integrated mathematical and financial modeling with
TRANSCRIPT
INTEGRATED MATHEMATICAL AND FINANCIAL MODELING WITH
APPLICATIONS TO PRODUCT DISTRIBUTION, WAREHOUSE
LOCATION AND CAPACITY PROBLEMS
by
SADIK COKELEZ, B.S., M.E.
A DISSERTATION
IN
BUSINESS ADMINISTRATION
Submitted to the Graduate Faculty of Texas Tech University in
Fulfillment of the Requirements for
the Degree of
DOCTOR OF BUSINESS ADMINISTRATION
Approved
May, 1986
C%^/^ ^ ACKNOWLEDGEMENTS
I take the opportunity of expressing my feelings and thanks with
sincere appreciation and gratitude for the exceptionally high caliber
supervision that Dr. James R. Burns has patiently endured. At the same
time, I've been lucky to have a scholar of Dr. Paul H. Randolph's
quality and recognition on my committee.
I am certainly indebted to Dr. Surya B. Yadav and Dr. Charles
Burford for their support and well-focused criticism. Dr. Cheryl A.
Segrist's and Dr. C. Tommy Moores's constructive suggestions, careful
reading of the material in this study, and corrections definitely have
helped accomplish this work.
Finally, I would like to thank Dr. Bob Davis and Dr. Arthur L.
Stoecker for their very valuable comments. Dr. Bob Davis's experience
and comments helped in clarifying the capabilities and limitations of
this study and gave it a new direction.
n
TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS 1i
ABSTRACT v
LIST OF TABLES viii
LIST OF FIGURES x
I. INTRODUCTION 1
Definition of an Integrated Linear Programming Model 1
Problem Statement 3
II. LITERATURE SURVEY 7
III. THE INTEGRATED AGRICULTURAL DECISION MODEL (lADM). . . . 17
The Conceptual Design of the lADM 17
The Operational Design of the lADM 19
Model 1. Integrated Mixed Integer Linear
Programming Model # . . . . 19
Model 2. Forecasting Model 28
Model 3. Net Present Value Model 29
Model 4. Agricultural Tax Model 30
IV. TEST PROBLEMS AND DATA 38
Origination of Test Problems and Data 38
Model Data Tables 39
Assumptions 60
m
PAGE
V. COMPUTATIONAL EXPERIMENTS ON LINDO 62
LINDO--An Interactive Linear Programming Package . . 62
Presentation of Results 62
Interpretation of the Results 63
VI. VALIDATION 92
Validation of Computational Results 92
Corroborative Analytical Deductions 93
VII. GENERAL 6UIDLINES FOR THE DESIGN OF INTEGRATED DECISION MODELS 101
VIII. CONCLUSIONS 106
Expected Contributions 106
Production Operations Management and Operations
Research 106
Agricultural Problems 107
Industrial Applications 108
BIBLIOGRAPHY H O
APPENDIX 1. THE USER'S MANUAL FOR THE COMPUTER PROGRAMS . . . . 114
APPENDIX 2. COMPUTER PROGRAMS 129
IV
ABSTRACT
The main objective of this study is to develop effective
integrated models in product distribution system design. The
integrated mixed Integer linear programming model developed in this
paper concurrently assesses the optimal solution of interrelated
problems. Conventional optimization models treat such problems separa
tely. This research has combined the existing models of subproblems
with minor modifications to achieve an overall objective. Existing
models were drawn from the areas of production operations management,
operations research, finance, and statistics. The research has pro
duced general guidelines for:
1. formulation of integrated decision models and their applica
tions to product mix and distribution system design,
2. warehouse location and capacity under diverse situations.
This thesis has contributed to production operations management
and operations research decisions by developing integrated models with
capabilities that serve to:
1. provide a high degree of coordination, adaptability, and
flexibility,
2. provide cost-effective model usage,
3. prevent suboptimality caused by treating the individual models
separately.
The integrated decisions regarding which warehouses to operate and
what quantity to ship from each warehouse have been the cornerstones of
product distribution system design. The warehouse location problem has
attracted much attention. Without warehouses, shipping direct from
factory to customers may result in higher costs due to the inability to
ship bulk and in long shipping time. Also, the warehouses act as
collection points for several factories, thereby enabling a mix of
products to be shipped to customers.
Existing warehouse location models do not integrate production
decisions and are useful only to agencies or middlemen who are in the
transportation or warehousing businesses, not producers themselves.
The models that treat production problems individually may give subop-
timal results and artifically-generated subjective supply figures; they
suffer from the artificial restrictions Imposed by individual models
such as subjectively predetermined supply figures, subjectively prede
termined warehouse capacity ranges or meeting all the demand even when
it is not profitable to do so. The integrated mixed Integer linear
model developed in this research is more comprehensive. For this
reason, there was a need for a more sophisticated and realistic
integrated model capable of handling diverse problems without imposing
the artificial restrictions mentioned above.
This research developed a unified and highly coordinated mixed
integer programming model to address product mix, transportation, ware
house location, warehouse capacity and overcapacity Issues con
currently. This unified model allows insertion, deletion, and choice
of individual models and it is very flexible. It has also been shown
through test problems that profits were much higher using the
integrated decision model developed in this paper than using conven
tional optimization techniques.
vi
Finally, this study extended the warehouse location problem by
analyzing various factors affecting warehouse location and distribution
Analyzing techniques required experiments on the computer, followed by
comprehensive mathematical proofs. The effects of an Increase or
decrease in distances among possible warehouse sites on the degree of
warehouse centralization were analyzed. In addition, the effects of
changes in resource consumption of products were studied. The analysis
ended with a study of relationship between warehouse location costs and
warehouse distribution and appropriate conclusions were drawn.
v n
LIST OF TABLES
PAGE
Table 4.1. Profits on Crops in Production Regions (dollars/acre) for All Cases 40
Table 4.2. Transportation Costs Between Production Regions and Demand Centers (dollars/ton) for All Cases . . . 40
Table 4.3. Regular Capacity Construction Costs at Production^Regions and Demand Centers (dollars/m ) for All Cases 41
Table 4.4. Fixed Warehouse Operating Costs at Production Regions and Demand Centers (dollars) for All Cases 41
Table 4.5. Water Usage of Crops (acres-feet/acre) for All Cases Except Case 5 41
Table 4.6. Water Availability at Production Regions (acres-feet) for All Cases 42
Table 4.7. Land Availability at Production Regions (in acres) for All Cases 42
Table 4.8. Crop Yields (tons/acre) for All Cases 42
3 Table 4.9. Volume-weight Values (m /ton) for All Cases 43
Table 4.10. Acres of Land Likely to Be Devoted to Each Crop in Each Region for All Cases 43
Table 4.11. Demand at Demand Centers (tons) for All Cases. . . . 43
Table 4.12. Transportation Costs Among Production Regions (dollars/ton) for Case 1 44
vm
PAGE
Table 4.13. Transportation Costs Among Demand Centers (dollars/ton) for All Cases 44
Table 4.14. Necessary Modifications for Handling Case 2 57
Table 4.15. Transportation Costs Among the Production Regions (dollars/ton) for Case 3 59
Table 4.16. Transportation Costs Among the Production Regions (dollars/ton) for Case 4 59
Table 4.17. Water Usage of Crops (acres-feet/acre) for Case 5 60
Table 5.1. The Results of Case 1 64
Table 5.2. The Results of Case 2 65
Table 5.3. The Results of Case 3. . . . 66
Table 5.4.. The Results of Case 4 67
Table 5.5. The Results of Case 5 69
Table 5.6. The Results of Case 6 70
Table 5.7. The Results of Case 7.c 72
Table 5.8. The Results of Case 7.a.. Case 7.b., and 7.d.(The Output of the Computer Program in Appendix 2). . . . 74
IX
LIST OF FIGURES
PAGE
FIGURE 1. Interactions Among the Decision Models 36
FIGURE 2. The Expanded Prototypical Integrated Model, Formatted for LINDO 45
CHAPTER I
INTRODUCTION
Definition of an Integrated Linear Programming Model
This research develops an integrated decision model that could be
used in effective product distribution system design and in analyzing
the factors affecting facility location and distribution. An
integrated linear programming model can be defined as a combination of
two or more interrelated linear programming models with capabilities
that serve to:
1. provide a high degree of coordination, adaptability, and
flexibility,
2. provide cost effective model usage,
3. prevent suboptimality caused by treating the Individual
interrelated models separately.
This research deals with the integration of the following interre
lated linear programming (LP) models:
1. Optimal product mix model. These models are used in finding
the optimal product mix when the objective is to maximize the
total profit that is subject to certain resource availa
bility constraints and possibly some others, such as demand
constraints.
2. Transportation models. The transportation models have the
objective of minimizing the total transportation cost subject
1
to meeting all customer demands at any cost while staying
within the supply limits.
3. Warehouse location models. These models deal with the deci
sions that must be made about trade-offs between transportation
costs and costs for operating distribution centers. The deci
sions concern the selection of warehouses to operate and the
quantity to ship from any warehouse to any customer,
4. Warehouse capacity models. These models are used to determine
the optimal warehouse capacities. Generally, they are
integrated with warehouse location models. For example. Brown
and Gibson combined warehouse location and warehouse capacity
models [7]. But these models suffer from artificial restric
tions, such as requiring the warehouse capacities to be within
subjectively predetermined ranges.
5. Warehouse overcapacity models. These models are extensions of
warehouse capacity models. This research has developed a method
to determine the warehouse overcapacities; it considered the
net present value of the savings gained from warehouse over
capacities over the economic life of a warehouse and the net
present value of the costs realized by warehouse overcapacities.
Forecasting and net present value techniques were used to deter
mine the objective function coefficients of the integrated mixed
integer linear programming model developed in this research. This
model is appropriate for vertically-integrated firms in agriculture and
other industries as well.
Problem Statement
The integrated decisions regarding which warehouses to operate and
what quantity to ship from each warehouse have been the cornerstones of
product distribution system design. The warehouse location problem has
attracted much attention [23]. Without warehouses, shipping direct
from factory to customers may result in higher costs due to the inabi
lity to ship bulk and in lengthy shipping times. Also, the warehouses
act as collection points for several factories, thereby enabling a mix
of products to be shipped to customers.
Existing warehouse location models do not integrate production
decisions and are useful only to agencies or middlemen in the transpor
tation or warehousing businesses who are not producers themselves.
Such models treat production problems separately which may give subop-
timal results and artificially-generated, subjective supply figures;
they suffer from the artificial restrictions Imposed by individual
models such as subjectively-predetermined supply figures, subjectively-
predetermined warehouse capacity ranges or meeting all the demand even
when it is not profitable to do so.
For example, in transportation models, the objective is to mini
mize the total transportation cost only. The profit losses by not
transporting and selling the products are not considered. Therefore, if
less than or equal to (<=) signs are used for all supply and demand con
straints, the values of the decision variables would automatically be
zero. To prevent this, the artificial restriction to meet all the demand
must be imposed. In the case of Integrated modeling, however, goods are
produced and transported to the extent that is profitable by consid
ering the revenues and transportation costs concurrently. Then, as
long as such decisions are profitable, the values of the decision
variables would never be zero. Also, the Integrated linear mixed
Integer model developed in this research is comprehensive. For this
reason, the model is capable of handling diverse problems without
imposing the artificial restrictions mentioned above.
Integrated linear programming models are quite large, which was
probably one of the factors that delayed their development and applica
tion. Because of the computing tine limitations of mathematical
programming techniques, many researchers turned to heuristic
approaches. The justification for using heuristic approaches is that
satisfactory solutions obtained by such methods require far less
computer time than optimal solutions. But, the user must be content
with suboptimal solutions.
With the recent advances in computer technology, integrated
linear programming models are easier to handle. For example, LINDO
(Linear Interactive Discrete Optimizer) [41], a computer package for
solving linear programs, is a user-friendly package capable of solving
problems with up to 4999 variables and 499 constraints (including the
objective function row). Some larger LINDO packages are also
available. Schrage [41] points out that the use of large linear
programming models has been restricted by two difficulties:
1. the cost of collecting the necessary input data and 2. the cost of solving really large LP models. The continuing
development by many firms of integrated Information and data base systems plus the continuing rapid reductions in the cost
of computer hardware are removing these two roadblocks. As continuing improvements are made in these technologies, the opportunities for profitably exploiting the power of LP will rapidly expand.
There are also some other computer packages such as MPS (Mathematical
Programming Solver) capable of handling a wide range of linear
programming problems.
The research in this study has also addressed the following
issues:
1. Should the warehouses be large and centralized, or small and
distributed?
2. Should the warehouses be sited close to the production regions
or close to the demand centers?
3. Should the product mixes consist of only a few enterprises per
region or should they be more diversified?
Kuehn and Hamburger [33] suggested that the warehouses should be
sited close to the demand centers in their heuristic approach to the
warehouse location problem. In the current study, that issue has been
analyzed in a quantifiable way and a procedure has been developed to
determine whether warehouses should be located at the production
regions or at the demand centers. This can be accomplished by making
minor changes in the parameters of the Integrated model.
The main objectives of this research are to develop an integrated
decision model that could be used in production distribution system
design and to analyze the factors that affect product distribution.
The specific objectives of this research are:
1. formulation of integrated decision models and their applica-
tions to designing product mix and distribution systems with
emphasis on warehouse location and capacity issues, and
2. analysis of the factors affecting the warehouse distribution
and developing theorems based on these analyses.
The primary Intended users of the integrated decision model would
be vertically-integrated firms such as agricultural co-operatives.
By deleting certain components of this multi-objective model and
changing the parameter and variable definitions slightly, it could be
used by farmers and transport owners as well. Although most farmers
act Independently and do not follow centrally-coordinated policies, it
is likely in the future that large, vertically-integrated firms will
eventually play an important role in agribusiness. As an example,
Mobil Oil and Shell Oil are now investing in agribusiness. The tools
developed in this research would benefit the users by providing them
with a cost-effective model usage, a high degree of coordination,
adaptability and flexibility, and optimal rather than suboptimal
results.
In Chapter III, an integrated agricultural decision model (lADM)
has been developed to analyze the product mix, warehouse location and
capacity Issues concurrently. The same model could be applied to
Industry as well without any major modifications. Then, by making
modifications on the parameters of the integrated model, factors
affecting the warehouse distribution are analyzed by the computer. The
review of previous research on integrated modeling, warehouse location,
capacity, and agricultural issues is discussed in the following chapter,
CHAPTER II
LITERATURE SURVEY
The plant or warehouse location problem has been the subject of
many articles that have appeared since the past century. Greenhut [23]
explains the history of location problems and the early approaches In
the following discussion. One of the earliest approaches to the loca
tion problem considered land rent and transportation costs as the only
determinants of location where the location is given and the type of
crop to be planted is determined assuming only one consuming center.
In another early approach, again as discussed by Greenhut [23], the
industry is given and the location is determined assuming several con
suming centers. Also, labor, transportation, and other general local
factors are taken into account. Later, demand determinants were
included in addition to cost determinants and the maximum profit con
cept emerged incorporating the cost of production at alternative loca
tions.
Francis and White [18] indicate that facility location problems
can be classified by whether the new facilities are considered to
occupy point locations or area locations, whether the solution space is
constrained or unconstrained, discrete or continuous, and whether the
distance measure is rectilinear or Euclidean, or another measure.
These problems can also be classified by whether a new facility is
dependent or independent of the locations of the remaining new facili
ties. Furthermore, the magnitude of the interactions between facili
ties, if any, can be static or dynamic, deterministic or
7
8
probabilistic. In addition, facility location problems can be classified
according to the type of objectives, such as minimizing total costs,
maximum costs, or distances, etc., the number of new facilities in
volved, and whether it is a single or multifacility location problem.
A sizeable amount of research has been conducted on the discrete
plant location problems. Often heuristic procedures were used; the
Kuehn-Hamburger heuristic program is one of the frequently referred
procedures [33]. It locates warehouses one at a time until no addi
tional ones can be added without increasing the total cost. Then the
solution is modified by evaluating the profit implications of dropping
individual warehouses or shifting them from one location to another.
The three principals of Kuehn-Hamburger program are outlined below:
1. Most geographical locations are not promising sites for a regional warehouse; locations with promise will be at or near concentrations of demand.
2. Near optimum warehousing systems can be developed by locating warehouses one at a time, adding at each stage of the analysis that warehouse which produces the greatest cost savings for the entire system.
3. Only a small subset of all possible warehouse locations need to be evaluated in detail at each stage of the analysis to determine the next warehouse site to be added.
The main disadvantage of this algorithm is that it does not guarantee
an optimal solution to a problem and it only considers demand centers
or locations near demand centers as possible warehouse sites. Feldman
et al. [17] developed a similar procedure. They assumed that ware
houses are assigned to all sites and individual warehouses are dropped
one at a time until no warehouse can be dropped without increasing
total cost.
Economides and Fok [13] studied the warehouse location problems by
analyzing the following alternatives for cost effectiveness:
1. Stationery stores to remain at the present location, under the existing operational mode,
2. Stationery stores to remain at the present location but to be upgraded to a modern, more efficient mode of operation,
3. Stationery stores to be relocated in the main-complex site, but retain the present mode of operation, or
4. Stationery stores to be relocated in the main-plant complex and to be upgraded to a modern, more efficient mode of operation.
Their model is a small-scale, mixed Integer programming model with 19
variables and 11 constraints which differs little from conventional
transportation and warehouse location models. They also state that the
model may easily be enhanced to incorporate one-time costs, provided
they have been properly discounted. Put these costs were considered
explicitly in a follow-up cash-flow analysis.
Brown and Gibson [7] developed a comprehensive model which con
verted both subjective and objective factors to dimensionless indices
in order to ensure compatibility between them. These factors were com
bined to yield the location measure of a given site that might be used
to select a single location, or might serve as input to a second model
to solve a multiplant location problem. The authors aimed at applying
current location theory, based on least total-cost site using con
sistent quantification techniques, to select the facility site. They
accomplished this objective in four steps:
1. classifying the location factors, 2. defining a general model in terms of the classification, 3. quantifying the terms of the general model,
4. formulating the general model.
The zero-one programming format utilized by Brown and Gibson selects
those sites at which production facilities should be constructed
10
together with their respective capacities that maximize the sum
of the location measures. At the same time, it satisfies any
constraint which management may specify, such as a minimum capacity
requirement and a maximum capacity expenditure.
Larson and Sadiq [34] considered the optimal location of p facili
ties in the presence of impenetrable barriers to travel where facility
users are distributed over a finite set of demand points. The weight
of each point is proportional to its demand intensity and each demand
point is assigned to the closest facility. The p-median problem is
concerned with finding the optimal locations for p facilities where the
objective is to minimize the distances between facilities and users.
The p-median problem always has an optimal solution with facilities on
the nodes and the search for an optimum is reduced to a combinatorial
one.
Klingman, et al., [32] examined the plant location problem of the
cotton-processing Industry which has experienced an excess gin plant
capacity. By considering the transportation requirements from farms to
gins, gin costs, and gin capacities, they developed a model to deter
mine which gins should be used for cotton. They calculated the
distances between the production origins and the plant locations from
aerial photos and constructed a matrix of the cost of transportation
from these origins to the plants. They emphasized alternative model
formulations. These models were capable of designating which gins
should be activated for processing cotton and how much cotton each farm
should ship each week to each gin so that the aggregated cost of
11
storage, transportation, and processing would be minimized.
Barman and Parkan [3] addressed the problem of finding a location
for the (m-i-l)st facility corresponding to a given total expected demand
on the network which already contained m facilities and determining
which demand points would be served by which facility. They also
pointed out that utilizing their methodology is possible in a situation
where there are already m facilities in the system and ml new ones are
to be offered by considering various location configurations of m-»-l,
m+2,..., m-i-ml facility systems sequentially.
Shier and Dearing [43] addressed a class of nonlinear location
problems. In their study, a single facility is to be placed on a net
work in order to minimize an aggregate cost function that is nonlinear
in travel distances.
Sule [47], on the other hand, presented simple heuristic methods
instead of complex optimization methods for the uncapacitated facility
location/allocation problem. Sule developed methods for:
1. Unlimited facility capacity without any fixed cost,
2. Unlimited facility capacity with a cost associated with
placing a facility in a location,
3. Multiperiod problems where demand and cost of assigning a
demand may change from period to period.
Sule's heuristic procedure is outlined below:
1. Formulate the total cost matrix. An entry ij in the total cost matrix represents the cost of allocating all demand from source i to location j.
2. Sum each column. The sum represents the total cost if demands from all sources are assigned to that location.
12
3. Assign the first facility to the location with minimum total cost.
4. If no more facilities are available for assignments, go to step 8, otherwise continue.
5. Determine the savings of moving each demand from the assigned locatlon(s) to a non-assigned locatlon(s). If there is no savings, mark it by '-' in the appropriate column.
6. Take a sum over each unassigned column. The sum represents the savings that could be achieved if an assignment is made in that location.
