APPLICATION OF THE REVISED SIMPLEX
METHOD TO THE FARM
PLANNING MODEL
By
WENHUIHUA
Bachelor of Arts
Hangzhou University
Hangzhou) China
1990
Submitted to the Faculty of the
Graduate College ofthe
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December) 1998
APPLICATION OF THE REVISED SIMPLEX
METHOD TO THE FARM
PLANNING MODEL
Thesis Approved:
Thesis Adviser
2J. F I~
ean ofthe Graduate College
ii
ACKNOWLEGEMENT
First of all, I would like to express my sincere gratitude to my th sis adviser, Dr.
K. M. George, and my committee members, Dr. Francis Epplin, Dr. George Hedrick. and
Dr. H. K. Dai for their guidance and suggestions during this thesis period of my graduate
program. This thesis would not have been possible without their help. I specifically
thank Dr. Epplin for his helping me choosing this interesting and real programsolving
topic. The experience developed through the discussions with these advisers has become
my lifelong memories and I hope it will benefit my future professional lite.
I also thank my husband. Dr. Junxiang Lu, for his understanding and support
during this critical stage of my life. To my parents. Yongxiang Hua and Zihua Zho\!, no
word can describe my appreciation. They help taking care of my sons, Alan and Willis.
enabling me to finish this degree. [hope this degree is one of the ways that [ say ''Thank
you" to my parents.
III
Chapter
TABLE OF CO TENT
Page
1. INTRODUCTION I
n. SIMPLEX METHOD AND REVISED
SIMPLEX METHOD: A REVIEW 4
2.1 Simplex Method 4
2.2 Revised Simplex Method 10
2.3 Sensitivity Analysis 17
III. DESIGN AND IMPLEMENTAnON OF
THE FARM PLANNING MODEL SYSTEM 20
3.1 The Components of the Farm Planning Model System 20
3.2 The System Design of Farm Planning Model System 21
3.3 Key Algorithtn 22
IV. A APPLICATION OF THE FARM PLANNING MODEL SYSTEM ......... 29
4.1 Farm Planning and the Farm Planning Model System 29
4.2 The OSU Enterprise Budgets 29
4.3 An Example of the Farm Planning Model 30
V. SUMMARY AND CONCLUSIONS 49
IV
LI T OF FIGURE
Figure Pag
2.1 The Solution Set for the Linear Program 5
2.2 Simplex Method to Solve Linear Program 9
3.1 Menu Organization (System View) 26
3.2 The Control Flow of the Farm Planning Model System 27
3.3 T11e Main Menu of the Farm Plaruling Model System 28
4.1 Farm Information Data Sheet.. 35
4.2 Production Activity: Native Pasture 36
4.3 Production Activity: Wheat for Grain Only 37
4.4 Production Activity: Wheat for Grain and Forage 3g
4.5 Production Activity: Grain GrazeOut 39
4.6 Production Activity: Oats 40
4.7 Production Activity: CowCalf.. 41
4.8 Production Activity: Stocker Steers 42
4.9 Production Activity: Stocker Steers GrazeOut 43
4.10 Production Acti vity: Slaughter Steers 44
4.11 The Solution of the Farm Planning Problem (in Matrix Form) 45
4.12 The Solution Report of the Farm Planning Problem (in Plain Text) 46
v
Figure Pag
4.13 The Solution of the ensitivity Analy i 47
4.14 The olution Report of the Sensitivity Analysis (in Plain Text) 48
vi
LIST OF TABLES
Table Page
4.1 Optimal Production Activities for the Example Farm Planning Problem 32
4.2 Resource Allocations for the Example Farm Planning Problem 33
4.3 Sensitivity Analysis for the Example Farm Planning Problem 34
VII
LIST OF APPENDICES
Appendix Page
1. Installation Procedure for the Planning Model System 53
VIII
CHAPTER I
lNTRODUCTION
The Farm Planning Model is used to determine optimal allocation of a farm's
limited resources such as land, labor and capital among alternative crop and livestock
enterprises. It helps farmers to decide what and how much will be produced in order to
make the optimal returns from the resources they have or have access to.
Farm Planning Model has been a topic of farm and agribusiness management
textbooks for a number of years [Barnard79; Castle72; Herbst86; Kay94; Osburn83 J.
However, while these farm management textbooks include descriptions and provide
graphical solutions of trivial models, methods for solving more realistic models have nol
been included [Epplin971.
Farm Planning Model uses linear programming method to solve the optimization
problem of allocating the scarce resources to the products in a manner such that profits
are a maximum, or alternatively, costs are a minimum.
Since the development of modern techniques of management, linear programming
has become an important tool of economics. It assumes a prominent position in
operations research and management science [Simonnard66]. Currently there are many
software systems solving the linear programming problem, such as integrated linear
programming solver in MSExcel, linear programming module in MATLAB, and the
General Algebraic Modeling System (GAMS). There are also smaJllinear programming
software designed specifically for farm planning such as MUSAH86 [Li85]. All of the
above mentioned software systems are relatively complex and require certain levels of
computer skills and knowledge of linear algebra and agricultural economics background.
For example, all of these software systems need users to set up the objective function and
the constraint matrix for the farm planning problem. This kind of inconvenience prevents
farmers from using these systems. In order to let the farmers solve farm planning
problem themselves, an easytouse software system for the farm planning problem is
needed. Windowsbased application systems require users to have few computer skills to
use these systems. The objective of this thesis is to develop a linear programming
software system to solve the farm planning problem, which is both easytouse and userfriendly.
For example, the proposed software system for the farm planning problem will
set up the objective function and the constraint matrix automatically for the users. The
entire software system includes four parls: the farm planning data sheets, the farm
planning model, the farm planning solver and the sensitivity analysis. The farm planning
data sheets allow the users to enter the relevant information of the f~1rm planning problem
(such as the amounts of resources and the prices of products and so on). The farm
planning model generates the objective function and the constraint matrix for the farm
