter ship waiting time. More than eighty thousand tons of extra grain are shipped through the port under the new functions. This causes 252 Table 5.6. Results of the Robustness Test Due to New Demand and Supply Functions TRANSPORTATION PORT PORT TOTAL COST COST INPUT THRUPUT SCENARIO (S) BALANCE SHIP COST (6) (tons) (tons) Original 178306164 72055 73460279 88979645 3045552 2906493 F“"Ct‘°"s (33184543) (10235) (30361543) (3523859) (143920) (118238) New 161232975 69061 56814650 90160379 3103107 2981750 F”"°t1°"s (25539016) (11002) (22161571) (3365487) (153415) (118886) STOCK-OUT TINES (years) RATIOS 0F SUPPLY TO OENANO RNN 1 RNR 2 RNN 3 RNR 4 RNN 1 RNN 2 RUN 3 RNN 4 Original .4508 .4084 .3459 .3610 .8298 .8412 .8670 .8525 F“"°t‘°"‘ (.0928) (.0853) (.0968) ( 0982) (.0360) ( 0414) (.0418) (.0405) New .4465 .4881 .3747 .3929 .8772 .8482 .8815 .8736 F“"°t‘°"s (.0502) (.0640) (.0785) (.0646) (.0386) (.0358) (.0465) (.0268) * Numbers inside parenthesis are the standard deviations. 253 not only an increase in fuel consumption, but also increases the cost of capital needed fOr carrying the extra grain. Another factor is the cost of capital in the initial stage of the capital development process. It was mentioned that the initial value of the supply curve is higher in the new version. This says that more capital is needed for the start of operations, or that more capital Should be acquired and probably kept for longer periods (because of TRLIMIT) in the pre-crisis stage, thus increasing the total transportation cost. The increase in the regional stockout measures is the direct conse- qunce of the new form of supply and demand curves. In the period of peak demand the supply is much lower than the original supply function. This causes stockouts to increase. . But the more uniform arrival of the grain creates the some kind of stability in the operation. It causes the reduction in the balance measure and the rise in the ratios of supply to demand. Of course, part of this good performance Should be credited to the higher amounts of supply available in the new scenario. The uniform ship arrival also causes the reduction in most of the standard deviations of performance measures. An important conclusion of the above test is with regard to the reduction of Ship waiting time cost and total cost due to more uniform arrival of the Ships. This suggests that in the time of crisis in a country, it is better that an international agency be selected as a main contact of all possible donors. This organization in cooperation with the decision makers in the involved country should arrange a more uniform arrival of the food. The second robustness test is based on population movements. It was stated in Chapter II, that the demand model can simulate the probable 254 pOpulation movement during famine crisis. By this model feature dif- ferent scenarios can be generated in order to test the policy robustness. The “Pareto better" policy was tested by letting the population move from the first and the second regions into the third and fourth ones, with more people moving into the fourth region than the third one. This was done by letting the population movement parameters have the following values: 81 = -.15, 82 = -.15, and B3 = .l. The test results are presented in Table 5.7 with MONRUN equal to ten. When the population moves, its effect will appear in the policy result after the new demand estimates are transmitted to the decision makers. This adds a great deal of error to already inherent estimation errors, resulting in a worsening of the balance criterion. The new (error causes the excess shipment of grain to the first and second regions and the lack of enough supply in the third and fourth regions. This can be observed by looking at the regional performance indices. The first two regions' stockout times and ratios of supply to demand improve as the ones of the second two regions' decline. The fourth region is hit harder because more people move into that region. The reduction in the total cost and the ship waiting cost is due to the shorter dis- tances the trucks should travel. AS more and more people move, larger quantities are shipped to the third and fourth regions. But these regions are closer to the port than the other two, less fuel consumption and faster capital turnover. The result is a high availability of capital at the port which allows the ships to be offloaded faster. Road breakdowns are used as the third robustness test for the selected policy. Different times and different routes were selected in order to test a variety of scenarios. Again MONRUN was set equal 255 Table 5.7. Results of Policy Robustness Test with Population Movement Scenario ‘ AVE PER SHIP PORT PORT TOTAL COST SHIP COST NAITINC TINE INPUT THRUPUT SCENARIO S BALANCE (4) (years) (tons) (tons) No. Pop. 178306164 72055 73480279 .0488 3045552 2906493 "°'°'°"t (33184545) (10235) (30361543) (.01921) (143920) (118238) Population 176848253 78732 71886902 .0478 3066386 2940004 "°'°'°"t (33052067) (4316) (29768132) (.01887) (149827) (117323) STOCK-OUT TINES (years) RATIOS 0F SUPPLY T0 OENANO RHH 1 RHH 2 RHH 3 RNH 4 RHH 1 RNH 2 RNN 3 RNH 4 No. Pop. .4508 .4084 .3459 .3610 .8298 .8412 .8670 .8525 "°"°""t (.0928) (.0853) (.0968) (.0982) (.0360) (.0414) (.0418) (.0405) Population .4364 .3772 .4135 .4620 .8387 .8529 .8354 .8072 "°'°'°"t (.0948) (.0937) (.0773) (.0761) (.0401) (.0480) (.0353) ' (.0304) * Nunbers in the parenthesis represent the standard deviations. 256 to ten and the effects of road breakdown on various performance criteria was observed. These results are tabulated in Tables 5.8. Routes number two and fOur are selected for breakdowns which occur either at times equal to .26 or .56. Since the average Ship waiting time and its cost, and the port input were the same for all of the cases, they are not reported. Instead, the total cost of transportation is given in the Table 5.8a.f A The excellent performance of the policy and the model is obvious. For better understanding of the result it is necessary to remember that the distances of new roads are _5_9_O_K_M for the secondnroute and M for the fourth one. Thus, the distance does not change for the second route, but it increases fifty percent for the fourth road. Another factor is the length of time the auxiliary-road is used, i.e. the time when the incident happens. Looking at the results of route number two, one can see that the total cost and balance are better for time equal to .56 than .26. This trend can also be seen for the other route. Small perturbations of the regional performance measures are in part due to the assumed policy of dispatching the full returning trucks from the broken road to the same regional warehouse. Before closing this section, it would be well to note that the Monte Carlo analysis by itself is a weak robustness test. All the results presented in this chapter are obtained as the model had been operating in the Monte Carlo mode. In this way, at every iteration a different sequence of random numbers is used, hence Slightly different scenarios are generated. 257 Table 5.8a. Mean and Standard Deviation of Overall Performance Indices ~' Resulted from the Road Breakdown Robustness Test TRANSPORTATION PORT TOTAL COST COST THRUPUT SCENARIO (3) BALANCE (5) (tons) No Breakdowns 178306164 72055 88979645 2906493 (33184545) (10235) (3523859) (118238) Breakdown (T = .26) ' Route #2 178420594 72378 89101607 2906501 (33167400) (9798) (3704836) (118251) Route #4 180506992 72541 91191194 2906473 (33476270) (9607) (8816501) (118209) Breakdown (T = .56) Route #2 178381512 72069 89058221 2906660 (33172857) (10213) (3637272) (118493) Route #4 179436276 72225 90101296 2906350 (33170913) (9995) (5877131) (118022) * Numbers in parenthesis represent the standard deviations. 2581 Table 5.8b. Regional Performance Measures Resulted from the Road Break- down Robustness Test STOCK-OUT TINES (years) RATIOS OF SUPPLY TO OENANO SCENARIO RHH 1 RNH 2 RHH 3 RHH 4 RNH 1 RHH 2 RNN 3 RNH 4 No Breakdowns .4508 .4084 .3459 .3610 .8298 .8412 .8870 .8525 (.0928) (.0853) (.0988) (.0982) (.0380) (.0414) (.0418) (.0405) Breakdowns T . .26, Route #2 .4502 .4073 .3454 .3601 .8298 .8412 .8670’ .8525 (.0944) (.0889) (.0971) (.0996) (.0360) (.0414) (.0417) (.0405) T - .26, Route #4 .4505 .4072 .3452 .3596 .8298 .8412 .8670 .8525 (.0937) (.0871) (.0972) (.1005) (.0358) (.0414) (.0417) (.0406) T . .58, Route #2 .4508 .4083 .3482 .3609 .8298 .8413 .8670 .8525 (.0928) (.0855) (.0965) (.0982) (.0380) (.0415) (.0418) (.0405) .56, Route #4 .4512 .4085 .3465 .3809 .8296 .8412 .8670 .8525 (.0920) (.0852) (.0964) (.0982) (.0357) (.0414) (.0417) (.0405) * Numbers in parenthesis represent the standard deviations. Sumary The model seems to perform well based on the reliability and expectedness of outputs. The control issue of the logistics system was discussed in some (detail in this chapter. After probing in the scope and the nature of the control problem, two important decisions were identified which Should be answered by the system decision makers. These were the questions of food allocation and capital acquisition. Some policies were designed for the solution of these problems such that a set of performance indices are optimized in pareto sense. The decision rules to implement a relief plan must stipulate what is to be done, when to do it, and at what rate. Generality and Simpli- city are also two desired features of any control policy. It was seen that all decisions are based on supply and demand information. Food distribution policies were based on estimated demands and regional Silo levels where capital development decisions were derived primarily from the expected rate of food arrival. Based on the fact that in a famine situation trucks and drivers are only needed to deliver foods and not to satisfy demand, it was concluded that other information can be used in designing capital acquisition policies. These were the port storage level and ship queue in the harbor. After many experiments with different overall policies as the related control parameters were perturbed, one policy was chosen as the "Pareto better" policy. The robustness of this policy was tested in different ways. An important conclusion of these tests was the sharp reduction in the Ship waiting time cost due to a more uniform arrival of the grain. A significant valid research project which was only a. 259 260 touched in passing is the optimization task of the current control problem. CHAPTER VI SUMARY AND CONCLUSIONS Sumary Famine relief logistics is viewed as a complex process involving the dynamic interactions of many subsystems. Necessarily simplified analytical models have been found which are of significant use for either explanation or prediction of system behavior. The purpose of this chap- ter is, first, to sumarize the foregoing chapters as one entity. Then, the major results of the study are presented, followed by observations concerning the practical utility of the model. Finally, the areas for further research are discussed. A sketch of various sub-systems involved in a famine relief, and their interconnections was discussed in Chapter I. In that introduction, an attempt was made to shed some light over the wide spectrum of issues and problems which are associated with the overall relief Operations. The economic, socio-political, and cultural bottlenecks were also ex- plained. Since the emphasis of this dissertation is on famine logistics, the tendency was more toward discussing the problems most likely to be encountered in that area of relief systems. To stress the importance of logistics in a food crisis, Dando (28) identifies "transportation famine" as one of the basic types_of this kind of disaster. In order to be able to define the problem under study, major famine 261 262 logistics sub-systems and linkages (Figure 1.1 ) were discussed in some detail. Exploring this structure, many points become clear which were used in the modeling process. _ Figure 1.2 clarifies the relationship between logistical goals and the obstacles which must be passed for achievement of them. Logistical system design could be based on either spatial or temporal economics. Here the design is more on temporal structure and economics. A hypothetical country with approximately a sixty million population was assumed, divided among four regions. This assumption is for modeling purposes and has no effect on general conclusions drawn from the study. The entire modeled logistics system