7. Make an assignment in a location which indicates the maximum savings. Transfer the demands that had contributed to this savings to the new location. This location now becomes an assigned location. Go to step 4.
8. All the assignments are made. Calculate the minimum cost and schedule.
In the case of multiperiod analysis, some adjustments would be
necessary in Sule's method. In that case, the demands and costs of
assigning demands (mainly transportation costs) may change. Projecting
demands and costs of assigning demands for each period, constructing
the total cost matrix for each period, and then determining the present
worth of each cost element in each total cost matrix becomes necessary.
In addition to the warehouse location issue, the degree or level
of warehouse centralization is also Important. Chorafas [9] discusses
warehouse centralization and decentralization. He suggests that
transshipment of products from a factory to a central warehouse, from
the central warehouse to a local warehouse, and then to another local
warehouse should be avoided to reduce cost and damage. He also
suggests that transportation linkages should be minimized. In addi
tion, the probability of error in delivering the right products to the
right destinations would Increase with the increasing number of ware
housing levels.
13
Edwards [14] points out that:
the general effect of transportation costs is to concentrate industries; a new plant locates near existing ones owing to orientation toward resources, markets, junctions, transhipment points, or median locations. Avoidance of high rent and the hope for establishing a local monopoly are examples of dispersive loca-tional forces causing new plants to decentralize and locate away from existing plants.
The research in this study concurrently utilizes both centralizing
factors, such as transportation costs, and decentralizing factors such
as warehouse construction and fixed warehouse operating costs men
tioned by Edwards, to determine warehouse locations.
Another Important aspect is warehouse capacity assessment and
expansion. Rocklin, et al., [40] derived the optimal solution of the
finite-horizon capacity expansion/contraction problem with demand
augmentation dynamics. If the demand exceeds the planned capacity of
the facility during any period, then additional capacity must be intro
duced within that period to meet the deficit. Rocklin, et al., found an
optimal strategy which minimizes the sum of capital, labor and main
tenance costs for N consecutive periods under uncertain demands.
Berry, et al., [4] described various capacity planning techniques
and some key managerial issues in choosing the appropriate technique.
These techniques are especially appropriate when dealing with complex
and continuous manufacturing control systems.
On the other hand, there has been little work done on integration
of decision levels in production planning. French [19] points out that
the problem facing the engineer-economist is to select shipping pat
terns, location, and number of plants to minimize some function of
14
total cost where the cost of concern here is for the total system. The
research in this study addresses the issues pointed out by French
concurrently and may be considered as an example of total system analy
sis since it can be used by diverse groups such as farmers, co
operatives, and transport owners.
Gelders and Wassenhove [21] point out that production planning
problems may be formulated as mixed integer linear programming
problems; but they have chosen to use a hierarchical approach. For
example, a medium-term planning model and a short-term planning model
can be Integrated to form a hierarchical planning model. The authors
have discussed hierarchical production planning systems, but have not
developed a method or algorithm capable of handling these problems.
In the other extreme, much has been written on mathematical models
and simulation in agriculture. Most of Earl 0. Heady's [1] (C.F.
Curtiss, Distinguished Professor of Agriculture at Iowa State
University) work deals with linear, integer, and dynamic programming,
PERT/CPM, inventory applications, and economic models in agriculture.
Various micro- and macro-agricultural economic models are discussed in
the "Proceedings of an East-West Seminar" by Heady [26]. Agricultural
resource requirements, resource adjustments, and farm programs are
extensively covered by Heady, Mayer, and Madsen [27], Dent and
Anderson [10] use statistical methods in systems analysis of agri
cultural problems, computer modeling, and simulation of crop-irrigation
systems.
The recent research by Stoecker et al, [46] discusses an efficient
15
computer-aided planning method using linear programming and dynamic
programming to determine the patterns of Investment in irrigation
systems which will maximize the expected net present value of future
returns.
Some applied mathematical programming books cite several examples
which may be used in an agricultural context, Bradley, et al,, [5] give
a mixed integer programming formulation of the warehouse location
problem in the simplest form. They discuss the possible extensions to
the model in their book. Applied Mathematical Programming, Bussey [8]
shows the general applications of the taxation and net present value
techniques in detail which, of course, can be extended and used in an
agricultural context, Johnson and Montgomery [28] discuss various
forecasting techniques such as linear regression, exponential
smoothing, etc. McClain [36] points out that restarting with limited
data distorts the weighting pattern of the exponential smoothing fore
casting technique. He introduces the declining alpha method, a new
technique that preserves the exponential weight pattern whereby the
smoothing constant is changed in each period by use of a formula.
The literature on decision support systems (DSS) generally deals
with commercial and Industrial, rather than agricultural, applications.
Bennet [2] discusses how to integrate optimization models with infor
mation systems for decision support. He emphasizes the importance of
embedding an optimization model within the context of a DSS. In their
recently published paper, Minch and Burns [37] present a framework
that facilitates the use of management science models in decision sup-
16
port systems. They conclude that the DSS could lower the development
effort and cost associated with the implementation of management
science models, while simultaneously helping to bring these tools
within reach of non-programming decision makers/users.
None of the works cited above dealt with diverse agricultural
problems concurrently, through the use of an Integrated decision model.
Until now, agricultural problems have been treated individually
rather than through an Integrated system for decision support.
Therefore, this research is original and promising in the sense that it
has contributed something new to the fields of agriculture, operations
research, and production operations management. Also, this study pro
vides a higher degree of coordination, adaptability, flexibility, and
cost-effective model usage as compared to any other approach discussed
in this chapter. Finally, this research extended the warehouse loca
tion problem, analyzed various factors affecting warehouse location
and distribution, conducted computer experiments and followed with
comprehensive mathematical proofs. The Integrated agricultural deci
sion model (lADM) developed in this research is presented and discussed
in the following chapter.
CHAPTER III
THE INTEGRATED AGRICULTURAL DECISION MODEL (lADM)
The Conceptual Design of the lADM
The lADM supports decision making through the Integration of
various models into a single coordinated system. Currently there are
not many efficient integrated approaches designed to handle complex
agricultural decision making processes. Recent articles in The
American Journal of Agricultural Economics were analyzed to support this
claim [11]. Most conventional operations research methods cannot treat
several interrelated problems concurrently. The agricultural problems
addressed by this research are highly Interconnected in nature.
The quality of farming decisions can be improved through the use
of the lADM. The flexible structure of the lADM allows incorporation
and treatment of several problems concurrently. Its adaptability makes
dealing with the diverse dynamic agricultural environments of today
possible. An lADM supports managerial judgement and improves the
effectiveness of agricultural problem solving. For all these reasons,
there was a need for a sophisticated lADM.
The lADM designed for this research consists of the following
models:
1, An integrated mixed integer linear programming model that
determines the optimal crop combination policy, optimal crop
17
18
distribution routes, optimal warehouse locations, and optimal
warehouse capacities and overcapacities,
2. Linear forecasting models that are used in predicting prices,
costs, and yields associated with agricultural products,
3. Net present value models that are used to analyze agricultural
cash flows,
4. An agricultural tax model.
The agricultural co-operatives are common in many European
countries and the U.S.A. They undertake activities which are in the
best Interest of their farmer members, and coordinate farming activi
ties such as crop distribution and marketing. Therefore, the agri
cultural co-operatives would construct warehouses in those locations
which would minimize the overall transportation costs. If the farmers
ship directly to demand centers, arrangements for special transpor
tation would be extremely costly, whereas a centrally coordinated
transportation system of the agricultural co-operatives could manage
the shipment at a much lower cost. Conceivably, the regional agri
cultural co-operatives could use the lADM to advise farmers what to
plant and could distribute and market their products.
The integrated model developed in this research might not be
appropriate for world-wide use unless necessary modifications are made
for specific cases. But it may prove to be useful on a regional scale
and for vertically-integrated firms in agriculture and other industries
as well. This model could prove to be useful especially in those
19
countries where the farmers would willingly Implement the recommen
dations of regional co-operatives and where there is a central policy.
The Operational Design of the lADM
The operational design phase is concerned with the details of
interactions among models and data, and with interactions of models
with each other. The mathematical representations of the models are
given in the following pages.
Model 1. Integrated Mixed Integer Linear Programming Model
This model is an integrated model consisting of the following sub
models:
1. Product mix model,
2. Transportation model,
3. Warehouse location model,
4. Warehouse capacity model,
5. Warehouse overcapacity model.
The first component in the objective function of Model 1 (see
n m Equation (0) p. 22), ( y I p..x.. ), is the total profit prior to
j=l 1=1 ^^ -^
transportation of the products. The parameter and variable definitions
are given in pp. 23-25. The second component,
n n m ( I I I c . .| x .j, )^ is the total transportation cost from
k=l j=l 1=1
20
production regions to the warehouses, whereas the third component,
s n m ^l 1 I ^ikf z.. ), is the total transportation cost from ware-
1=1 k=l i=r*^* ^^^ n
houses to the demand centers. The component, I h.w. , is the total k=l ^ ^
n warehouse construction cost whereas the component, Y f.y^, is the
k=l ^ ^ n
total fixed warehouse operating cost. The component, V h.o,., is the k=l ^ ^
u n total warehouse overcapacity cost. The final component, V Y \..o,.
t=l k=l ^^ ^
is the total savings associated with warehouse overcapacities.
The constraints are shown in pp. 22-23. Constraint set (1) is a
set of resource availability constraints such as water availability,
capital availability, etc., for each production region. Constraint set
(2), a set of supply constraints, guarantees that the amount of a cer
tain crop produced in a certain production region is equal to the
amount of that crop consumed in that production region plus the total
amount of that crop shipped from that production region to all ware
houses. Conversion factor y.. is used to convert acres of crops pro-
duced to tons of crops transported.
Constraint set (3) guarantees that no shipment of any crop can be
made from any production region to a specific production region if a
warehouse is not constructed in that specific region. Constraint set
(4) is used to ensure that the total amount of a certain crop shipped
from all production regions to a certain warehouse is equal to the
21
total amount of that crop shipped from that warehouse to all demand
centers.
Constraint set (5) is a set of demand constraints which ensures
that the total shipment of a certain crop from all warehouses to a spe
cific demand center cannot exceed the demand of that crop in that spe
cific demand center. Constraint Set (6) guarantees that no shipment of
a crop can be made to a demand center from a certain production region
if no warehouse is constructed in that production region.
Constraint sets (7) and (8) are respectively used to drive ware
house capacity and warehouse overcapacity in a specific region to zero
if no warehouse is constructed in that region. Constraint set (9) for
ces the total warehouse capacity to be at least as large as the total
average crop supplies. Conversion factors 6- and y-- are used to con
vert acres of crop supplies to cubic meter equivalents in warehouse
capacity assessment. Constraint set (10) forces the total warehouse
capacity to be large enough to accommodate the forecasted crop
supplies.
Constraint set (11) forces the warehouse capacity in a specific
region to be greater than or equal to the total amount of all crops (in
cubic meters) shipped from all regions to that specific warehouse.
Constraint set (12) ensures that -the warehouse overcapacities should be
large enough to handle a forecasted crop surplus in excess of total
warehouse capacity. Constraint set (13) is used to calculate the opti
mal overall warehouse capacity in a region which is the sum of regular
22
warehouse capacity in that region plus the warehouse overcapacity in
the same region.
Constraint set (14) shows how much of each crop produced in a cer
tain region is likely to be consumed there. The variable u.. is the
amount of crop 1 in tons that is produced and consumed in region j,
whereas g.. is its corresponding numerical value. Therefore, only
production in excess of u.. can be shipped. (See constraint set 2.)
Constraint set (15) defines the binary warehouse location variables.
If a warehouse is constructed in a specific region the value of the
binary variable is 1; otherwise it is zero. All unnumbered constraint
sets are non-negativity constraints. The integrated mixed Integer
linear programming model is shown below:
n m n n m s n m n Max I I p . j . X . j - I I I C i j k ^ i j k - I I I ^ t k £ ^ i k £ - I V k
j = l 1=1 k=l j = l i = l 1=1 k=l 1=1 k=l
n n u n
- I Vk - 1 \ \ ^ I I kt°k k=l k=l t = l k=l (0)
s . t .
m y a • • X • •
^4i i j g i j < bjg j = l , 2 , , , , , n g = l , 2 , . , , , r (1)
n
^j "Ji^ijk - ^ij^ij = 0 1=1,2 , . , , ,m j = l , 2 , , , . , n (2)
n < 0 1=1,2 , . . . ,m k = l , 2 , . . . , n (3)
23
n s
5^Nik " l^ 3=1 -^ 1=1
ik£ = 0 1=1,2 , . . . ,m k = l , 2 , . . . , n (4)
n
k = l ^^'' < d
U 1=1,2 , , , , ,m £ = 1 , 2 , . , , , s (5)
| l ' ik£ - ^l^'^u^h s s L^ i l c . - (
V
°k-Myk
n
k = l ^
< 0
< 0
< 0
n m
1=1,2 , , , , ,m k = l , 2 , . , , , n (6)
k = l , 2 , . . . , n
k = l , 2 , . . . , n
',1 i^l^i^iJ^Uo
(7)
(8)
( 9 )
Iw, k = l
m n ^k " ^ J^PiXTjk
i = l j = l
n m
^^1 Ji«inj<'iji
> 0 k = l , 2 , . . , , n
( 1 0 )
( 1 1 )
u n
t = l k=l ^
u. . i j
u n m n
= w, +o, k = l , 2 , . . . , n
= 0 or 1 k = l , 2 , . . . , n
( 1 2 )
( 1 3 )
= g . j 1=1,2 , . . . ,m j = l , 2 , . . . , n (14)
( 1 5 )
^ j
X. i j k
ik£
w,
> 0
> 0
> 0
> 0
> 0
> 0
-^ i , j
•V- 1, j .k
¥ i , k , £
Y k
Y k
Y k
IJ
iiq " ^"lount of resource g needed to produce one acre of crop 1
24
where
p.j • = forecasted profit per acre on crop 1 in production region
j for the coming year,
X.., = acres of production region j to be allocated to crop 1,
a. . = " 9
in production region j.
b. = total amount of resource g available in production region
j.
c.., = forecasted cost of shipping one ton of crop 1 from produc
tion region j to warehouse k, based on an analysis of past
years' data.
X... = amount of crop 1 in tons to be shipped from production
region j to warehouse k.
d.. = forecasted cost of shipping one ton of crop 1 from ware
house k to demand center z, based on analysis of past
years' data.
z.. = amount of crop 1 in tons to be shipped from warehouse k to
demand center i, 3
h. = forecasted construction cost per m in the region where
" k
warehouse k is to be constructed.
3 = regular capacity in m of warehouse k.
f. = forecasted fixed operating cost of warehouse k.
y. = binary variable which is equal to 1 if warehouse k is
operated and 0 if it is not operated.
3 0. = overcapacity in n of warehouse k.
25
X| ^ = the net present value of the forecasted savings Incurred
in year t per unit overcapacity in the region where ware
house k is to be located as a result of not subcontracting
for overcapacity.
u.. = amount of crop 1 in tons that is produced and consumed in
region j.
Y^ • = forecasted yield factor in tons/acre for crop i in region
j based on an analysis of past years' data.
M = a very big number. 3
p. = experimentally-determined conversion factor in m /ton for
crop 1. (Note: s- is not the same as the crop density
because of the higher volume caused by air space in crop
piles).
d. = forecasted demand in tons for crop 1 at demand center i, 11
q..p, = average amount of land in acres in production region j
allocated to crop 1 over the past several years.
q!., = forecasted amount of land in acres in production region j ^ijl
allocated to crop 1 in year 1 (next year).
^ijt = those values of the forecasted acres of land in production
region j allocated to crop 1 in year t for which there is
n m n ,
a crop surplus, i.e., I I B-y-jq-V^ > y w, . Here q^j^
is the forecasted acreage in production region j allocated
to crop 1 in year t. 3
V. = optimal capacity in m of warehouse k.
26
g.jj = numerical value in tons, of crop 1 that is produced and
consumed in production region j.
The warehouses should be capable of accommodating
n m n m "'' t^l TjSiYijqijo.J^ .I^B^Y,jq,'ji}. depending on q^^^ and
The optimal total capacity is:
n n I V. = y (W.->-0K). Due to possible forecasting errors and possible
k=l " k=l " '
unexpected outcomes, keeping the warehouse capacities somewhat larger
in order to handle future crop supplies is appropriate. There is no
way of precisely calculating future crop supplies. Therefore, crop
supplies for any year should be forecasted to assess the over
capacities. The total crop supplies in excess of total regular ware
house capacities would Indicate the amount of additional capacity
needed.
A value of 1 for a warehouse location variable indicates that a
warehouse should be located, but does not indicate how many warehouses
should be built. Since the integrated decision model is capable of
finding the corresponding capacities, the number of warehouses can be
determined easily. Suppose y =1 and w,=3000 cubic meters. If the most
appropriate capacity is 1000 cubic meters for a warehouse in that
region because of economical, constructional, and zoning restrictions,
then three warehouses at a capacity of 1000 cubic meters each would be
buiIt.
27
This model is designed for similar products which require similar
storage conditions and which could be stored in the same warehouse.
However, the case of dissimilar products could be treated yery easily by
modifying warehouse capacity variables. Orginally, w. was defined to be:
3 w. = capacity in m of warehouse k.
By defining w. to be:
3 w.. = capacity in m of warehouse k that should be constructed for
crop 1.
and by using w.. variables instead of Wj variables, an extension to the
multiproduct storage case can be made without changing the model.
On the other hand, if the user does not prefer to base the results
of his warehouse location on one year's optimal crop combination
policy, the optimal crop profit component
n m ( I I P--x, • ) and resource availability constraints, i.e., con-j = l 1=1 " ^
straint set (1), may be omitted and the following constraints may be
imposed:
x. . > q.: • i=l,2,...,m j=l,2,...,n
x. . > q. . i=lf2 m j=l,2,.,.,n
In addition, choice of average costs, revenues, etc., instead of fore
casted costs, revenues, etc., based on several years' data is possible.
Then, this revised model can be solved on LINDO and the warehouse loca
tions can be determined in advance. The solution to this model would
determine in what regions the warehouses should be located. Let the
optimal warehouse location variables, y. , be:
28
y| = P| k=l,2,...,n
where pj is the value of y^ and is a constant which is either 0 or 1.
Now the optimal y^ values are added to the original Integrated mixed
integer linear programming model as constraints and the original model
is resolved. In this way, warehouse locations would not be based on
one year's optimal crop combination policy. Even if the user does not
use this procedure, the model would still not be very sensitive to
relative price changes as constraint sets (9) and (10) force the model
to take into account the amount of each crop likely to be planted in
each region based on past several years' data.
Model 2. Forecasting Model
There are some yery fine forecasting models. This research does
not propose to develop a sophisticated forecasting model as it is
beyond its scope. The forecasting model is included here to show what
agricultural components would be forecasted, how forecasting models
would relate to the linear programming models and how they would
interact with integrated mixed Integer linear programming model com
ponents.
In this research, linear models of the form shown below were used
to forecast various parameters:
^ j t - ''' ^ j ( t - i ) ' 't
where
Y.. = orice or cost of crop 1 in production region j at time t ijt ^
29
a = trend constant
b = one-period lag coefficient
^ij(t-l) ~ P" "" ^ 0^ ^ost of crop 1 in production region j at
time t-1
G^ = random error component.
The cash-flow in the current period is assumed to be linearly related
to and dependent on the cash-flow in the previous year. The above
equation analyzes the interactions between cash flows.
Forecasting equations for transportation costs, crop yields, crop
supplies and demands, warehouse construction and fixed operating costs
would be similar with certain modifications in the subscripts.
Model 3. Net Present Value Model
The net present value model for calculating the crop profits per
acre is shown below:
where
p.. = the net present value of the profit per acre of crop 1 in
production region j.
r-.^ = income per acre of crop 1 in production region j at time 1J t
t.
c!. = cost per acre of crop i in production region j at time t. IJ t
e = discount rate.
30
t = the point in time under consideration, i.e.,
t=0,l,2,...,u'.
The land preparation, planting, harvesting, and other costs are
incurred at different time points for each crop and region and they are
projected to the present time at a certain discount rate. The discount
rate is assumed to remain constant for all time points. The p.. values
calculated using the model above would constitute the coefficients of
the first component of the objective function of the mixed Integer li
near programming model. The agricultural season is assumed to start in
October when wheat is planted in most places. Therefore, October 1 is
taken as the starting point and is denoted by t=0. The net present
value models for transportation and warehouse costs would be similar
with certain modifications in the subscripts; here the incomes (r..^)
would always be zero atall times since there are only cost components.
Model 4, Agricultural Tax Model
Even though lADM is primarily designed for vertically-integrated
firms such as co-operatives, a tax model for farmers was developed as well
in addition to the tax model for the co-operatives. Since the co-opera
tives would supposedly advise farmers on what to plant, it is Important
that co-operatives should also be concerned with the amount of tax the
farmers would pay. The tax model for the farmers is discussed below.