plalming problem automatically from the information the users enter in the farm planning
data sheets. The farm planning solver solves the farm planning problem to return the
optimal solution back to the same constraint matrix generated in the part of the farm
plalming model. Thi.s part also generates a plain text solution report which is easily
understood by farmers. The optimal solution provides the users with the optimal value
2
for the farm planning problem and its associated allocation of the products produced and
the resources used. The sensitivity analysis gives the ranges of variation of coefficients
( ) for which the optimal solution remains optimal. A plain text sensitivity analysis
report is also generated. The farm planning model system is implemented using Visual
Basic 5.0 under the Windows 95 environment.
3
CHAPTER II
SIMPLEX METHOD AND REVISED SIMPLEX METHOD: A REVIEW
As discussed in the previous chapter, linear programming is an important tool of
economics and already has demonstrated its value as an aid to decision making in
business, industry, and government. There are many methods used to solve the linear
programming problem, such as the Graphical Method, the Systematic TrialandError
Method, the Vector Method, and the Simplex Method. Among these methods, the
Simplex Method and its variant, the Revised Simplex Method, are the most powerful and
most popular ones [Loomba64]. Simplex Method and Revised Simplex Method are
described in this chapter. Sensitivity analysis is also discussed at the end of this chapler.
2.1 Simplex Method
The Simplex Method was first proposed in 1947 by G. B. Dantzig [Murtagh81 J.
It observes that the solution set of such linear program is convex, that is, the solution set
of a linear program of n variables can he represented as a convex polygon in an nspace.
This is illustrated in Figure 2.1, the shaded area is the solution set. Furthermore, ira
maximum or minimum value of the sol ution exists. it will be at a corner of this polygonal
region. The Simplex Method must visit corners of the solution set to find the maximum
value. In other words, the Simplex Method is an iterative procedure for determining
4
basic feasible solutions to a system of equations and testing each solution for optimality
[Childress74]. That is, the Simplex Method begins at an arbitrary corner of the basic
solution set. At each iteration, the Simplex Method selects the variable that will produce
the largest change towards the maximum (minimlm1) solution. That variable replaces one
of its components that is most severely restricting it, thus moving the Simplex Method to
a different corner of the solution set and closer to the final solution. In addition, the
Simplex Method can determine when no solution actually exists.
y
3
2.5
Ol l.. ="' ~
2 4 x
Figure 2.1 The Sol utian Set for the Linear Program:
3x + 2y s: 6
5x + 8y s: 20
5
The general form of linear programming is formalized in (2.1).
maximize
subject to:
"
Z= Le;%;
./=1
/I
La,x;:::;bj (i=I,2, ... ,m<n)
/=1
Xj ~ 0 (j =1, 2, ... ,n) (2.1 )
where, Z represents the value to be optimized, that is, either maximized or minimized. n
is the number of activities, m is the number of potentially scarce resources. The
coefficients Cj represent the marginal change in the value of the objective function Z
resulting from a one unit change in activity j. The variables Xj represent a choice variable
which represents the level of activity j. The solution of the model provides the "optimal"
level of activity j (j = 1,2,00,n). The coefficient ajj represents the inputoutput coefficient
which indicates the amount of resource i required to produce a unit of activity j. The
variable bi represent the initial quantity of resource or other constraint b available for
allocation to the alternative activities, for i = 1,2, ... , m. These statements comhined
represent a linear program, to which we seek a solution of optimal profit or minimum
cost.
The Simplex Method operates only upon the standard form of the linear
programming problem that includes inequality constraints and nonnegative variables. To
solve the linear programming problem in (2.1) using the Simplex Method, we need to
change (2.1) to the standard form of the linear programming by adding slack variables. A
slack variable means the amount by which the lefthandside of the inequality falls short
of the righthandside, and it plays a very important role in the solution of linear
programming problem. With the introduction of the slack variables Xnt !, Xn • 2, ... , Xn1m,
6
the initial basic feasible solution (BFS) will be the solution of the linear program where
the following holds:
Xj = 0
Xj = bj _
1l
(j=I,2, ... ,n)
(j= n+l, n+2, ... , n+m)
where Xj (j = 1, 2, ... , n) are nonbasic variables and Xj (j = n+ 1. n+2, ....n+m) are basic
variables (or slack variables). Once a solution to the linear program has been found.
successive improvements are made to the solution. In particular. one of the nonbasic
variables (with a value of zero) is chosen to be increased so that the value of the cost
1/
function, Z = :LCJG decreases. That variable is then increased. maintaining the
1=1
equality of all the equations while keeping the other nonbasic variables at zero, until one
of the basic (nonzero) variables is reduced to zero and thus removed from the basis. At
this point, a new solution has been determined at a different corner of the solution set.
The process is then repeated with a new variable becoming basic as the other becomes
nonbasic. Finally, the Simplex Method results in one of the following three situations.
First. a solution may occur where no nonbasic variable will decrease the cost, in whicb
case the current solution is the optimal solution. Second, a nonbasic variable might
increase to infinity without causing a basicvariable to become zero, resulting in an
unbounded solution. Third, no solution may actually exist and the Simplex Method must
abort [Murtagh81].
The following is a demonstration of the SimpLex Method. Assume there are two
activities and two resource constraints,
7