and its various components along with the explanation of the assumptions made, are described in Chapter II. This model consists of six major parts. The port, four regional warehouses and roads, supply and demand, information and data acquisi- tion component, capital develOpment model, and the cost function. All policy experiments are based on this model. Due to the fact that capital develOpment decisions are part of overall logistical policies, a further complementary description of this part of the model was discussed in Chapter V. Available information and its communication play a. vital role in the successful implementation of the designed policies. There is no need to stress the importance of accurate data, since the subject has been discussed in various chapters in detail. Due to the imortance of the quality and quantity of information on one hand and the general Shortage of data. on 'famine, Specially' in 'the case of a third world country on the other hand, there is an im- mense need to extract maximum benefit from the gathered infor- mation. In an attempt to come to grips with the error 263 involved in the available data, the use of some kind of filtering method was seen necessary. To achieve this aim, a detailed discussion and analysis of various existing estimation approaches was made, and has been reported in Chapter III. Two estimation models resulted from the above search. These were the Extended Kalman filter (parameter identification via state augmenta- tion) and the (3'8 tracker with adaptive tracking feature (time-varying B.parameter-.). Since little is known about the demand function, encoun- tered in a famine, it is obvious that its details are hardly known. From past experiences and some conunon sense knowledge, various related characteristics can be identified. In order for an estimation procedure to be chosen for the famine information system, it Should perform well, on the average, for all different demand functions possible. To do this test, a demand model was designed (Equation 3.19) which can repre- sent a wide spectrum of demand functions. The demand function described in Chapter II (Equation 2.49) is one member of that family. The selected filters were then tested on sample functions of the demand model (Equa- tion 3.19). The result was the selection of the adaptive o-B tracker for use in the logistics model. This choice resulted from extensive tests based on different conditions which are comon in the case of famine relief efforts. When high uncertainty exists regarding the initial values of the demand model's state variables and the model tra- jectories are partially known the adaptive 0- B tracker performs far better than the Extended Kalman filter. (Figures 3.5 - 3.12). The validity of the logistics model developed in chapters II and III, was tested and proved ’in Chapter IV. Various consistency tests were performed. Apart from the validation goal, these tests may serve 264. other purposes. They provide an indirect way to test policy Options. One or more parameters could be changed to reflect a particular policy goal and the consequences thus Simulated. Logical or theoretical incon- sistencies of the model are revealed through sensitivity analysis. ;The results of the above tests can also suggest data collection priori- ‘ties by indicating those parameters which are of greatest consequence to the performance of the model. In Short, the above tests and their results may add to one'S understanding of and insights into both the model and the corresponding real system. One of the main objectives of this thesis is the design and experi- mentation of different.control policies. This subject was discussed in Chapter V. Service performance and total cost expenditure were used as the basis for the development of different performance measures which were used in the process of policy evaluation, leading to the selection of the "Pareto-better" policy. The model's applicability to policy formulation was demonstrated in Chapter V, where the results of a series of computer runs examining various combinations of policy Options were analyzed. These policies are composed of two different but highly inter- connected decision rules, meaning the food allocation and capital acqui- sition decisions. The existence of several conflicting objectives in the model makes the control problem more complex. Since no optimization procedure was used in arriving at the best policy alternative, the selected policy is just a preference based on the model's assumptions. But by systemati- cally investigating policy alternatives, the range of choice and the relationship between alternatives and the relative values of the objec- tives were identified. Note that the process of finding the better 265 filtering technique (Chapter III) is part of the control process, since decision on the quality and quantity of the information is one of the policy entry points of the model. Chapter V concludes with the results of several robustness tests conducted on the "Pareto-better" policy. Major Results and Conclusions By knowing that any result obtained is a natural consequence of the goals set forth for this study, they are repeated here. There are two main objectives in this dissertation: modelling and control. In light of these aims various inferences and results are reported following the same arrangement of the chapters, i.e., modeling, estimation and control. The most important design parameter of the port subsystem is the ship offloading rate. This parameter has a significant influence on policy implications. These are based on the sensitivity tests of Chapter IV and policy runs of Chapter V. A ten percent increase in the ship offloading rate (RMS) resulted in a sixty percent reduction in average per ship waiting time. Another rough calculation showed that the ratio of offloading rate to arrival rate should be at least 1.6 to 1.8. The vehicle loading rate of the equipment does not influence the model out- put, primarily due to other existing bottlenecks in the system. Even so, this rate Should be at least as great as the expected grain arrival rate. The port's storage capacity is effective in the Short run and it is not a good policy option for long-run objectives. At the regional warehouse level, the storage role is to equalize supply and demand, and their capacities have minimum effect. This makes the maximum truck unloading rate (RMSS) the only important parameter at the RWH's. The 266 effect of this parameter on system performance is two-fold. 0n the one hand it limits the regional supply rate, and on the other hand it influences capital turnover. The second effect is the most important one, because a higher unloading rate makes the delay of trucks shorter and capital availability at port higher. But there is a limit beyond which the extra unloading capacity is useless. It is usually given that better information should lead to a better performance of the system. This assumption can be used to study and test model validity and policy structure. The experiments of Chapter IV Show that the above statement is true regarding the current model. In fact, given the assumed cost coefficients, it is quite advantageous to have better quality with higher frequency. Increasing the quality and guantity of available information will lead to lower cost, better performance, and service. But, there exists a range of problems, such as cultural, political and logistical ones, that complicate the task of information gathering in a third world country framework, thus making the availability of more data harder. The results of analysis of various estimation and filtering tech- niques in Chapter III suggest important insights into the question of what filtering method should be used in order to capture most of a given data set. Given the complete knowledge of the structure of the model. generating the information, the Extended Kalman filter outperforms any other filter (Table 3.2). ' But this performance degrades, as less and less is known about the original demand model. On the contrary, the adaptive a-B tracker Shows a consistent performance under different circumstances. The two methods were tested for robustness under two conditions. The first condition was when the trajectories of the model 267 generating the stochastic process are partially known. The second was a test on transient initial conditions in which high uncertainty existed regarding the initial values of the demand model's state variables. The above conditions are quite comon with any disaster relief operation. Under these conditions the adaptive o-B tracker performed well and the Extended Kalman filter did a very poor job. Tables 3.3 and 3.4 summarize the above results. Several inferences can be made regarding the results and implica- tions of various policy designs. It was mentioned in Chapter V that the findings of the policy experiments are the basis for further Opti- mization work. By formulating different control policies and testing them, the most important policy design variables were identified. These were estimated regional demands, port storage level, expected food arri- val rate, number of ships in the harbor waiting to be unloaded and the amount of grain on these ships. It was concluded that the port's storage level has enough information needed for capital acquisition policies. This variable along with the expected food arrival were successfully used to estimate the desired number of trucks and drivers. The concept of well stocked regional storages proved to be a good underlying assumption for the design of food distribution policies. Even in the FAPl policy, which did not use any information on demand, above concept leads to good clearance of port from grain. This fact is illustrated with a low ship waiting time and cost associated with this policy (Table 5.2). The comparison of the two food distribution policies shows the importance of the data on regional demand not only for overall performance of the logistics system but also on the balanced distribution of the food. The badly balanced allocation of food under 268 the first policy (FAPl) gives witness to this fact. Even under the various scenarios tested for policy robustness, the error caused by the use of regional estimated demand as the only basis for food alloca- tion decisions was very low. In fact, the general logistical policies' overall performances were satisfactory considering the quality and quan- tity of different, data available for decision making (Tables 5.2 and 5.3) The importance of the port's offloading capacity was demonstrated again. It was seen that whenever port storage is very low and there are ships waiting to be unloaded, the port's offloading capacity limit has been reached. The policy implication of this state is that acquisi- tion of any extra capital is useless. Another important result was obtained by changing the supply function. This was one of the robustness tests conducted on the I'Pareto better" policy. In this new supply func- tion (Figure 5.3) the grain arrival rate was more uniform than the previous one (Figure 2.5). Although the change was only for the peak of the crisis, the results were significant. The ship waiting cost, and consequently the total cost were reduced substantially. This result suggests the importance of the formation of an international body in the time of crisis in order to manage more uniform delivery of aid to the stricken country. Finally a general conclusion which was observed through this study was the excellent ability of computer simulation as an invaluable tool in the study of complex processes. A model developed by simulation can be used in designing various policies and obtaining their relevant outputs for comparison and use in the real world decision-making process. The use of a computer allows comparison of various situations quickly, 269 examining results and varying initial conditions and policy combina- tions. Futher Analysis of the Model The purpose of this section is to sumarize some of the major features of the model and to discuss various advantages and disadvan- tages associated with it. It is hoped that these explanations will be helpful for possible users of the model and its results. From various discussions and analysis of the previous chapters it can be concluded that, although the model as presented here needs more work, it can provide important contributions to the famine relief logistics planning and the