The tax model for the co-operatives is discussed at the end of this
section. As mentioned earlier, not only the vertically-integrated
31
firms, but also the farmers and the transport owners, could use the same
model with minor modifications in the parameters.
Taxes are based on cash flows in a calendar year. Assuming that
farmers buy inputs such as seeds, fertilizers, etc. as needed in each
agricultural season, they would not have to store them for the
following year. Thus, they avoid storage costs and costs of capital
associated with extra input purchases. Individual farmers generally do
not ship their own crops themselves. Therefore, the co-operatives, not
farmers, are assumed to pay for transportation costs. This research
considers the effect of taxes on the profits of individual farmers
obtained as a result of direct crop revenues and costs. Therefore,
taxes could be based on cash flows rather than an accrual method.
Certain crops are planted in one year and harvested in the
following year. Therefore, the agricultural season must be segregated
into two periods; i.e., the period between Oct. 1 and Dec. 31, and
Jan. 1 and Sept. 30 of the following year. Taxes associated with agri
cultural cash flows between Oct. 1 and Dec. 31 for farmer z are given by:
Dec.31 n m
Dec.31 n m
^^ I I I (^jt-Sjt)^zij > 0 t=o j=l 1=1 ^^^ ^ -^
Dec.31 n m < 0
''- .^, • 1 It i.it' zi.i
J
uec..3i n m ^
z T, = amount of taxes associated with agricultural cash flows
between Oct. 1 and Dec. 31, for farmer z.
32
a^ = tax rate for farmer z.
X x . . = ^^J X. . ziJ b. iJ
jgi
Here,
I
^zij ~ ^ " " acres that farmer z devotes to crop 1 in region j
as a result of the optimal crop combination policy,
^zi ~ ^°^a^ farmland farmer z possesses in region j.
b. = total farmland availability in region j.
In the same way, taxes between Jan. 1 and Sept. 30 of the
following year are given by:
„ Sept.30 n m , ,
" z " ^ 5 ^ I ^^-It'^iit^^zii^^z ^ Jan.l j=l 1=1 ^J^ ^J^ ^^J ^
Sept.30 n m i f y y y (r. .^-c.*.^)x'•. >
Jan.l j=l 1=1 ^J^ ^J^ ''^ 0
Sept.30 n m
0 if I I I ( jt-Sjt) zlj < 0 Jan.l j=l i=l ^J^ 'J ^^^
where
. H T = amount of taxes associated with agricultural cash flows
between Jan. 1 and Sept. 30 of the following year, for
farmer z.
The net present value of T is given by:
P V T ; = T ; (l+e)-'<'
where
k' = number of points in time between Oct. 1 and the taxation
t i me.
33
PVT^ = the net present value of taxes associated with agri
cultural cash flows between Oct. 1 and Dec. 31, for farmer
z.
In the same way,
PVr = T^ (Ue)-(^'^"''
where
n = number of points in a calendar year.
PVT = the net present value of taxes associated with agri
cultural cash flows between Jan. 1 and Sept. 30 of the
following year.
Note that T is Incurred one year after T is incurred. Finally,
II
PVT = PVT^ + PVT^
where
PVT = the net present value of taxes associated with agri
cultural cash flows over the whole calendar year.
The expanded form for PVT is:
Dec.31 n m , • PVT^ = (( I I I {r^jt-Sjt''<zij'»z)n-e)-'
t=o j=l i=l
Sept.30 n m /, • "v
^ (( I I I (^•J•t-^ijt)XziaK)(l-e)•'' '" > Jan.l j=l 1=1
Therefore, the after-tax net present value of overall profits for farmer z is:
34
n m
^ j=l 1=1 J J
Dec.31 n m • ( ( I I I {r^jt-c' )x' .)aJ(Ue)-^
t=o j=l i=l 'J"- 'J' zij z
I I Sept .30 n m /L 'u. • \
Jan.l j=l 1=1
where
^'""z = after-tax net present value of the overall profits for
farmer z.
The agricultural co-operatives would also pay for warehouse
construction and transportation costs. Therefore, the components of
the objective function of the Integrated mixed Integer linear
programming model associated with warehouses and transportation costs
do not appear in the above tax model which is developed solely for
individual farmers. However, the after-tax net present value of
overall profit for a co-operative would be given by:
ATPV = I (r -cj(l+e)"^ - ( I (r.-cj) a) (1+e)"''" t=o ^ ^ t=o ^ "-
where
r. = revenue of the co-operative at time period t
c = expenditure of the co-operative at time period t
a = tax rate for the co-operative
e = discount rate
35
n' = number of periods in a calendar year
k' = number of periods between Jan. 1 (t=o) and the taxation ti me
next year (April of the following year in many countries).
The details of the interactions of various models with each other
are shown in Figure 1. As can be seen from Figure 1, past crop prices
and costs are analyzed to forecast the profits on crops in the next
agricultural season. The net present values of the forecasted profits,
which will later constitute the coefficients of the first component of
the objective function in Model 1, are calculated for each crop and
each region. The taxes would be predicted based on the forecasted
prices and costs of the crops that are in the optimal solution of
Model 1. The taxes would be projected into the present, subtracted
from the before-tax profit to get the after-tax net present value of
the overall profit.
This chapter discussed the components of lADM, their relationship
to each other and the mathematical models for those components. The
models shown in Figure 1 were integrated, expanded, and tested by using
the data presented in the following chapters. Several real life cases
were developed and analyzed by conducting computational experiments on
the computer.
36
FbRECAstiNG MODEL
FORECASTEC J PRICES
P0ft£CASTiN(5 MODEL
INFLATION
INTEREST RATES
3
FORECASTED COSTS
T "*
r
1
1
>
DISCOUNT RATE
1
THE NET PRESENT VALUE MODEL
A
THC NST PRESENT VALUE TAXATION MODEL A A
<
THC NET PRESENT VALUE OF THE FORECASTED PROFITS
pRmtKD TAXES
1 1
1 1 1 1
- - 1
1
-TAX RATE
V SOLUTION
— >
FUTURE SAVINGS ASSOCIATED WITH WAREHOUSE OVERCAPACITIES
—>
FORECASTING MODEL >
FORECASTEq FUTURE SAVINGS ->
THE NET PRESENT VALUE MODEL
TRmrr— PRESENT VALUE OF THE FORECASTED SAVINGS
PAST CROP YIELDS IN ACRES
3
FORECASTING MODEL 3
FORECASTED YIELDS IN ACRES
AVERAGE CROR YIELDS IN ACRES
- 3
FORECASTED CROP YIELDS IN M3/ACRE
AVIHAGE CROP YIELDS IN M3/ACRE
Figure 1 - Interactions Among the Decision Models
37
IHL HLl PRESENT VALUE OF THE FORECASTED PROFITS
"Donr AVAIL ABILITY
TXPTTXr AVAILABILITY
SiULUIlUN
TATION COSTS
ULHANU
— 3
LINLAR PROGRAMMING mOlL FOR DETERMINING THE OPTIMAL CROP
COMBINATION POLICY
I TRAHSPORIAtlUN MODEL FOR OETERMININC OPTIMAL CROP DISTRIBUTION ROUTES
mt Nti PRESENT VALUE OF THE FORECASTED SAVINGS
TTJRECTSTW CROP YIELDS IN M^/ACRE
INTEGRATED MATHEMATICAL PROGRAMMING MODEL
--.zi
INTtlSLR t>> U(;tWIHlMS MDULL m DETERMINING OPTIMAL WAREHOUSE LOCATIONS. CAPACITIES, AND OVERCAPACITIES
MIXED INTEGER .LINEAR PROGRAMMING MODEL
YIELDS IN M3/ACRE
TTTtlJ WAREHOUSE OPERATING COSTS
UAKLHUUbL CONSTRUCTION COSTS
Figure 1. Continued
CHAPTER IV
TEST PROBLEMS AND DATA
Origination of Test Problems and Data
Computational experiments on the computer were conducted to deter
mine the optimal crop combination policy, optimal distribution routes,
warehouse locations, warehouse capacities, and the degree of warehouse
centralization. The effects of varying distances on warehouse central
ization were analyzed. The following six broad and comprehensive cases
were analyzed and the appropriate guidelines were determined for each
case:
1. The distances among the production regions are comparable to
the distances between production regions and demand centers,
and the warehouses are sited at production regions.
2. Case 1 with the modification that the warehouses are now sited
at demand centers.
3. Case 1 with the modification that the distances among the pro
duction regions are now very small.
4. Case 1 with the modification that the distances among produc
tion regions are now very large.
5. Case 4 with the modification that the resource consumption of
the products are now significantly increased.
6. Case 1 with interrelated problems treated separately.
For each of the cases a test problem was constructed for solution
38
39
on the computer. In addition to the above cases, the following cases
were developed to exercise all components of the lADM and demonstrate
its effectiveness as an Integrated module:
7. a. Using the forecasting component, the crop yields, acres of
land likely to be devoted to each crop in each region,
the demand on each crop at each region is forecasted.
All cost components and revenues are also forecasted.
b. Net present values of the forecasted cost components and
profits are calculated.
c. The results of 7.a. and 7.b. are input Into the integrated
mathematical programming model and the integrated model is
resolved.
d. The optimal solution is input into the agricultural tax model
The solutions to the test problems would significantly change
depending on the nature of the data. Using real data would provide an
answer for only one specific case which may not be representative of
diverse situations. Therefore, several tables of fictitious data were
used to develop guidelines in a broader context.
Model Data Tables
The following fictitious data presented in Tables 4.1 through 4.13
were used for the first case and the data were modified for each of the
other cases accordingly:
40
Table 4.1 Profits on Crops in Production Regions (dollars/acre) for All Cases
Crop
1
2
3
4
5
1
200
100
150
250
300
Prodi
2
210
105
160
270
330
jction
3
190
95
140
220
270
Reg ion
4
200
105
155
260
320
5
185
95
145
220
265
Table 4.2 Transportation Costs Between Production Regions and Demand Centers (dollars/ton) for All Cases
Production Region
1
2
3
4
5
1
5
4
5
6
3
2
4
6
6
4
5
Demand Center
3
5
6
5
3
6
4
6
4
3
4
2
5
3
5
6
2
3
41
Table 4.3 Regular Capacity Construction Costs at Production^Regions and Demand Centers (dollars/m ) for All Cases
Production Demand
Region Cost Center Cost
1 25 1 25
2 25 2 25
3 25 3 25
4 50 4 50
5 25 5 25_
Table 4.4 Fixed Warehouse Operating Costs at Production Regions and Demand Centers (dollars) for All Cases
Production Demand
Region Cost Center Cost
1 1000 1 1000
2 1000
3 1000
4 1000
5 1000
Table 4.5 Water Usage of Crops (acres-feet/acre) for All Cases Except Case 5
Crop Water Usage
1 .6
2 1.0
3 .8
4 1.5
5 1.8
2
3
4
5
1000
1000
1000
1000
42
Table 4.6 Water Availability at Production Regions (acres-feet) for All Cases
Production Region
1
2
3
4
5
Water Avallability
900000
3800000
2200000
400000
1600000
Table 4,7 Land Availability at Production Regions (in acres) for All Cases
Production Region Acres of Land
1
3
4
5
1000000
4000000
2000000
3000000
2000000
Table 4,8 Crop Yields (tons/acre) for All Cases
Crop
1
2
3
4
5
1
1
2
4
8
10
Production
2
1.2
2.3
4.5
9
12
3
.9
1.8
3.5
7
8
Peg-Ion
4
1
2.1
4
8.1
9.9
5
1.2
2.4
4.4
9
12
43
Table 4.9 Volume-weight Values (in m^^/ton) for All Cases
Crop Volume-weight Values
1
2
3
4
5
1.5
2.0
2.5
.8
1.2
Table 4.10 Acres of Land Likely to Be Devoted to Each Crop in Each Region for All Cases
Crop
1
2
3
4
5
1
500000
100000
200U00
100000
100000
Production Region
2
1000000
1000000
1500000
200000
300000
3
500000
400000
800000
200000
100000
4
2500000
200000
100000
100000
100000
5
1000000
100000
100000
600000
200000
Table 4.11 Demand at Demand Centers (tons) for All Cases
Crop
1
2
3
4
5
1
10000000
20000000
30000000
60000000
80000000
2
10000000
21000000
35000000
70000000
95000000
Demand Cent
3
8000000
20000000 '
25000000
50000000
60000000
er
4
9000000
25000000
32000000
60000000
75000000
5
12000000
25000000
34000000
65000000
96000000
Total
49000000
111000000
156000000
305000000
406000000
44
Table 4.12 Transportation Costs Among Production Regions (dollars/ton) for Case 1
Production Region
1
2
3
4
5
1
-
4
5
6
3
Product
2
4
-
6
4
5
ion
3
5
6
-
3
6
Region
4
6
4
3
-
2
5
3
5
6
2
-
Table 4.13 Transportation Costs Among Demand Centers (dollars/ton) for All Cases
Demand Center
1
2
3
4
5
1
-
4
5
6
3
2
4
-
6
4
5
Demaf id Center
3
5
6
-
3
6
4
6
4
3
-
2
5
3
5
6
2
-
The expanded prototypical model based on the preceding data
is given on the following pages for Case 1 in Figure 2.
45
MAX
200X^1 +
+ 95X^3 ^
+ 145X35 +
+ 330X^2 ""
210X^2 ^
105X24 +
260X4^ +
270X53 ^
190X^3 +
96X25 ^
270X^2 "•
320X54 +
200X^4 +
150X3^ ^
220X^3 -
266X55 -
186X^5 +
I6OX32 -
26OX44 -*
100X21 "*-
140X33 -
220X45
4X 112 - 6X
3X 116 4X 212
- 6X 213 6X 214
- 3X215 '
_ 6X 314 . 3X 316
4X 412 - 6X 413
- 6X
. 6X 613 - 6X 614
. 3X 616 4X 121
- 4X 221
- ^^326
. 6X 223 . 4X 224
- 6X 226
. 4X,o, - ^^423 - 4X
421 424
4X 524 - 6X 626
- 6X 131 - 6X
. 6X 232 . 3X 234
6X
6X 432 - 6X^31
- 6X535- ^h41
. 3X0.- - 2X246
236
- 3X434
132
5^331
414
6Xi23
4X321
5X426 '
3Xi34
113
4X312
3X415
4X
106X22
I66X34
f 300X51
- 6X^14
- 6X313
- 4X
124 '
6X323 -
4X 621
- 6X 332
- 6X135 -
3X334 "
- 6X 436 - 6X 631
. 6X 632
612
6X125
4X324
6X523
5^231
6X336
3X534
bXi - 4X 142
- 3X 143 - 2X
6X
243 341
- 4X 342
146
- 3X343
- 4X 442 3X;,.. - 2X445
6X
U43 641
. 4X 542
. 6X241
- 2X345 -
- 3X543 -
4X242
6X441
2X546
3X 6X 162 6X
- 3X 161
- 2X254
- 6X,.o - 2X^54
163 2X 164
3X,
361 6X 362
- 6X353 -
- 3X
^463 661
6X 662
261
2X354
6^563
bX
61 113 . 6Z 114
- 31 116 - 6Z
•252
- 3X451
- 2X554
- 42
- 6X 263
6X452
- 61
- 62 214 32215
62 311 42 312
- 62 411
- 5^613
- 42 412
- 62514
62413
3^516 -
, 62 414
211
- 62313
. 32,1, - ^^611 -416
42 121 . 62 122
111
6^213
3^316
- ^^612
62i23- ^^124
212 '
- 62314 -
3 .^^ Tnteqrated
, T.e Expanded P-^f/;! .00^ Figure 2. J,;^! .Formatted for
46
5Z
6Z
4Z
- 5Z
5Z
6Z
125
322
424
131
233
335
^^532
4Z
- 6Z
3Z
2Z
- 5Z
2Z
144
341
443
545
252
354
- 3^551
- lOOOY^
- 25 W,
4Z
6Z
5Z
221
323
- 6Z
4Z
425
6Z
3Z
5Z
- 5Z
132
234
431
533
2Z
- 4Z
- 4Z
145
342
444
3Z
- 6Z
- 3Z
- 5Z
151
253
355
552
lOOOY,
222
324
4Z
- 5Z
6Z
6Z
3Z
521
133
235
- 6Z
5Z
- 6Z
432
6Z
3Z
534
241
343
2Z 445
5Z
- 2Z
- 3Z
152
254
451
- ^^553
- lOOOY^
3Z
- 5Z
223
325
522
134
331
4Z
4Z
6Z
6Z
- 6Z
5Z 433
6Z
- 4Z
- 4Z
535
242
344
^^541
- 6Z
3Z
5Z
2Z
153
255
452
554
25W^
224
421
523
135
332
3Z
- 6Z
3Z
2Z
- 4Z
434
141
243
345
2Z
3Z
6Z
3Z
542
154
351
453
5Z
6Z
4Z
5Z
5Z
225
422
524
231
333
- 4Z
6Z 435
4Z 142
4Z
6Z
3Z
244
441
3Z
5Z
543
155
352
555
25Wo
2^454
lOOOY
321
6Z
5Z
- 6Z
3Z
5Z
3Z
423
525
232
334
531
143
2Z
4Z
245
442
4Z
3Z
- 6Z
544
251
353
1
25W.
3^455
IOOOY2
SOW,
Figure 2. Continued
47
S . t .
0.6X11 + X21
0.6X
, CIV + l . S X t
« ov , + l . b A 4 i
+ ^21 " . . ^ 1.8X
^ 900000
^ 3800000
62 2200000
V + 0.8X33 * I '^'^tS 400000
, . 0.8X34 + ^ - ^ ^ 4 1600000
° - ' ' ^ * '* 0 8X 1 > ^ - ^ ^ B ^ -'' ^ ^ innnooi
' X21 - " - M 1.8X,
^ X + 0.8X32 ^ ^ • ^ ' ^ ^ 1? 22 , cv + l.SX
. X - 0.8X33 - ^ - ^ ^ 3 0.6X^3 + ^ 3 ^^
^31
^32 "*"
^33 "*"
X 4 1 •*•
^42 "*"
^43 "*"
X44 "*•
^ 1
^62
^46 "
^ 3
^54
^56
X^l + ^21 ""
X^2 ^ ^22 ^
Xi3 - h2 "
Xi4 - ^24 •"
Xi5 - ^ 6 '
^ . Xii3 ^ ^ 1 ^ ' ' ^ ^ '
"" * T '• Z • >.» * •"• *";" U^l ^ H U ^ ' ^ X514 ^ ^616
V + X512 ^ ^ 1 3 ^ ' U51 + H u ^^'-
1000000
4000000
2000000
3000000
. 2000000
. Xii
- 2X21
4X 31
. 8X41
- 10X51
0
0
0
: 0
= 0
^ ^ Xi24 " ^26 ^ ^ X122 ^23 ^24
U12 21 ^^-^ + X 3 % 4 * ^ ^ U22 221 '222 22^ ^ ^^^ , X325 •
V + X002 J*"
0,2 > 21 ' '522 523
1.2X12 "
2.3X22 ^
. 4.6X32
(2)
(3)
(4)
(6)
9X 42
. 12X52
0
0
: 0
= 0
0
, , o continued f igure ^ .