Maximize
Subject to:
(2.2)
Rewrite (2.2) into the standard form of the linear programming by adding nonnegative
slack variables X" X4,
maXImIze
Subject to: =40
+ 1 X4 = 120
The matrix or Simplex tableau of (2.3) is
Basic Variables RHS XI X2 Xl X'I
C 4 5 0 0 J
0 XJ 40 2 0
0 X4 120 4 3 0
(2.3)
The abbreviation RHS denotes the "right hand side" coefficient. To make the solution to
be feasible, every entry in the RHS column must be nonnegative. The step by step
sequence of operations at every iteration is as follows (Figure 2.2):
Step I: Select the activity (column) Xc with the smallest (Zj  Cj), which contributes
most to the objective function.
8

Step 2: For every coefficient 3;c in the Xc column, compute R; = RHS/3;c' Select as the
variable :x. to leave the basis the one which is defined by the row with the
smallest such R; .
Step 3: Let 3,.c denotes the "pivot" element, the coefficient at the intersection of the Xr 
row and the Xccolumn. For every element 3,.j in the pivot row, the new value is
Initial solution:
Basic Variables R RHS Xl X2 X, X4
C 4 5 0 0 J
0 X, 20 40 2 0
0 X4 40 120 4 3 0
Zj 0 0 a 0 0
Zj  CJ 4 5 0 0
First iteration:
5 X2 40 20 1/2 1/2 0
0 X4 24 60 5/2 0 3/2
Z 100 5/2 5 5/2 ()
J
ZC 3/2 0 5/2 ()
J I
Second iteration: Optimum solution
5 Xl 8 0 4/5 1/5
4 XI 24 0 3/5 2/5
Z 136 4 5 8/5 3/5 J
Figure 2.2 Simplex Method to Solve Linear Program (2.3). The optimal solution is
Z = 136, Xl = 24, X2 = 8 with Xl = X4 = O.
9
a.,j' = a.,j / a.,c Let this corresponding Xrenters the basis. The pivot element at
each iteration is underlined.
Step 4: Let aij denotes any element not in the pivot row and a,c the element in the same
row and the pivot column, the new value of Cl;j is
Step 5: If there are any negative coefficients in the (Z·  C) row, begin the next iteration .I J
of step J. Otherwise terminate, a solution is found.
2.2 Revised Simplex Method
Since the Simplex Method procedure is laborious and timeconsuming, researches
have developed a more efficient matrixoriented approach called the Revised Simplex
Method (RSM).
The Revised Simplex Method describes linear programs as matrix entities and
presents the Simplex Method as a series of linear algebra computations. Instead of
spending time updating tableau at the end of each iteration. the RSM does its heavy
calculation at the beginning of each iteration, resulting in much less at the end. The
formulation of the Revised Simplex Method is as follows rLocks74J.
Maximize
Subject to:
Z=C'X
AXsb
X20 (2.4)
where C is a given n x 1 component vector, Cr is a transformation of C, which is I x n .
10
3,j' = 3,j / a,.c. Let this corresponding Xr enters the basis. The pivot element at
each iteration is underlined.
Step 4: Let aij denotes any element not in the pivot row and a;c the element in the same
row and the pivot column, the new value of aij is
a;j' = a;j  (a;c)(a,.j)
Step 5: If there are any negative coefficients in the (Zj  Cj ) row, begin the next iteration
of step 1. Otherwise terminate, a solution is found,
2.2 Revised Simplex Method
Since the Simplex Method procedure is laborious and timeconsuming, researches
have developed a more efficient matrixoriented approach called the Revised Simplex
Method (RSM).
The Revised Simplex Method describes linear programs as matrix entities and
presents the Simplex Method as a series of linear algebra computations. Insteacl of
spending time updating tableau at the end of each iteration, the RSM does its heavy
calculation at the beginning of each iteration, resulting in much less at the end. The
formulation of the Revised Simplex Method is as follows [Locks741,
Maximize
Subject to:
Z=cTx
AX~b
x~o (2.4 )
where C is a given n x 1 component vector, Cf is a transformation of C, which is I x n .
fO
c
ell
X is an n x 1 vector of unknowns,
x
X,
A is a given m x n coefficient matrix,
c.] .
all ([12 (/I"
a21 an 02// '
A
alii I Umn
b is a given m x 1 component column vector,
b
bill
and 0 is an ncomponent null vector.
1\
In the RSM, X can be partitioned into XN and XB, which is
XN is called the vector of nonbasic variables, Xo is called the vector of basic variables.
That is,
.xl
.x, + J
X,+m
(2.4) now becomes:
Maximize Z=C1X
Subject to: [A,I] [~]~ b
X ~ 0 (2.5)
where I is the In x m identity matrix. (A, I' is the tableau of the initial iteration of the
Simplex Method. The basic solution of (2.5) is an m x I subvector X, of [~].
Associated with Xn is the m x m nonsingular basis matrix B, consisting of the columns
of [A, I] associated with the basic variables. The initial basic feasi ble sol ution of the
RSM becomes:
12
(2.6)
Since B is nonsingular, the basic solution for (2.6) is obtained by premultiplying both
sides by B1
,
(2.7)
Premultiplying both sides of (2.5) by B1
, we have the corresponding expression in terms
of the entire simplex tableau,
B1 [A, I] [XNJ= [B1 A, n'] [XN l= nI b.
XII XIIJ
(2.8)
The augmented standard form of the linear programming problem includes one
additional basic variable, Z, that is included in every basic solution. The augmented
statement of the problem corresponding to (2. 5) is
(2.9)
The augmented vector of basic variables is [ZJ . Let ell denote the row mvector of
Xli
objectivefunction coefficients for XB• The augmented basis matrix is
Then the inverse of the Bo is
B1 = [1 n a
Premultiplying both sides of (2.9) by Bo·1
, we therefore obtain
13
I
CnB AC
I
B A
(2.10)
The equation (2.10) shows that for every iteration the entire simplex tableau is a function
of n\ which is m x m submatrix formed by the slackvariable columns.
There are several ways of making the changeorbasis calculations from one
iteration to the next. A simpler method, which used in the RSM, is to identify the basis
matrix B as the submatrix of [A, II, associated with the basic solution Xu and invert it to
get B'I, and premultiply it by an elementary transformation matrix, E. E is identical to an
identity matrix except for one column, called the TJvector.
Let aij , i= I, ... , m, j= I, ... , n, n+ 1, ... , n+m, denotes any coefficient of the
submatrix [BIA, BIl of the simplex tableau, and suppose that at the current iteration XI
leaves the basis and Xk enters, then a,'k is the "pivot" element. The TJvector is
arK
1
11 =
arl'"
where the number 1 denotes the rth row. The E matrix is the identity matrix with the
rth column replaced by the llvector. The new B'I is obtained simply by,
I I
B E B m:w  old'
14
To solve the linear prgramming problem in (2.2) using the RSM. it is to,
Maximize [4,5][;:]
subject to [~
The augmented standard form of (2.11) is
(2.11 )
z
[X3] with XB == .
X4
At the first iteration, X2 enters the basis, it replaces Xl' the new basis matrix is
To get R 1
, we first form the llvector
Then
15
and
and
also
B'A~[}~ ~l[~ ~]~[i ~l
B'b ~ [_~~ ~l[I~OO]~ [~~]
(2.12)
(2.13)
since one of the coefficients calculated in (2.13) is negative, the variable with the most
negative coefficient, XI' enters the basis. It replaces X4 , the pivot is 5/2.
then
16
and
also
l4 1] _I _ 5"  5" _ 8 3
CBB  [5,4] _ ~ ~  [5' 5]
B'A~l}~ i][~ ~]~[~~]
B'b ~ l}~ i][l:OO]~ [:4]
(2.14)
(2.15)
since all of the Zrow coefficients in (2.15) are nonnegative, iterations terminate and the
optimal solution is obtained.
2.3 Sensitivity Analysis:
"Sensitivity analysis" is also called as "postoptimality analysis" [Lock74]. Most
of the coefficients which appear in an linear programming (LP) problem are not known
exactly, and in practice are usually best estimates of the value that the coefficient should
be [Murtagh81]. The sensitivity analysis is important to decision makers, since it gives
17