policy-making process. Most_of the existing models in the literature dealing with the logistics have two distinct characteristics. One, they are discrete time, meaning that all entities have been modeled individually. Second, they are at a micro level, simulating the logistics of a business company. In this dissertation, the logistics systems has been looked upon from a macro point of view, thus the existing flows have been modeled at the aggregate level. In addition, the discrete modeling of the port and its interconnections with the continuous time inland transportation system provides the desired framework which can be utilized for macro level decision making. Using an operational model is a major step forward in the task of managing a logistics system. A more direct input to the policy development process is the capability of the model to explore the conse- quences and implications of a wide range of logistics policy options. As discussed in Chapter V, different policies can be tested on the current model. The sensitivity analysis of Chapter IV illustrates an 270 important application of the model to policy formulation when there is uncertainty inherent in the quality of the available information. In this way, the model can be used to evaluate the sensitivity of the policies to data uncertainty, for example, the upper limit on the capital acquisition rate (TRLIMIT). In the model description of Chapter II, it was said that since there is little information on this parameter, the model can be utilized in order to get an estimate about the range of it. This is essential information for system planners who should take any action possible to provide the necessary amount of capital needed for the fulfilment of the allocation policies which may include the use of government authority power. In this study, significant steps forward are made in the modeling of the famine logistics system. The discrete time port model has been interconnected with the continuous time inland transportation system along with a distribution network and regional warehouses. Transship- ments are possible in the case of an emergency when one of the roads becomes impassable and population) movement can give a wide range of possibilities for policy experimentation. It is also possible to gener- ate different Ship arrival patterns. Detailed analysis of the behavior of the simulated system under a range of assumptions and policy conditions provides a comprehensive view of the complex and dynamic logistics system under study. This can contribute to an improved understanding and sharpened intuitions regarding relief operations in general as well as the particular logis- tics system itself. Insofar as the simulated system correctly represents relevant behavioral patterns of the real system, this heightened under- standing can be a valuable asset in reducing some of the uncertainty 271 policy makers necessarily face. The sampling component, added to the simulation model, allows study of results of a given information quality without specifying the details of surveillance and processing. Since the model has not been adequately validated against real famine data and its background is a hypothetical country, the numerical results of this study should be looked upon as indicators of the nature of expected outcomes, not as actual recomenda- tions. The main drawback of the model can be seen in the development of the cost function. Since the total cost is one of the main perfromance criterion used in policy evaluations, more attention is needed for this part of the model. A real-world data base is not available for much of the cost data that would allow comprehensive model validation and policy experimentation. There are some unrealistic assumptions in the model which Should be kept in mind in analyzing policy results. In this model no constraints have been assumed on fuel, spare parts, and maintenance, although it is easy to incorporate them. Also, the question of needed money and technology has not been addressed. Thus, it may be desirable, if the model is to be implemented, to give high priority to modifying the current model to realistically reflect actual input constraints. The discussions of Chapter I led to the conclusion that the food crisis can happen in any part of the world. Even though the third world countries are more susceptible to famine, they enjoy a wide spectrum of different cultures, political and economic settings. These factors are quite important and must be taken seriously in the planning and decision making processes. Thus it is probably never going to be 272 possible to have a detailed model that addresses a particular food crisis in a particular region. In light of above facts, the value of less specific models Such as the current one is in their ability as a tool for decision makers and planners. These models can give general guidelines for crisis management under various circumstances and scenarios. They provide a decision maker with more information, help him to identify new and economically feasible policy Options, and sharpen his intuition, thus making for better decisions. But the policy decision maker, in evaluat- ing simulated results, must be aware of the assumptions and simplifica- tions built into the model. He must appreciate limitations that exist with regard to the quesitons the model is capable of addressing. As part of the pre-planning stage these models can also be used as training devices for the perspective peOple involved in the managing of relief Operations. Improvements and Extensions Any modeling effort of human behavior can never be finished. Famine relief operations simulation is of this type. The people are involved in all aspects of any relief effort and, indeed, it is done to save other peOple. Based on this fact, in response to the changing world, input data, structural and casual relationships and even the problem definition may have to be revised from time to time. But any modifica- tion and extension Should be decided upon after a cost-benefit analysis. There are several areas of the current model which need further development and research in order to improve its performance and conform more closely to real world behavior. The first area of work concerns 273 the development of a cost function. Not only does the aggregate level of the current one need more detailed analysis and modification but there also is a severe need for information on, numerical values for cost coefficients. The importance of this area becomes clearer in light of the poor financial situation of third world countries, and the deci- sion on the policy choice. It was said that there are many noninferiOr solutions to a multi-objective problem. Thus, the total cost becomes an important factor in the selection of one of these noninferior solu- tions. The above discussion should not undermine the general need for accurate data in other parts of the logistics system. One of the results of the sensitivity analysis and policy experi- ments stages was the importance of the role that some extra number of trucks or drivers could play in improvement of the system performance. The capital market mechanism has not been modeled in this study and its effects are considered as exogenous inputs to the decision making component of the system (Figure 5.2). Even though the current capital development model (Figure 2.6) simulates important elements of this process, it leans more toward the policy design and control parts of the logistics model rather than the market interactions. There is a need for further development of the mechanism of this market in order to model its reaction to policy inputs in more detail. This brings up, again, the question of an upper limit on the capital acquisition rate (TRLIMIT). There iS a serious lack of data on this rate. Other less serious Shortcomings of this component is the equal acquisition delay and TRLIMIT for both types of capital. Many features of the current model are in aggregated form. One such case is the truck repair shop. No distinction is made between 274 the possible various repair needs. An average constant delay has been assumed for all trucks. This needs a more detailed modeling in order for the model to portray the real world better. There are also some constraints which have not been modeled at all. These are: fuel, spare parts and maintenance inputs. Fuel iS'very critical considering the worldwide energy crisis and that the high prices of energy have made poorer countries more vulnerable to famine. One more factor for explora- tion is the driver "attrition". There is a truck attrition rate in the model. The decision making process has been modeled continuously with constant control parameters. This continuity refers to the fact that the control values are computed at each discrete model time interval, DT. As DT shrinks, decisions are made more and more continuously. The possibility of time-varying control parameters lead to the use of dynamic programing, which should be explored as an extension to this model. Another natural extension, regarding the control and decision- making process is the optimization work which was mentioned in a previous chapter. It was said that the multi-objectivity feature of the control problem poses new difficulties for Optimization. There is usually a tendency to convert the multi-objective problems to single-objective ones, by some weighting method, since the latter is much easier and many procedures exist for its solution. The subject of multi-criterion optimization which is also known as Pareto optimization regarding the current study, is by itself a separate research topic due to the volume of work and the freshness of the subject. In what follows, it is tried to portray some of the advantages of this approach to the Single- criterion one. 275 The consideration of many goals in the planning process accomplishes several major improvements in problem solving. Since the model, such as the current one, is most likely to be used in the decision-making and planning processes, multi-objective programming and planning promotes more apprOpriate roles for the participants in the above processes. The single-objective approaches often expand the analyst's role, result- ing in a decrease in the decision maker's control of decision situations. Since all single-objective models require that all policy effects be measurable in terms of a Single unit, the burden of decision making, not the decision of weighting function, squarely falls on the shoulders of the analyst or the model. Multi-objective approaches pursue an explicit consideration of the relative value of policy impacts. By systematically investigating policy alternatives, the range of choice and the relationship between alternatives and the relative values of the objectives are identified. In this manner the responsibility of assigning relative values remains where it belongs - with the decision makers. Regardless of the actual nature of the decision-making process, multi-objective approaches can be useful in promoting the explicit con- sideration of value judgments which are implicitly made in the applica- tion of single-objective approaches. The~ unambiguous identification of an optimal alternative is the result of single-objective methods which are predicted on a unique measure of effectiveness. This leaves the decision makers in the position of accepting or rejecting this sole alternative identified as the best. It is generally true, however, that multi-objective approaches will present to decision makers a range of choice larger than the one "optimal" solution. 