(6)
(7)
(8)
(9)
(10)
( U )
(12)
(13)
(14)
(16)
(16)
(17)
(18)
(19)
(20)
48
^13 ^ ^131 •*• ^132 ^ ^133 ^ ^134 " ^135 " ^'^^
^23 ^ ^231 ^ ^232 ^ ^233 "*" ^234 "*" ^235 " ^'^^
^33 ^ ^331 •*• ^332 "*" ^333 "*" ^334 ^ ^335 " ^'^^
^43 ^ ^431 " ^432 ^ ^433 " ^434 " ^435 " ^^
^53 " ^531 ' h32 " ^533 ' ^534 ^ ^535 " ^^
13
23
33
43
53
0
0
0
0
0
(21)
(22)
(23)
(24)
(25)
^14 ^ ^141 ^ ^142 ^ ^143 ^ ^144 ^ ^145
^24 " ^241 •*• ^242 ^ ^243 " ^244 ^ ^245
^34 " ^341 ^ ^342 "" ^343 "" ^344 " ^345
'44 ^ ^441 " ^442 " ^443 "" ^444 " ^445
^54 ^ ^541 "" ^542 "" ^543 "" ^544 " ^545
14
- 2.IX
4X
24
34
- 8.IX 44
- 9.9X 54
0
0
0
0
0
(26)
(27)
(28)
(29)
(30)
Ui5 ^ ^151 ' hs2 ' hs3 ^ 154 ^ ^55 " ^'^^
^25 ^ ^ 2 5 1 " ^252 ^ ^253 ^ ^254 ^ ^255 " ^-^X
35 ' hbl " ^352 " ^353 ^ % 4 " ^355 " ^'^^
U45 ^ ^451 ^ ^452 ^ ^453 " % 4 ^ ^455 " " ^
U55 " ^551 ^ ^552 ^ ^553 ^ ^554 ^ ' SSS " ^ X
15
25
35
45
55
= 0
= 0
= 0
= 0
= 0
(31)
(32)
(33)
(34)
(35)
- 999000000Y, < 0 ^ 1 1 ^ hzi •" ^131 "" ^141 "• ^151
^211 ^ ^221 ^ ^231 ^ ^241 ^ ^251 " ' ' ' ' ' ' ' ' ' '
h n "• ^321 ^ ^331 "• ^341 ^ % 1
^411 ^ hzi "*• ^431 ^ ^441 " ^451
^511 •*• ^521 ^ h3l ^ ^541 ^ hb\
- 999000000Y
- 999000000Y
- 999000000Y
< 0
< 0
< 0
< 0
(36)
(37)
(38)
(39)
(40)
Figure 2. Continued
49
S l 2 ^ hzZ '' 132 •" 142 "" 152 " 999000000Y2 *^ ^ ^^^^ ^32 ^ ^142 ^ hb2 ' 999OOOOOOY2
^232 " 242 •*• 252 " 999000000Y2 ^
^332 •*• 342 •*• 352 " 999000000Y2 ^
^212 ^ ^222 ^ h32 ^ ^242 " 252 " 999000000Y2 ^ ^ • - * « - «-t-c- cjc C^C C06 Z
S12 •" 322 "• 332 "• 342 "" 352 • 999000000Y2 *
X412 ^ X422 "• 432 "• 442 "• 452 " 999000000Y2 <
^512 •" 522 "• 532 " 542 " 552 " 999000000Y2 <
00*+ ott 03H H
• X434 + X^4^ + X^5^ - 99900000UY^ <
^ X534 + X54^ + X55^ - 999OOOOOOY4 <
> ^135 " ^145 ^155 - 999OOOOOOY5 <
. ^235 ^245 ^255 " 999000000Y5 <
+ Xooc + Xoy. + Xocc - 999000000Yc <
(42)
'2 < 0 (43)
'2 < 0 (44)
'2 < 0 (45)
^113 •" 123 •" 133 "" 143 ^153 " 999OOOOOOY3 < 0 (46)
^213 "" 223 " 233 " 243 " 253 " 999OOOOOOY3 < 0 (47)
^313 ^ h23 •*" 333 " 343 " 353 " 999OOOOOOY3 < 0 (48)
^413 "• 423 "• 433 "" 443 453 " 999OOOOOOY3 < 0 (49)
^513 "• 523 ^533 ^543 ^553 " 999OOOOOOY3 < 0 (50)
^114 "" 124 "" 134 "• 144 "" 154 " ^ggOOOOOOY^ < 0 (61)
^214 " 224 •" 234 "" 244 " 254 ' ^ggOOOOOOY^ < 0 (62)
^314 "• 324 "" 334 "" 344 "" 354 " 999000000Y^ < 0 (53)
^414 "" 424 •" 434 "" W "" 454 " 99900000UY^ < 0 (54)
^514 •" 524 "• 534 "" 544 "" 654 " ggOOOOOOY^ < 0 (55)
^115 ^ ^125 ^135 " ^145 ^155 " 999OOOOOOY5 < 0 (56)
^215 ^ ^225 ^235 ^245 ^255 " 999000000Y5 < 0 (67)
^315 ^ ^325 ^335 ^345 ^355 " 999OOOOOOY5 < 0 (68)
^ 415 " ^425 X435 ^ ^445 ^455 " 999OOOOOOY5 < 0 (69)
^515 ^ ^525 "• 535 ^545 ^555 " 999OOOOOOY5 < 0 (60)
Figure 2. Continued
50
^lll"^^12l'^^13l'^^14l'^^15r^lir^ll2"^113'^114"^116
^21l"^^22l'^^23l"*'^24l'^^25r^2ir^212'^213"^214"^216
^31l"*"^32l"*'^33l'*"^34l'*"^36r^3ir^312"^313"^314'^315
^41l"*'^42l"^^43l"*"^44l"^^46r^4ir^412'^413"^414"^416
^51l'^^52l'*'^63l"*"^54l'^^66r^5ir^512'^513"^514"^615
^112'*"^122"^^132'*'^142"^^162'^12r^l22'^123'^124"^126
^212'*"^222"^^232"^^242'*"^262"^22r^222"^223"^224"^226
^312"^^322"^^332'^^342'^^362"^32r^322"^323"^324"^325
^412"^^422"*"^432'*'^442"*'^462'^42r^422"^423"^424"^426
^612"^^522"^^532"^^642"^^662"^62r^522'^523"^624"^626
^113''^123"'^133'"^143''^163"^13r^l32"^133"^134"^135
^213"^^223'^^233"'^243"'^253"^23r^232"^233"^234"^235
^313'"^323''^333''^343'"^363-^33r^332"^333"^334-^335
^413'^^423'^^433"^^443"^^453"^43r^432"^433"^434"^436
^13'"^523''^533'"^543"'^553"^53r^532"^533"^534-^b36
^114'^^124"^^134'^^144"^^154"^14r^l42"^143"^144"^146
^214"^^224'^^234"^^244'^^254"^24r^242'^243'^244"^245
^314"'^324'^^334'^^344"^^354-^34r^342"^343'^344"^345
^414'^^424"^^434"^^444'*'^454"^44r^442"^443"^444"^445
^514'*'^524'*'^534"^^544"^^554"^54r^542'^543"^544"^646
= 0
= 0
•- 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
= 0
(61)
(62)
(63)
(64)
(66)
(66)
(67)
(68)
(69)
(70)
(71)
(72)
(73)
(74)
(75)
(76)
(77)
(78)
(79)
(80)
Figure 2. Continued
51
''ll5*''l25*''l35*'*145*''l55'^15r^l52"^153"^154"^155 ^ ^ ' '
''215*'*225*'*235'^''245*'*255'^25r^252'^253'^254"^255 " " * '
''315*''325*'*335*'*345*''355'^35r^352"^363'^354"^355 ' " ' '
'*415*'*425*''435*''445*'*455"^45r^452'^453"^454"^455 " ° f^"'
''515*'*525'^'*535'^'*545*''555'^55r^552"^553'^554"^555 " ° ' '
^111 * ^121 • 131 ^ ^141 * ^151 * 10000000 (86)
211 ' hzi ' hzi ' hM ' % 1 * 2°"°°°"° <«^'
311 * hzi ^ ^331 " ^341 ^ ^351 * ^'^°°'^°°° ^^^^
^411 •" 421 * hz\ "• 441 "• 451 < 60000000 (89)
^511 ^ ^521 ^ ^531 * ^541 * ^551 < 80000000 (90)
^ 1 1 2 ^ ^ 1 2 2 * ^ 1 3 2 * ^ 1 4 2 ^ ^ 2 < 1°™°°"° '^1'
^ 2 1 2 * ^ 2 2 2 * ^ 2 3 2 * ^ 2 4 2 * ^ 2 5 2 ' 2100°°°° <^2'
^ 3 1 2 * ^ 3 2 2 * ^ 3 3 2 * ^ 3 4 2 * ^ 2 < ^5000000 (93)
Z412 * ^422 * ^432 * Z442 * Z452 < 'OO^OO" ''*'
^ 5 1 2 * ^ 5 2 2 * ^ 5 3 2 * ^ 5 4 2 * ^ 2 < ^^000000 (95)
^113 * Zl23 * ^133 * ^143 * ^153 < ^000000 (96)
^ 2 1 3 * ^ 2 2 3 * ^ 2 3 3 * ^ 2 4 3 * ^ 3 < ^0000000 (97)
(98)
(99)
^ 3 1 3 * ^ 3 2 3 * ^ 3 3 3 * ^ 3 4 3 * ^ 3 5 3 < ^5000000
^413 * ^423 * Z433 * Z443 * Z453 < 50000000
^513 * ^523 * Z533 * Z543 * Z553 < ^OO^OOO" (1°°'
Figure 2. Continued
62
^114 ^ ^124 •*• 134 ^ ^144 ^ ^154 ^
^214 ^ ^224 ^ ^234 ^ ^244 " 264
^314 •*• 324 " 334 " 344 ^ ^354
^414 " 424 " 434 " 444 ^ ^464
^514 " 524 ^ ^634 " 644 ^ ^664
9000000
< 25000000
< 32000000
< 60000000
< 76000000
(101)
(102)
(103)
(104)
(106)
^116 ^ ^125 ^ ^136 ^ ^146 ' ^165 < 1^000000
^216 " ^226 ' ^236 " ^246 " ^266 < ^6000000
^315 ^ ^325 ' ^335 ^ ^346 ^ ^365 < ^4000000
^416 ' ^426 ^ ^435 ^ ^445 ' ^466 < ^^^^OOOO
^616 ^ ^626 ' ^636 ' ^546 ^ ^666 < ^^^^^OOO
(106)
(107)
(108)
(109)
(110)
^111 ^ ^112 " 113 ^ ^114 " 115
^211 ^ ^212 " 213 "" 214 " 216
^311 ^ hl2 "" 313 •" 314 ^ his
^411 " 412 "*• 413 " 414 ^ ^416
^511 "" 612 "" 613 "• 514 "" 615
49000000Y, < 0
llOOOOOOY
- 166000000Y
- 305000000Y
- 406000000Y
< 0
< 0
< 0
< 0
(111)
(112)
(113)
(114)
(115)
^121 ^ h22 ^ h23 ^ ^124 ^ ^125
^221 "*• ^222 "*• ^223 ^ ^224 ^ ^225
^321 " ^322 ^ h23 ^ ^324 ^ ^325
Z421 + 2^22 •*• ^423 " ^424 " ^425
^521 ^ ^522 ^ h23 ^ ^524 ^ ^525
49000000Y2 < 0
IIIOOOOOOY2 < 0
15b000000Y2 < 0
305000000Y2 < 0
4O6OOOOOOY2 < 0
(116)
(117)
(118)
(119)
(120)
Figure 2. Continued
53
121)
122)
123)
^31 ^ ^132 ^ ^133 ^ ^134 ^ ^135 ' 49OOOOOOY3 .< 0
^231 ^ ^232 ^ ^233 ^ ^234 ^ ^236 " IIIOOOOOOY3 < 0
^331 ^ ^332 ^ ^333 ^ ^334 ^ ^335 " I66OOOOOOY3 < 0
^431 ^ ^432 •" 433 "" 434 "" 436 " 3O6OOOOOOY3 < 0 (124)
^31 ^ ^532 ^ ^633 " ^634 ^ ^636 " ^06000000Y3 < 0 (126)
^141 "" 142 "" 143 "" 144 "" 146 " 49OOOOOOY4 < 0 (126)
^241 "• 242 "" 243 " 244 "" 246 " m^OOOOOY^ < 0 (127)
^341 ^ ^342 - 343 ^ ^344 ^ ^345 ' 156000000Y^ < 0 (128)
Z44I "• 442 "" 443 " ^444 " ^446 " 306000000Y^ < 0 (129)
^41 ' ^542 ^ ^643 " ^544 ^ ^646 " 406000000Y^ < 0 (130)
^161 •" 152 ^ ^163 " ^154 ^ ^156 " ^^OOOOOOYs < 0
^251 ^ ^262 ' hs3 ' 254 ' 265 " IIIOOOOOOY5 < 0
^351 ^ ^352 ^ ^363 ^ ^354 ^ ^365 " I56OOOOOOY5 < 0
^461 ^ ^462 ^ ^453 ^ % 4 ^ ^466 7 3O6OOOOOOY5 < 0
^551 ^ ^552 ^ ^653 ^ ^654 ^ ^656 " 4O6OOOOOOY5 < 0
131)
132)
133)
134)
136)
W^ - 999000000Yj < 0 (136)
W2 - 999OOOOOOY2 < 0 (137)
W3 - 9990OOOOOY3 < 0 (138)
W^ - 999OOOOOOY4 < 0 (139)
W5 - 999OOOOOOY5 < 0 (140)
Wi + W2 + W3 + W4 + W5 > 63226000 (141)
Figure 2. Continued
64
V I . 1.6Xiil •
4X211
10X311
\^.
1.8X121
4.6X221
. 1.36Xi3i
. 3.6X231
1.6X141
4,2X241
10X341 ocv - 8.76X331
. 11.26X321 6.48X441 ^ „ . - 6.6X431
, . . 7.2X421 6.4X411 ^ ^.6X531
. 11.88X541
- 1.8X151
- 4,8X251
. 11^61
. 7.2X451
- 14,4X551
> 0 (142)
^, . 1.36X132 ' - 1.8X122
1.6X112 ^ 3.6X232 " . 4,6X222
^212 ^ . 8.76X332 . 11.26X322 6.48X442
^ . 6.6X432 _ 14.4X552 7.2X422 ^ 11,88X542
4X<
10X312
6.4X412
1 2 ^ 1 2
1.6X142
4,2X242
10X342
- 1.8X152
, 4.8X252
. 11X352
. 7.2X452
14.4X522 9.6X532 0
(143)
U. 1.6X113
4X213
1.6X143
4,2X243
10X343
u. o - 1-^^^133 • 1.8X123
, - 3.6X233 4.6X223
- 8.76X333 , ^ , . 11.26X323 ^ 6.48X443 1^^313 ^ . 6.6X433
, 7.2X423 6.4X413 , 9.6X533
. 14.4X523 12X513
, 11.88X543
. 1.8X153
. 4,8X253
. 11X353
. 7.2X453
- 14.4X553
> 0 (144)
Fig^ re 2. Cont"* inued
65
W. 1.6X
4X
lOX
6.4X
12X
114
214
314
414
514
1.8X
4.6X
- 11.25X
7.2X
14.4X
124
224
324
424
624
- 1.35X
- 3.6X
- 8.76X
6.6X
134
234
334
1.6X 144 1.8X 164
4.2X
lOX
9.6X
434
634
- 6.48X
- 11.88X
244
344
444
544
4.8X
IIX
7.2X
264
364
454
- 14,4X 664
> 0 (145)
W, 1,5X
4X
lOX
6,4X
12X
116
215
315
416
516
1.8X
4,6X
- 11,26X
7,2X
14.4X
U 11
U
U
U
21
31
41
U
U
51
12
U
U
U
U
22
33
42
52
100
200
300
600
800
100
210
360
700
950
126
226
326
426
625
- 1.36X
- 3.6X
- 8.76X
5.6X
9.6X
135
236
336
436
636
1.6X 146
4.2X 246
lOX.
- 6.48X
345
446
- 1.8X
4.8X
IIX
166
266
365
- 11.88X 646
^•^^456
14.4X555
> 0 146)
147)
148)
149)
150)
161)
162)
153)
164)
155)
156)
Figure 2. Continued
66
U
U
U
13
23
32
U
U
U
U
U
43
63
14
24
34
U
U
U
U
U
44
64
16
26
36
U
U
46
66
80
200
250
600
600
90
250
320
600
760
120
260
340
650
960
167)
168)
169)
160)
161)
162)
163)
164)
166)
166)
167)
168)
169)
170)
171)
Figure 2. Continued
67
Tabular data for Cases 2 through 6 appear in Tables 4.14 through 4.17.
Table 4.14. Necessary Modifications for Handling Case 2
Variable
^111
^211
^311
^411
^611
^122
x ^222
X ^322
X422
X ^622
^133
^233
^333
^433
Xcoo
Old Coeff.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
New Coeff.
-5
-5
-6
-6
-6
-6
-6
-6
-6
-6
-5
-6
-5
-6
-5
Variable
^111
^211
^311
^411
^611
^122
^222
^322
Z422
^522
^133
^233
^333
^433
Z - i
Old Coeff.
-5
-5
-6
-6
-6
-6
-6-
-6
-6
-6
-5
-6
-5
-5
-5
New Coeff.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 4.14. cont.
68
144
^244
'344
^444
'644
165
'266
'366
^456
^655
0
0
0
0
0
0
0
0
0
0
-4
-4
-4
-4
-4
-3
-3
-3
-3
-3
144
•244
•344
•444
•644
165
•266
•366
•465
•555
4
4
4
4
4
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
69
Table 4.16. Transportation Costs Among the Production Regions (dollars/ton) for Case 3 (See Table 4.12 for comparison)
Produ Reg
1
2
3
4
6
ction ion
1
-
.04
.05
.06
.03
ProdL
2
.04
-
.06
.04
.05
jction
3
.06
.06
-
.03
.06
Region
4
.06
.04
.03
-
.02
5
.03
.05
.06
,02
-
Table 4.16 Transportation Costs Among the Production Regions (dollars/ton) for Case 4 (See Table 4,12 for comparison)
Production Region
Production Region
1
2
3
4
-
400
500
600
300
400
-
600
400
500
500
600
-
300
600
600
400
300
-
200
300
500
600
200
^
60
Table 4.17 Water Usage of Crops (acres-feet/acre) for Case 5
Crop Water Usage
1 600
2 1000
3 800
4 1600 (*)
6 1800
* Water usage of crop 4 in region 4 was taken to be 340.
Assumptions
All parameters of the models are assumed to be constant through
time; for example, water usage of a crop, amount of water available,
and incomes on crops are assumed to remain constant over a specific
period of time. Most crops are sold within a few months after har
vesting. Prices of commodities are relatively stable for vertically-
integrated firms during such a short period of time. Therefore, it is
reasonable to assume that the incomes remain stable during a specific
period of only a few months. Another assumption is that there are no
interactions between the activities that would change the total usage
of some resource.
61
In the test problems, warehouse construction costs and fixed
warehouse operating costs were assumed to be the same at the produc
tion regions and the demand centers. Such an assumption was necessary
for a fair comparison of locating the warehouses at the production
regions against locating the warehouses at the demand centers.
This chapter discussed the test problems (cases), the data used
for each test problem, the assumptions regarding the test problems,
and the reasons behind these assumptions. Also, the entire Integrated
mixed Integer linear program developed in the previous chapter was
expanded and modified for each problem using the data presented in this
chapter. The computer package used in computational experiments and
the results of the experiments with the test problems are discussed in
the following chapter.
CHAPTER V
COMPUTATIONAL EXPERIMENTS ON LINDO
LINDO--An Interactive Linear Programming Package
Large linear programming problems that require long calculations
can be solved by a computer package called Linear Interactive Discrete
Optimizer (LINDO) [41]. LINDO permits the user to quickly input an LP
formulation and solve it. It also permits the user to make minor modi
fications of the problem and repeat the process.
LINDO is an interactive, command-oriented and user friendly
package that is designed to solve linear programming problems with up
to 4999 variables and 499 constraints; some larger LINDO packages are
also available. In LINDO, there is a wide range of commands that can
be executed at any time. For example, there are certain commands that
will" allow for the storage and retrieval of model data. These commands
along with those for editing model data greatly facilitated the
accomplishment of this research.
Presentation of Results
All test problems were solved using the LINDO computer package
discussed in the previous section. The results of all seven cases are
summarized in table form. The u. . values are the same as the right-
hand sides of the constraints 147 through 171 in Figure 2 in all cases,
so they are not repeated here. With the exception of u^ • values, if
62
63
no variable appears in the tables, the values for those variables can
be assumed to be zero. Interpretation of the results is presented in
the following section of this chapter. For the most part, positive
basis variables and their associated values are exhibited in Tables 6.1
through 6.7. However, for the reader's convenience, all values asso
ciated with warehouse location (y, ) and warehouse capacity variables
(W| ) are displayed.
Interpretation of the Results
For Cases 1, 2, and 3 the warehouses should be constructed only
at the production regions. In Case 1, the distances among the produc
tion regions are comparable to the distances between the production
regions and demand centers (see Table 4,12),
As a result of the analysis of Case 1, in which the distances
among the production regions are comparable to those between the
production regions and the demand centers, the LINDO solution
indicated that the warehouses should be- constructed in four out of five
production regions (see Table 6.1.). Therefore, the warehouses
should be distributed under these specific circumstances. Warehouse
capacities vary significantly from region to region as generated by
LINDO. The optimal crop combination policy and warehouse capacities
would depend yery much on the nature of the data; Case 1 and Case
7.C, are compared in this regard at the end of this section.
Table 5.1. The Results for Case 1
64
Variable
h h h u h \
h "3
\
\
hi
^12
^ 3
^14
^ 5
^21
^22
^23
^24
^26
^31
^32
^33
Value
1
1
1
0
1
1499366
8639164
47769628
0
5317852
999670
3999696
1399786
666949
1999666
100
91
111
119
104
75
66
100
Max Z =
Variable
^34
^3b
^41
X42
^43
X44
^45
^51
^52
^53
^b4
^55
^111
^122
^133
^145
^165
^633
^116
^121
^134
^164
^634 = 342746624
Value
80
77
75
78
71
74
72
80
79
599932
76
80
999670
4799636
1259728
665859
2399480
4798854
999570
4799536
1259728
3065339
4798854
65
Table 5.2. The Results for Case 2
Variable Value Variable Value
W.