the range of variation over the product which the contribution margin can vary without
causing a change in the optimal value.
The sensitivity analysis in the farm planning problem consists of (l) changes in
the coefficients (Cj ) in the objective function, (2) changes in the righthandside values
(bi) in the resource constraint inequalities, and (3) changes in the inputoutput coefficients
in (2.1) [Murtagh8l]. This thesis only investigates the changes in the coefficients (Cj ) in
the objective function, since coefficients (C) in the objective function represent input
costs and the output prices that a fann production involves and changes in these
coefficients occur most frequently. Farmers also mostly concern the changes in Cj while
remaining their optimal returns unchanged. The sensitivity analysis involving changes in
resource constraints and inputoutput coefficients are much more complicated.
According to Murtagh [Murtagh81], the changes in the coefficients (Cj ) affect the
"sensitivity" of production in two ways: through nonbasic variables and through basic
variables.
(1) Nonbasic Variables:
The change in the coefficient eCJ) of the nonbasic variable affects the reduced
cost of that variable only. To perform sensitivity analysis, an arbitrary numerical
quantity 6 is added to Cj to see how far 8 can vary before a change of basis is
necessary. That is, the range over which can vary and the current solution remains
optimal is given by:
C=C+8. . J
Let d,denotes the jth element of the reducedcost vector,
18
II
II•I•