276 It was mentioned that there are, generally, infinitely many non- inferior solutions to a multicriterion optimization problem, and one noninferior solution is as good as another. Decision makers, considering the existing circumstances, select the most satisfying noninferior solu- tion. This is quite important, considering the generality of the current model, and diversity of conditions different relief operations face. A general rule for decision making which is assumed here is that more information (carefully presented) is better than less information. The decision to accept or reject a Single optimal alternative is an uninformed decision. Informed, rational .decision making ‘requires a knoweldge of the full range of possibilities. This can be provided by multiobjective analysis. Finally, models or the analyst's perception of'a' problem will be more realistic if many objectives are considered. Different approaches have been suggested for the handling of this type of problem. For example, see (54), (83). (99). and (102). The process of selection of the best means of transportation has not been modeled in the current study. This is a possibility for exten- sion of the current model. Various modes of transportation, one mode or a combination of modes, should be modeled. In the case of the avail- ability of more than one mode, the results of this extension could be used in the selection of the better mode. Also, in most cases, more than one means of transportation is utilized in order to deliver the allocated food to different regions. In the current study a single mode, meaning the trucks, has been modeled. One further factor not explored in this study but which has a large effect, is the distribution of grain on ships; the distribution used for the Bangladesh case (Figures 2.2 and 2.3) is certainly open to change for other ports. The current model also uses one grain equivalent figure 277 and has no crop breakdowns. This is done for Simplicity, but logic generally dictates that others should be handled similarly. The dis- aggregation in modeling could be extended to the demand function. A more accurate portrayal would be the result of identifying various popu- lation groups such as rural and urban. Another important modification of the demand function is the introduction of randomness into the demand model. Facility location is one of the modern logistical activities. The number, size, and geographical arrangement of facilities and ware- houses bear a direct relationship to the service performance capabilities and corresponding logistical cost outlay (11, Chapter 2). The current model can easily be modified and used for the purpose of finding optimum regional warehouse locations. The subroutine SILOS in Appendix B can be utilized for any number and size RWH. The geographical location can be modeled by changing the distances from the port. Another problem area which would call for an extenSion of the model is the transshipments issue. The current model can handle random break- downs of any road and at any time. But no transshipments are possible from one RWH to the other. This can give extra flexibility to the system managers for emergency cases, because it is desirable that the control policies would lead to an optimum food allocation for which no transshipment becomes necessary. Finally, the hierarchical character- istic of the control problem can be used in order 'to utilize a vast amount of literature on multi-level control for further research. Bryds et al (14) present a technique for steady-state optimization of an important class of hierarchical control structures, namely continuous processes. Note that with the exception of ship arrivals at port, the 278 rest of the model is in a continuous time mode. Concluding Remarks In what has passed, some of the shortcomings of this study have been discussed and means by which they can be dealt with in order to improve the model's predictive and prescriptive capabilities have been suggested. It was seen that some, if not most, of these shortcomings arise from the lack of needed information. This problem exists no matter what kind of technique is used. Nonetheless, it has been reasoned that the system simulation analysis as used here, with its flexible approach to many of the methodological problems found in studying famine relief operations, provided an improved framework for not only policy analysis but also gave a better understanding of the real system itself. There are tremendous tasks to be accomplished in any relief effort. Even with limiting the scope of the current study to the role of a logistics system, many complex components have been noted. There still remains, however, the task of actual implementation of the model. Many political and cultural obstacles, some of which were discussed in Chapter I, hinder the implementation feasibility. Conflicts. between social classes, politicians, religions or regions have always been the cause of the unequal distribution of food in the world. These factors must be taken into consideration when designing allocation policies and plan- ning relief programs. It must be stressed that the current model yields usable estimates of the consequences of several policy strategy alternatives. In the future, when more and better information becomes available, further research could correct current inadequacies. The experience and lessons 279 learned in the present work and others like it will be valuable in future modeling and relief efforts. APPENDICES APPENDIX A NUMERICAL COST COEFFICIENTS The total cost was one of the main criterion in the process of selecting a better policy in Chapter V. It is always used in logistical systems evaluation. The equations of Chapter II, merely presented the mathematical relationships among various components of the total cost and their assumed structures. Those equations (2.58 - 2.74) explained the rationale of the assumed mathematical forms and defined different variables. But the values of the parameters and the unit costs were left undefined. These values are needed for the total cost computation of Chapter V. This appendix is intended to fill the gap between Chapter II formu- lations and the analysis of Chapter V. In what follows, different unit costs are redefined and their numerical values are discussed. These values are based on limited available information and intuitive judge- ment. The lack of data on third world countries is apparent, but, since various logistical policies are judged on relative total cost, these numerical values do not harm the process of finding the pareto Optimum solution for the control problem in this study. The fuel unit cost is calculated as follows. It is assumed that the cost per gallon of diesel is $2 (approximately $.53/liter) and a truck can travel 5 miles per gallon. This means approximately one kilo- meter per .47 of a liter. Thus CFUEL = unit fuel cost = .47 * .53 = .2491 (S/truck/KM) ,0 280 281 A truck imported to a third world country costs $40,000, and has a life span of 10 years (considering road conditions of these countries). its depreciation value for one year has been used for the truck rental cost. CRENT = rental cost = 4000 ($/truck/year) Other transportation costs are as follows. CDWAGE = driver wage = 5475 ($/driver/year) The driver's wage is based on $5 per driver each shift. A Shift is eight hours. An average repair cost has been assumed for trucks. CRPIR = average truck repair cost = 200 ($/truck/service) CFRPIR = fixed cost of repair shop = 2000 ($/year) Another logistical cost is the inventory cost. The 'following numerical values have been assumed for it. 145 ($/ton/year) CSTRG = average unit inventory cost CFSTRG = fixed cost of inventory 5000 ($/year) The loading and unloading of trucks were assumed to be dorie by manpower. A ten ton truck consists of 200 bags of grain. On the aver- age, it usually takes two men three hours to load or unload a truck, or six hours per man. Manpower cost assumed in this study is four dollars per man per shift (eight hours). As was discussed in Chapter II, 'HT a famine Situation part of the wage is paid in food and labour is generally cheap in 'such a crisis. Thus, the above manpower cost 282 translates to fifty cents an hour per man. Consequently, the cost of unloading or loading a truck becomes three dollars (6 * .5). This means that the cost of loading/unloading of a ton of grain cost $.3 (truck capacity is ten tons). Hence, CLOAD = unit loading cost = .5 * .6 = .3 ($/ton) CULOAD = unit unloading cost = .3 ($/ton) CFLOAD = fixed loading cost = 1000 ($/year) CFULOAD = fixed unloading cost = 1000 ($/year) The following has been assumed for sampling cost. Knapp (64) gives a detailed discussion on this type of cost. CSMPL = unit sampling cost = 2000 ($/survey/region) CFSMPL = fixed sampling cost = 4000 ($/year) The last item in the total cost calculation is the Ship waiting cost. The contribution of this cost is an important part of the total cost. In this study, it has been assumed that this cost is proportional to the capacity of the ship and other important ship characteristics such as Speed, which is assumed to be the same for all ships. The numerical value of the waiting cost is based on the cost of transporting a ton of grain from the donor country to the port of destination. This cost is $50 for a ton of grain when the travelling time is six weeks. So the Ship waiting time cost becomes CSHIPW = unit cost of ship waiting time = 50 * 52/6 = 433.33 ($/ton/year) 283 The above numerical values remain unchanged throughout the study. APPENDIX B FORTRAN Computer Program 284 PROGRAM MAlN( INPUT.0UTPUT,TAPET,TAP62,TAPE}.TAPE4,TAPE§.TAP66. l TAPE7,TAPE8 ) COMMON / BLOCK / DUR.DT.DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVLl, PRTVL2,SAMPT,ALPHA,BETA,CCOP,SUMOEL.TRLlMlT, BETl,BETZ,BET3,DELD.SDDEM.BETSMPL.SPDFUL.SPDMTY, CPRST8,CPEPA.CPQUE.CPTNO.QUEPLAC.POP(4).TATTC COMMON / SYSVAR / T.ROUTE(5.5).TROUTE.TTBS.TOR1OP,TTRIOP.TR(4). . TRP0L(4),SUMSTOC,SUMRT,SUMR2.NSP,NOTSNTP,OEM(4), OEMEST(4),TCRC,TORC,CAPwN,le,TwT,RCAPwH(4), TOP(4),XCT(4).PTSTRC(4),AVTONS, . TRSHOLO,CONVPAC,TTSTRO(l6),RLOAO(4),RUNLOA0(4), PTSTR6(4).RT5TR8(4).0POL.TPOL.TTIRS.TOOL. TOBs.ST06.RwST06(4).Rl.Rz.SRl(4).SR2(4),ATTRATE COMMON / COP / DELCDP,OELCDPP,KCDP,TRLOST,YPAST,TRMIN,TYD,DYD, l STRGCDP.TRLACK.DRLACK.DYPAST,DSTGCDP COMMON/ ARRIVE / TRUCKAR,DELINN,DELINNP,KOP,RT(6),RD(3).DELRPR, l DELRPRP.KTP COMMON / FAC / TlOT,IOUTTOT,ST,OOCN,NSS,PARwT,TlNPUT,TlOCAP,TlORMs COMMON_/ UNI / A1,A2.A3,Dl,D2,Pl,Cl,RMS,TONSH(150) COMMON / SILO / RSTBLST(4).PROOEM(4).TSUPPLY(4),NP,TRP(4),RMSS(4), RPT(lo,4),TOEMANO(4),RTRUPUT(4).TOPR(4),TRN(4), RET(10,4),OELE(4),OELPE(4).NE,TRNP(4),kR,STN0UT(4) ,RTR(lo,4),soEVSO(4),TAR(4),TSR(4),CIQS(4).CR(4) ,RTTP(TO,4),RTTR(TO,4).SROUTE(4),BRFL6(4).TBRKON, BALANCE COMMON / TRNSS / NT,AUXRM(3,4),AUXRP(3,4),5TART(4).ENOELO(4,4) COMMON / OEMOEsT / 00(4),Pl,TO£E.BlAs,ENlO(4),BETOEM(2).OEV UN—fi O‘U‘It’U-DN—P \flvF'WN—I 1 ,DTOTALoTDEH COHHON / DECIDE / T1DTR,TDR,DDR,THRUPUT.TTRUPUT,DTRUPUT.STGLST,RMT l ,TlDGR.TIDDR.TIDRHT,CCTRL(A) COMMON / COST / CDWAGE.CRPIR,CFRPIR,CRENT,CFUEL,CFTRNS.CFSTRG, CSTRG.CFLOAD.CLOAD.CFULOAD.CULOAD.CFSMPL.CDRWAGE. CRPAIR,CRNTR,CFUELS,TCTRNS,CVAINV,CVLOAD,CVULOAD. CVSMPL,CSHTPw.TCSHlP,TOTCOST,CSMPL COMMON / AVE / MONRUN,NAVE,M0NTTME,MON,lNTOTM(4),leM(4),STocM(4), AVTwTM(4),TIOTM(4),TNRUPM(4).TlNPM(4),TlOTRM(4), lOUTM(4),TlBCM(4),PARlM(4),STKOTMT(4),STKOTM2(4), STNOTM3(4).STNOTM4(4).RSTOCMI(4).RSTOOM2(4). RSTOCM3(4),RSTOCM4(4),TTRUPM(4).OTRUPM(4).TTBSM(4), TOBSM(4),RTRUPMT(4),RTRUPM2(4),RTRUPM3(4), RTRUPM4(A),PRODEM1(h),PRODEM2(4),PRODEM3(4), PROBEM4(4),SOEVOMT(4),SOEVOM2(4).SOEVOM3(4), SBEVOM4(4),TTOCRM(4),TlOBRM(4),VAR(2O),SOEV(2O). T10RM5M(4).TTORMTM(4),TT(2O,3o),PARlOT,AVTwT, TCSHTPM(4),TCTRNSM(4),TOTCSTM(4),BALANCM(4) COMMON / FOOD / YRTONS COMMON / CAL / QGRW.QGRAP COMMON / PQUE / PTSR,PTAR,PDAR,PCIQS,PC1QSD OATA NVAR,NRUN,MONRUN,MONT1ME / 9.1.1.4 / DATA ROUTE/ o.o,400..590.,4BO.,400.,4OO.,O.O,190..330.,400..590., l l90.,o.o,ll6.,33o.,480.,33o.,l16.,o.o,l7o.,4oo., 2 400.,330.,170.,o.o / VON-e ~moowa~uas~u- C C * * * BEGIN RUN LOOP C nnnnn on no nnn 285 00 500 IRUN I 1,NRUN * * DEFINE PARAMETERS UNCHANGED THRU SIMULATION RUN * * * RUN PARAMETERS DUR I 1 0T I 1./h380. DETPRT I 0.0 SELPRT I 1. BEGPRT I .25 PRTCHG I 2. PRTVLl I .25 PRTVLZ I .25 NAVE I IRUN TGRC I 10. TDRC I 1. * DATA FOR PORT RMTD I 13700. RMT I RMTD*365. CAPWH I 200000. YRTONS I 3000000. NDTSKIP I 10 RMSH I 6A0. RMS I RMSH*24.*365. STGLST I .1 ALPHA I .05 BETA I .8 8 DATA FOR REGIONAL WAREHOUSES TRSHOLD - .02 DO I I-l,4 RCAPwN(I)-5oooo. RSTGLSTII) - .l DELF(|) - l./(2.*365.) DELPF(|) - DELF(I) 1 CONTINUE * DATA FOR SHIPS AVTONS I 18500. P1 I .86 A1 I AOOO. A2 I 27000. A3 I 55000. 01 I A2-A1 02 I A3-A2 Cl I 1./1h60. CIHR I C1*1460.*6. * DATA FOR REGIONAL DEFICIT AND * DEMAND SHIFTS PARAMETERS BETI I 0.0 BETZ I 0.0 DEMAND n on nn nn nnn nnn nnnn * t 286 BET3 I 0.0 PI I h. * ATAN(1.) TDEF I 3200000. 4 DATA FOR SAMPLING ANO ESTIMATION OF DEMANDS SAMPT - 14./365. BETBEM(T) - .2363 BETOEM(2) - .1133 OEV - 2250000. 