W.
W.
W
W,
11
12
13
14
15
'21
'22
'23
'24
'26
'31
'32
'33
1
0
0
0
1
26806672
U
0
0
36420628
749852
3999696
1791443
665949
1999666
100
91
111
119
104
75
56
100
'34
35
41
42
43
44
46
51
^52
53
^54
'55
'116
'121
'131
'146
155
'615
•531
111
155
•511
•565
80
77
75
78
71
74
72
249898
79
208274
76
80
749762
4799536
1612219
666869
2399480
2498179
1666596
6411766
3816091
1665695
2498179
Max Z = 330371648
66
Table 6.3. The Results for Case 3
\/ar1able Variable
h h h \
h S ^2
^ 3
^4
\
hi
^ 2
^ 3
^ 4
^ 6
^21
^22
^23
^24
^25
^31
X-„
Value
1
0
0
u .
1
1723638
U
0
0
61502364
999670
3999696
1399786
665949
1999666
100
91
111
119 •
104
75
56
Value
'34
'36
41
42
43
44
46
'61
52
'53
'54
'55
'111
121
125
'135
146
'156
^535
115
154
•554
80
77
75
78
71
74
72
80
79
599932
76
80
999570
124602
4674934
1269727
665869
2399480
4798863
1124172
9000000
4798853
'33 100
Max Z = 358997824
67
Table 6.4. The Results for Case 4
Variable Value
W.
W,
W.
W
W.
11
12
13
14
15
'21
'22
'23
X, 24
'26
'31
Variable Value
1499356
8639164
47769628
998789
4319063
999670
3999696
1399786
666949
1999666
100
91
111
119
104
76
35
'41
42
43
44
45
"51
^52
'53
54
'55
111
122
'133
'144
'155
^633
115
121
134
145
77
75
78
71
74
72
80
79
599932
76
60
999570
4799536
1259727
665869
2399480
4798854
999570
4799536
1259727
666869
68
Table 6.4. continued
Variable Value
X32 66
X33 100
^34 80
Max Z = 319107616
Variable
^164
^634
Value
2399480
4798854
69
Table 5.5. The Results for Case 5
Variable
^1
'2
h U h h '2
'3
\
^5
^ 1
^12
^13
^14
^ 5
^21
^22
^23
^24
^26
^31
Value
1
1
1
0
1
1059
63217434
3470
0
4038
806
5675
2946
90
1969
100
91
111
119
104
76
Max Z =
Variable
^32
^33
^34
^36
X41
X42
^43
X44
^46
^51
^52
^53
^64
^55
^111
X122
^133
^166
Z1I6
^124
^134
^154
-1678083710
Value
56
100
80
77
76
78
71
74
72
80
79
76
76
80
706
6710
2670
2243
706
6710
2670
2243
70
Variable
Table 6.6. The Results for Case 6
Value Variable
^42
^43
X44
^46
^51
X52
^63
^54
^55
^111
^122
^133
^14b
^155
^611
^522
^633
^555
^115
^121
^134
Zi C/l
Value
78
71
74
72
249898
1166668
833226
76
333232
749762
3399748
1049762
665869
1999698
2498179
13997872
6666208
3997818
749762
3399748
1049762
2665557
w.
w,
w.
w
w.
11
12
13
14
15
'21
'22
'23
'24
'26
'31
'32
1
1
1
0
1
31102776
207688896
65403180
0
62166824
749862
2833207
1166492
665949
1666616
100
91
HI
119
104
76
56
'33 100 •516 2498179
Variable
^34
^35
X41
71
Table 6.6. Continued
alue
80
77
75
Max Z =
Variable
^624
^634
^564
-7094670320
Value
13997872
6666208
3997818
72
Table 5.7. The Results for Case 7.c
iriable
^1
h h u h
Value Variable
^43
X44
^45
^61
^62
Value
63
70
65
249913
1166580
w.
w.
w.
w
w,
11
12
13
^ 14
^ 5
'21
'22
^23
'24
'25
'31
'32
'33
1249462
71514728
10129
14005
16144
749868
2833223
1166511
666005
1666631
91
78
96
114
89
68
49
92
"53
64
66
111
'122
133
144
'156
'611
'522
^633
'555
116
121
134
145
•154
•515
833239
67
333243
824754
4533068
1049780
732616
1999717
2748246
14697968
741522A
4331196
824754
4633058
1049780
732516
1999717
2748246
73
Table 5,7. Continued
Variable
^34
^36
^41
X42
Value
73
72
60
70
Max z •-
Variable
^521
^534
^554
= 131908744
Value
14697968
7416224
4331196
74
Table 6,8, The Results for Cases 7,a,, 7,b,, and 7,d,
CROP
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
REGION
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
6
PROFIT
265
178
183
214.
164.
88.
92.
100
96
88
162
169
146
174
144
261
287
211
263
234
.6
.6
.9
.2
.4
.4
.0
.1
.1
.4
.3
.6
.7
.2
.6
.6
.1
.9
.1
.3
*See Appendix 2 for the actual output of the computer program.
76
Table 5.8. Continued
CROP
6
5
6
6
5
FROM REGION
2
2
2
2
2
3
3
3
3
3
REGION
1
2
3
4
5
TO REGION
1
2
3
4
5
1
2
3
4
6
1
2
3
4
5
PROFIT
317,6
372,0
272.3
316,6
273,0
TRANSPORTATIO
0.0
3.9
4,9
6.3
3.6
4,0
0.0
6.4
4.2
5.2
5.4
5.7
0.0
3.6
6.9
76
Table 5.8. Continued
FROM REGION
4
4
4
4
4
5
6
5
5
5
FROM REGION
1
1
1
1
1
2
2
2
2
2
TO
•
REGION
1
2
3
4
6
1
2
3
4
5
TO DEMAND CE
1
2
3
4
5
1
2
3
4
5
TRANSPORTATION COST
5.7
4.1
3.5
0.0
1.8
3.2
5.1
6.0
2.2
0,0
5,1
3,9
4,9
6.3
3.5
4.0
5.8
6.4
4.2
5.2
77
Table 5.8. Continued
FROM REGION TO DEMAND CENTER TRANSPORTATION COST
3 1 5.4
3 2 6.7
3 3 4.8
3 4 3.5
3 5 5.9
4 1 5,7
4 2 4,1
4 3 3.6
4 4 4.1
4 5 1.8
5 1 3.2
6 2 5.1
6 3 6.0
6 4 2.2
6 5 2.9
CROP REGION FORECASTED CROP YIELD
1 1.1
2 1.6
3 0.9
4 1.1
6 1.2
78
Table 5.8. Continued
CROP REGION FORECASTED CROP YIELD
2 1 2.2
2 2 2.7
2 3 2.1
2 4 2.2
2 6 2.8
3 1 4.4
3 2 5.1
3 3 3.8
3 4 4.4
3 6 4.7
4 1 10.0
4 2 10.0
4 3 7.9
4 4 8.6
4 5 10.0
6 1 11.0
6 2 12.6
5 3 8.9
6 4 11.2
5 5 13.0
79
Table 6 .8 . Continued
CROP
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
REGION
1
2
3
4
6
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
FORECASTED ACf
460001.0
900002.0
500000.0
2600000.0
900002.0
125000.1
1000000.0
400000.0
200000.0
100000,0
200000,0
1600007.8
824984.2
100000.0
150000.0
100000.0
200000.0
176000.0
100000.0
660000.0
80
Table 6.8. Continued
CROP
5
5
5
5
5
CROP
2
2
2
2
2
3
3
3
3
3
REGION
1
2
3
4
5
DEMAND CENTER
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
FORECASTED ACRE
125000.0
300000.0
99999.6
100000.0
200000.0
DEMAND IN TONS
11000050.0
10900000.0
8999976.0
9319931.0
12357118.U
20500034.0
23000000.0
21000200.0
34000940.0
34000940.0
38998120.0
35333360.0
27000000.0
36000672.0
34600000.0
81
Table 5.8. Continued
CROP DEMAND CENTER DEMAND IN TONS
4
4
4
4
4
5
5
6
5
6
REGION WAREHOUSE CONSTRUCTION COST
1 27.1
2 26.4
3 28.6
4 60.4
6 32.0
1
2
3
4
5
1
2
3
4
5
61000000.0
71333336.0
54999840.0
64498920.0
72998664.0
82667088.0
96000000.0
63997312.0
76334168.0
98000000.0
82
Table 5.8. Continued
REGION WAREHOUSE FIXED OPERATING COST
1 1067.7
2 1067.7
3 994.9
4 983.6
5 1002.4
NET PRESENT VALUE OF THE OVERALL TAXES FOR FARMER Z = 622646.8
Prior to dealing with Case 2, some modifications were necessary.
X.., was originally defined to be the amount of crop 1 in tons to be ijk ^ J r
shipped from production region j to warehouse k, i.e., from production
region j to production region k where a warehouse is constructed. If
warehouse k is built in production region j, j will be equal to k and
there will be no cost associated with the shipment of crop 1 from j to
k. Thus, X. .. where j=k would have zero coefficients in the objective IJK
function. On the other hand, z., was originally defined to be the
amount of crop 1 in tons shipped from production region k where a ware
house is located to the demand center i. For this reason, z-j would
not have zero coefficients in the objective function even if k=ji. For
example, production region 3 is not the same location as demand center
3 and there is some transportation cost associated with it.
Now, reverse the variable definitions, that is, define x..| to be
the amount of crop 1 shipped from production region j to demand center
83
k where a warehouse is to be located and z.. to be the amount of crop
1 shipped from demand center or warehouse k to demand center i. With
this minor modification in definition, changing any of the constraints
is not necessary, but minor changes in the objective function must be
made. Using the data presented earlier, the coefficients of x. .. where
j=k would be revised; they would no longer be zero. Since the defini
tions are reversed, the coefficients of z.. where k=£ are now set to
zero. In summary, x coefficients where j=k were interchanged with
z.. coefficients where k=Ji (see Table 4.14). LINDO allowed these
minor modifications without rewriting any part of the linear program.
Case 2 is the same as Case 1 with the requirement that the warehouses
should be located at demand centers. The comparison of Case 1 and Case
2 would depend yery much on the nature of the data. In this specific
instance, warehouses are to be constructed at two out of five demand
centers, according to the LINDO solution (see Table 5.2.). Since the
objective function value is higher in Case 1, the warehouses should be
located at the production regions for these specific data.
In Case 3, the distances among the production regions are Mery
small as compared with the original problem (Case 1). Therefore, the
objective function coefficients of the relevant variables of the origi
nal problem were revised using Table 4.16 accordingly. Logically,
the warehouses would be expected to be more centralized and larger.
The cost of shipping from one production region to the other is now
yery small allowing economical transportation to the centralized
warehouse(s). If the warehouses were distributed, then we would pay
84
more in fixed costs and also pay for the extra land. In the case of
centralized warehouse construction, the capacity of a warehouse can
easily be expanded by increasing the height of the building in order to
avoid paying for the extra land. In Case 1, centralizing the ware
houses was not appropriate, because the production regions were more
widely separated from each other. In addition, the high cost of
shipping from other production regions to the production regions where
more centralized warehouses are to be constructed would outweigh the
other economic advantages of centralized warehouse construction. The
test problem for Case 3 verified these predictions. The LINDO solution
requires only two warehouses to be constructed Instead of four, which
indicates that decreased distances favor warehouse centralization as
predicted earlier (see Table 6.3.).
For the fourth case, the distances among the production regions
were very large as compared to those in the original problem.
Necessary changes were made using Table 4.16. The warehouses would be
expected to be more distributed than those in the original problem.
The LINDO solution suggests that warehouses should be constructed at
each production region indicating that the increased distances favor
warehouse decentralization as predicted (see Table 6.4.).
Case 6 analyzed the effect of increases in the technological coef
ficient matrix, i.e., increases in the resource consumption of the pro
ducts on the degree of warehouse centralization. Theoretically, the
water consumption by the crops was assumed to increase tremendously.
The technological coefficients of the decision variables of the water
86
availability constraints of the original problem were modified using
Table 4.17. Then, the use of a test problem showed that such an
increased resource consumption favors warehouse centralization (see
Table 6.6.). In the original problem, four warehouses are to be
constructed. Now, only three warehouses are constructed, indicating a
tendency towards warehouse centralization. If the products consume
more resources, then the production level would drop. A decrease in
production would cause a decrease in transportation. Consequently,
fewer warehouses would be needed and this would discourage warehouse
dispersion. Similarly, a decrease in resource usage of the products
would favor warehouse decentralization. Technology is developing at a
rapid pace. Improved and more efficient technology would probably
result in a reduction of resource usage by the products. Thus, a trend
towards warehouse decentralization can be expected in the future.
Case 6 dealt with solving each of the interrelated problems
separately and then concurrently so that the results could be compared.
The results are summarized in Table 6.6. The optimal crop combination
and optimal crop distribution, warehouse location and capacity problems
were solved separately. The optimal crop combination problem was
solved first. Then, the optimal solution was used as an input to the
transportation problem, supplying the data to the right-hand sides of
the supply constraints. These results were compared to the results
obtained from the integrated mathematical programming model. Then, the
solutions to the individual problems were compared with the solution
obtained by lADM. Solving the interrelated problems individually
86
resulted in suboptimal solutions, contrary to solving the problems by
lADM, which resulted in optimal solutions. This was demonstrated
through the use of test problems. The optimal profit is higher under
the lADM option indicating that the lADM gives better results than the
conventional optimization techniques (compare the objective function
values in Table 6.1. and Table 6.6.). All the observations and find
ings based on the test problems were generalized through mathematical
proofs in the "Corroborative Analytical Deductions" section of Chapter
VI.
For Cases 7.a. and 7.b., the output of the computer program in
Appendix 2 is presented in Table 5.8. The first part of the computer
program uses linear regression to forecast the crop prices and crop
costs including subcomponents such as planting cost, harvesting cost,
etc., for each production region and each crop. It also forecasts the
transportation costs for each crop from each production region
(possible warehouse site) to the other production regions (possible
warehouse sites) and the transportation costs for each crop from each
production region to the demand centers. In addition, the first part
of the program forecasts the crop yields in each production region,
the acres of land likely to be devoted to each crop in each region, and
the demands for each crop at each demand center using past data. The
second part of the program forecasts the future warehouse construction
and fixed operating costs for each region using linear regression (see
Table 5.8.).
The third part of the program calculates the net present values of
87
the forecasted crop prices, forecasted crop cost component values,
forecasted crop transportation costs among production regions, and
forecasted crop transportation costs between production regions and
demand centers. The fourth part of the program computes the net pre
sent values of the forecasted crop profits which are based on forecasted
crop prices and forecasted crop cost component values. These are the
profit figures prior to the transportation of crops to demand centers.
The fifth part of the program computes the net present values of the
forecasted warehouse construction and forecasted fixed warehouse
operating costs. The net present values of the profits, transportation
costs, and warehouse-related costs are used as inputs to the objective
function of the Integrated mixed Integer linear agricultural decision
model (see Table 6.8.).
The sixth and seventh parts of the program calculate the taxes and
the net present values of the taxes associated with forecasted crop
prices and forecasted crop costs between October 1 - December 31, and
January 1 - September 30, for farmer z respectively, where October 1 is
taken to be the starting point of the agricultural season (see Table
6.8).
The results of this computer program are later incorporated as the
parameters of lADM into the integrated mathematical programming model
(Case 7.C.). The incorporation of forecasting and net present value
analysis significantly affected the values of the optimal crop com
bination decision variables (see Table 5.7.), and also changed the
88
optimal basis variables related to transportation, warehouse location,
and warehouse capacity. Case 7.c. is the same problem as the original
problem (Case 1) with only a few changes to the coefficients of the
integrated model as a result of Incorporating forecasting and net pre
sent value considerations; but the outcomes are significantly dif
ferent. In Case 1, only the data pertaining to the most recent year
were used as inputs to the Integrated model. However, in Case 7.c.,
the data were extrapolated to the future, and the extrapolated data and
the net present value coefficients were incorporated into the integrat
ed model. As mentioned earlier, this affected the optimal crop combin
ation policy, warehouse capacity, and other decision variables signifi
cantly. Since the projected transportation costs were higher in Case
7.C., the warehouses were more decentralized than those in Case 1.
Finally, the new optimal LINDO solution (solution to Case 7.c) was
used as input to the tax model (see the computer program in Appendix
2 ) . As an example, the taxes for a farmer who has 10,000 acres of land
in production region 1 and no other land were calculated (see Table
6.8). The total land in production region 1 is 1,000,000 acres (see
Table 4.7.). Therefore bg^ = 1,000,000. For optimal x.jj values where
j=l, see Table 7.c. Using,
x I
X . . = u^ iJ
Z1J bg^
zij X.. (see Model 4, pg.31)
we have:
89
X iL (^ \ . 10,000
^zll = F T : ^^ll) = 1,000,000 (^^9868) = 7^^8.68 11
jl ^ ^ ^ ^ ^ 'z21 b^^ ^"21^ " 1,000,000
^^ (x ) = iQ»ooo ( . _ ^^?V 1 nnn nnn \ 91j - 0.91
^31 = ^ ( 3i) = -umS ' '«' = °- «
"341 = ('<4l) = l.OOoiogg ' '°^ ' °-'
\^1 - ET; ("51' = l.OOMOO <24^«13) = 2499.13
All other variables x . . where j^l would be zero, since farmer z does
not have land in any other production region. Therefore, the optimal
acres would be used as Inputs to the tax model by extending the input
data values with the x . . values shown above. The net present value
of taxes at a tax rate of 20% and a discount rate of .016 per bimonthly
period would be $622546.80.
To summarize, the following general results were found:
1. Profits were much higher when integrated decision models were
used. The integrated model avoids some of the artificial
restrictions of the transportation model, such as meeting the
demand exactly; rather, the demand is met only to the extent
that is profitable. In the transportation problem, if less
than or equal to (<=) signs are used for all constraints, the
values of all decision variables would automatically be zero.
90
since the objective is to minimize the transportation costs
regardless of the loss from not transporting and selling the
products. Therefore, the transportation model, by itself. Is
not yery powerful. In the case of Integrated modeling, pro
duction and transportation are generated to the extent that
they are profitable and the values of decision variables would
never be zero as long as these decisions are profitable.
Integrated modeling considers profits and transportation costs
concurrently.
2. An increase in distances between possible warehouse sites
favors warehouse decentralization, whereas a decrease in
distances between possible warehouse sites favors warehouse
centralization.
3. An Increase in resource usage by all products favors warehouse
centralization, whereas a decrease favors warehouse decentra
lization. Since improved technology in the future may
reduce resource consumption by products (crops that are
drought-resistant and require less water due to improved
technology, for example), a tendency toward warehouse
decentralization could be expected.
Interestingly, the objective function value of Case 5 is negative
(see Table 5.5.). Due to the hypothetical Increased resource consump
tion by products, the production and consequently the profit on the
crops would be small. The constraint sets (9) and (10) (see Model 1,
p. 23) force the warehouse capacities to be large enough to accom-
91
modate the expected crop supplies based on an analysis of past data.
If constraint sets (9) and (10) are omitted, the warehouse capacities
would only be controlled by constraint set (11) and would turn out to
be much smaller in the case of increased resource consumption by pro
ducts. Since the warehouse capacities are not based on a specific
year's data, as in the case of a possible increase in resource consump
tion by products, they would still be yery large. As a result, the
warehouse-related costs are well above the profits on crops and produce
a negative objective function value. However, if certain conditions,
such as constraint sets (9) and (10) are not required, then the objec
tive function value of an Integrated model would never be negative.
The objective function value of Case 6 is also negative, because
the product mix and the transportation problems are treated separately.
Transporting the products without considering revenues might result in
cost overruns. However, in the case of integrated modeling, production
and transportation take place to the extent that they are profitable
and, therefore, the objective function value is much higher (see Table
6.1. and Table 5.6.).
This chapter was devoted to presentation and Interpretation of the
results of the test problems developed in the preceding chapter. The
validation of lADM is also based on these test problems and discussed
in the following chapter.