then
= Zj  (Cj + 8)
= d. _s: J u.
Where d, is the reduced cost at the current optimum. For a nonbasic variable, the
range 8 is
ct) < 8 ~ d,.
The change beyond these limits will make the original solution nonoptimal, since
the reduced cost of a nonbasic variable becomes negative.
(2) Basic Variables
The change in the coefficient of the basic variable affects the reduced cost of the
non basic variables. For a basic variable, the range 8 is
j d i } .C· { d i I maXI ~u ~min f
;(a,,·O  aij ijui/' 0  ai;
where a,j = (B'aj );. If there is no (liJ < 0, then 0 < ct), and if there is no (Xij > O. then
8 > ct).
19
•

CHAPTER III
DESIGN AND IMPLEMENTATION
OF THE FARM PLANNING MODEL SYSTEM
3.1 The Components of the Farm Planning Model System
The farm planning model system includes four parts: farm planning datasheets.
farm planning model, farm planning solver and farm planning sensitivity analysis (see
Figure 3.3). The farm planning model system also contains a menu bar for tile handling
and an online help menu. The first part is farm planning data sheets. It has 9 data sheets
for alternative crop and livestock production activities. The information for these data
sheets is from the individual enterprise budgets of the corresponding production
activities. Alternative crops have five data sheets ( with example data displayed in Figure
4.2  4.6): Native Pasture Data Sheet, Wheat for Grain Only Data Sheet, Wheat for
Forage and Grain Data Sheet, Graze Out Data Sheet and Oats Data Sheet. Alternative
livestock activities have four data sheets (with example data displayed in Figure 4.7 
4.] 0): CowCalf Data Sheet, Stocker Steers on Winter Wheat Pasture Data Sheet, Stocker
Steers on GrazeOut Wheat Pasture Data Sheet and Slaughter Steers Data Sheet. Another
data sheet about the farm's available resources and their prices is called Farm Information
Data Sheet ( with example data displayed in Figure 4.1).
The second part is a farm planning model that generates the o~jective function
and the constraint matrix for the linear programming of the farm planning problem ( with
20

example data displayed in Figure 4.11). The objective function is represented by the row
·'optimal". The b in (2.5) is represented by the column RHS. The rest of the matrix in
Figure 4.11 correspond to A in (2.5).
The third part is the farm planning solver which solves the farm planning model
and returns the optimal solution back to the same constraint matrix of Figure 4.11 in the
second part. This optimal solution includes the optimal value of the objective function,
the optimal amount of production activities and resource allocation. which the farmer
should use and produce to maximize hislher profit.
The final part of the system is the sensitivity analysis. This part gives the range of
variation of these coefficients for which the optimal solution remains optimal. These
coefficients in this study include the coefficients of objective function (prices of products
and costs of inputs).
3.2 The System Design of the Farm Planning Model System
The layout of the whole farm phuming model system is shown in Figure 3.1.
Figure 3.2 descrihes the control flow of the farm planning model system or the
relationship among the four parts of the farm planning model system. The first part
provides all the necessary data sheets that are required to generate the o~iectivc ft.mction
and the constraint matrix in part two. Part three solves the farm planning model using the
revised simplex method. The fi.nal part is the sensitivity analysis when the optimal
solution is found in the third part. Figure 3.3 shows the initial screen of the farm
planning model system. The command buttons at the top of the screen correspond to the
di fferent parts of this system.
21