8 CONTROL PARAMETERS CPEFA - l. CPTNO - .06 CPQUE - o.O QUEFLAG - 5. * ROAD BREAKDOWN TBRKDN I 2. R I .h * * POLICY PARAMETERS 1 SPDFUL I 35. SPDMTY I AO. ' * READ RUN PARAMETERS PRINT 901, IRUN PRINT 905, CAPNM.RMSH,RMTD,C1HR,YRTONS,P1,DT PRINT 906, RMS.RMT PRINT 9l4, RCAPwH(l),RCAPwH(2),RCAPwH(3).RCAPNH(4),RMSS(I) RMss(2).RMss(3).RMss(h) ZTDEF - l.l * YRTONS PRINT 916, BETDEM(1).BETOEM(2),DEV,SAMPT,ZTDEF.BET1,BET2.BET3 NITER I DUR / OT + .OOOOOOOOOOOI *** START MONTE CARLO LOOP *** DO ASO MRUN I 1 , MONRUN * DEFINE INITIAL VALUES * DATA FOR PORT SUMAT I 0.0 TPOL I TRMIN DPOL I TRMIN DOCK I 0. N55 I O NSP I 3 TIDT I O. TIDTR I O. TIDGR I 0.0 TIDDR I 0.0 TIDCAP I 0.0 TIDRMS I 0.0 287 TIORMT - 0.0 IwL - 0 TNT - o. PARwT-o. INTOT - o INPART - O IOUTTOT - o TINPUT-o. THRUPUT - O. STOG - 40000. TEMPCl - Cl TTRUPUT - o. DTRUPUT - o. TOR - 0.0 DDR - 0.0 t * QUEUES AT PORT PTAR - o.o POAR - 0.0 PTSR - 0.0 PCIQS - O.o PCIQSD - 0.0 * * DATA FOR REGIONAL HAREHOUSES DO 5 I I 1 ll XGT(I) - o.o TRN(I) - o.o TRP(I) - 0.o TAR(I) - 0.0 TSRII) - o.o TDPR(|) - 0.0 SOEVSO(I) - 0.0 RTRUPUT(I) - 0.0 STKOUT(|) - 0.0 TRNP(I) - 0.0 RWSTOG(I) - llooo. TRPOL(I) - 0.0 CIQS(I) - 0.0 TDEMAND(I) - 0.0 TSUPPLY(I) - 0.0 PROOEM(I) - 0.0 RLOAo(I) - o.o RUNLOAD(I) - 0.0 PTSTRG(I) - 0.0 FTSTRG(I) - 0.0 RTSTRG(|) - 0.0 BRFLGII) - o.o START(I) - 0.0 00 4 J - I,4 ENDFLG(|.J) - 0.0 4 CONTINUE 5 CONTINUE 00 7 J-l,4 DO 6 I-I,lo RPT(|,J) - 0.0 riri race cars (western nnn can 288 RFT(I.J) I 0.0 RTR(I.J) I 0.0 RTTP(I,J) - 0.0 RTTR(|.J) - 0.0 6 CONTINUE 7-CONTINUE 00 8 K - 1.150 TOMSH(K) - 0.0 8 CONTINUE DO 9 J I 1.16 TTSTRG (J) I 0.0 9 CONTINUE BALANCE I 0.0 DATA FOR COSTS TRUCKS ANO ORIVERS wHICH wE HAVE To PAY EOR THEIR SERVICES TTRIOP - o.o TORIOP - 0.0 TOTAL OISTANCE TRAVELLEO BY TRUCKS TROUTE - O.o INCREMENTAL SUM OF SERVICES OF STORAGES AND LOAOING ANO UNLOAOING FACILITIES SUMSTOG - 0.0 SUMRT - 0.0 SUMR2 - 0.0 * GRAIN ON SHIPS wAITING AT PORT QGRw - 0.0 QGRAP - 0.0 * TIME AND PRINT DATA T I 0.0 MON I 1 PRTIME I BEGPRT PRTVL I PRTVL] 48* INITIAL CAPITAL OEVELOPMENT PROCESS 88* CALL CAPITAL( YO ) *** BEGIN TIME LOOP *** DO 400 ITER I 1 , NITER 'CALL MODEL CALL EXGEN( T,SUMAT,AVTONS,INTOT,INPART,IWL ) CALL FACPORT *** ALLOW FOR DOWN TIME *** IF(NSP.LT.NDTSKIP) GO TO 15 NSP I 0 GO TO 25 15 CONTINUE nn nnn nnn nnn noon 25 80 90 289 *** CHECK DOCKING *** CALL DOCKY( DOCK.TEMPC1.R1.RMS.C1,DT ) **** CHECK TRUCK AND DRIVER **** CALL ARAIVALI TDR , DDR ) CALL DEMAND CHECK FOR ROAD BREAKDOWN IF( T .GT. TBRKON ) THEN RANOOM SELECTION OF ROAO |F( R .GT. .75 ) XGT(1) - 1.0 IF( R .GT. .5 .ANO. R .LE. .75 ) ch(2) IF( R .GT. .25 .ANO. R .LE. .5 ) ch(3) IF( R .LE. .25 ) xGT(4) - 1.0 ENDIF 1.0 1.0 CALL CONTROL DO 80 I - 1.4 CALL SILOS(|) CONTINUE TRUCKAR - TRNP(1) + TRNP(2) + TRNP(3) + TRNP(4) CALL CALCULT 86* CHECK PRINT TIME 84* IF(T.LT.PRTIME-.OOOOOOOI) GO TO 90 PRINT RESULTS IF( T .GT. PRTCHG - .000000001 ) PRTVL I PRTVLZ PRTIME I T + PRTVL CALL COSTS CALL AVERAGE( IRUN,INTOT,INPART ) |F( SELPRT .EQ. 0.0 ) GOTO 90 PRINT SELECTED VARIABLES CALL SELPRNT( DUR ) CONTINUE IF( T .LT. .9999999 ) GO T0 100 VARIABLE OBSERVATION FOR CONSTRUCTION OF ITS DISTRIBUTION TT(1,MRUN) - TIDT TT(2.MRUN) - TIOCAP TT(3,MRUN) - TIOGR TT(4,MRUN) --AVTwT TT(5.MRUN) - TIOTR TT(6.MRUN) I TIDDR 290 DO 95 I . I". TT(1+6,MRUN) - PR00EM(I) TT(1+10,MRUN) - STKOUTII) 95 CONTINUE TT(15,MRUN) - TINPUT TT(16.MRUN) - THRUPUT TT(17.MRUN) - TCSHIP TT(18,MRUN) - TCTRNS TT(19.MRUN) - TOTCOST TT(20.MRUN) - BALANCE 100 CONTINUE I400 CONTINUE 1650 CONTINUE C c PRINT MONTE CARLO AVERAGES c O CALL MONPRNT( OETPRT ) C 500 CONTINUE STOP C C FORMAT STATEMENTS C 901 FORMAT(38H l NON- OEEAULT PARAMETER VALUES FOR RUN,12./. 1 ") 905 FORMAT("O",5X."PORT PARAMETERS",/. 6x, " --------------- ",/. l GRAIN STORAGE CAPACITY AT PORT (TONS) " ,FlO.,/, 2 " SHIP UNLOAOING RATE (TONS/HR) ".12x, F6. 0. /. 3 " PORT TRUCK LOAOING RATE (TONS/BAY) ",6X,F6.0,/, 4 " OOCKING TIME (HRS) ".ZOX,F6.2,/, 5 " TOMS OE GRAIN ARRIVING PER YEAR ", 7x,Elo.o,/, 7 " SERVICE GENERATION PARAMETER FOR SHIPS ",2x,56.2,/, 8 " DT (TIME INCREMENT) ",lBX.FlO.6 ) 906 FORMAT(" SHIP UNLOAOING RATE (TONS/YR) ",8X,F12.0,/, " PORT TRUCK LOAOING RATE (TONS/YR) " 4x, F12. o ) 914 FORMAT("O".5X."R. w. H. PARAMETERS",/, 6x," ----------------- " ,/, STORAGE CAPACITY AT IST RWH (TONS)", FlO.,/, " STORAGE CAPACITY AT 2N0 RwH (TONS)",FlO.,/, " STORAGE CAPACITY AT 3R0 RWH (TONS)",FlO../, " STORAGE CAPACITY AT 4TH RWH (TONS)",FlO.,/, " MAx TRUCK UNLOAOING RATE AT lST RwH (TONS/YR)",FlO.,/ ," MAx TRUCK UNLOAOING RATE AT 2N0 RwH (TONS/YR)",F10../ ," MAx TRUCK UNLOAOING RATE AT 3RD RwH (TONS/YR)", FlO../ ," MAx TRUCK UNLOAOING RATE AT 4TH RwH (TONS/YR)". Flo. ) 916 FORMAT("O",5X. "ESTIMATION, SAMPLING ANO OEMANO PARAMETERS"./. 6x, .. ----------------------------------------- II,/, " BETAI I”,F9.6,/," BETAz -",F9.6,/," OEV -",E10.,/, " SAMPLING INTERVAL (YEARS)".F9.6,/, " ExPECTEO TOTAL OEMANO (TONS)".FlO.,/, " REGIONAL POPULATION MOVEMENT COEFFICIENTS". 3(2X.F5-3)) d GNO‘WrUN-l O‘U’lL-UJN—I END nn nnn WP 10 DON-I U‘mk'UUN—P 1 291 SUBROUTINE CONTROL COMMON / BLOCK / DUR,DT,DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVLT, PRTVL2,SAMPT,ALPHA,BETA,CCDP.SUMDEL,TRLIMIT, BETI,BET2.BET3.DELD.SDDEM.BETSMPL,SPDEUL.SPDMTY. CPRSTG,CPEPA,CPQUE,CPTND.QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,R0UTE(5,5),TROUTE,TTB$.TDRIOP.TTRIOP.TR(4). TRPOL(4),SUMSTOG.SUMR1,SUMR2.NSP,N0TSKIP,DEM(4), DEME5T(4),TGRC,TDRC.CAPwH,IwL,TwT,RCAPwH(4), TDP(4),xGT(4).PTSTRG(4),AVTONS, TRSHOLD.CONVPAC.TTSTRG(16),RLOADI4),RUNLOAD(4),_ - PTSTRG(4).RTSTRG(4),DPOL,TPDL,TTIRS,TDOL, TDBS.$TOG.RwSTOG(4).R1.R2.SR1(4).SR2(4).ATTRATE COMMON / DECIDE / TIDTR.TDR.DDR.THRUPUT.TTRUPUT.DTRUPUT.STGLST,RMT ,TIDGR.TIDDR.TIDRMT.CCTRL(4) COMMON / PQUE / PTSR.PTAR.PDAR,PCIQS,PCIQSD DIMENSION GNEED(4) . GRwH(4) . RSTGMTY(4) DATA CCTRL / 48.95 / IF( T .GT. DT ) GOTO 5 Do 4 I - 1,4 RSTGMTY(I) - CCTRL(I) 8 RCAPwH(I) CONTINUE TDR - o.o TGRwH - 0.0 TOTDEM - 0.0 - TOTNEED - 0.0 CALL FOODARI T . YM ) CALL CONVDEL YD - YM 8 CONVFAC QUE - FLOAT(IWL) - QUEFLAG IF( QUE .LT. o.o ) QUE - o.o COMPUTING TOTAL NUMBER OF TRUCKS DESIRED SCALE I TRSHOLD * CAPWH ASTOG I (STOG - SCALE) / TGRC IF( ASTOG .LT. 0.0 ) ASTOG I 0.0 CAPNEED I CPEFA*YD + CPQUE*(QUE*AVTONS/TGRC) + CPTND*ASTOG CALL CAPITAL( CAPNEED ) CALL CHOICE( DT,RMT,TIDGR,TIDTR,TIDDR,TIDRMT ) FOOD ASSIGNMENT DO 10 I I 1.4 IF( DEMEST(I) .LE. 0.0 ) DEMESTII) I .001 TOTDEM I TOTDEM + DEMEST(I) CONTINUE REST - R2 - TOTDEM ALLOCATION OF EXTRA AID IF( REST .GT. 0.0 ) THEN R2 8 R2 - REST FULL STORAGES DO NOT GET EXTRA ALLOCATION DO ‘2 I .191. GNEED(I) - DEMESTII) no nnn nnn 292 IF( RWSTOG(I) .GE. RSTGMTY(I) ) GNEED(I) - .OOOOOI TOTNEED - TOTNEED + GNEED(I) 12 CONTINUE EXTRA A10 15 ALLOCATED PROPORTIONAL TO ESTIMATED DEMAND DO 15 J - 1,4 GNEED(J) - ( GNEED(J)/TOTNEEO ) 8 REST 15 CONTINUE EMDIF DO 20 1 - 1.4 IF( REST .LE. 0.0 ) GNEED(I) - O.o GRWHII) - GNEED(1) + ( DEMEST(I)/TOTDEM ) 8 R2 TDP(I) - GRwH(I) / TGRC TGRWH - TGRwH + GRWH(|) TDR - TDR + TDP(1) 20 CONTINUE DDR - TDRC8TDR IF( REST .GT. 0.0 ) R2.- R2 + REST PORT OUTPUTS THRUPUT - THRUPUT + DT8TGRwH 'TTRUPUT - TTRUPUT + DT8TDR DTRUPUT - DTRUPUT + DT8DDR STOG - STOG + DT8(R1 - TGRWH - STGLST8STOG) IF( STOG .LT. 0.0 ) STOG - o.o QUEUES AT PORT PTSR I PTSR + DT*TDR PCIQS I PCIQS + TPOL PCIQSD I PCIQSD + DPOL RETURN END nnnnnnnnnnnnn 16 VON-P O‘W’UN—P 1 I 293 SUBROUTINE CAPITAL( YD ) COMMON / BLOCK / DUR,DT,DETPRT,SELPRT.BEGPRT,PRTCHG,PRTVL1, PRTv12,SAMPT,ALPHA,BETA,CCDP,SUMDEL.TRLIMIT, BETl.BET2,BET3.DELD.SDDEM.BETSMPL,SPDEUL.SPDMTY. CPRSTG,CPEEA.CPQUE,CPTND,QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,ROUTE(5,5),TROUTE,TTBS.TDRIOP.TTRIOP,TR(4), TRPOL(4),SUMSTOG.SUMRI.SUMR2.NSP.NDTSKIP,DEM(4), DEMEST(4),TGRC,TDRC,CAPNH.INL.TwT,RCAPwH(4), TOPI4),XGT(4),PTSTRG(4),AVTONS, TRSHOLD.CONVEAC,TTSTRG(16),RLOAD(4),RUNLOAD(4). ETSTRG(4).RTSTRG(4).DPOL.TPOL.TT1RS.TDOL. TDBS.STOG.Rw5TOG(4),R1,R2,SR1(4),SR2(4),ATTRATE COMMON / COP / DELCDP.DELCOPP.KCDP.TRL05T.YPAST.TRMIN,TYD,DYD, STRGCDP.TRLACK,DRLACK,DYPAST,DSTGCDP COMMON / PQUE / PTSR,PTAR,PDAR.PCIQS,PCIQSD DIMENSION RCDPT(3) . RCDPD(3) DATA CCDP.KCDP.TRLOST.TRMIN.TRLIMIT.TATTC / 4OOO..3,.1,O.0. 123000.,.25 / THIS SUBROUTINE SIMULATES THE CAPITAL DEVELOPMENT PROCESS IN TOTAL OPERATIONS . ( ACQUSITION OF TRUCKS/DRIVERS ) TATTC I TRUCK ATTRITION RATE DELCDP I ACQUSITION DELAY TRLOST I LOST FACTOR TRMIN I INITIAL NUMBER OF TRUCKS IN THE SYSTEM CCDP I CONTROL PARAMETER TRLIMIT I LIMIT ON RATE OF ACQUSITION STRGCDP I INVENTORY 0F TRUCKS IN TRANSIT DSTGCDP I INVENTORY OF DRIVERS IN TRANSIT IF( T .GT. 0.0 ) GOTO 20 DELCDP I 14. / 365. DELCDPP I DELCDP DSTGCDP I 0.0 STRGCDP I 0.0 U I 0.0 YN I 0.0 DU I 0.0 DYN I O. O TRLACK I 0 DRLACK I 0. | n ) ) DO 5 RCDPTII RCDPD(I CONTINUE YPAST I TRMIN OYPAST I TRMIN CALCULATING THE INITIALLY NEEDED CAPITAL CALL FOODAR(T , YM ) CALL CONVDEL YD I YM * CONVFAC TYD I ( 1. + DT*TATTC ) * YD DYD I YD YDINT I YD O O 1 3 0.0 0.0 nonnnn non no 20 25 30 294 CDPFLAG I 0.0 GOTO 25 EXECUTION PHASE ADJUSTING FOR TRUCKS IN REPAIR SHOP AND DRIVERS 0N LEAVE AND TRUCK ATTRITION TYD I YD + TTIRS TYD I I 1. + DT*TATTC ) * TYD DYD I YD + TOOL Z I TRLOST * YPAST ATTRATE I TATTC * YPAST YDOT I U + YN - Z YDOT I YDOT - ATTRATE Y I YPAST + DT*YDOT IF( Y .LT. 0.0 ) Y I 0.0 CHANGE I Y - YPAST YPAST I Y TPOL I TPOL + CHANGE + TRLACK DZ I TRLOST * OYPAST DYDOT I DU + DYN - DZ DY I OYPAST + DT * DYDOT IF( DY .LT. 0.0 ) DY I 0.0 DCHANGE I DY - OYPAST OYPAST I DY DPOL I DPOL + DCHANGE + DRLACK * QUEUES AT PORT IF( CDPFLAG .LT. l. ) GOTO 30 IF( CHANGE .GT. 0.0 ) THEN PTAR I PTAR + CHANGE ENDIF IF( DCHANGE .GT. 0.0 ) THEN POAR I POAR + DCHANGE ENDIF CONTINUE CHECK FOR INITIAL ACCUMULATION OF CAPITAL IF( TPOL .GE. YDINT .AND. CDPFLAG .EQ. 0.0 ) THEN CDPFLAG I 1. GOTO 40 ENDIF TRLACK I 0.0 DRLACK I 0.0 IF( TPOL .LT. 0.0 ) THEN TRLACK I TPOL TPOL I 0.0 ENDIF IF( DPOL .LT. 0.0 ) THEN DRLACK I DPOL DPOL I 0.0 ENDIF C nnn 40 295 CONTROL ERRORT I TYD - Y X I CCDP * ERRORT IF( X .LE. 0.0 ) THEN W I 0.0 YN I X ELSE IF( X .LT. TRLIMIT ) W I X IF( X .GE. TRLIMIT ) W I TRLIMIT YN I 0.0 ENDIF ERRORD I DYD - DY OK I CCDP * ERRORD IF( DX .LE. 0.0 ) THEN DW I 0.0 DYN I OX ELSE IF( Dx .LT. TRLIMIT ) Dw - DX IF( DX .GE. TRLIMIT ) Dw - TRLIMIT DYN - 0.0 ENDIF CAPITAL ACQUISITION DELAY IOTU - 1’ CALL DELVF( w,u.RCDPT,STRGCDP.DELCDP.DELCDPP.DT.IDTU.KCDP ) CALL DELVF( DW.DU.RCDPD.DSTGCDP.DELCDP.DELCDPP,DT,IDTU.KCDP ) IF( CDPFLAG .EQ. 1. ) GOTO A0 TTRIOP I TTRIOP + TPOL TDRIOP I TDRIOP + DPOL GOTO 25 CONTINUE RETURN END nnnn mm 296 SUBROUTINE CONVDEL THIS SUB COMPUTES THE CONVERSION FACTOR FOR CAPITAL OEVELOPMENT PROCESS COMMON / BLOCK / DUR,DT,DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVLI. PRTVL2,SAMPT,ALPHA,BETA,CCDP,SUMDEL.TRLIMIT, BETI, BET2, BET3, DELD, SDDEM, BETSMPL, SPDFUL, SPDMTY, CPRSTG. CPEFA, CPQUE, CPTND. QUEFLAG, POP(4), TATTC COMMON / SYSVAR / T, ROUTE(5, 5), TROUTE, TTBS, TDRIOP, TTRIOP, TR(4), TRPOL(4),SUMSTOG,SUMR1,SUMR2,NSP,NDTSK1P, DEM(4), DEMEST(4),TGRC,TDRC.CAPwH,IHL,TWT,RCAPwH(4), TDP(4),XGT(4),PTSTRG(4),AVTONS, TRSHOLD.C0NVEAC.TT5TRG(16),RLOADI4),RUNLOAD(4), ETSTRG(4),RTSTRG(4),DPOL.TPOL,TTIRS,TDOL. TDBS.STOG,RwSToG(4),R1,R2,SR1(4),SR2(4),ATTRATE COMMON / SILO / RSTGLST(4),PRODEM(4).TSUPPLY(4).KP.TRP(4).RMSS(4). RPT(IO,4),TDEMANDI4).RTRUPUT(4),TDPR(4),TRN(4), RPT(lo,4),DELE(4).DELPElh).KE.TRNP(4),KR,STKOUT(4) ,RTR(10.4).SDEVSD(4).TAR(4).TSR(4).CIQS(4),GR(4) .RTTP(IO.4).RTTR(TO.4).SROUTE(4).BRELG(4).TBRKDN. BALANCE COMMON / TRNss / KT,AUXRM(3.4).AUXRE(3.4).START(4).ENDELG(4.4) DIMENSION DISDEL(4).ESTIME(4).H(4).DUMDEL(4).DUMSTG(4) DATA POP / 20..20..lo..lo. / DATA IELG.DUMDEL.DUMSTG / O.480.O.48O.O / O‘WPWN-P VIN-i Ul-PWN-o TW - o.o SUMDEL - 0.0 IF( T .GT. 0.0 ) GOTO 15 TRAVEL DELAY AND EXPECTED SERVICE TIME DO 5 I - 1,4 DISDEL(I) - DELAY(SPDFUL . ROUTE(I+1.1)) + 1 DELAY(SPDMTY . ROUTE(I+1.1)) EXPECTED SERVICE TIME PER DT ESTIMEII) - l./(RMss(I)/TGRC) HEIGHTS FOR INITIAL CAPITAL DEVELOPMENT PROCESS w(I) - POP(I) Tw-Tw+W(I) 5 CONTINUE DO 10 I - 1.4 DEL - ESTIMEII) + DISDEL(I) + DELF(I) SUMDEL - SUMDEL + (W(l)/TW)*DEL TO CONTINUE GOTO 35 15 CONTINUE CHECK FOR ROAD BREAK DOWN AND DELAY-WEIGHT ADJUSTMENTS IF( T .GT. TBRKON ) THEN TBRKON I TBRKON + OUR PERMANENT DELAY CORRECTIONS OO 18 I I 1,4 IF( XGT(I) .GE. 1. ) THEN OELP I DELAY(SPOFUL , ROUTE(I+1,1)) nnnn nnn 297 DELR - DELAY(SPDMTY , ROUTE(|+l,l)) DISDEL(1) - DISDEL(I) + DELAY(SPDFUL , SROUTE(I)) + l DELAY(SPDMTY . SROUTE(I)) - DELP - DELR IFLG - I GOTO 19 ENDIF 18 CONTINUE ENDIF 19 IF( IFLG .EQ. o ) GOTO 20 TEMP. CORRECTIONS IF( BRFLG(IFLG) .LT. 4. ) THEN IF( ENDFLG(1.1FLG) .LT. 1. ) THEN DUMDEL(IELG) - DUMDEL(IELG) + DELR/2. DUMSTG(IFLG) - DUMSTG(IFLG) + TTSTRG(IFLG) ENDIF IF( ENDFLG(2,IFLG) .LT. l. ) THEN DUMDEL(IFLG) - OUMDEL(IFLG) + DELR / 