CHAPTER VI
VALIDATION
Validation of Computational Results
The optimal crop combination and optimal crop distribution, ware
house location and capacity problems were solved separately. The solu
tions to the individual problems were compared with the solution
obtained by lADM. Solving the Interrelated problems individually
resulted in suboptimal solutions, solving the problems by lADM resulted
in optimal solutions. This was shown by using test problems. The
overall profit was much higher under the lADM option, indicating that
the lADM is superior to conventional optimization techniques (compare
objective function values in Table 6.1. and Table 5.6.).
lADM Includes any components or decisions found in separate sub
models. Therefore, any solution generated by lADM would always be at
least as good as those generated by separate submodels. Since lADM
takes into account all cost and revenue components and decisions that
any single separate model would contain, plus many more, it can ana
lyze all possible combinations concurrently and more thoroughly. In
general, this would result in better solutions than the solutions of
separate models; or the solution would be at least as good as those of
separate models as discussed above.
lADM has also permitted more cost-effective model usage. Solving
the problems separately required taking the outputs of one problem and
using them as inputs to the other. For example, the values of the
92
93
decision variables of the optimal crop combination problem were used as
the right-hand sides of the supply constraints of the optimal crop
distribution problem. This means that the user has to solve the first
problem and use the solution to that problem as data for the second
problem and then solve the second problem. Then, the user has to com
bine the objective function values of both problems to assess the
overall objective function value. This is inefficient and impractical.
But if the user chooses to use lADM, the results can be obtained
directly and they will be optimal rather than suboptimal.
Corroborative Analytical Deductions
The computer-based empirical research was followed by analytical
deductions to support and validate the empirically determined obser
vations of the previous chapter. Several theorems relevant to those
observations are presented and proved In this section.
Theorem 1. Increased distances among the possible warehouse sites
favor warehouse decentralization.
Proof: Let
C = transportation cost coefficient row vector of length m
Z = transportation decision variable column vector of
length m
Vy = total number of warehouses to be operated under present
ci rcumstances.
94
f = fixed cost of operating (locating, constructing, etc.) a
warehouse (assumed to be the same at eyery region) where
f>0 (The warehouse facilities may already exist so major
construction may not be necessary.)
C = transportation cost coefficient row vector of length m
under Increased distances
Z' = transportation decision variable column vector of length
m under increased distances
5 y' = total number of warehouses to be operated under Increased
distances
CZ = the inner product of the transportation cost vector with
the decision variable vector Z where "CZ" is apparently
the total transportation cost
C'Z' = the total transportation cost under Increased distances
fly = total warehouse fixed operating cost under present
circumstances
tyy = total warehouse fixed operating cost under Increased
distances.
The total transportation cost under Increased distances would
always be greater than or equal to total transportation cost under
normal distances. If supply and demand constraints have equal signs,
then the overall values of the transportation variables would be the
same under increased distances; as a result, total transportation cost
would 1nt:rease as the distances increase. If certain demand or supply
targets do not have to be met, then the Increased distances which ulti-
96
mately result in increased transportation costs might cause a some
reduction in the overall values of the transportation decision
variables, but such a decrease would never be enough to overcome the
overall effect of the increased distances. If the values of the
transportation variables are decreased more and more, the overall
transportation cost would decrease. In addition, revenues might drop
as a result of transporting less and thus, selling less.
The optimization techniques always provide the best solution
(i.e., minimum total transportation cost possible); the solution
obtained under Increased distances (and thus. Increased transportation
costs), would never be better (i.e., smaller) than under normal distan
ces. So, C'Z' > CZ or C'Z' - CZ > 0. The increase in total transpor
tation cost is given by C'Z' - CZ where C'Z'- CZ > 0. The change in
the number of warehouses is given by ly* - ly. The change in the total
transportation cost per unit change in the total number of warehouses
is:
C'Z' - CZ
)>' - ly
The fixed cost of operating a warehouse is f. The optimization
techniques would necessitate a change in the warehouse distribution
only if the above ratio is greater than the fixed operating cost per
warehouse that is equal to f; it would be worthwhile to relocate the
warehouses only if the change in total transportation cost per unit
change in the total number of warehouses is greater than the fixed cost
of operating a unit warehouse; i.e., if
96
LI ~ CZ > f where f > 0
ir - ly
> 0 C'Z' - CZ
It was earlier shown that the numerator, C'Z' - CZ, is positive.
Therefore, the denominator should also be positive in order for the
above inequality to hold in the same direction. Therefore, [y' - ly >
0 or ly > ly which clearly Indicates that the warehouses should be more
distributed.
Corollary 1, A decrease in distances among the possible warehouse
sites favor warehouse centralization.
Proof: The proof follows directly from the converse of the previous
situation. Theorem 1 and Corollary 1 apply evenly to production
regions and demand centers. Proofs are general and are based on any
possible warehouse site with no reference to supply or demand centers.
For this reason, if the warehouses are sited at the demand centers,
results identical to those for production regions can be expected.
Theorem 2. An Increase in resource usage of all products (larger tech
nological coefficients) favors warehouse centralization.
Proof: Let
B = basis square coefficient matrix of size n of the product
model under present circumstances
97
B = basis inverse of the production model at optimality under
present circumstances
b = column vector length of n for the right-hand sides of the
production resource constraints under present circumstances
D = column vector of length d for the right-hand sides of the
demand constraints under present circumstances
A = basis square coefficient matrix of size (n + d) of the
transportation model under present circumstances
A~ = basis inverse of the transportation at optimality under
present circumstances
X = basis production decision variable column vector of
length n
C = transportation cost vector of length (n + d) under
present circumstances
Z = basic transportation decision variables column vector of
length (n + d) under present circumstances
ly = total number of warehouses to be operated under present
ci rcumstances
f = fixed cost of operating (locating, constructing, etc.)
a warehouse (assumed to be the same at every region)
where f > 0 under present circumstances
B' = basis square coefficient matrix of size n of the produc
tion model under increased resource consumption
B'"'^ = basis inverse of the production model at optimality
under Increased resource consumption
98
b = (remains the same under increased resource consumption)
D = (remains the sane under increased resource consumption)
A = (remains the same under increased resource consumption)
A = (remains the same under Increased resource consumption)
X' = basic production decision variables column vector of
length n under Increased resource consumption
C = (remains the same under Increased resource consumption)
V = basic transportation decision variables column vector of
length (n + d) under Increased resource consumption
ly^ = total number of warehouses to be operated under increased
resource consumption
Now,nB'ii > iiBii. Therefore,
HB' « > IIBB
nB''" ii < nB'- n
llX'n = ll(B'"- )bii < iiXii = ii(B"- )bii.
The X' values constitute the new reduced right-hand sides of the
transportation supply constraints which automatically cause a reduction
in the Z values:
BX'B < BXII
X' •g-]ll < HL-Q
il[- _]il is the combined column vector of length (n+d) which contains ^ both X and .D
[-^-]« < »[-^-]n where
flZ'n = nA"k-5-]« < »Z«=nA-k-5-]B
CZ' < CZ.
It has just been shown that CZ' < CZ. It follows that CZ' - CZ < 0.
99
It would be worthwhile to relocate the warehouses only if the
change in the total transportation cost per unit change in the total
number of warehouses is greater than the fixed cost of operating a unit
warehouse, i.e., if
CZ' - CZ
CZ' - CZ
> f > 0
T — I r ^ > 0
ly - ly
It was earlier shown that the numerator, CZ' - CZ, is negative.
Therefore, the denominator should also be negative in order for the
whole ratio to be positive. This implies that Jy' - ly < 0 and con
sequently ly* < [y, which indicates that the Increased resource con
sumption favors warehouse centralization, as was to be shown.
Corollary 2. A decrease in resource usage of all products (smaller
technological coefficients) favors warehouse decentralization.
Proof: The proof follows directly from the converse of the situation
in Theorem 2.
Theorem 3. An Increase in warehouse fixed operating costs favors ware
house centralization.
Proof: Let
M = capital allocation to be used for warehouse fixed
operating expenses
f = usual fixed cost of operating a warehouse
y = total number of warehouses under usual fixed warehouse
location costs
f = increased fixed cost of operating a warehouse
100
ly' = total number of warehouses under Increased fixed warehouse
location costs.
For any given fixed amount of money allocated to warehouse fixed
operating expenses, M,
M = f Jy = f ly'
f
Since f > f , < 1 and consequently
I
< 1 y
ly' < h
which indicates that an Increase in warehouse fixed operating costs
favors warehouse centralization.
Corollary 3. A decrease in warehouse fixed operating costs favors
warehouse decentralization.
Proof: The proof follows directly from the converse of the situation
in Theorem 3.
In this chapter, the superiority of lADM over the traditional
optimization methods was discussed. Also, the empirically determined
observations of the previous chapter were validated through mathemati
cal proofs. Since the use of Integrated modeling was validated, it was
worthwhile to discuss the general guidelines for the design of these
models in the following chapter.
CHAPTER VII
GENERAL GUIDELINES FOR THE DESIGN OF INTEGRATED DECISION MODELS
In real life situations, deciding on multiple Issues which require
the Integration of Interrelated problems is often necessary. The deter
mination of the optimal crop combination, optimal crop distribution
routes, warehouse locations and capacities are all different but
related problems. This research has combined these problems by using a
single integrated model.
First of all, the objectives of related problems should be com
bined in a single objective function. One of the objectives Is to
maximize the profits from the crops. Another objective is to minimize
the transportation costs for the crops. These two objectives can
easily be combined by multiplying the objective function of the
transportation problem by "-1" and then adding it to the naximization
objective function of the optimal crop combination problem. Therefore,
the transportation, warehouse capacity, and warehouse location cost
minimization objective functions were all multiplied by "-1" and then
added to the maximization objective function involving profits on crops
(see Model 1, Equation (0)).
Another important issue in Integrating the models is non-
linearity. Some objective function components may be nonlinear, but
nonlinearity should be avoided whenever possible. If avoiding the
nonlinearity without loss of credibility and realism in the model is
101
102
Impossible, then the nonlinearities should be treated separately. For
example, the net present value model is nonlinear and should not be
combined directly with the LP models. The net present values of crop
profits should be calculated separately and the results used as Inputs
to the integrated LP objective function.
In another case, even though the net present value Inputs (xkt)
associated with overcapacities varies with t, x.^ for each year is used
as coefficient of o^ for that year in the objective function and then
X| ^ values are summed over the years (see Model 1, Equation (0)).
Therefore, the problem does not become nonlinear, x.^ values should
be forecasted for each year t and the net present value considerations
should be incorporated prior to using x.^ values as coefficients in the
objective function.
In another situation, nonlinearity was avoided by taking the
construction costs as linear. In this case, the warehouse capacity
objective function was easily Integrated with the other objective func
tion components of f odel 1. The construction costs are linear; this is
not an assumption. In most instances, the construction firms actually
3 charge a fixed amount for each m without a discount for larger
buildings. Even if they offer a discount at certain discrete levels,
this doesn't violate linearity unless the discount pattern itself is
nonlinear. Therefore, such considerations can usually be incor
porated into the model without difficulty. On the other hand, the
construction firm's costs of construction would decrease as the size of
the construction becomes larger. Although the costs would be nonlinear
103
for the construction company, in general, the construction company
would still charge the agricultural or Industrial firms a fixed amount 3
for each m it has actually constructed.
The first major step in integration of several LP problems
is to combine the objective functions of the Interrelated problems in an
appropriate manner. Of course, caution should be exercised to avoid
nonlinearity.
The second major step is to combine the constraints in an
appropriate way. In addition to the agricultural resource availability
constraints, supply and demand constraints for the transportation
problem, warehouse capacity and warehouse location constraints were
Included in the Integrated model. But some modifications were made in
the constraints. Since the values for the crop production decision
variables would be the supply figures, x.. variables would constitute
the right-hand sides of the supply constraints. For simplex implemen
tation on LINDO, X. . variables were transfered to the left-hand side of
the constraints as -x. . so that there were no variables on the right-
hand sides (see Model 1, constraint set (2)). The x., variables are
expressed in acres and the transportation variables (x ,-| ) ^re
expressed in tons. Therefore, appropriate conversion factors (y. .)
were put in front of x.. variables to make the appropriate transition
from acres to tons.
Also incorporated was an additional set of constraints that
require the total amount of each crop shipped from all production
regions to a warehouse to be equal to the total amount of each crop
.1
shipped from that warehouse to all demand centers (see Model 1, con
straint set (4)). This is because a shipment from a warehouse is only
as much as that specific warehouse receives. These constraints are
usually referred to as "conservation constraints."
Two additional sets of constraints were incorporated into the
model. These constraints prevent the shipment of products either to a
production region if no warehouse is constructed there, or to demand
centers from a production region where no warehouse is constructed (see
Model 1, constraint sets (3) and (6), respectively).
Other sets of constraints v/ere added to drive the regular ware
house capacities and overcapacities to zero if no warehouse is
constructed (see Model 1, constraint sets (7) and (8), respectively).
Finally, another set of constraints was added to make the warehouse
capacities greater than or equal to the total optimal amount of prod
ucts shipped to those warehouses (see Model 1, constraint set (11)).
Another approach to multiple objective linear programming is goal
programming. Goal programming is used for optimization problems that
contain multiple conflicting objectives. A specific goal for each
objective is set and a solution that minimizes the weighted sum of
deviations from the set of stated goals is sought. The deviations in
the goal programming objective carry ordinal priority weights.
This study dealt with multiple objectives that could easily be
converted to each other. All the objectives were either maximizing
profit or minimizing cost that could be transformed into each other
simply by multiplying by (-1). Goal programming would be more suit-
105
able where there are conflicting objectives that cannot be easily com
bined in a single objective function and where there is a desired
level of attainment for each goal. The user must state an ordinal pre
ference ordering among his goals and also a target value for each
goal; such decisions would obviously involve subjectivity.
The main disadvantages of goal programming are that it Involves
subjectivity, permits intentional deviations from the target values to
occur, and it does not find a global optimum. It finds a feasible set
of optimal solutions to the priority 1 level subproblem. For all these
reasons, it would be preferable to integrate the multiple objectives in
a single objective function as was done in this study rather than
using goal programming.
CHAPTER VIII
CONCLUSIONS
In this research, general guidelines for the design of integrated
decision models were developed. A specific application of integrated
modeling to product mix and distribution system design was analyzed,
tested, and validated. This chapter concludes the findings of the
research with expected contributions to production operations manage
ment, operations research, agriculture, and Industry.
Expected Contributions
Production Operations Management and Operations Research
This research has contributed to production operations management
and operations research in the following ways:
1. The integrated linear programming model assesses the optimal
solution by solving interrelated problems concurrently. Most
mathematical programming models treat such interrelated
problems separately [7]. This research has combined the
existing models of subproblems with minor modifications to
achieve an overall objective. Existing models were drawn from
the areas of operations research, production operations
management, finance, and statistics.
2. As indicated in Chapter III, the lADM is highly adaptive and
flexible. Its flexibility allows the incorporation or deletion
106
107
of individual models or special considerations, and the choice
of individual models. For example, the warehouse capacities can
be based on average crop yields or forecasted crop yields by
omitting one constraint, or on a combination of average and
forecasted crop yields. If the warehouses are to be located
at demand centers Instead of production regions, this can be
achieved simply by modifying certain objective function coef
ficients and the variable definitions. These components or
constraints can easily be eliminated or modified by setting
certain parameters or variables equal to zero and by inter
changing certain parameters without changing the model, as
Indicated earlier. Therefore, the lADM is an Integrated,
unified, and highly coordinated system with potential applica
tion in a diverse and broad range of agricultural and
industrial contexts. It has the ability to deal with special
situations.
3. A different approach to warehouse capacity assessment was
developed. This approach uses the weight and volume rela
tionships of the individual crops in the assessment of ware
house capacities.
Agricultural Problems
The research has contributed to the modeling of agricultural
problems in the following ways:
108
1. A special original agricultural tax model capable of assessing
the taxes associated with agricultural activities and their
effect on agricultural economics has been developed.
2. The integrated agricultural decision model permits cost-
effective model usage and helps to increase agricultural
productivity. The concurrent use of various models and
system flexibility result in cost-effective model usage.
Conventional agricultural optimization methods solve interre
lated problems separately; preparing and solving the indivi
dual models, and then combining the solutions to assess the
overall solution, requires more time and effort. Such a
flexible, adaptive, and efficient application is probably uni
que in agriculture, because it provides the answers to several
agricultural problems concurrently by combining diverse tech
niques such as economic analysis, statistics, and operations
research.
Industrial Applications
The lADM concept would also contribute significantly to Industry.
As mentioned earlier, no major changes are necessary prior to imple
menting industrial test problems. The same basic principles that apply
to agriculture would apply to Industry, too. The industry, like its
agricultural counterpart, must be a vertically integrated one.
Finally, this research has produced general guidelines for:
109
1. Formulation of integrated decision models and their applica
tions to product mix and distribution system design,
2. Warehouse location and capacity under diverse situations.
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Ill
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APPENDIX 1
USER'S MANUAL FOR THE COMPUTER PROGRAM
Overview
This program computes the parameters of the integrated agri
cultural decision model. It is an integrated program consisting of
forecasting, net present value analysis, and tax analysis segments.
Inputs
The Inputs are crop prices, costs, yields, supplies, and demands,
warehouse-related costs, periods of incurrences of cash flows, discount
rate, and tax rate.
Outputs
The outputs are the forecasted crop yields, supplies, and demands,
the net present values of the forcasted profits on the crops, crop
transportation costs, warehouse construction costs, warehouse fixed
operating costs, and taxes.
Relationships Between the Outputs and the Integrated Agricultural Decision Model Parameters
Forecasted crop yields are used as conversion factors (y..) in
constraint set (2) of Model 1 (see p. 22). The supply forecasts are
114
115
used in warehouse capacity assessment (see q.., on the right hand side
of the constraint set (10)). The demand forecasts are used as the
right-hand sides of constraint set (5). The net present values of the
profits on the crops, crop transportation costs, warehouse construction
and fixed operating costs are all used as the objective function coef
ficients of lADM (see Model 1, Equation (0)).
Major Program Segments
The first part of the program computes the forecasts for the crop
prices and crop costs including subcomponents such as planting cost,
harvesting cost, etc., for each production region and each crop using
linear regression. It also forecasts the transportation costs for each
crop from each production region (possible warehouse site) to the other
production regions (possible warehouse sites) and the transportation costs
for each crop from each production region (possible warehouse site) to
the demand centers. The first part of the program also forecasts the
crop yields in each production region, the acres of land likely to be
devoted to each crop in each region, and the demands for each crop at
each demand center based on past data using linear regression. The
second part of the program forecasts the future warehouse construction
and fixed operating costs at each region using the same forecasting
technique in the first part.
The third part of the program calculates the net present values of
the forecasted crop prices, forecasted crop cost component values,
forecasted crop transportation costs among production regions, and
116
forecasted crop transportation costs between production regions and
demand centers. The fourth part of the program computes the net
present values of forecasted crop profits based on the forecasted crop
prices and forecasted crop cost component values. These are the profit
figures prior to the transportation of crops to the demand centers.
The fifth part of the program computes the net present values of ware
house construction and warehouse fixed operating costs.
The sixth part of the program calculates the taxes and their net
present values associated with the forecasted crop prices and forecasted
crop costs between October 1 and December 31 for farmer z where October
1 is taken to be the starting point of the agricultural season. The
optimal solution obtained by solving the Integrated model is used as
input to the tax model. The taxes would be dependent upon the optimal
profit and therefore also upon the optimal acreage. The final part of
the program calculates the taxes and their net present values assso-
ciated with the forecasted crop prices and forecasted crop costs between
January 1 and September 30 of the coming year.
Data Input Preparation
First, an input data file is created. Then each data point is
written on a separate card or line. The user can choose the data,
although the data should be entered in a certain order. The user does
not have to make any changes in the program, but only needs to revise
or create his input data file by typing the numerical data points. For
reader convenience, the description of each data point is provided in
117
the example that follows. This example shows the order in which the
data should be entered.
Example: Suppose we are dealing with two crops (NUMBER OF
CR0PS=2), two regions (NUMBER OF REGI0NS=2), two demand centers (NUMBER
OF DEMAND CENTERS=2), and two years of data (NUMBER OF YEARS OF
DATA=2). Suppose we want to forecast:
1. Crop cost components,
2. Crop prices,
3. Transportation costs from the production regions to the warehouses,
4. Transportation costs from the warehouses to the demand centers,
5. Crop yields,
6. Acres of land likely to be devoted to each crop in each
region,
7. Demand of each crop at each demand center.
Here, NUMBER OF CROP FORECASTS = 7.
And suppose that we also want to forecast:
a. Warehouse construction costs,
b. Fixed warehouse operating costs.
Thus, NUMBER OF WAREHOUSE FORECASTS = 2.
Let DISCOUNT RATE = .016 for a two-month period. Let the pre
dicted tax rate for farmer z be 20% for this year and also for next
year. There are three months or 1.6 periods (approximately 2 periods)
between October 1 and December 31. Thus, PERIODS OCTOBERl TO
DECEMBER31 = 2. Assuming that the taxation is incurred in April 1 of
next year, PERIODS OCTOBERl TO TAX-TIME NEXTYEAR = 3 since there are 3
118
two-month Intervals between October 1 of this year and April 1 of next
year. There are 6 two-month periods in a year. Therefore, PERIODS IN
A YEAR = 6. If the user wants to be more precise and if he has
reliable data, he might divide a year into 12 periods where each period
is one-month or he might even use weeks. The order that the data
should be entered for the example above is:
DATA POINT DATA DESCRIPTION
7 NUMBER OF CROP FORECASTS
2 NUMBER OF CROPS
2 NUMBER OF REGIONS
2 NUMBER OF REGIONSl (This is always the
same as NUMBER OF REGIONS. It is used
to avoid resetting NUMBER OF REGIONS
and making modifications In the
program).