3.3 Key Algorithm
a. Global variables
The whole system has 10 data sheets. The II arrays of global variables are
declared. There is one array for each of the ten data sheet, and there is an additional
array called MtxarrayO, that holds data for fann planning model (i.e. objective
function and constraint matrix). The global arrays are listed below:
Global MtxarrayO as double
Global wheatforageO as double
Global grazeoutO as double
Global natpasO as double
Global oatsO as double
Global wheatgrainO as double
Global fanninfoO as double
Global cowO as double
Global stksteerO as double
Global stkgrazeoutO as double
Global ssteerO as double
/* it holds data for farm planning model */
/* it holds data for wheatforage data sheet */
/* it holds data for grain grazeout data sheet */
/* it holds data for native pasture data sheet */
/* it holds data for oats data sheet */
/* it holds data for wheat for grain only data sheet */
/* it holds data for farm information data sheet"/
/ .. it holds data for cowcalf data sheet */
/* it holds data for stocker steers data sheet */
/* it holds data for stocker steer grazeout data sheet */
/* it holds data for slaughter steer data sheet .. /
b. Farm planning model construction
The farm planning model is to link the abovementioned 10 data sheets that are
represented by forms of tables. In the complete farm planning model, column IUIS
represents the resource endowments and the rest of the columns represent either a
production activity or a production rule. For example, column 4 in the hum planning
model represents the resource requirements for production activity cowcalf, which is
the information from data sheet of cowcalf. A production rule is either usage must
be less than purchase or sell must be less than production. Therefore all columns
together match the linear programming in (2.1).
22

c. Revised Simplex Method
J. Find the column with the smallest c".1
•
Min + c( I , I)
k+I
for i + I to n
if Min> c( I ,i) then
Min +c( I ,i)
k + i
endif
nexti
I*c( I, i) (Ire the objective coefficients*1
1* k is the column number, which is initialized with I *1
1* n altematives, i.e. column *1
I*the column with the smallest cj *1
1* m row *1
1* rth row *1
2. Find the row with the smallest R· (R;= RHSj / aik )
Min + B_b (1,1)1 A (I,k) I*B_b (j, 1) is the array for the RHS value*1
1* which is assigned by the Mtxarray(j,O),*/
1* I ~ j ~ m. A(i, j) are assigned by the*1
/'" Mtxarray(i,j), I~ i ~ m, l~j ~ n "'I
r + l /* r is the row number, which is initialized with I "'I
for j + I to m /* m is the number of resource constraints "'I
if Min> B_bU, I) / AU, k) then
Min + B_b(j, I) 1A(j, k)
r + j /* the row with the smallest Rj *1
endif
next j
3. Calculate TJvector. (ajk =ajk / ark)
for j + I to 111
ifj +1" then
11 U. I) + I / A(r. k)
else
11 (j, I) +  A(j, k) 1 A(r, k)
endif
next j
4. Calculate the B 1
•
1* B is the submatrix of A that is associated with basic variables *1
call matrixmultiply (m, m, BoO, m, B10, BinvO )
1* This function multiplies two matrices. m stands for the *1
/* number ofrows of the matrix. BoO is an III x m matrix, *1
1* which is initialized with an identity matrix, and its rth column's *1
1* value are assigned by llvector. */
/* BIO is an m x m identity matrix. B,nvO is the inverse matrix of B, */
/* which is an m x m matrix. */
23

sub matrixmultiply (byval m as integer, byval 11 as integer. AO as double,
byvall as integer, BO as double, CO as double)
for i ~ I to m
for j ~ I to I
C(i,j) ~ 0
for k ~ I to n
C(i, j) ~ C(i, j) + A(i, k)* B(k, j)
next k
next j
next i
end sub
5. Calculate the CB B1
•
1* CB are the objective coefficients for the basic variables */
call matrixmultiply ( I. m, CB I O. 111, B;II.0, CBO )
1* CBIO is the matrix that holds objective coefficients for the basic variables *1
1* CSO = CB 10 x B;II'O */
6. Calculate the Cn BIA  C.
1* A is the inputoutput coefficient matrix. C is the matrix that holds */
/* objective coefficients associated with nonbasic variables. *1
1* and its values are assigned by Mtxarray(O, i), I::; i ::; n */
call matrixmultiply (I,m, CBO, n, AO, CBAO )
1* CBA = CSO x A() */
forj ~ 1 to n I*n columns */
C,(1.j) ~ CBA( I,j)  C( Ij)
nextj
7. Calculate the BIA.
call matrixmultiply (rn, m, B;IIvO, n, AO. A I () )
/* A I() = 8,"vO X A() */
8 Calculate the 13 l b.
/*b is the RHS which is assigned by Mtxarray (j,D). I::; j ::; m *1
call matrixmultiply (m. 111, BinvO, 1, bO, B_bO)
1* B_bO = BinvO X bO *1
9. Calculate CJ) BIb.
CBb~O
for i ~ I to 111
CBb~CBI(I,i)* B_b(i, 1)+CBb
next i
24