2. DUMSTG(|FLG) - DUMSTG(IFLG) + TTSTRG(IELG+4) ENDIF IF( ENDFLG(3.IFLG) .LT. l. ) THEN DUMDEL(1ELG) - DUMDEL(IFLG) + OELP/2. DUMSTG(IFLG) - DUMSTG(IFLG) + TTSTRG(IFLG+8) ENDIF . IF( ENDELG(4,IPLG) .LT. l. ) THEN DUMDEL(IFLG) - DUMDEL(IFLG) + DELP / 2. DUMSTG(IFLG) - DUMSTG(IFLG) + TTSTRG(IFLG+12) ENDIE ENDIF IF( BRFLG(|FLG) .GE. 4. ) IFLG - O 20 CONTINUE WEIGHTS AFTER FOOD ARRAIVAL DO 25 l I 1,4 W(I) I TRPOL(I) + PTSTRG(I) + FTSTRG(I) + RTSTRGII) + OUMSTG(I) OUMSTG(I) I 0.0 Tw-TW+W(I) 25 CONTINUE QUEUE DELAY AT RWH Do 30 I - 1.4 IF( CIQS(I) .EQ. O.o ) THEN X - 0.0 ELSE x - CIQS(I) / TAR(I) ENDIE DEL - DT8X + ESTIME(I) + DISDEL(I) + DELF(|) + DUMDEL(1) DUMDEL(1) - 0.0 IF( W(l) .EQ. 0.0 ) THEN Y - 0.0 ELSE Y - W(|) / TW 298 ENDIF SUMDEL I SUMDEL + Y * DEL 3O CONTINUE C C CONVERSION FACTOR 'C 35 CONVFAC I SUMDEL / TGRC RETURN END nnnnnnn * I I I 20 25 299 SUBROUTINE FOODAR( T , Y ) * THIS SUBROUTINE GENERATES FOOD ARRAIVAL RATE SCENARIO . THE AREA UNDER THE CURVE REPRESENTS TOTAL AMOUNT OF AID . ALSO . IT IS USED FOR CALCULATING THE DESIRED NUMBER OF TRUCKS IN THE TOTAL SYSTEM AT ANY TIME . AND GENERATING STOCHASTIC INTERARRIVAL TIME FOR SHIPS . * COMMON / FOOD / YRTONS DIMENSION XTAB(21) , YTAB(21) DATA XTAB/o.o..l,.15,.2,.25..3..35,.4,.45,.5, .54,.6,.65,.7,.75,.8,.85,.9..94,.96,1./ DATA YTAB/1.o,l.o,l.3.2.l,2.9.3.8,4.7,4.9,5.1,5.35,5.5,5.4o, 5.05,4.1,3.15,2.2,1.25,.59,.19,.11,.001/ DO 20 I-2.21 IF( T .GT. XTAB(I)) GOTO 20 Y - (T-XTAB(1-1))8(YTAB(I)-YTAB(I-1))/(XTAB(I)-XTAB(1-1)) + YTAB(I-I) Y - Y8YRTONS/3. GOTO 25 CONTINUE RETURN END 3': nnnn loo 1 300 SUBROUTINE EXGEN( CLOCK.SUMAT.AVTONS,INTOT,INPART,IWL ) THIS SUB GENERATES EXPONENTIAL ARRIVAL TIMES AND DUAL-UNIFORM SHIP TONNAGE COMMON / UNI / A1,A2,A3,Dl.02,P1,CI.RMS.TONSH(150) COMMON / CAL / QGRw.QGRAP IF(CLOCK.LT.SUMAT) Go TO 1 IEXOUT - l R - RANF() CALL FOODAR( CLOCK,YRTONR ) T - CLOCK + AVTONS/(2.8YRTONR) IF( T .GT. 1. ) T - 1. CALL FOODAR( T . YRTONR ) EAT - AVTONS/YRTONR AT - -EAT8AL0G(R) SUMAT - SUMAT + AT COMPUTING THE SHIP LOAD R - RANF() IF( R .GE. Pl ) THEN TONSH(IWL+1) - (1.-R)802/(l.—P1) + A2 ELSE TONSH(IWL+1) - A1 + R8DI/Pl ENDIF QGRAP - QGRAP + TONSH(|WL+l) INTOT - INTOT + IEXOUT INPART - INPART + IEXOUT IwL - IWL + IEXOUT IF( IwL .GE. 150 ) THEN PRINT loo STOP ENDIF ' FORMAT(”1",5X,"TOO MANY SHIPS ARE WAITING") RETURN END on 70 75 ND“ 10 15 20 WN-I O‘U'lt'WN—fi 301 SUBROUTINE FACPORT COMMON / BLOCK / DUR.DT.DETPRT.$ELPRT.BEGPRT.PRTCHG,PRTVLT, PRTVL2,SAMPT,ALPHA.BETA.CCDP.$UMDEL.TRLIMIT, BETl,BET2.BET3.DELD.SDDEM.BETSMPL.SPDEUL.SPDMTY, CPRSTG.CPEEA.CPQUE.CPTND,QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,ROUTE(5.5).TROUTE,TTBS,TDRIOP,TTRIOP,TR(4), TRPOL(4).SUMSTOG.SUMR1.SUMR2.NSP,NDTSK1P,DEM(4), DEMEST(4),TGRC,TDRC,CAPwH,INL,TwT,RCAPwH(4), TDP(4),XGT(4).PTSTRG(4).AVTONS. TRSHDLD,CDNVEAC.TTSTRG(16).RLOAD(4),RUNLDAD(4), ETSTRG(4).RTSTRG(4).DPOL.TPOL.TTIRs.TDOL. TDBs.STOG.Rw5T0G(4).RI.R2.SR1(4).SR2(4).ATTRATE COMMON / FAC / TIDT.IOUTTDT.ST.DOCK,NSS,PARwT,T1NPUT,TIDCAP,TIDRMS COMMON / UNI / AT,A2,A3,DT,02,P1,C1,RMS,TONSH(150) 888 CHECK DOWN TIME 888 1E(NSP.LT.NDTSKIP-I) GO To 75 IF(NSS.EQ.1) Go TO 70 TIDT - TIDT+DT GO TO 30 TwT - TWT+IWL*OT PARwT - PARWT+IWL*DT Go TO 30 CONTINUE nan CHECK SERVICE STATION 888 IF(NSS.EQ.1) GO TO 10 IF(IWL.NE.O) Go TO 5 TIDT - TIDT+OT RI-o. . Go TO 30 IwL - IWL-l Nss - 1 was GENERATE SERVICE TIME 888 ST - c1 + TONSH(1) / RMS TINPUT - TINPUT + TONSH(1) IF( IWL .LT. 1 ) GOTO 9 Do 8 J - l.le TONSH(J) - TONSH(J+1) CONTINUE DOCK - 1. GO TO 15 888 CHECK WAITING LINE 888 IF(IWL.EQ.O) Go To 20 TWT - TwT+IwL8DT PARwT-PARwT+1wL8DT *** CHECK STORAGE VS. CAPACITY *** IF(STOG.GE.CAPWH) GO TO 35 *** CHECK REMAINING SERVICE TIME *** IF(ST.GT.DT) GO TO 25 RI I ST*RMS/DT IOUT I 1 N55 I 0 GO TO 50 25 ST - ST-DT n 30 35 4O 20 30 302 R) I RMS TIDRMS I TIDRMS + OT IOUT I 0 GO TO A0 R1 I O. IOUT I O TIDCAP I TIDCAP+OT CONTINUE IOUTTOT I IOUTTOT+IOUT RETURN END SUBROUTINE DOCKY( DOCK.TEMPCI,RI,RMS.CI,DT ) THIS SUBROUTINE COMPUTES SHIP OFF-LOADING RATE IF(DOCK.EQ.O.) GO TO 30 IF(TEMPCI.LT.DT) GO TO 20 TEMPCl I TEMPCl-OT RI IO. GO TO 30 RI I (OT-TEMPC1)*RMS/DT DOCK I O. TEMPCl I.CI RETURN END 303 . SUBROUTINE ARAIVAL ( TDR . DDR ) c 8 C C WN-I U‘U‘PWNI— 1 * THIS SUB COMPUTES THE NET INPUT RATES INTO REPAIR SHOP AND TRUCK / DRIVER POOLS . k 8 8 COMMON / BLOCK / OUR,OT,OETPRT,SELPRT,BEGPRT,PRTCHG.PRTVL], PRTVL2,SAMPT,ALPHA.BETA.CCOP,SUMDEL,TRLIMIT, BETI,BET2.BET3,DELD,SDDEM.BETSMPL.SPOFUL,SPDMTY, CPRSTG,CPEFA,CPQUE,CPTNO,QUEFLAG,POP(A).TATTC COMMON / SYSVAR / T.ROUTE(5.5).TROUTE,TTBS.TDRIOP,TTRI0P,TR(4), TRPOL(A),SUMSTOG.SUMR1,SUMR2.NSP,NDTSKIP,OEM(A), DEMEST(A){TGRC,TDRC,CAPWH,IWL,TWT,RCAPWH(A), TDPIh).XGT(A).PTSTRGIA)oAVTONSo TRSHOLD.CONVFAC,TTSTRG(16),RLOAO(A),RUNLOAO(A), FTSTRG(A),RTSTRGIA).DPOL,TPOL,TTIRS.TDOL. TOBsoSTOG,RWSTOG(A),RI,R2,SRI(A),SR2(A),ATTRATE CDMMON/ ARRIVE / TRUCKAR,DELINN.DELINNP,KDP,RT(6),RD(3).DELRPR, DELRPRP,KTP COMMON / PQUE / PTSR,PTAR,POAR,PCIQS,PCIQSD DATA KDPoKTP / 3.6 / IF( T .GT. DT ) GOTO 4 TRUCK REPAIR AND DRIVER DELAYS AT PORT DELRPR - 5./365. DELRPRP - DELRPR DELINN - 2./365. DELINNP - DELINN 88* INITIAL TRUCK/REPAIR AND DRIVER/LEAVE AT PORT TTIRS - O. ' TDDL - o. TTBS - 0.0 TDBs - 0.0 TRUCK/l DRIVER _ARRAIVAL RATES RD(1) - 0.0 RD (2) - 0.0 RD(3) - O.o TRUCKAR - 0.0 Do 3 JIl , KTP .RT(J) - 0.0 CONTINUE CONTINUE IDTU - 1 DRIVEAR - TDRC 8 TRUCKAR TRUCKRN - TRUCKAR 8 ALPHA IF( NSP .GT. 1 ) THEN HOLD - 0.0 GDTO 5 ENDIF ’ IF( NSP .LE. 0 ) THEN HOLD - TRUCKRN TRUCKRN - o.o GOTO 10 ENDIF IF( T .LT. 280T ) GOTO 5 TRUCKRN - TRUCKRN + HOLD **** 5 IO 10 15 20 30 304 CALL DELVF(TRUCKRN,TRUCKRD,RT,TTIRS ,OELRPR,DELRPRP,OT,IOTU,KTP) TRAR I TRUCKAR - TRUCKRN R3 I TRAR + TRUCKRO - TOR PTAR I PTAR + OT*( TRAR + TRUCKRO ) TPOL I TPOL + DT * R3 TTBS I TTBS + OT*TRUCKRO DRIVEIN I DRIVEAR * BETA CALL DELVF(DRIVEIN,ORIVERO ,RO,TO0L .DELINN,OELINNP ,OT,IOTU ,KDP) DRAR I DRIVEAR - DRIVEIN RA I DRAR + ORIVERO - DDR PDAR - PDAR + DT8( DRAR + DRIVERD ) DPOL - DPOL + OT 8 R4 TDBs - TDBS + DT8DRIVERD RETURN END SUBROUTINE DELVF( RIN,RDUT,R,STRG,DEL,DELP,DT,IOTU,K ) DIMENSION R(l) FK - FLOAT(K) B - 1. + (DEL - DELP)/(DT8EK) IDT - l. + 2. 8B8DT8EK/DELP IF( IDT .LT. IDTU ) IDT - IDTU A - PK8DT/(DELP8EL0AT(IDT)) OELP - DEL . KMl - K - 1 Do 20 JIl.lDT IF( K .EQ. l ) GOTO 15 Do 10 1-1,KM1 R(I) - R(I) + A8(R(I+1) -B8R(l)) CONTINUE R(K) - R(K) + A8(RIN -B8R(K) ) CONTINUE STRG - o. 00 30 I-1.K STRG - STRG + R(I)8DEL/EK CONTINUE ROUT - R(l) RETURN END nnnn * O‘U‘lt‘wN—P 305 SUBROUTINE CHOICE( OT,RMT,TIOGR,TIDTR.TIDDR.TIORMT ) * THIS SUB SIMULATES THE ASSIGNMENT OPERATION AT THE PORT . IT CALCULATES THE OUTPUT RATES OF THE PORT . '* 8 COMMON / SYSVAR / T,RDUTE(5.5),TROUTE.TTBS,TDRIOP.TTRIOP,TR(4), TRPOL(4),SUMSTOG,SUMR1,SUMR2,NSP,NDTSKIP,DEM(4), DEMEST(4),TGRC.TDRC.CAPwH,IwL,TwT,RCAPwH(4), TOP(4),XGT(4),PTSTRG(4).AVTONS, TRSHDLD.CONVEAC.TTSTRG(16),RLDAD(4),RUNLOAD(4), ETSTRG(4).RTSTRG(4).DPDL.TPDL.TTIRS.TDDL. TDBS.ST0G.RNST0G(4).R1.R2.SRI(4),SR2(4),ATTRATE SCALE - TRSHOLD 8 CAPwH IF( NSP .GE. NDTSKIP .OR. STOG .LE. SCALE ) THEN R2 - 0.0 TIDGR - TIDGR + DT IF( TPOL .LE. 0.0 ) TIDTR - TIDTR + DT IF( DPOL .LE. 0.0 ) TIDDR - TIDDR + DT GOTO 10 ENDIF IF( TPOL .LE. 0.0 ) THEN R2 I 0.0 TIDTR I TIDTR + OT IF( DPOL .LE. 0.0 ) TIDDR I TIDDR + OT GOTO 10 ENDIF IF( DPOL .LE. 0.0 ) THEN R2 I 0.0 TIDDR I TIDDR + OT GOTO 10 ENDIF DO I O. OPO I (TGRC*OPOL)/TORC ROD I CHECK( OP0,0T,RMT,OO ) TT I O. TPO I TGRC * TPOL RTT I CHECK( TPO.DT.RMT,TT ) SS IO. RSS I CHECK( STOG,OT,RMT,SS ) CODE I OO*TT *SS IF( CODE .EQ. I. ) THEN R2 I RMT TIDRMT I TIDRMT + OT GO TO 10 ENDIF R2 I ROD IF( R2 .GT. RTT ) R2 I RTT IF( R2 .GT. RSS ) R2 I RSS 10 306 IF( R2 .EQ. RSS ) TIDGR I TIDGR + OT IF( R2 .EQ. ROO ) TIDDR I TIDDR +-OT IF( R2 .EQ. RTT ) TIDTR I TIDTR + OT RETURN END FUNCTION CHECK( DATA.OT,RMT,W ) X I DT*RMT IF( DATA .GE. X ) W I 1. CHECK I OATA / DT RETURN END nnn nn nnn 307 SUBROUTINE SILOS ( I ) COMMON / BLOCK / DUR.DT.DETPRT.SELPRT.BEGPRT.PRTCHG,PRTVLl, PRTVL2,SAMPT,ALPHA,BETA.CCDP.SUMDEL.TRLIMIT, BETl,BET2.BET3.DELD,SDDEM.BETSMPL.SPDFUL.SPOMTY, CPRSTG.:PEEA,CPQUE.CPTND.QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,RDUTE(5.S).TROUTE,TTBS,TDRI0P,TTRIOP,TR(4), TRPOL(4),SUMSTDG.SUMR1,SUMR2,NSP,NDTSKIP,DEM(4), DEMEST(4),TGRC,TDRC,CAPwH,IHL,TwT,RCAPwH(4), TDP(4).xGT(4).PTSTRG(4),AVTONS. TRSHOLD.CONVEAC.TTSTRG(16).RLOAD(4).RUNLOAD(4). ETSTRG(4),RTSTRG(4).DPOL.TPOL.TTIRS.TDOL. TDBS.STOG.RwSTOG(4).R1.R2.SR1(4).SR2(4).ATTRATE COMMON / SILO / RSTGLST(4).PRODEM(4),TSUPPLY(4),KP,TRP(4),RMSS(4), RPT(lo,4),TDEMAND(4),RTRUPUT(4).TDPR(4),TRN(4), RET(10,4),DELE(4),DELPE(4),KE,TRNP(4),KR,STKOUT(4) ,RTR(Io,4),SDEVSD(4).TAR(4),TSR(4),CTQS(4),GR(4) ,RTTP(lo,4),RTTR(10,4),SROUTE(4),BRELG(4),TBRKDN. BALANCE DIMENSION COUNT(4) DATA KF,KP,KR.RMSS / 1.6.6.2oooooo..2oooooo.,loooooo.,loooooo. / DATA SROUTE / 780..590..57o.,650. / OWG'WN-I DUN-I erN—I IF( T .GT. OT ) GOTO I TOTDEM I 0.0 TOTSUP I 0.0 SUM I 0.0 I CONTINUE * * DELAYS OF TRUCKS AND DRIVERS RETURNING TO PORT * * IOTU I 4 CHECK FOR ROAD BREAKDOWN AND TRANSSHIPMENT IF( XGTII) .LT. I. ) GOTO 2 DELR I DELAY( SPOMTY . SROUTE(I) ) DELPR I DELR CALL DELVF( TRN(I),TRNP(I).RTTR(1.I).RTSTRGII).DELRoDELPRoDTo I IOTU , KR ) GDTO 3 2 CONTINUE DELR - DELAY( SPDMTY , ROUTE(1+I,1) ) DELPR - DELR CALL DELVF( TRN(1),TRNP(I),RTR(1,1),RTSTRG(I),DELR.DELPR.DT, l IOTU . KR ) 8 8 8 DELAYS DUE TO OVERNIGHT STAYS OF DRIVERS AT R.w.H. 3 IDTU - 1 CALL DELVF( TDPR(I).TRN(I).RFT(1.I).FTSTRG(I).DELFII).DELPF(|). 1 DT.|DTU.KF ) DOWN TIME FOR SILOS IF( NSP .GE. NDTSKIP ) THEN nnn nnn 308 SR1(I) - 0.0 SR2(1) -o.o SUP - 0.0 TDPR(I) - 0.0 RLOAD(1) - O.o RUNLOAD(I) - 0.0 GOTO 15 ENDIF **** UNLOAOING AND LOADING OPERATIONS TRPOL(I) - TRPOL(I) + DT8TRP(I) GR(|) - TGRC 8 TRPOL(I) / DT CHECK FOR MAx RATE OF UNLOAOING IF( GR(I) .GT. RMSS(1) ) THEN TGR - RMSS(I) ELSE TGR - GR(I) ENDIF SATISFYING THE DEMAND REST - DEM(I) - TGR IF( REST .GE. 0.0 ) GOTO 10 STORING EXCESS FOOD IF( RWSTOG(I) .GE. RCAPwH(I) ) THEN SR1(1) - 0.0 GOTO 5 ENDIF REST - ABS(REST) CHECK FOR CAPACITY ACAP - (RCAPwH(1) - RWSTOG(I))/OT IF( ACAP .LT. REST ) REST - ACAP SR1(I) - REST 5 5R2(I) - 0.0 SUP - DEM(I) TDPR(I) - (DEM(I) + SR1(I)) / TGRC RLOAD(1) - DEM(I) RUNLOAD(I) - DEM(I) + SR1(|) GOTO 15 IO SRIII) I 0.0 SUPPLYING EXCESS DEMAND CHECK FOR GRAIN IN STORAGE SCALE - TRSHOLD8RCAPwHII) ASTOG - (RWSTOG(I) - SCALE) / DT IF( ASTOG .LT. 0.0 ) ASTOG - o.o IF( ASTOG .LT. REST ) THEN SR2(I) - ASTOG STKOUTII) - STKOUT(1) + OT ELSE SR2(1) - REST ENDIF SUP - TGR + SR2(I) TDPR(I) - TGR / TGRC RLOAD(I) - TGR + SR2(I) IN REGIONAL WAREHOUSES nnn nn nnn nn nnn 15 20 22 I 309 RUNLOAD(I) I TGR MEASURES OF PERFORMANCE - SUPPLY AND DEMAND COUNT(I) - SUP / DEM(I) TOTDEM - TOTDEM + DEM(I) TOTSUP - TOTSUP + SUP IF( 1 .LT. 4 ) GOTO 22 TOTPRO - TOTSUP / TOTDEM DO 20 JK - 1.4 DUMMY - DEMEST(JK)8AMAX1((TOTPRO - COUNT(JK)) . 0.0) SUM - SUM + DUMMY SDEVSO(JK) - SDEVSD(JK) + OT8DUMMY CONTINUE BALANCE - BALANCE + DT8SUM TOTDEM - 0.0 TOTSUP - o.o SUM - o.o CONTINUE TSUPPLY(1) - TSUPPLY(I) + SUP TDEMAND(I) - TDEMAND(I) + DEM(I) PRODEM(I) - TSUPPLY(|) / TDEMAND(I) RTRUPUT(I) I RTRUPUT(I) + OT * SUP 'RWSTOG(|) I RWSTOGII) + DT*(SR1(I) - SR2(I)-RSTGLST(I)*RWSTOG(I)) IF( RWSTOGII) .LT. 0.0 ) RWSTOG(I) I 0.0 * TRUCKS AND DRIVERS RETURNING BACK TO PORT * * * TRPOL(I) I TRPOL(I) - DT*TDPR(I) CALCULATIONS FOR QUEUES CIQS(I) - CIQS(I) + TRPOL(I) TAR(I) - TAR(I) + DT8TRP(I) TSR(1) - TSRII) + DT8TDPR(I) **** DELAYS FROM PORT TO REGIONAL WAREHOUSES **** IOTU I 4 CHECK FOR ROAD BREAKDOWN IF( XGT(I) .LT. l. ) GOTO 25 CHECK FOR TRUCKS REMAINING ON THE OLD ROAD IF( BRFLG(I) .LT. 4. ) THEN CALL TRNSHIP( I , RFTR . RMTR ) ENDIF DELPR - DELAY( SPDFUL . SROUTE(I) ) DELPPR - DELPR CALL DELVF( TDP(I),TRP(I),RTTP(1,I),PTSTRG(I),DELPR,DELPPR,DT, IDTU . KP ) TRPII) I TRP(I) + RFTR an an 310 COST CALCULATIONS FOR DISTANCES TRAVELED TROUTE I TROUTE + DT*(TRP(I)+TRNP(I)'RFTR-RMTR)*SROUTE(I) RFTR I 0.0 RMTR I 0.0 GOTO 30 25 CONTINUE DELPR I DELAY( SPDFUL e ROUTE( I+l . 