2 NUMBER OF DEMAND CENTERS
2 NUMBER OF SUB COMPONENTS
2 NUMBER OF SUB COMPONENTSl (Again, this
is always equal to NUMBER OF SUB
COMPONENTS).
2 NUMBER OF YEARS OF DATA
2 NUMBER OF WAREHOUSE FORECASTS
0.016 DISCOUNT RATE
4 NUMBER OF CROP FORECASTS IN NPV (It is
equal to 4, because the net present
119
values of the four forcasted elements,
i.e., 1., 2., 3., and 4. in the above
example are calculated. The other
elements, 6., 6., and 7. are not
money related forecasts; so their net
present values can't be taken),
2 NUMBER OF PROFIT FORECASTS (It is
equal to 2, because only the forecasted
elements 1. and 2. are used in calcu
lation of profits prior to transpor
tation of crops).
2 NO OF WAREHOUSE FORECASTS IN NPV (It
is equal to 2, because the net pre
sent values of two forecasted ele
ments, a and b in the example above,
are calculated).
0 SUM OF CASH FLOWS THIS YEAR
.2 TAX RATE FOR FARMER Z THIS YEAR
2 PERIODS OCTOBERl TO DECEMBER 31
3 PERIODS OCTOBERl TO TAX-TIME NEXT YEAR
2 NUMBER OF CROP FORECASTS IN TAX
0 SUM OF CASH FLOWS NEXT YEAR
.2 TAX RATE FOR FARMER Z NEXT YEAR
6 PERIODS IN A YEAR
120
PRICE OF CROP 1 IN REGION 1 IN YEAR T=-2 (the user would
start using his own data starting from here on).
PRICE OF CROP 1 IN REGION 1 IN YEAR T = -1
PRICE OF CROP 1 IN REGION 2 IN YEAR T = -2
PRICE OF CROP 1 IN REGION 2 IN YEAR T = -1
PRICE OF CROP 2 IN REGION 1 in YEAR T = -2
PRICE OF CROP 2 IN REGION 1 IN YEAR T = -1
PRICE OF CROP 2 IN REGION 2 IN YEAR T = -2
PRICE OF CROP 2 IN REGION 2 IN YEAR T = -1
COST COMPONENT 1 OF CROP 1 IN REGION 1 IN YEAR T = -2
COST COMPONENT 1 OF CROP 1 IN REGION 1 IN YEAR T = -1
COST COMPONENT 2 OF CROP 1 IN REGION 1 IN YEAR T = -2
COST COMPONENT 2 OF CROP 1 IN REGION 1 IN YEAR'T = -1
COST COMPONENT 1 OF CROP 1 IN REGION 2 IN YEAR T = -2
COST COMPONENT 1 OF CROP 1 IN REGION 2 IN YEAR T = -1
COST COMPONENT 2 OF CROP 1 IN REGION 2 IN YEAR T = -2
COST COMPONENT 2 OF CROP 1 IN REGION 2 IN YEAR T = -1
COST COMPONENT 1 OF CROP 2 IN REGION 1 IN YEAR T = -2
COST COMPONENT 1 OF CROP 2 IN REGION 1 IN YEAR T = -1
COST COMPONENT 2 OF CROP 2 IN REGION 1 IN YEAR T = -2
COST COMPONENT 2 OF CROP 2 IN REGION 1 IN YEAR T = -1
COST COMPONENT 1 OF CROP 2 IN REGION 2 IN YEAR T = -2
COST COMPONENT 1 OF CROP 2 IN REGION 2 IN YEAR T = -1
COST COMPONENT 2 OF CROP 2 IN REGION 2 IN YEAR T = -2
COST COMPONENT 2 OF CROP 2 IN REGION 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
121
TO PRODUCTION REGION 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP I FROM PRODUCTION REGION 2
TO PRODUCTION REGION 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO PRODUCTION REGION 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
122
TO PRODUCTION REGION 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO PRODUCTION REGION 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO DEMAND CENTER 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO DEMAND CENTER 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO DEMAND CENTER 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 1
TO DEMAND CENTER 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO DEMAND CENTER 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO DEMAND CENTER 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO DEMAND CENTER 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 1 FROM PRODUCTION REGION 2
TO DEMAND CENTER 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO DEMAND CENTER 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
TO DEMAND CENTER 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 1
123
TO DEMAND CENTER 2 IN YEAR T = -2
TO DEMAND CENTER 2 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO DEMAND CENTER 1 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO DEMAND CENTER 1 IN YEAR T = -1
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO DEMAND CENTER 2 IN YEAR T = -2
TRANSPORTATION COST OF CROP 2 FROM PRODUCTION REGION 2
TO DEMAND CENTER 2 IN YEAR T = -1
YIELD OF CROP 1 IN REGION 1 IN YEAR T = -2
YIELD OF CROP 1 IN REGION 1 IN YEAR T = -1
YIELD OF CROP 1 IN REGION 2 IN YEAR T = -2
YIELD OF CROP 1 IN REGION 2 IN YEAR T = -1
YIELD OF CROP 2 IN REGION 1 IN YEAR T = -2
YIELD OF CROP 2 IN REGION 1 IN YEAR T = -1
YIELD OF CROP 2 IN REGION 2 IN YEAR T = -2
YIELD OF CROP 2 IN REGION 2 IN YEAR T = -1
ACRES OF LAND DEVOTED TO CROP 1 IN REGION 1 IN YEAR T = -2
ACRES OF LAND DEVOTED TO CROP 1 IN REGION 1 IN YEAR T = -1
ACRES OF LAND DEVOTED TO CROP 1 IN REGION 2 IN YEAR T = -2
ACRES OF LAND DEVOTED TO CROP 1 IN REGION 2 IN YEAR T = -1
ACRES OF LAND DEVOTED TO CROP 2 IN REGION 1 IN YEAR T = -2
ACRES OF LAND DEVOTED TO CROP 2 IN REGION 1 IN YEAR T = -1
ACRES OF LAND DEVOTED TO CROP 2 IN REGION 2 IN YEAR T = -2
ACRES OF LAND DEVOTED TO CROP 2 IN REGION 2 IN YEAR T = -1
12-
DEMAND OF CROP 1 AT DEMAND CENTER 1 IN YEAR T = -2
DEMAND OF CROP 1 AT DEMAND CENTER 1 IN YEAR T = -1
DEMAND OF CROP 1 AT DEMAND CENTER 2 IN YEAR T = -2
DEMAND OF CROP 1 AT DEMAND CENTER 2 IN YEAR T = -1
DEMAND OF CROP 2 AT DEMAND CENTER 1 IN YEAR T = -2
DEMAND OF CROP 2 AT DEMAND CENTER 1 IN YEAR T = -1
DEMAND OF CROP 2 AT DEMAND CENTER 2 IN YEAR T = -2
DEMAND OF CROP 2 AT DEMAND CENTER 2 IN YEAR T = -1
WAREHOUSE CONSTRUCTION COST IN REGION 1 IN YEAR T = -2
WAREHOUSE CONSTRUCTION COST IN REGION 1 IN YEAR T = -1
WAREHOUSE CON.STPUCTION COST IN REGION 2 IN YEAR T = -2
WAREHOUSE CONSTRUCTION COST IN REGION 2 IN YEAR T = -1
FIXED WAREHOUSE OPERATING COST IN REGION 1 IN YEAR T = -2
FIXED WAREHOUSE OPERATING COST IN REGION 1 IN YEAR T = -1
FIXED WAREHOUSE OPERATING COST IN REGION 2 IN YEAR T = -2
FIXED WAREHOUSE OPERATING COST IN REGION 2 IN YEAR T = -1
PERIOD OF INCURRENCE OF PRICE (REVENUE) OF CROP 1 IN REGION 1
PERIOD OF INCURRENCE OF PRICE (REVENUE) OF CROP 1 IN REGION 2
PERIOD OF INCURRENCE OF PRICE (REVENUE) OF CROP 2 IN REGION 1
PERIOD OF INCURRENCE OF PRICE (REVENUE) OF CROP 2 IN REGION 2
PERIOD OF INCURRENCE OF COST COMPONENT 1 OF CROP 1 IN REGION 1
PERIOD OF INCURRENCE OF COST COMPONENT 2 OF CROP 1 IN REGION 1
PERIOD OF INCURRENCE OF COST COMPONENT 1 OF CROP 1 IN REGION 2
PERIOD OF INCURRENCE OF COST COMPONENT 2 OF CROP 1 IN REGION 2
PERIOD OF INCURRENCE OF COST COMPONENT 1 OF CROP 2 IN REGION 1
.:5
PERIOD OF INCURRENCE OF COST COMPONENT 2 OF CROP 2 IN REGION 1
PERIOD OF INCURRENCE OF COST COMPONENT 1 OF CROP 2 IN REGION 2
PERIOD OF INCURRENCE OF COST COMPONENT 2 OF CROP 2 IN REGION 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 1 TO PRODUCTION REGION 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 1 TO PRODUCTION REGION 2
PERIOD OF INCURRENCE OF TRANSPORTATION CO.ST OF CROP 1 FROM
PRODUCTION REGION 2 TO PRODUCTION REGION 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 2 TO PRODUCTION REGION 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 1 TO PRODUCTION REGION 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 1 TO PRODUCTION REGION 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION-REGION 2 TO PRODUCTION REGION 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 2 TO PRODUCTION REGION 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 1 TO DEMAND CENTER 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 1 TO DEMAND CENTER 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 2 TO DEMAND CENTER 1
12-
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 1 FROM
PRODUCTION REGION 2 TO DEMAND CENTER 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 1 TO DEMAND CENTER 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 1 TO DEMAND CENTER 2
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 2 TO DEMAND CENTER 1
PERIOD OF INCURRENCE OF TRANSPORTATION COST OF CROP 2 FROM
PRODUCTION REGION 2 TO DEMAND CENTER 2
PERIOD OF INCURRENCE OF WAREHOUSE CONSTRUCTION COST IN REGION 1
PERIOD OF INCURRENCE OF WAREHOUSE CONSTRUCTION COST IN REGION 2
PERIOD OF INCURRENCE OF FIXED WAREHOUSE OPERATING COST IN REGION 1
PERIOD OF INCURRENCE OF FIXED WAREHOUSE OPERATING COST IN REGION 2
After running the program with the above data the user would feed
the results of this program as Inputs to the mixed Integer linear
programming model, expand the model according to his needs, enter LINDO
on a terminal, type his expanded model exactly as it appears, and run
LINDO package program. Suppose we want to solve the following mixed
Integer linear program on a VAX terminal:
Max 2x.. + X2
s.t. X, + 2x2 <= 2
^1 = 0 or 1
^2 >= 0
1^7
The user would enter LINDO and a $ sign would appear on the
screen. Subscripting the variables is not necessary when typing the
linear program. The steps are outlined below:
$LINDO (Hit "RETURN")
:MAX 2X1 + X2 (Hit "RETURN")
ST (Hit "RETURN")
?X1 + 2X2 <= 2 (Hit "RETURN")
?END (Hit "RETURN")
:INTEGER XI (Hit "RETURN")
:G0 (Hit "RETURN")
Then the solution would appear on the screen.
Of course, the linear program for our sample would be much
larger. The amount of tax is dependent on the optimal LINDO solution
of lADM. Therefore, after getting the results of the linear
programming model, the user should extend the data of the computer
program by incorporating the LINDO output. The LINDO solution would
generate values for the entities below; these values would follow the
previous data and become a part of the data base:
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 1 (To be
multiplied by COST COMPONENT 1 OF CROP 1 IN REGION 1)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 1 (To be
multiplied by COST COMPONENT 2 OF CROP 1 IN REGION 1)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 2 (To be
multiplied by COST COMPONENT 1 OF CROP 1 IN REGION 2)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 2 (To be
9C
multiplied by COST COMPONENT 2 OF CROP 1 IN REGION 2)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 2 IN REGION 1 (To be
multiplied by COST COMPONENT 1 OF CROP 2 IN REGION 1)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 2 IN REGION 1 (To be
multiplied by COST COMPONENT 2 OF CROP 2 IN REGION 1)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 2 IN REGION 2 (To be
multiplied by COST COMPONENT 1 OF CROP 2 IN REGION 2)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 2 IN REGION 2 (To be
multiplied by COST COMPONENT 2 OF CROP 2 IN REGION 2)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 1 (To be
multiplied by PRICE OF CROP 1 PRODUCED IN REGION 1)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 1 IN REGION 2 (To be
multiplied by PRICE OF CROP 1 PRODUCED IN REGION 2)
OPTIMAL ACRES THAT FARMER Z DEVOTES TO CROP 2 IN REGION 1 (To be
multiplied by PRICE OF CROP 2 PRODUCED IN REGION 1)
OPTIMAL ACRES THAT FARMER 7 DEVOTES TO CROP 2 IN REGION 2 (To be
multiplied by PRICE OF CROP 2 PRODUCED IN REGION 2)
The user would run the computer program with the above extended data
obtained from LINDO solution (without deleting any previous data) and
obtain the final output of the tax analysis.
APPENDIX 2
COMPUTER PROGRAMS
/* THIS PROGRAM USES CROP PRICE, COST, YIELD, SUPPLY, AND DEMAND
DATA, WAREHOUSE-RELATED COST DATA, PERIODS OF INCURRENCES OF CASH
FLOWS, DISCOUNT RATE AND TAX RATE AS INPUTS. THE OUTPUTS ARE
FORECASTED CROP YIELDS, SUPPLIES, AND DEMANDS, NET PRESENT VALUES
OF THE PROFITS ON THE CROPS, THE CROP TRANSPORTATION COSTS, AND
WAREHOUSE-RELATED COSTS. THESE OUTPUTS APE FED INTO THE
INTEGRATED AGRICULTURAL DECISION MODEL (lADM) AND lADM IS SOLVED
ON LINDO. THEN THE OUTPUTS OF THE LINDO SOLUTION ARE INCORPORATED
AS FURTHER DATA AND THE COMPUTER PROGRAM IS RERUN TO ASSESS THE
TAXES AS THE AMOUNT OF TAX WOULD BE DEPENDENT ON THE OPTIMAL LINDO
SOLUTION. THE MAJOR PROGARM SEGMENTS ARE FORECASTING, NET PRESENT
VALUE ANALYSIS, AND TAX ANALYSIS. EACH SEGMENT IS COMMENTED IN
DETAIL. */
FORE
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
PROCEDURE OPTIONS (MAIN);
NUMBER_OF_CROP_FORECASTS) FIXED;
NUMBER_OF_CROPS) FIXED;
NUMB€R_OF_REGIONS) FIXED;
NUMBER_0F__REGI0NS1) FIXED;
NUMBER_OF_ DEMAND__CENTERS) FIXED;
NUMBER_OF_SUB_COMPONENTS) FIXED;
NUMBER_0F_SUB_C0MP0NENTS1) FIXED;
NUMBER_OF_YEARS_OF_DATA) FIXED;
NUMBER_OF_WAREHOUSE_FORECASTS) FIXED;
NO_OF__WAREHOUSE_FORECASTS__IN_NPV) FIXED;
129
130
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
NUMBER_OF_PROFIT_FORECASTS) FIXED;
NO_OF_WAREHOUSE_FORECAST_IN_NPV) FIXED;
NO_OF_CROP_FORECASTS_IN_TAX) FIXED;
N,I,J,L,T) FIXED;
CROP_DATA (15,16,16,15,16)) FLOAT;
SUM1,SUM2,SUM3,SUM4) FLOAT;
MEAN1,MEAN2) FLOAT;
A (16,15,16,16),B (15,15,16,16)) FLOAT;
CROP_FORECAST (15,16,16,15)) FLOAT;
WAREHOUSE_CASH_FLOW_DATA (15,15,15)) FLOAT;
A2 (15,15), B2 (15,15)) FLOAT;
WAREHOUSE_CASH_FLOW_FORECAST (16,16)) FLOAT;
CROP_PERIOD_OF_INCURRENCE (16,16,15,15)) FIXED;
DISCOUNT_RATE) FLOAT;
CROP_PRESENT_VALUE (15,16,15,15)) FLOAT;
CROP_NET_PRESENT_VALUE (15,15)) FLOAT;
SUM_OF_CROP_PRESENT_VALUES) FLOAT;-
WAREHOUSE_PERIOD_OF_INCURRENCE (15,15)) FIXED;
WAREHOUSE_PRESENT_VALUE (15,15)) FLOAT;
SUM_OF_CASH_FLOWS_THIS_YEAR) FLOAT;
TAX_RATE_FOR_FARMER_Z_THIS_YEAR) FLOAT;
PERI0DS_0CT0BER1_T0_DECEMBER31) FIXED;
PERIODOCTOBERITOTAXTIMENEXTYEAR) FIXED;
NUMBER_OF_OPTIMAL_CROPS) FIXED;
OPTIMAL_ACRES_FOR_FARMER_Z (15,16,15,16)) FLOAT;
ACTUAL_CROP_CASH_FLOW THIS YEAR (16,15,15,15)) FLOAT;
.31
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
DCL
TAX__FOR_FARMER__Z_THIS_YEAR) FLOAT;
NPV_TAX__FOR_FARMER_Z_THIS_YEAR) FLOAT;
SUM_OF_CASH_FLOWS_NEXT_YEAR) FLOAT;
TAX_RATE_FOR_FARMER_Z_NEXT_YEAR) FLOAT;
PERIODS_IN_A_YEAR) FIXED;
ACTUAL_CROP_CASH_FLOW_NEXT_YEAR (15,16,15,15)) FLOAT;
TAX_FOR_FARMER_Z_NEXT_YEAR) FLOAT;
NPV_TAX_FOR_FARMER_Z_NEXT_YEAR) FLOAT;
NPV_OF_OVERALL TAX FOR FARMER Z) FLOAT;
DCL INFILE FILE STREAM INPUT;
DCL OUTFILE FILE STREAM OUTPUT;
OPEN FILE (INFILE) INPUT;
OPEN FILE (OUTFILE) OUTPUT;
GET
GET
GET
GET
GET
GET
GET
GET
GET
GET
GET
GET
GET
FILE
FILE
FILE
FILE
FILE 1
FILE 1
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
(INFILE)
(INFILE)
(INFILE)
[INFILE)
[INFILE)
[INFILE)
INFILE)
INFILE)
INFILE)
INFILE)
INFILE)
INFILE)
INFILE)
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
LIST (
NUMBER_OF_CROP_FORECASTS);
NUMBER_OF_CROPS);
NUMBER_OF_REGIONS);
NUMBER_0F_REGI0NS1);
NUMBER_OF_DEMAND_CENTERS);
NUMBER_OF_SUB_COMPONENTS);
NUMBER_0F_SUR_C0MP0NENTS1);
NUMBER_OF_YEARS_OF_DATA);
NUMBEP_OF_WAREHOUSE_FORECASTS);
DISCOUNT_RATE);