/* for iteration"/
for i ~ I to In
for j ~ 1 to m
B1(i, j) ~Binv ( i, j)
nextj
next i
II. Sensitivity analysis
(a) for nonbasic variables
min ~ C1(I,j) /* C](I,j) ~ CBA(I,j)  C(lj), I~j ~ 11 */
max ~ IE + 30
(b) for basic variables
min ~ C1(l, j) / A I (p, j) /"'p is the row number for the basic variable, I ~ j ~ n */
max ~ C1(I,j)/ Al(p,j)
25
 •
Solution
Report
Sensitivity
Analysis
Report
Adjustable
Cells
Native Pasture
GrazeOut
Oats
Wheat for Forage and Grain
Stocker Sleer on GrazeOut
Slaughter Steer
Stocker Steer ....I~~
Figure 3.1 Menu Organization (System View)
26

Choice of Data Sheets
Farm Planning Model
( Matrix Form)
.Ir
Solver
( Revised Simplex Method)
solution not found
solution found
Farm Planning Model
(Matrix Form)
Sensitivity Analysis
solution not found
solution found
,Ir
Report End
Figure 3.2 The Control Flow of the Farm Planning Model System
27

Figure 3.3 The Main Menu of the Farm Planning Model System
28

CHAPTER IV
AN APPLICATION OF THE FARM PLANNING MODEL SYSTEM
4.1 Farm Planning and the Farm Planning Model System
Farm Planning is to determine optimal allocation of a farm's limited resources
such as land, labor and capital among alternative crop and livestock enterprises. It helps
farmers to decide what and how much will be produced to make the optimal returns from
the resources they have or have access. The farm planning model system can be used to
help farmers in conducting such kinds of decisionmaking  to maximize returns from
their production activities given the amount of resources available to them. In order to do
so, relevant information is needed, such as the prices of farm production outputs, the
amount of resources a farm has or has access, the prices of these resources and farm
production inputs and so on.
4.2 The OSU Enterprise Budgets
Enterprise budgets provide such kind of information for different number of
production activities. Enterprise budgets have been developed by OSU agricultural
economist in four principal types of budgets used in farm decision making [Doye88a].
These four types of budgets are: whole farm, cash flow, enterprise and partial budgets.
Enterprise budgets project the costs and returns for an activity or activities  raising
29

livestock, producing grain, growing vegetable and so on  for some period, generally one
year. OSU enterprise budgets are made available to producers through County Extension
offices and area agricultural economics specialists.
The enterprise budget incorporates information about a specific resource,
management practices and technology used in the production process. For instance,
separate enterprise budgets are specified for different calving seasons and feeding
systems in cowcalf operations[Doye88]. For the details of the OSU Enterprise Budgets,
please refer to Doye[Doye881, Doye88b].
4.3 An Example of the Farm Planning Model
The following example is a typical farm planning problem. This farm planning
problem has two types of production alternatives: alternative stocks and alternative crops.
These two production alternatives include nine production activities: Native Pasture,
Wheat for Grain Only, Wheat for Forage and Grain, Grain GrazeOut , Oats, CowCalf,
Stocker Steers, Stocker Steers on GrazeOut, and Slaughter Steers. Each production
activity provides with information on how much labor, land, capital, fertilizer, machinery,
insurance, insecticide, seed etc. are needed to produce one unit of this product. Figure 4. I
provides the information about a farm's total available resources, such as land, labor,
capital and their prices. The data sheets in figures 4.2 through 4.10 provide enterprise
budget information for the abovementioned nine production activities.
Figures 4.11 and 4.12 provide the solution of the example farm planning problem.
The solution of the farm planning problem is returned in two forms. Figure 4.11 provide
the solution in the matrix form. The first row of Figure 4.11 provides the optimal
30