1 ) ) DELPPR I DELPR CALL DELVF( TOP(I),TRP(I).RPT(I,I),PTSTRG(I),DELPR,OELPPR.DT, I IOTU , KP ) CALCULATIONS FOR COST - SUM OF DISTANCES TRAVELED TROUTE I TROUTE + DT*(TRP(I) + TRNP(I)) * ROUTE(I+I,I) 3O CONTINUE RETURN END FUNCTION DELAY( SPEED . DISTANC ) W I DISTANC / (SPEED * 24. ) DELAY I W/365. RETURN END nn non non 311 SUBROUTINE TRNSHIP( I , RFTR , RMTR ) COMMON / BLOCK / DUR, OT,DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVL1, PRTVL2, SAMPT, ALPHA, BETA. CCDP, SUMDEL,TRL1MIT, BETI. BET2, BET3, DELD, SDDEM, BETSMPL, SPDFUL, SPDMTY, CPRSTG.CPEPA.CPQUE.CPTND,QUEPLAG,PDP(4).TATTC COMMON / SYSVAR / T,ROUTE(5.5).TROUTE,TTBs,TDRI0P,TTRIOP,TR(4), TRPOL(4),SUMSTOG.SUMR1.SUMR2,NSP,NDTSKIP,DEM(4), DEMEST(4),TGRC,TDRC,CAPwH,IwL,TWT,RCAPwH(4). TDP(4),XGT(4),PTSTRGI4),AVTONS, TRSHOLD.CONVEAC,TTSTRG(16),RLOAD(4),RUNLOAD(4), ETSTRG(4),RTSTRG(4),DPOL,TPOL,TTIRs.TDOL. TDBS,STOG,RHSTDG(4),R1,R2,SR1(4),SR2(4),ATTRATE ‘COMMON / SILO / RSTGLST(4),PRODEM(4),TSUPPLY(4),KP,TRP(4),RMSS(4), RPT(10,4),TDEMAND(4).RTRUPUT(4),TDPR(4),TRN(4), RET(10,4),DELE(4).DELPE(4).KE.TRNP(4),KR,STKOUT(4) ,RTR(Io,4),SDEVSD(4),TAR(4),TSR(4).CIQS(4),GR(4) ,RTTP(10,4),RTTR(TO.4).SROUTE(4).BRELG(4).TBRKDN. BALANCE COMMON / TRNSS / KT,AUXRM(3,4),AUXRE(3.4),START(4).ENDPLG(4,4) DATA KT / 3 / U‘U‘I?U~|N-‘ VON—I \flJ-IUJN—P IF( START(I) .GT. 0.0 ) GOTD l5 START(I) I 1.0 COSTI I 0.0 COSTZ I 0.0 DO 10 J I I,KT K I 7 - J AUXRM(J.I) I RTR(K,I) RTR(K.I) I 0.0 AUXRF(J,|) I RPT(K,I) RPT(K,I) I 0.0 10 CONTINUE 15 CONTINUE DUMMY VARIABLES FOR DELAY AND COST RIN I 0.0 TROAD I 0.0 EMPTY TRUCKS RETURNING TO PORT IF( ENDFLG(1.I) .GT. 0.0 ) GOTO 20 IOTU I A DELR I DELAY( SPDMTY , ROUTE(I+1,1) ) DELPR I DELR CALL DELVF( RIN. RMTR, RTR(1, I) ,TTSTRG(I). DELR. DELPR, OT, IOTU, KR ) TRNP(I) I TRNPII) + RMTR TROAD I TROAD + RMTR IF( TTSTRGII) .LE. 0.0 ) THEN BRFLGII) I BRFLGII) + l. ENDFLG(1.|) I I. ENDIF EMPTY TRUCKS TURNING BACK TO RWH 8‘3an 4‘1an 312 20 IF( ENOFLG(2.|) .GT. 0.0 ) GOTO 25 IOTU I 8 DELTSM I DELR/2. OELTSMP I DELTSM IF( COST) .LT. l. ) THEN DO 22 J I 1,KT TROUTE I TROUTE + (DELTSM/KT)*AUXRM(J.I)*(J/KT)*ROUTE(I+1,1) 22 CONTINUE COSTI I l. ENDIF CALL DELVF( RIN.ROUT,AUXRM(1,I),TTSTRG(I+4),DELTSM,DELTSMP,DT, l IDTU , KT ) EMPTY TRUCKS DO NOT STAY OVERNIGHT TRN(1) - TRN(1) + ROUT IF( TTSTRG(I+4) .LE. 0.0 ) THEN BRFLG(I) - BRFLG(I) + 1. ENDFLG(2,I) - 1. ENDIF FULL TRUCKS COMING To RWH 25 IF( ENOFLG(3,I) .GT. 0.0 ) GOTO 30 IOTU - 4 DELPR - DELAY( SPDFUL . ROUTE(I+1.1) ) DELPPR - DELPR . CALL DELVF( RIN.RETR.RPT(1,I),TTSTRG(I+8).DELPR,DELPPR,DT, l IOTU , KP ) TROAD - TROAD + RETR IF( TTSTRG(I+8) .LE. 0.0 ) THEN BRFLG(I) - BRFLG(I) + l. ENDFLG(3.I) - 1. - ENDIF FULL TRUCKS TURNING BACK TO PORT 30 IF( ENDFLG(A,I) .GT. 0.0 ) GOTO 35 IOTU I 8 DELTSF I DELPR/2. DELTSFP I DELTSF IF( COSTZ .LT. I. ) THEN O0 32 J I IoKT TROUTE I TROUTE + (DELTSF/KT)*AUXRF(J,l)*(J/KT)*ROUTE(I+1,I) 32 CONTINUE COSTZ I 0.0 ENDIF CALL DELVF( RIN.ROUT,AUXRF(1,I),TTSTRG(I+12).DELTSF.OELTSFP,DT, l IDTU . KT ) TDP(I) - TDP(1) + ROUT IF( TTSTRG(I+12) .LE. 0.0 ) THEN BRFLG(I) - BRFLG(I) + 1. ENDELGL4,I) - l. non 313 ENDIF SUM OF THE DISTANCES TRAVELED 35 TROUTE I TROUTE + DT*TROAD*ROUTE(I+I,1) RETURN END nnn nnnn n on MN 314 SUBROUTINE COSTS THIS SUBROUTINE COMPUTES ACCUMULATED COST AT ANY TIME COMMON / BLOCK / DUR,DT,DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVL1, PRTVL2,SAMPT,ALPHA,BETA,CCDP,SUMDEL.TRLIMIT, BETl.BET2,BET3,DELD.SDOEM.BETSMPL,SPOFUL.SPOMTY, CPRSTG.CPEEA.CPQUE,CPTND,QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,ROUTE(5.5).TRDUTE,TTBS,TDR1OP,TTR10P,TR(4), TRPOL(4),SUMSTOG,SUMR1,SUMR2.NSP,NDTSKIP,DEM(4), DEMEST(4),TGRC,TDRC.CAPNH.INL,TwT,RCAPwH(4), TDP(4),XGT(4),PTSTRG(4),AVTONS, TRSHOLD.CONVEAC,TTSTRG(l6),RLOAD(4),RUNLOADI4), ETSTRGI4).RTSTRG(4).DPOL.TPOL.TTIRS.TDOL. TDBS.STOG.Rw5TOG(4),R1,R2.SR1(4),SR2(4),ATTRATE COMMON / COST / CDWAGE,CRPIR,CFRPIR,CRENT,CFUEL.CFTRNS.CFSTRG. l CSTRG,CELDAD.CLOAD,CPULDAD.CULDAD,CESMPL,CDRwAGE, CRPAIR,CRNTR,CFUELS,TCTRNS,CVAINV,CVLOAD,CVULOAD. CVSMPL,CSHIPw,TCSH1P,TOTCOST,CSMPL COMMON / CAL / QGRw,QGRAP DATA CDWAGE,CRPIR,CFRPIR,CRENT,CFUEL,CFSTRG,CLOAO.CSTRG.CULOAO. I CFLOAD,CFULOADoCSMPL.CFSMPL.CSHIPW / 5575.,200.,2000.,A000., 2 .2491,5000...3.1A5.,.3,IOOO.,IOOO..2000.,4000.,433.33 / TRANSPORTATION COSTS - DRIVERS wAGES CDRWAGE - CDwAGE 8 OT 8 TDRIOP TRUCK REPAIR COSTS CRPAIR - CRPIR 8 TTBS RENTED TRUCKS COSTS CRNTR - CRENT 8 OT 8 TTRIOP FUEL COST CFUELS - CFUEL 8 TROUTE TOTAL VARIABLE COST OF TRANSPORTATION CVTRNS I CDRWAGE + CRPAIR + CRNTR + CFUELS FIXED COST OF TRANSPORTATION CFTRNS I ( T / DUR ) * CFRPIR TOTAL COST OF TRANSPORTATION TCTRNS I CFTRNS + CVTRNS INVENTORY COSTS CVAINV I CSTRG * DT * SUMSTDG LOADING FACILITIES COSTS CVLOAD I CLOAD * SUMR2 UNLOAOING FACILITIES COSTS CVULOAD I CULOAD * SUMRI INFORMATION COSTS CVSMPL I A. * ( T / SAMPT ) * CSMPL TOTAL SHIPS WAITING TIME COST TCSHIP I CSHIPW * OT * QGRW TOTAL VARIABLE COST OF OPERATIONS on 315 TVCOST I CVTRNS + CVAINV + CVLOAD + CVULOAD + CVSMPL + TCSHIP TOTAL FIXED COST OF OPERATIONS TFCOST I (T/DUR)*(CFRPIR + CFSTRG + CFLOAD + CFULOAD + 4.*CFSMPL) TOTAL COST OF OPERATIONS TOTCOST I TFCOST + TVCOST RETURN END 316 SUBROUTINE CALCULT C THIS SUBROUTINE KEEPS TRACK OF VARIABLES NECESSARY FOR C COST CALCULATIONS C COMMON / BLOCK / OUR.DT.DETPRT,SELPRT,BEGPRT,PRTCHG,PRTVLI, I PRTVL2,SAMPT,ALPHA,BETA,CCDP,SUMDEL.TRLIMIT, 2 BETI,BETZ.BET3,0ELD.SDDEM.BETSMPL,SPOFUL,SPDMTY, 3 CPRSTG.CPEFA,CPQUE.CPTND,QUEFLAG,POP(A),TATTC COMMON / SYSVAR / T,ROUTE(5,5),TROUTE,TTBS.TDRIOP,TTRIOP.TR(A)o 1 TRPOL(A),SUMSTOG.SUMR1.SUMR2,NSP,NDTSKIP,OEM(A), 2 DEMEST(A),TGRC.TORC.CAPWH.IWL,TWT,RCAPWH(A), 3 TDP(4),XGT(4),PTSTRG(A),AVTONS, A TRSHOLD,CONVFAC,TTSTRG(16).RLOAD(A),RUNLOAD(A), 5 FTSTRG(A),RTSTRG(A).DPOLoTPOLoTTIRS.TDOLo 6 TDBS.STOG.RWSTOG(A),RI,R2,SR1(A),SR2(A),ATTRATE COMMON / CAL / QGRW.QGRAP C TRIOP I 0.0 CL I 0.0 CUL I 0.0 00 5 K- 1 , 4 TRIOP -TRIOP+TRPOL(K)+PTSTRG(K)+ETSTRG(K)+RTSTRG(K) l +TTSTRG (K) +TTSTRG (K+4) +TTSTRG (Ki-B) +TTSTRG (Ki-12) CL - CL + RLOADIK) CUL - CUL +-RUNLOAD(K) 5 CONTINUE DRIOP - TDRC 8 TRIOP + DPOL TRIOP - TRIOP + TPOL + TTIRS TDRIOP - TDRIOP + DRIOP TTRIOP - TTRIOP + TRIOP SUMSTDG - SUMSTDG + STOG + RWSTOG(1) + Rw5T0G(2) + RWSTOG(3) + .1 RwSTOG(4) SUMRI - SUMRI + OT 8 CUL SUMR2 - SUMR2 + OT 8 CL QGRAP - QGRAP - 0T 8 R1 IF( QGRAP .LE. 0.0 ) QGRAP - 0.0 QGRw - QGRw + QGRAP RETURN END nnnn nn nnnn 317 SUBROUTINE DEMAND * * THIS PROGRAM GENERATES THE DELAYED ESTIMATED- STOCHASTIC REGIONAL FOOD DEFICIT A 8 COMMON / BLOCK / 0UR.DT.DETPRT,SELPRT,BEGPRT.PRTCHG,PRTVLI. PRTVL2,SAMPT,ALPHA,BETA,CCDP.SUMDEL.TRLIMIT, BETl,BET2.BET3.DELO.SDDEM.BETSMPL.SPOFUL.SPDMTY, CPRSTG,CPEEA.CPQUE.CPTN0.QUEELAG,POP(4),TATTC COMMON / SYSVAR / T,ROUTE(5,5),TRDUTE,TTBS.T0RIOP.TTRIOP.TR(4). TRPOL(4).SUMSTOG.5UMR1.SUMR2,NSP.NDTSKIP.0EM(4). DEMEST(4).TGRC,TORC,CAPHH,IwL.TWT.RCAPwH(4), TDP(4),XGT(4),PTSTRG(4).AVTDNS, TRSHOLD,CDNVEAC,TTSTRG(l6).RLOADI4).RUNLOAD(4). ETSTRG(4),RTSTRG(4),DPDL.TPDL,TTIRS,T00L. TDBS.ST0G.RNSTOG(4).R1.R2.SR1(4),SR2(4),ATTRATE COMMON / DEMDEST / 00(4),PI,T0EE.BIAS.ENID(4).BETDEM(2).DEV l .DTOTAL.T0EM DIMENSION ALE(4) . Rl(5o,4) . DATA DD,SDDEM,BIAS / .4..4..I,.1,.15,o.o / DATA DEM.DEMEST / 480.0 , 480.0 / UN‘ U‘WFUJN-I IF( T .GT. OT ) GOTO 3 INITIAL DEMAND DTOTAL I .2*2.*TDEF TDEM I ACOSII. - DTOTAL/TDEF)/(2.*PI) INITIAL VALUES FOR REGIONAL DEMANDS DO 2 II1,A ENID(I) I DD(|) * DTOTAL 2 CONTINUE ESTIMATION DELAY DELD I 2./365. 3 CONTINUE CALCULATING WEIGHTS FOR REGIONAL DEMANDS (TIME VARYING) ALF(I) - 00(1) + BETI 8 T ALF(2) - 00(2) + BETz 8 T ALF(3) - 00(3) + BET3 8 T ALE(4) - l. - ( ALF(l) + ALF(2) + ALF(3) ) IF( ALE(4) .LT. 0.0 ) ALE(4) - 0.0 ESTIMATION AND DATA PROCESSING OF REGIONAL FOOD DEFICIT INCLUDING TRANSMISSION DELAY IF( T .LT. TDEM ) GOTD 5 IF( T .GT. .96 ) GOTO 5 DTOTAL - TDEF 8 I 1. - C05( 2.8PI8T ) ) 5 CONTINUE DO 10 1-1.4 DEM(I) - ALE(1) 8 DTOTAL DEVS - 00(1) 8 DEV IF( DEM(I) .LE. DEVS ) BETSMPL - BETDEM(1) IF( DEM(I) .GT. DEvs ) BETSMPL - BETDEM(2) DUMMY - DEMEST(I) CALL SAMPL( DEM(I),DEMEST(I),RI(1,1),ENID(1),SAMPT,DELD,BIAS, 318 I SDDEMoloOToToBETSMPL ) IF( DEMEST(I) .LT. 0.0) DEMEST(I) I DUMMY IO CONTINUE RETURN END nonnnnnnn nnnnn On nnn on 21 20 run- 319 SUBROUTINE SAMPL( VAL,VALEST,VALAR,ENIT,SAMPT,DEL,BIAs,SD,NK, 0T.T.BETA ) VAL - ACTUAL VALUE , VALEST - ESTIMATE OF VAL VALAR - ARRAY OF INFORMATION IN DELAY PIPLINE ENIT - INITIAL ESTIMATE VALUE SAMPT - SAMPLING INTERVAL (YEAR) BIAS - MEASUREMENT BIAS SD - MEASUREMENT STANDARD DEVIATION NK - COUNTER , NUMBER OF ITEM MEASURED DEL - DELAY LENGTH. DIMENSION HDLD(12),NCNT(12),NSAMP(12),NN(12).VALAR(I) DIMENSION YP(12) . YY(12) . YD(Iz) . NMLVAL(4I) REAL NMLVAL DATA N/so/ DATA NMLVAL/~3.5.-I.96,-1.645,-1.439.-1.281,-1.15,-I.o37.-.925, -08‘919-07559-067‘..-o598.-o52hg’o‘05hg".386,-0312.-0253 ,-.189,-.126,-.056.0.o,.056,.126..189,.253..312..386, .454,.524,.598,.674..755..84l,.925,1.O37.1.15.1.281. 1.439.1.645,l.96,3.5 / IF( T .GT. DT+.OOOOl ) Go To 20 INITIALIZATION OF ARRAY AND COUNTERS DO 21 KK - I,N VALAR(KK) - ENIT HOLD I MEASURED VALUE HELD UNTIL NEXT SAMPLE TIME NCNT I NUMBER OF DTS SINCE LAST SAMPLING NSAMP I NUMBER OF DTS BETWEEN SAMPLING NN I NUMBER OF OTS DELAY LAST HOLDINK) I 0.0 NCNT(NK) I O NSAMP(NK) I O NN(NK) I DEL/OT + .5 YY(NK) I ENIT YD(NK) I 0.0 EXECUTION PHASE NCNT(NK) - NCNT(NK) + 1 IF( NCNT(NK) .LT. NSAMP(NK) ) GOTO 1 SAMPLING PRECEDURE Y IS STANDARD NORMAL RANDOM VARIABLE NSAMP(NK) I SAMPT/OT + .5 R I RANFI) Y I TABLIEI NMLVAL.0.0..025,AO,R ) HOLDINK) I VAL*(1. + SD*Y) + BIAS DATA PROCESSING PHASE ALPHA - 2.8SQRT(BETA) - BETA YP(NK) - YY(NK) + SAMPT8YD(NK) 320 YY(NK)- YP(NK) + ALPHA8(HOL0(NK) - YP(NK)) YD(NK) - YD(NK) + (BETA/SAMPT)8(HOL0(NK) - YP(NK)) NCNT(NK) - o CONTINUE CALL V0T0LI( YY(NK),VALEST,VALAR.N.NN(NK).0EL.0T ) RETURN END FUNCTION TABLIE( VAL,SMALL,DIFF,K,DUMMY ) DIMENSION VAL(I) DUM - AMINI(AMAX1(DUMMY - SMALL,o.o),FLDAT(K)801FF) 1 - l. + DUM/DIFF IF( I .EQ. K+l) I-K TABLIE - (VAL(I+1) - VAL(I))8(DUM - FLOAT(I-1)8DIFF)/DIFF + VAL(I) RETURN END 000 321 SUBROUTINE VDTDLI( v1N.VDUT.V1NT,N,NN,DEL,DT ) N - MAXIMUM SIZE OF ORDER NN - SIZE OF ORDER AT TIME (T-DT) DIMENSION VINT(l) NNNEw - DEL/OT + .5 IF( NNNEw .LT. 2 ) NNNEw-z IF( NNNEw .GT. N ) NNNEw-N VOUT - VINT(I) NDIF - MNNEW - NN IF( NDIF .LE. 0 ) GOTO 4 DEL INCREASES . RECENT DATA HELD LONGER DD 3 II-I.NDIF VINT(II+NN) - VINT(NN) CONTINUE DEL UNCHANGEO , CURRENT DATA KEPT DEL SHRINKS , OLDEST DATA SAVED NN - NNNEw DD 6 I-2,NN VINT(I-I) - VINT(I) VINT(NN) - VIN RETURN END O‘U’Ik‘WN—I 1 mrwn—o WN-i dmmummrwn—a 322 SUBROUTINE AVERAGE( IRUN,|NTOT.INPART ) COMMON / SYSVAR / T.ROUTE(595).TROUTE,TTBS,TORIOP,TTRIOP,TR(A), COMMON / FAC / TRPOL(4),SUMSTOG.SUMR1,SUMR2,NSP,NDT5KIP,DEM(4), DEMEST(4),TGRC.TDRC.CAPwH,IwL,TwT,RCAPwH(4), TDP(4),XGT(4),PTSTRG(4),AVTONS, TRSHOLD.CONVFAC.TTSTRG(16),RLOAD(4),RUNLOAD(4), FTSTRG(4).RTSTRG(4).0POL.TPOL.TTIRS.TDOL. TDBS,5TOG,Rw5TOG(4).RI.R2.SR1(4).SR2(4),ATTRATE TIDT,IOUTTDT,ST,DDCK,Nss,PARwT,TINPUT,TIDCAP,TIDRMS COMMON / DECIDE / TIDTRoTDR.DDR,THRUPUT,TTRUPUT,DTRUPUT,STGLST,RMT ,TIDGR,TIDDR.TIDRMT.CCTRL(4) COMMON / SILO / RSTGLST(4).PRODEM(4).TSUPPLY14).KP.TRP(4).RMSS(4). RPT(IO,4),TDEMAN0(4).RTRUPUT(4),TDPR(4),TRN(4), RFT(IO,4),DELF(4).DELPF(4),KF,TRNP(4).KR,STKDUT(4) ,RTR(IO,4),SDEVSD(4),TAR(4),TSR(4),CIQS(4),GR(4) ,RTTP(IO,4),RTTR(IO,4),5ROUTE(4),BRFLG(4),TBRKDN, BALANCE COMMON / COST / CDWAGE,CRPIR,CFRPIR,CRENT,CFUEL,CFTRNS.CFSTRG, COMMON / AVE / IF( NAVE .NE. NAVE I O tit CSTRG.CFLOAD.CLOAD.CFULOAO.CULOAO.CFSMPL.CDRWAGE. CRPAIR,CRNTR,CFUELS,TCTRNS,CVAINV,CVLOAD,CVULOAD, CVSMPL.CSHIPw,TCSHIP,TOTCOST,CSMPL MONRUN,NAVE.MONTIME.MON,INTOTM(4),IwLM(4),STOGMI4), AVTHTM(4),TIDTM(4),THRUPM(4),TINPM(4),TIDTRM(4), IDUTM(4),TIDCM(4),PARIM(4),STKOTMI(4),STKOTM2(4), STKOTM3(4),STKOTM4(4),RSTDGM1(4),RSTOGM2(4), RSTOGM3(4).RSTOGM4(4),TTRUPM(4),DTRUPM(4),TTBSM(4). TDBSM(4).RTRUPMI(4),RTRUPM2(4),RTRUPM3(4), RTRUPM4(4),PRODEM1(4),PRODEM2(4),PRODEM3(4), PRODEM4(4),SDEVDMT(4),SDEVDM2(4),SDEVDM3(4). SDEVDM4(4),TIDGRM(4).TIDDRMI4).VAR(2D).SDEv(2o). TIDRMSM(4),TIDRMTM(4),TT(2D,3O),PARIDT,AVTwT, TCSHIPM(4).TCTRNSM(4).TOTCSTM(4).BALANCM(4) IRUN ) GOTO 5 INITIALIZE AVERAGES 88* DO 2 III.MONTIME IWLM(I) - O AVTwTM(I)-o TIDTM(I) - O. STOGM(I)-o THRUPM(I) -o.o TINPMII) - O.o INTOTM(I) - D IOUTM(|)IO‘ TIDCM(I)-O TIDTRM(I)-O TIDGRMII) I 0.0 TIDORMII) I 0.0 TIDRMSMII) I O TIORMTMII) I O PARIM(1)IO TTRUPMII) I O. DTRUPMII) I O. .O .O 323 TTBSM(I) - TDBSM(I) - RTRUPM1(I) RTRUPM2(I) RTRUPM3(I) RTRUPM4(I) STKOTM1(I) STKOTM2(1) STKOTM3(I) 5TKOTM4(I) RSTOGMIIII RSTDGM2(I) RSTOGM3(I) RSTOGM4(I) PRODEM1(I) PRODEH2(I) PRODEM3(I) PRODEM4(I) SDEv0M1(I) SDEVDM2(I) SDEv0M3(I) SDEv0M4(I) TCTRNSM(I) TCSHIPM(1) TDTCSTM(I) BALANCM(1) CONTINUE DO 3 I - 1.20 VAR(I) - 0.0 CONTINUE CONTINUE AVTwT - TWT/INTOT PARIDT-PARwT/INPART PARWTIO. INPART - O IWLM(MON) - IWLMIMON)+IWL AVTwTM(MON) - AVTWTM(MON)+AVTWT/MONRUN TIOTM(MON) - TIDTM(MON)+TIDT/MONRUN STOGM(MDN) - STOGM(MDN)+STOG/MONRUN THRUPM(MON) - THRUPM(MON)+THRUPUT/MONRUN TINPM(MON) - TINPM(MON) + TINPUT/MONRUN INTOTMIMON) - INTOTM(MON)+INTOT IOUTM(MON) - IOUTM(MON)+IOUTTOT TIDCM(MON) - TIDCM(MON)+TIDCAP/MONRUN TIDTRM(MON) - TIDTRM(MON)+TIDTR/MONRUN