NO_OF_CROP_FORECASTS_IN_NPV);
NUMBER_OF_PROFIT_FORECASTS);
NO OF WAREHOUSE FORECAST IN NPV);
132
GET
GET
GET
GET
GET
GET
GET
GET
GET
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
FILE (
'INFILE;
'INFILE;
[INFILE]
[INFILE;
[INFILE^
'INFILE
[INFILE
'INFILE;
[INFILE'
1 LIST (
) LIST (
1 LIST (
) LIST (
) LIST (
) LIST (
) LIST (
1 LIST (
) LIST (
SUM_OF_CASH_FLOWS_THIS_YEAR);
TAX_RATE_FOR_FARMER_Z_THIS_YEAR);
PERI0DS_0CT0BER1_T0_DECEMBER31);
PERIODOCTOBERITOTAXTIMENEXTYEAR);
NO_OF_CROP_FORECASTS_IN_TAX);
NUMBER_OF_OPTIMAL_CROPS);
SUM_OF_CASH_FLOWS_NEXT_YEAR);
TAX_RATE_FOR_FARMER_Z_NEXT_YEAR);
PERIODS IN A YEAR);
THIS PART OF THE PROGRAM COMPUTES THE FORECASTS FOR CROP PRICES
(N = 2) AND CROP COSTS (N = 1) INCLUDING SUBCOMPONENTS SUCH AS
PLANTATION COST, HARVESTING COST, ETC., FOR EACH PRODUCTION REGION
AND EACH CROP USING LINEAR REGRESSION. IT ALSO FORECASTS THE
TRANSPORTATION COSTS FOR EACH CROP FROM EACH PRODUCTION REGION TO
THE OTHER PRODUCTION REGIONS (N = 3), THE TRANSPORTATION COSTS FOR
EACH CROP FROM EACH PRODUCTION REGION TO THE DEMAND CENTERS
(N = 4), THE CROP YIELDS IN EACH PRODUCTION REGION FOR EACH CROP
(N = 6), ACRES OF LAND LIKELY TO BE DEVOTED TO EACH CROP IN EACH
REGION (N = 6), AND DEMANDS IN TONS FOR EACH CROP AT EACH DEMAND
CENTER (N = NUMBER_ 0F_ CROP_FORECASTS WHICH IS EQUAL TO 7 HERE)
USING PAST DATA. THE SUPPLY FORECASTS ARE USED IN WAREHOUSE
CAPACITY ASSESSMENT. SINCE WAREHOUSE CAPACITY ASSESSMENT IS A
STRATEGIC ISSUE IT WOULD NOT BE APPROPRIATE TO RELY ON THE SUPPLY
FIGURES GENERATED BY THE AGRICULTURAL DECISION MODEL ONLY; HENCE
PAST DATA ARE ANALYZED. */
> 1
NUMBER_OF_REGIONS = NUMBER_0F_REGI0NS1;
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NUMBER_OF_CROP_FORECASTS;
IF (N = NUMBER_OF_CROP_FOPECASTS)
THEN DO;
NUMBER_OF_REGIONS = NUMBER_OF_DEMAND_CENTERS;
NUMBER_OF_SUB_COMPONENTS = 1 ;
END;
ELSE NUMBER_OF_REGIONS = NUMBER_OF_REGIONS;
IF (N = 1) THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
IF (N = 3)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_REGIONS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
IF (N = 4)
THEN NUMBER_OF_SUB_COMPOENTS = NUMBER_OF_DEMAND_CENTERS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
DO T = 1 TO NUMBER_OF_YEARS_OF_DATA;
GET FILE ( INF ILE) LIST (CROP_DATA ( N , I , J , L , T ) ) ;
END;
END;
END;
•J
END;
END;
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F__SUB_C0MP0NENTS1;
NUMBER_OF_REGIONS = NUMBER_0F_REGI0NS1;
DO N = 1 TO NUMBER_OF_CROP_FORECASTS;
IF (N = NUMBER_OF_CROP_FORECASTS)
THEN DO;
NUMBER_OF_REGIONS = NUMBER_OF_DEMAND_CENTERS;
NUMBER_OF_SUB_COMPONENTS = 1 ;
END;
ELSE NUMBER_OF_REGIONS = NUMBER_OF_REGIONS;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
IF (N = 3)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_REGIONS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
IF (N = 4)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_DEMAND_CENTERS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBFR_OF_SUB_COMPONENTS;
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
SUMl = 0:
SUM2 = 0
SUM3 = 0
:35
SUM4 = 0;
DO T = 2 TO NUMBER_OF_YEARS_OF_DATA;
SUMl = SUM1 + (CR0P_DATA (N,I,J,L,T-1)*CROP_DATA (N, I,J,L,T));
SUM2 = SUM2+CR0P_DATA (N,I,J,L,T);
SUM3 = SUM3+CR0P_DATA (N,I,J,L,T-1);
SUM4 = SUM4+(CR0P_DATA (N,I,J,L,T-1)*CROP DATA (N,I,J,L,T-lT);
END:
MEANl = SUM2/(NUMBER_0F_YEARS_0F_DATA-1);
MEAN2 = SUM3/(NUMBER_0F_YEARS_0F_DATA-1);
IF (SUM4-(MEAN2*SUM3) = 0)
THEN B (N,I,J,L) = 0;
ELSE B (N,I,J,L) = (SUM1-(MEAN1*SUM3))/(SUM4-(MEAN2*SUM3));
A (N,I,J,L) = MEAN1-(B(N,I,J,L)*MEAN2);
CROP_FORECAST (N,I,J,L) = A (N,I,J,L)+B (N,I,J,L)*
CROP_DATA (N,I,J,L,T-1);
END;
END;
END;
END;
/* THIS PART OF THE PROGRAM FORECASTS THE FUTURE WAREHOUSE
CONSTRUCTION (N = 1) AND FIXED OPERATING COSTS AT EACH
PRODUCTION REGION (N=NUMBER OF WAREHOUSE FORECASTS WHICH IS
EQUAL TO 2 HERE) USING LINEAR REGRESSION, PART OF THE PROGRAM
WAS REWRITTEN WITH MINOR MODIFICATIONS TO PROVIDE CLARITY OVER
THE SUBSCRIPTS. */
13c
NUMBER__OF_REGIONS = NUMBER_0F_REGI0NS1;
DO N = 1 TO NUMBER_OF_WAREHOUSE_FORECASTS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO T = 1 TO NUMBER_OF_YEARS_OF_DATA;
GET FILE (INFILE) LIST (WAREHOUSE_CASH_FLOW_DATA (N,J,T))
END;
END;
END;
DO N = 1 TO NUMBER_OF_WAREHOUSE_FORECASTS;
DO J = 1 TO NUMBER_OF_REGIONS;
SUMl = 0;
SUM2 = 0;
SUM3 = 0:
SUM4 = 0;
DO T = 2 TO NUMBER_OF_YEARS_OF_DATA;
SUMl = SUM1+WAREH0USE_CASH_FL0W_DATA (N,J,T-1)*
WAREHOUSE_CASH_FLOW_DATA (N,J,T);
SUM2 = SUM2+WAREH0USE_CASH_FL0W_DATA (N,J,T);
SUM3 = SUM3+WAREH0USE_CASH_FL0W_DATA (N,J,T-1);
SUM4 = SUM4+WAREH0USE_CASH_FL0W_DATA (N,J,T-1)*
. WAREHOUSE_CASH_FLOW_DATA (N,J,T-1);
END;
MEANl = SUM2/(NUMBER_0F_YEARS_0F_DATA-1);
MEAN2 = SUM3/(NUMBER_0F_YEARS_0F_D.ATA-1);
IF (SUM4-(MEAN2*SUM3) = 0)
THEN B2 (N,J) = 0;
137
ELSE B2 (N,J) = (SUM1-(MEAN1*SUM3))/(SUM4-(MEAN2*SUM3));
A2 (N,J) = MEAN1-(B2(N,J)*MEAN2);
WAREHOUSE_CASH_FLOW_FORECAST (N,J) = A2 (N,J)+B2 (N,J)*WAREHOUSE_ CASH_FLOW_DATA (N,J,T-1);
END;
END;
/ * THIS PART OF THE PROGRAM CALCULATES THE NET PRESENT VALUES OF THE
FORECASTED CROP PRICES (N = 2 ) , FORECASTED CROP COST COMPONENT
VALUES (N = 1 ) , FORECASTED CROP TRANSPORTATION COSTS BETWEEN
PRODUCTION REGIONS (N = 3 ) , AND FORECASTED CROP TRANSPORTATION
COSTS BETWEEN THE PRODUCTION REGIONS AND THE DEMAND CENTERS
(N = NO_OF_CROP_ FORECASTS_IN_NPV WHICH IS EQUAL TO 4 HERE. * /
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NO_OF_CROP_FORECASTS_IN_NPV;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1;
IF (N = 3)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_REGIONS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
IF (N = 4)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_DEMAND_CENTERS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS:
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER OF REGIONS;
13.S
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
GET FILE ( INF ILE) LIST (CROP__PERIOD_OF_INCURRENCE ( N , I , J , L ) ) ;
END;
END;
END;
END;
NUMBER_OF_SUB__COMPONENTS = NUMB ER_OF_SUB_COMPONE NTS 1 ;
DO N = 1 TO NO_OF_CROP_FORECASTS_IN_NPV;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
IF (N = 3)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_REGIONS;
ELSE NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS
IF (N = 4)
THEN NUMBER_OF_SUBCOMPONENTS = NUMBER_OF_DEMAND_CENTERS;
ELSE NUMBER_OF_SUBCOMPONENTS = NUMBER_OF_SUBCOMPONENTS;
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBEP_OF_SUB_COMPONENTS;
IF (N = 1)
THEN CROP_PRESENT_VALUE ( N , I , J , L ) = -CROP_FORECAST ( N , I , J , L ) *
1/((1+DISC0UNT_RATE)**(CR0P_PERI0D_0F_
INCURRENCE ( N , I , J , L ) - 1 ) ) ;
ELSE CROP PRESENT VALUE ( N , I , J , L ) = CROP FORECAST ( N , I , J , L ) *
139
1/((1+DISC0UNT_RATE)**(CP0P_PFRI0D_0FJNCURRENCE
(N,I,J,D-D);
END;
END;
END;
END;
/•* THIS PART OF THE PROGRAM COMPUTES THE NET PRESENT VALUES OF THE
FORECASTED CROP PROFITS BASED ON FORECASTED CROP PRICES (N =
NUMBER_OF_PROFIT_FORECASTS WHICH IS EQUAL TO 2 HERE), FORECASTED
CROP COST COMPONENT VALUES (N = 1). THESE ARE THE PROFIT FIGURES
PRIOR TO TRANSPORTATION OF CROPS TO DEMAND CENTERS. NET PRESENT
VALUES OF PROFITS COMPUTED BELOW AND NET PRESENT VALUES OF
TRANSPORTATION COSTS COMPUTED ABOVE WILL BE INPUTS TO THE MIXED
INTEGER LINEAR INTEGRATED AGRICULTURAL DECISION MODEL. */
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
SUM_OF_CROP_PRESENT_VALUES = 0;
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NUMBER_OF_PROFIT_FORECASTS;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB__COMPONENTS = 1 ;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
SUM_OF_CROP_PRESENT_VALUES = SUM_OF_CROP_PRESENT_VALUES+CROP_
PRESENT VALUE ( N , I , J , L ) ;
i'^M^^'--
END;
END;
CROP_NET_PRESENT_VALUE (I,J) = SUM_OF_CROP_PRESENT_VALUES;
END;
END;
I* THIS PART OF THE PROGRAM COMPUTES THE NET PRESENT VALUES OF THE
FORECASTED WAREHOUSE CONSTRUCTION (N = 1) AND FORECASTED FIXED
WAREHOUSE OPERATING COSTS (N = NO_OF_WAREHOUSE_FORECAST_IN_NPV)
WHICH IS EOUAL TO 2 HERE. */
DO N = 1 TO NO_OF_WARFHOUSE_FORECAST_IN_NPV;
DO J = 1 TO NUMBER_OF_REGIONS;
GET FILE (INFILE) LIST (WAREHOUSE_PERIOD_OF_INCURRENCE (N,J));
END;
DO J = 1 TO NUMBER_OF_REGIONS;
WAREHOUSE_PRESENT_VALUE (N,J) = WAREHOUSE_CASH_FLOW_FORECAST (N,J)*
1/((1+DISC0UNT_RATE)**(WAREH0USE_PERI0D_0F_INCURRENCE(N,J)-1));
END;
END;
/* THIS PART OF THE PROGRAM CALCULATES THE TAX AND THE NET PRESENT
VALUE OF THE TAX ASSOCIATED WITH FORECASTED CROP PRICES (N = NO_OF_
CROP_FORECASTS_IN_TAX WHICH IS EOUAL TO 2 HERE) AND FORECASTED
CROP COSTS (N = 1) BETWEEN OCTOBER 1 AND DECEMBER 31 FOR FARMER Z
WHERE OCTOBER 1 IS TAKEN TO BE THE STARTING POINT OF THE
AGRICULTURAL SEASON. THE OPTIMAL SOLUTION OBTAINED BY SOLVING THE
INTEGRATED LINEAR MODEL IS FED INTO THE TAX MODEL BECAUSE TAX
WOULD BE DEPENDENT UPON THE OPTIMAL PROFIT AND HENCE THE OPTIMAL
ACREAGE. * /
NUMBER_OF_SUR_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NO_OF_CROP_FORECASTS_IN_TAX;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
DO I = 1 TO NUMBER_OF_OPTIMAL_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
GET FILE ( INF ILE) LIST (OPTIMAL_ACPES_FOR_FARMER_Z
( N , I , J , L ) ) ;
END;
END;
END;
END;
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NO_OF_CROP_FORECASTS_IN_TAX;
IF (N = 1)
THEN NUMBER_OF_SUB_COMPONENTS = NUMBER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
DO I = 1 TO NUMBER_OF__OPTIMAL_CROPS;
DO J = 1 TO NUMBER__OF_REGIONS;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
IF (CROP_PERIOD OF INCURRENCE ( N , I , J , L ) <
^ - . * . - . •
t^M--
1 " ' ^
•
PERI0DS_0CT0BER1_T0_DECEMBER31)
THEN ACTUAL_CROP_CASH_FLOW_THIS_YEAR ( N , I , J , L ) = ( ( - 1 ) * * N )
CROP_FORECAST (N,I,J,L)*OPTIMAL_ACPEAS_FOR_FARMER_Z
( N , I , J , L ) ;
ELSE ACTUAL_CROP_CASH_FLOW_THIS_YEAR ( N , I , J , L ) = 0;
SUM_OF_CASH_FLOWS_THIS_YEAR = SUM_OF_CASH_FLOWS_THIS_YEAR +
ACTUAL_CROP_CASH__FLOW_THIS_YEAR ( N , I , J , L ) ;
END;
END;
END;
END;
IF SUM_OF_CASH_FLOWS_THIS_YEAR > 0)
THEN TAX_FOR_FARMER_Z_THIS_YEAR = SUM_OF_CASH_FLOWS_THIS_YEAR*TAX_
RATE_FOR_FARMER_Z_THIS_YEAR;
ELSE TAX_RATE_FOR_FARMER_Z_THIS_YEAR = 0;
NPV_TAX_FOR_FARMER_Z_THIS_YEAR = TAX_FOR_FARMER_Z_THIS_YEAR*
1/((1+DISC0UNT_RATE)**(PERI0D0CT0BER1T0TAXTIMENEXTYEAR-1));
/ * THIS PART OF THE PROGRAM CALCULATES THE TAX AND THE NET PRESENT
VALUE OF THE TAX ASSOCIATED WITH FORECASTED CROP PRICES (N = NO_OF_
CROP_FORECAST_IN_TAX WHICH IS EOUAL TO 2 HERE) AND FORECASTED CROP
COSTS (N = 1) BETWEEN JANUARY 1 AND SEPTEMBER 30 OF THE COMING
YEAR. * /
NUMBER_OF_SUB_COMPONENTS = NUMBER_0F_SUB_C0MP0NENTS1;
DO N = 1 TO NO_OF_CROP_FORECASTS_IN_TAX;
IF (N = 1)
143
THEN NUMBER_OF_SUR_COMPONENTS = NUMRER_OF_SUB_COMPONENTS;
ELSE NUMBER_OF_SUB_COMPONENTS = 1 ;
DO I = 1 TO NUMBER_OF_OPTIMAL_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_SUB_COMPONENTS;
IF (CROP_PERIOD_0F_INCURPENCE ( N , I , J , L ) >
(PERI0DS__0CT0BER1_T0_DECEMRER31-1))
THEN ACTUAL_CROP_CASH_FLOW_NEXT_YEAR ( N , I , J , L ) =
((-1)**N)*CR0P_F0RECAST ( N , I , J , L ) *
OPTIMAL_ACRES_FOR_FARMER_Z ( N , I , J , L ) ;
ELSE ACTUAL_CROP_CASH_FLOW_NEXT_YEAR ( N , I , J , L ) = 0;
SUM OF_CASH_FLOWS_NEXT_YEAR = SUM_OF_CASH_FLOWS_NEXT_YEAR +
ACTUAL_CROP_CASH_FLOW_NEXT_YEAR ( N , I , J , L ) ;
END;
END;
END;
END;
IF (SUM_OF_CASH_FLOWS_NEXT_YEAR > 0)
THEN TAX_FOR_FARMER_Z_NEXT_YEAR = SUM_OF_CASH_FLOWS_NEXT_YEAR*
TAX_RATE_FOR_FARMER_Z_NEXT_YEAR;
ELSE TAX_FOR_FARMER_Z_NEXT_YEAR = 0;
NPV_TAX_FOR_FARMER_Z_NEXT_YEAR = TAX_FOR_FARMER_Z NEXT_YEAR*
1/((1+DISC0UNT_RATE)**(PERI0D0CT0BER1T0TAXTIMENEXTYEAR
+PERI0DS_IN_A_YEAR-1));
NPV_OF_OVERALL__TAX_FOR_FARMER_Z = NPV_TAX_FOR_FARMER_Z_THIS_YEAR
+NPV_TAX_FOR_FARMER_Z_NEXT_YEAR;
!U
PUT FILE (OUTFILE) SKIP(3) EDIT ('CROP','REGION','PROFIT')
(X(8),A,X(17),A,X(15),A);
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
PUT FILE (OUTFILE) SKIP EDIT (I,J,CROP_NET_PRESENT_VALUE (I,J))
(X(8),F(1,0),X(20), F(1,0),X(20),F(9,1));
END;
END;
PUT FILE (OUTFILE) SKIP (3) EDIT ('FROM REGION','TO REGION',
'TRANSPORTATION COST') (X(8),A,X(15),A,X(10),A);
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_REGIONS;
PUT FILE (OUTFILE) SKIP EDIT (J ,L,CROP_PRESENT_VALUE (3,1,J,L))
(X(8),F(1,0),X(20),F(1,0),X(20),F(9,1));
END;
END;
PUT FILE (OUTFILE) SKIP (3) EDIT ('FROM REGION','TO DEMAND CENTER',
'TRANSPORTATION COST') (X(8),A,X(9),A,X(5),A);
DO J = 1 TO NUMBER_OF_REGIONS;
DO L = 1 TO NUMBER_OF_DEMAND_CENTERS;
PUT FILE (OUTFILE) SKIP EDIT (J,L,CROP_PRESENT_VALUE (4,1,J,L))
(X(8),F(1,0),X(20),F(1,0),X(20),F(9,1));
END;
END;
PUT FILE (OUTFILE) SKIP (3) EDIT ('CROP','REGION',
'F0RECASTED_CROP_YIELD') (X(8),A,X(17),A,X(7),A);
1^5
DO I = 1 TO NUMBER__OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
PUT FILE (OUTFILE) SKIP EDIT (I,J,CROP_FORECAST ( 5 , I , J , 1 ) )
( X ( 8 ) , F ( 1 , 0 ) , X ( 2 0 ) , F ( 1 , 0 ) , X ( 2 0 ) , F ( 9 . 1 ) ) ;
END;
END;
PUT FILE (OUTFILE) SKIP (3 ) EDIT ('CROP','REGION','FORECASTED_ACRES_
PLANTED') ( X ( H ) , A , X ( 1 7 ) , A , X ( 7 ) , A ) ;
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_REGIONS;
PUT FILE (OUTFILE) SKIP EDIT ( I , J , CROP_FORECAST ( 6 , I , J , 1 ) )
( X ( 8 ) , F ( 1 , 0 ) , X ( 2 0 ) . F ( 1 , 0 ) , X ( 2 0 ) , F ( 1 0 , 1 ) ) ;
END;
END;
PUT FILE (OUTFILE) SKIP (3 ) EDIT ('CROP*,'DEMAND_CENTER',
'DEMAND_IN_TONS') (X (8 ) , A , X ( 1 7 ) , A , X ( 1 0 ) , A ) ;
DO I = 1 TO NUMBER_OF_CROPS;
DO J = 1 TO NUMBER_OF_DEMAND_CENTERS;
PUT FILE (OUTFILE) SKIP EDIT (I,J,CROP_FORECAST ( 7 , I , J , 1 ) )
( X ( 8 ) , F ( 1 , 0 ) , X ( 2 0 ) , F ( 1 , 0 ) , X ( 2 0 ) , F ( 1 0 , 1 ) ) ;
END;
END;
PUT FILE (OUTFILE) SKIP ( 3 ) EDIT ('REGION','WAREHOUSE_CONSTRUCTION_
COST') ( X ( 8 ) , A , X ( 1 6 ) , A ) ;
DO J = 1 TO NUMBER OF REGIONS;
:] r^fe^:" "^
146
PUT FILE (OUTFILE) SKIP EDIT (J,WAREHOUSE_PRESENT_VALUE (1,J))
(X(8),F(1,0),X(20),F(9,1));
END;
PUT FILE (OUTFILE) SKIP (3) EDIT ('REGION','WAREHOUSE_FIXED_OPERATING_
COST') (X(8),A,X(15),A);
DO J = 1 TO NUMBER_OF_REGIONS;
PUT FILE (OUTFILE) SKIP EDIT (J,WAREHOUSE_PRESEr'T_VALUE (2,J))
(X(8),F(1,0),X(20),F(9,1));
END;
PUT FILE (OUTFILE) SKIP (3) LIST (' NET_PRESENT_VALUE_OF_THE_OVEPALL_
TAX_FOR_FARMER_Z = ' ,NPV_OF_OVERALL_TAX_FOR_FARMER_Z);
END FORE;