TIDGRM(MON) - TIDGRM(MON) + TIDGR/MONRUN TIDDRM(MON) - TIDDRM(MON) + TIDDR/MONRUN TIDRMSM(MON) - TIDRMSM(MON) + TIDRMS/MONRUN TIDRMTM(MDN) - TIDRMTM(MDN) + TIDRMT/MONRUN PARIM(MON) - PARIM(MON)+PARIDT/MONRUN TTRUPM(MDN) - TTRUPM(MDN) + TTRUPUT DTRUPM(MON) - DTRUPM(MON) + DTRUPUT TTBSM(MON) - TTBSM(MON) + TTBS TDBSM(MON) - TDBSM(MON) + TDBs RTRUPM1(MON) - RTRUPM1(MON) + RTRUPUT(I) / MONRUN IIIIIIIIIIIIIIIIIIIIIIIIOO OOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOO RTRUPM2(MON) RTRUPM3(MON) RTRUPM4(MON) STKOTM1(MON) STKOTM2(MON) STKOTM3(MDN) STKOTM4(MDN) RSTOGMIIMON) RSTOGM2(MON) RSTOGM3(MON) RSTOGM4(MON) PRODEMI(MDN) PRODEM2(MON) PRODEM3(MON) PRODEM4(MON) SDEVDMI(MDN) SDEVDM2(MON) SOEVOM3(MON) SDEVDM4(MON) TCTRNSM(MON) TCSHIPM(MDN) TOTCSTM(MON) BALANCM(MON) MON - MON+1 RETURN END RTRUPM2(MON) RTRUPM3(MON) RTRUPM4(MON) STKOTM1(MON) STKOTM2(MON) STKOTM3(MDN) STKOTM4(MDN) RSTOGM1(MON) RSTOGM2(MON) RSTOGM3(MON) RSTOGM4(MON) PRODEM1(MDN) PRODEM2(MON) PRODEM3(MON) PRODEM4(MON) SDEVDMI(MDN) SDEVDM2(MON) SDEVDM3(MON) SDEVDM4(MON) TCTRNSM(MON) TCSHIPM(MDN) TOTCSTM(MON) BALANCM(MON) +++++++++++++++++++++++ 324 RTRUPUT(Z) / MONRUN RTRUPUT(3) / MONRUN RTRUPUT(4) / MONRUN STKOUT(I) / HONRUN STKOUT(2) / MONRUN STKOUT(3) / MONRUN STKOUT(4) / MONRUN RWSTOG(1) / MONRUN RWSTOG(2) / MONRUN RHSTOG(3) / MONRUN RNSTOG(4) / MONRUN PRODEM(I) / MONRUN PRODEM(2) / MONRUN PRODEM(3) / MONRUN PRODEM(4) / MONRUN SDEVSD(I) / MONRUN SDEVSD(2) / MONRUN SDEVSD(3) / MONRUN SDEVSD(4) / MONRUN TCTRNS / MONRUN TCSHIP / MONRUN TOTCOST / MONRUN BALANCE / MONRUN nnn 325 SUBROUTINE SELPRNT( DUR ) COMMON / SYSVAR / T,ROUTE(5.5),TROUTE,TTBS,TDRIOP.TTRIOP,TR(4), TRPOL(4).SUMSTDG.SUMRI.SUMR2.NSP.NDTSKIP.0EM(4). DEMEST(4),TGRC,T0RC,CAPwH,IwL,TwT,RCAPwH(4), TDP(4),XGT(4).PTSTRG(4),AVTONS, TRSHDLD,CONVFAC,TTSTRG(l6),RLDAD(4),RUNLOAD(4), FTSTRG(4).RTSTRG(4),DPDL.TPOL.TTIRS.TDOL. TDBS.STOG.Rw5TOG(4),R1,R2,SR1(4),SR2(4),ATTRATE COMMON / CDP / DELCDP,DELCDPP,KCDP.TRLOST.YPAST,TRMIN,TYD,0YD. 1 STRGCDP.TRLACK.DRLACK,DYPAST,DSTGCDP COMMON / SILO / RSTGLST(4).PRODEM(4).TSUPPLY(4),KP,TRP(4),RMSS(4), RPT(IO,4),T0EMAN0(4),RTRUPUT(4),TDPR(4),TRN(4), RFT(IO.4).0ELF(4).DELPF(4).KF.TRNP(4).KR.STKOUT(4) ,RTR(10.4).SDEVSD(4),TAR(4),TSR(4),CIQS(4),GR(4) ,RTTP(10,4),RTTR(10,4),SROUTE(4),BRFLG(4),TBRKDN, BALANCE - - COMMON / COST / CDwAGE.CRPIR,CFRPIR.CRENT.CFUEL.CFTRNS,CFSTRG, l CSTRG.CFLOA0.CLOAD.CFULOAD.CULOAD,CFSMPL.CDRwAGE. CRPAIR,CRNTR,CFUELS.TCTRNS,CVAINV,CVLOAD,CVULOAD, 3 CVSMPL.CSHIPw.TCSHIP.TOTCDST.CSMPL COMMON / PQUE / PTSR,PTAR.PDAR,PCIQS,PCIQSD mmrmN—o U‘l-PUJN—o PRINT 901, T PRINT 902 - PRINT 909, TPOL,TTIRS,YPAST,TRLACK.STRGCDP.TTRIOP PRINT 913. DPOL.TDOL.DYPAST.DRLACK PRINT 904, (PTSTRGII),I-l,4).(FTSTRG(I),I-I.4).(RTSTRG(I),I-I,4) DO 6 I I 1.4 IF( XGT(I) .LT. l. ) GOTO 6 TBR I TBRKON - OUR PRINT 907, I,TBR IF( BRFLGII) .GE. A. ) GOTO 6 PRINT 906, I,TTSTRG(I),TTSTRG(I+A),TTSTRG(I+8),TTSTRG(I+12) 6 CONTINUE PRINT 905. (TRPOL(I) . 1-1.4) PRINT 915 PRINT 916, (TARII),1-1.4),(TSR(I),I-I.4).(CIQS(I),I-I,4) PRINT 917, PTAR,PDAR.PTSR,PCIQS,PCIQSD PRINT 919 w PRINT 920. CDRWAGE,CRPAIR,CRNTR,CFUELS,TCTRNS, l CVAINV,CVLOAD.CVULOAD.CVSMPL.TCSHIP.TOTCOST FORMAT STATEMENTS 5901 FORMAT("I"o2X."SELECTED AND NON MONTE CARLO VARIABLES AT TIME". I F9-60/93x9” “no 2 "m") 902 FORMAT("O",5X,"DATA ON CAPITAL",/.6X," IIIIIIIIIIIIIII ") 90M FORMAT("O",5X,"TRUCKS AND DRIVERS ON THE ROAD"./o2X, 2 "PTSTRG(I)I",FIO..NX,"PTSTRG(2)I",FIO.,NX,"PTSTRG(3)I", 3 F10.,NX,"PTSTRG(A)I".FIO.,/,2X,"FTSTRG(I)I",FIO.,NX, A "FTSTRG(2)I",FIO.,AX,"FTSTRG(3)I",FIO.,AX."FTSTRG(A)I", 326 5 F10.,/,2X,"RTSTRG(I)I",FIO.,4X,"RTSTRG(2)I",F10.,AX, 6 "RTSTRG(3)I”,F10.,AX,"RTSTRG(A)I",FIO.) 905 FORMAT("O",5X,"REGIONAL POOLS",/.IX."TRPOL(I) I",FIO.,AX. I "TRPOL(Z) I",FIO..AX,“TRPOL(3) I".FIO.,4X,"TRPOL(A) I", 2 F10.) 906 FORMAT("O",2X."TTSTRG OF",12,2X,4F10.) 907 FORMAT("O".2x."THERE HAS BEEN A BREAK DOWN IN ROAD #".12. l " AT TIME",F9.6) 909 FORMAT("O",5X,"NUMBER 0F TRUCKS AT PORT -",F12.,/, 6x,"NUMBER OF TRUCKS IN REPAIR SHOP -",F10.,/, 6X,"TOTAL TRUCKS IN THE SYSTEM -".2x,Flo.,/, 6X."EXCESS TRUCK IN THE SYSTEM I",2X.FlO.,/. 6X,"TRUCK AQUSITION IN TRANSITI",2X,FIO.,/, 6X,"TOTAL DT-HOURS OF TRUCK USE -".2x.Flo.) 913 FORMAT("O".5X,"TOTAL DRIVERS AT PORT -",F12.,/,6x, "NUMBER OF DRIVERS ON LEAVE I".F12../.6X. "TOTAL DRIVERS IN THE SYSTEM I",F12../.6X, "EXCESS DRIVER IN THE SYSTEM -",F12. ) 915 FORMAT("O",5X."DATA ON QUEUES"./.6X." -------------- ") 916 FORMAT("O",5X,"QUEUES AT REGIONAL SlLOS",/.3X,"ARRAIVAL RATES", 1 1X,4FIO.,/,3x."SERVICE RATES",1X,4FIO.,/,3x, 2 “SUM OF THE QUEUES".4F10.) 917 FORMAT("O",5X,"PORT QUEUES",/.3X,"PTARI",F12..2X."PDARI", 1 F12.,2X,"PTSRI",F12..2X,"PCIQSI".F12.,2X,"PCIQSDI",F12.) 919 FORMAT(“O“,5X,"COSTS IMFORMATION",/,6X." ------------------ ") 920 FORMAT("O",2X,"DRIVERS WAGE I",lX,FlO.,/,3X,"TRUCKS REPAIR -", FlO.,/.3X.“TRUCKS RENT I",2X,FlO.,/,3X,"FUEL COST -".3x. F11../.3X."TOTAL COST OF TRANSPORTATION -",Flz../.3X, “INVENTORY EXPENSE I".2X,FlO.,/.3X."LOADING COST -",7X, FIO.,/,3X,"UNLOADING COST I",5X,FlO.,/,3X,“COST OF ", "INFORMATION I",FlO.,/,3X,"SHIP WAITING COST I",lX,Fll.,/, 3X,"TOTAL COST OF OPERATIONS -".F12.) WS‘WN—O UNI-I O‘U’it‘WN-fi RETURN END 327 SUBROUTINE MONPRNT( DETPRT ) COMMON / AVE / MONRUN,NAVE,MONTIME,MON,INTOTM(4),IWLM(4),STOGM(4), AVTWTM(4),TIDTM(4),THRUPMI4).TINPM(4),TIDTRM(4), IOUTM(4),TIDCM(4).PARIN(4),STKOTMI(4),STKOTM2(4), STKOTM3(4),STKOTM4(4),RSTOGM1(4),RSTOGM2(4), RSTOGM3(4).RSTOGM4(4).TTRUPM(4).0TRUPM(4).TTBSM(4). TDBSM(4),RTRUPMI(4),RTRUPM2(4),RTRUPM3(4), RTRUPM4(4),PRODEMI(4),PRODEM2(4),PRODEM3(4), PRODEM4(4),SDEVDM1(4),SDEVDM2(4),SDEVDM3(4), SDEVDM4(4),TIDGRM(4),TIDDRM(4),VAR(2D),SDEV(2O), TIDRMSM(4),TIDRMTM(4),TT(20,3D),PARIDT,AVTWT, TCSHIPM(4),TCTRNSM(4).TOTCSTM(4).BALANCM(4) ~mm-aa~mrw- DO 470 MON-I.MONTIME 1WLM(M0N) - 1WLM(M0N)/MONRUN INTOTM(MON) - INTOTM(MON)/MONRUN IOUTM(MON) - IOUTM(MON)/MONRUN TTRUPM(MDN) - TTRUPM(MDN)/MONRUN DTRUPM(MON) - DTRUPM(MON)/HONRUN TTBSM(MON) - TTBSM(MON) / MONRUN TDBSM(MON) - TDBSM(MON) / MONRUN T - FLOAT(MON)/FLOAT(MONTIME) IF( DETPRT .EQ. 1. ) GOTO A70 . PRINT 910. MONRUN . T PRINT 900 PRINT 912,1WLM(MON),AVTWTM(MON),TIDTM(MON),STOGM(MON).THRUPM(MON) 2 .TINPM(MON) PRINT 902, INTOTM(MON),IOUTM(MON) PRINT 903. TIDCM(MON).TIDGRM(MON).TIDTRM(MON).TIDDRM(MDN) 1 ,PARIM(MON),TIDRM$M(MON).TIDRMTMIMON) PRINT 904, TTRUPM(MDN),DTRUPM(MON).TTBSM(MON).TOBSMIMON) PRINT 905, RTRUPMI(MON),RTRUPM2(MON),RTRUPM3(MON),RTRUPMA(MON) PRINT 908. RSTOGMl(MON),RSTOGM2(MON),RSTOGM3(MON),RSTOGMA(MON) l ,STKOTMI(MON).STKOTM2(MON).STKDTM3(MON),STKDTM4(MON) 2 ,PRODEMI(MON),PRODEM2(MON).PRODEM3(MON).PRDDEM4(MON) PRINT 922. SDEVDMI(MDN),SDEVDM2(MON),SDEVDM3(MDN).SDEVDM4IMON), I BALANCM(MON) PRINT 921, TCSHIPM(MDN),TCTRNSM(MON),TOTCSTM(MON) 47o CONTINUE IF( MONRUN .LE. 1 ) RETURN M I A 00 A80 ITII.MONRUN VAR(I) I VAR(1)+((TT(1,IT)- TIDTMIM))**2)/MONRUN VAR(2) - VAR(2)+((TT(2.IT)- TIDCM(M))882)/MONRUN VAR(3) - VAR(3)+((TT(3.1T)-TIDGRM(M))882)/MONRUN VAR(4) - VAR(A)+((TT(A.IT)-AVTWTM(M))**2)/MONRUN VAR(5) - VAR(5)+((TT(5.IT)-TIDTRM(M))882)/MDNRUN VAR(6) - VAR(6)+((TT(6,IT)-TIDDRM(M))882)/MONRUN VAR(7) - VAR(7)+((TT(7.IT)-PRODEM1(M))882)/MONRUN VAR(B) - VAR(8)+((TT(8,IT)-PRODEM2(M))882)/MONRUN VAR(S) - VAR(9)+((TT(9.IT)-PRODEM3(M))882)/MONRUN VAR(IO) I VAR(10)+((TT(IO,IT)-PRODEMA(M))**2)/MONRUN nan 328 VAR(II) - VAR(II)+((TT(II.IT)-STKOTMI(M))882)/MONRUN VAR(Iz) - VAR(12)+((TT(12,IT)-STKOTM2(M))882)/MONRUN VAR(I3) - VAR(13)+((TT(I3,IT)-STKOTM3(M))882)/MONRUN VAR(I4) - VAR(I4)+((TT(14.IT)-STKOTM4(M))882)/MONRUN VAR(15) - VAR(15)+((TT(15.IT)-TlNPM(M))**2)/MONRUN VAR(16) - VAR(16)+((TT(16,IT)-THRUPM(M))882)/MONRUN VAR(17) - VAR(17)+((TT(17,IT)-TCSHIPM(M))882)/MONRUN VAR(IB) - VAR(18)+((TT(18,IT)-TCTRNSH(M))882)/MONRUN VAR(19) - VAR(19)+((TT(19,IT)-TOTCSTM(M))882)/MDNRUN VAR(2O) - VAR(2O)+((TT(2O,IT)-BALANCM(M))882)/MDNRUN A80 CONTINUE DO A85 IT I 1.20 A85 SDEV(IT) I SQRTIVAR(IT)) PRINT 907. ( VAR(KT) , SDEV(KT) , KT - 1,14 ) PRINT 909. ( VAR(KT) , SDEV(KT) . KT - 15,20 ) PRINT 925 00 490 IT - I.MDNRUN PRINT 923. ( TT(KT,IT) , KT - 1,14 ) 490 CONTINUE .PRINT 926 00 495 IT - I.MDNRUN PRINT 924, ( TT(KT,IT) , KT - 15,20 ) 495 CONTINUE FORMAT STATEMENTS 900 FORMAT("O".5X."PORT DATA AND PERFORMANCE MEASURES"./.6x. I ll .................................. H'/’ 1 lox,"LENGTH OF”.lOX,"AVERAGE PER-SHIP",AX, 2 "IDLE TIME OF",lOX,"STORAGE",lOX."THRUPUT“,13X,“INPUT",/, 3 lOX,"WA|T LINE".10X."WAIT TIME(YRS)",6X,"SHIP SERVICE-CENTER" 4 ,3X,"AT PORT",lOX,"(PORT)",1AX,“(PORT)") 902 FORMAT(1HO."NUMBER OF SHIPS IN".IS." NUMBER OF SHIPS OUT",15) 903 FORMAT("O","IDLE TIME OF DFFLOAD EQUIP/SHIPS DUE TO OVERAGE ". 1 "STORAGE CAPACITY“,F9.6./. " IDLE TIME OF TRUCK/DRIVER " 2 ."DUE To SHORTAGE OF GRAIN",14X.F9.6,/, 3 " IDLE TIME OF DRIVER/LOAD EQUIP CAUSED BY ". 3"SHORTAGE OF TRUCKS". 5x,F9.6./." IDLE TIME OF TRUCKS/LOAD EQUIP", 4" DUE TO SHORTAGE 0F DRIVERS". 7x,F9.6./." AVERAGE SHIP WAIT TIME 5FOR SERVICE CENTER (LAST PERIOD)". 9X,F9.6./." TOTAL TIME WHEN ". 6 ”PORT IS WORKING AT LIMIT UNLOAOING CAPACITY". 5X.F9.6,/, 7" TOTAL TIME WHEN PORT IS WORKING AT LIMIT LOADING CAPACITY". 7x, 8 F9.6) 904 FORMAT("O",9X." NUMBER OF TRUCKS BEING UTILIzED -".F14.,/, 10x." NUMBER OF DRIVERS BEING UTILIZED-",FI4../. 10x." TOTAL NUMBER OF TRUCKS REPAIRED -".F14../. 10X," TOTAL NUMBER OF DRIVERS ON LEAVE-",Fl4.) 905 FORMAT("O".5X,"OATA AND PERFORMANCE INDICES ON REGIONAL SILOS"./. 6x," ---------------------------------------------- ",/, llx,"GRAIN THRUPUT FROM RWHI (TONS) I",FlA.,/. llX."GRAIN THRUPUT FROM RwH2 (TONS) -".F14../. ,l WN—i DON-0 ' 329 A 11X,"GRAIN THRUPUT FROM RWH3 (TONS) I",FIA.,/, 5 IIX,"GRAIN THRUPUT FROM RWHA (TONS) I",FIA.) 907 FORMAT("1",15X,"VARIANCES AND STANDARD DEVAITIONS AT TIME.1.0"w/o 15x,”--.--. I 1 ”,/, AX,"IDLE TIME OF SHIP SERVICE CENTER".27X,2F9.5,/, AX,"IDLE TIME OF OFF-LOADING EQUIP/SHIP DUE TO FULLHoIXo "STORAGE",2F9459/9AX,"IDLE TIME OF TRUCKS/DRIVERS DUE". " TO EMPTY STORAGE",IIX.2F9.5,/,AX, "SHIP WAIT TIME FOR SERVICE CENTER".26X,2F9.5,/. AX,"IDLE TIME OF DRIVER/LOAD EQUIP DUE TO SHORTAGE OF "9 "TRUCKsquFSoSA/oAX,"IDLE TIME OF TRUCK/LOAD EQUIP DUE", " TO SHORTAGE OF DRIVERS",2F9.5,/, AX,"RATIO OF SUPPLY TO DEMAND AT RWH)".IOX,2F9.5./, AX,"RATIO OF SUPPLY TO DEMAND AT RWHZ".IOX,2F9.5./, AX,"RATIO OF SUPPLY TO DEMAND AT RWH3".IOX,2F9.5,/. AX,"RATIO OF SUPPLY TO DEMAND AT RWHA".IOX.2F9.5./, AX,"STOCKIOUT TIME AT RWH)",IOX,2F9.5,/, AX."STOCKIOUT TIME AT RWHZ".IOX,ZF9.5,/, AX,"STOCK'OUT TIME AT RWH3",IOX,2F9.5,/, AX,"STOCKIOUT TIME AT RWHA",IOX,2F9.5) 908 FORMAT("O",IOX," STORAGE AT R .H. 1 (TONS) I",FIA.,/, 11X," STORAGE AT R 2 (TONS) I".F1A../. IIX," STORAGE AT R. (TONS) I",FIA.,/, 11X," STORAGE AT R (TONS) I".FIA.,/. A A A O‘U'Ik‘UN—P—PUDQNU‘U'IG'UN—l-fi 11X." STOCK-OUT . 1 (YEARS) I",F1A.7,/, 11X," STOCK-OUT . 2 (YEARS) I".F1A.7,/, 11X," STOCK-OUT . 3 (YEARS) I",FIA.7,/, 11X," STOCK-OUT A . A (YEARS) I",FIA.7,/, 11X," RATIO OF SUPPLY TO DEMAND AT RWHII",F1A.7,/, 11X," RATIO OF SUPPLY TO DEMAND AT RWH2I"9F1A.7,/, 11X." RATIO OF SUPPLY TO DEMAND AT RWH3I",F1A.7,/, 11X," RATIO OF SUPPLY TO DEMAND AT RWHAI",FIA.7) 909 FORMAT("O",3X,"TOTAL GRAIN INPUT (PORT)".AX,2F20.,/, AX."TOTAL GRAIN THRUPUT (PORT)".2X.2F20.o/o AX,"SHIP WAITING COST",11X.2F20.,/, AX."TOTAL COST OF TRANSPORTATION".2F20.o/o AX,"TOTAL COST OF OPERATIONS",AX,2F20-w/o AX, "BALANCE DISTRIBUTION INDEX (SYSTEM)".2F20. ) 910 FORMAT("I". 6X, "MONTE CARLO AVERAGES FOR", I3," RUNS AT TIME", F9. 6, l /, 7X, " 'o 2 I'm") 912 FORMAT(IHO, 12X, 13, lOX,F10. A, 15X, F5. 3, 12X, F10. 0. 8X, F10. O, 10X, F10. ) 921 FORMAT("O",5X, "DATA ON COST",/, 6X," ------------ ",/. 12X,"SHIP WAITING COST (DOLLARS) I".11X.F12.,/, 12X."TOTAL COST OF TRANSPORTATION (DOLLARS) I".FIZ., /,12X."TOTAL COST OF OPERATIONS (DOLLARS) I".AX, F12.) 922 FORMAT("O".10X."BALANCE DISTRIBUTION MEASURES FOR FOUR SILOS ARE". 1 /.5X,AF20.,/.IIX,“ANO FOR TOTAL SYSTEM IS",F20.) 923 FORMAT("O",2X,IAF8.5) 92A FORMAT("O",2X.6F1A.) 925 FORMAT("1",15X."OBSERVATIONS ON SELECTED RANDOM VARIABLES"./o . I IOX," ”9/9 2 IAX,"VARIOUS IDLE TIMES AT PORT".IAX,"RATIOS OF SUPPLY", 3 h .H .H H .H N-‘NOQNO‘U‘IPUJN—P U’IPUJN—P PWN—i 330 3 " TO DEMAND",11X,"STOCK-OUT TlAES",/,1Ax, h ll .......................... Il’lhx," .................... ll, 5 u ...... ",IIX," ............... II) 926 FORRAT("O",5X,"GRAIN INPUT",2x,"PORT THRUPUT",AX,"SHIP c057".hx, I "TRANS COST",AX,"TOTAL COST",5x,"BALANCE",/,6X, II ........... ",ZX," ............ ll’hx," ......... Il'hx’ 3 II .......... 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