production activities and the first column of Figure 4.11 are the resources that are used to
attain the above optimal. The maximum anlount of protit is $77164.30. Figure 4.12
provides the solution in plain text form, which is easily understood by farmers. Figure
4.13 is the result of the sensitivity analysis. Figure 4.14 provides the sensitivity analysis
report in plain text form that is easily understood by farmers. Tables 4.1 and 4.2
summarize the solution of this farm planning problem. Table 4.3 is the summary of the
sensitivity analysis.
31
Table 4.1 Optimal Production Activities for the Example Farm Planning Problem
Production Activities:
24.5 heads
398.9 heads
o
o
573.7 bu.
226.3 bu.
600 aums
oo 322.7 hrs.
oo
860.8 hIs.
$90.000.00
o
31 cwt. (7.35 heads)
21.4 cwt. (2.45 heads)
3.3 cwt. (0.24 heads)
1,692.2 cwt. (387.23 heads)
J ewt. (0.50 heads)
2,708.7 ewt. ( 98.92 heads)
o
o
o
2,5842.3 bu.
oo
132.9 aLllns
220.3 aums
187.9 aums
CowCalf
Stocker Steers
Stocker Steers on Graze Out
Slaughter Steers
Wheat for Grain Only
Wheat for Grain and Forage
Native Pasture
Oats
Grain Graze Out
Hire Labor (JanFebMar)
Hire Labor (AprMayJun)
Hire labor (JulAugSep)
Hire labor (OctNovDec)
Borrowed Capital
Sell Steer Calves (45)
Sell Heifer Calves (45)
Sell Commercial Cows
Sell Aged Bulls
Buy Steer Calves (45)
Sell Heifer Calves (67)
Sell Steer Calves (67)
Sell Steer Calves (78)
Buy Steer Calves (78)
Sell Slaughter Steer
Sell Wheat
Sell Oats
Pasture Transfer from 1SI Season to 2"d Season
Pasture Transfer from 2"d Season to 3"J Season
Pasture Transfer from 3'll Season to 4'1> Season
Pasture Transfer from 41
1> Season to 1SISeason
32
Table 4.2 Resource Allocations for the Example Farm Planning Problem
Resources
Land for Pasture
Land for Crop
Labor (JanFebMar)
Labor (AprMayJun)
Labor (JulAugSep)
Labor (OctNovDec)
Own Capital
Borrowed Capital
Pasture balance in 151 Season
Pasture balance in 2"d Season
Pasture balance in 3'd Season
Pasture balance in 41h Season
Balance for Steers 437
Balance for Heifer 422
Balance for Commercial Cows
Balance for Aged Bulls
Balance for Heifer 605
Balance for Steers 665
Balance for Steers 1065
Balance for Wheat
Balance for Oats
Balance for Steers 764
Required
600 acres
800 acres
450 hrs.
276 hrs.
450 hrs.
450 hrs.
$9,990.00
$90,000.00
oaaa
o
aa
oa
o
ooo
o
33
Available
600 acres
800 acres
450 hrs.
450 hr5.
450 hrs.
450 hrs.
$10,000.00
$90,000.00
o
oo
a
o
o
ooooo
o
()
o
Table 4.3 Sensitivity Analysis for the Example Farm Planning Problem
Production Activities:
CowCalf
Stocker Steers
Stocker Steers on Graze Out
Slaughter Steers
Wheat for Grain Only
Wheat for Grain and Forage
Native Pasture
Oats
Grain Graze Out
Hire Labor (JanFebMar)
Hire Labor (AprMayJun)
Hire labor (JulAugSep)
Hire labor (OctNovDec)
Borrowed Capital
Sell Steer Calves (45)
Sell Heifer Calves (45)
Sell Commercial Cows
Sell Aged Bulls
Buy Steer Calves (45)
Sell Heifer Calves (67)
Sell Steer Calves (67)
Sell Steer Calves (78)
Buy Steer Calves (78)
Sell Slaughter Steer
SeJl Wheat
Sell Oats
Pasture Transfer from Isl Season to 2nd Season
Pasture Transfer from 2"d Season to 3"J Season
Pasture Transfer from 3'd Season to 4lh Season
Pasture Transfer from 41h Season to 1s'Season
34
Reduced Cost
oo
27.3
73.86
o
o
o
37.81
79.63
o
7.23
2.75
oo o
oooo
o
o
o
oooo
4.81
oo
o
Range of Variation
8.74 ~ 81.98
92.11 ~ 12.98
27.3~IE+30
73.86 ~ IE + 30
150.19~3.27
3.27 ~ 68.37
IE+30~IE+30
37.81 ~ IE + 30
79.63 ~ IE + 30
2.29  23.76
7.231E+30
2.75IE+30
10.1722.84
200000 ~ IE+ 30
0 IE + 30
6.9  64.75
10.01 93.9
64.33  603.67
()  1.8
72.19  677.51
J3.57  1.91
01E+30
03.57
6.32  1E + 30
25.03  0.55
0.69  1E + 30
4.81IE+30
4.81  2.5R
4.6J  1.27
4.76  1.7
Iii Farm Infolmation Data Sheet  8~ft3
1 0
0 1 J
Hours
450
450
.8 .
10000 
90000 ...
.09
6.5
2
.8
o .1
JFM: Labor Available in the 1st Season
MJ: Labor Aveilable in the 2nd Season
JAS: Lebor Aveilable in the 3rd Season
OND: Labor Available in the 4th Season
Wheat for Forage and Grain Only
Native Pasture
Wheatfor Grein Only
GrazeOut
Land for Crop:
Land for Pasture:
Labor/Season:
Capital Need for the Hired Labor:
Hired Lebor Efficiency:
Unconsumed Pasture Transfered to Next Season:
Operating Capital:
MBXimum Borrowed Cepital:
Borrowed Interest Rete:
Wage for Hired Lebor/Hour:
Figure 4.[ Farm Information data Sheet
35
.. Native Paslme Data Sheel~~ ~[i] Il:i
Operating Inputs Units Price Quantity Value
Prescribed Fire: Acre 2
Mach. Fuel. Lube, Rep: Dol.
3.69
Annual Op. Capital: Dol .0176
Labor/Season: Hrs. 1.56
Hours Hours
JFM JAS
AMJ OND
Production
Pasture/Month: Aums
Aums Aums
JFM JAS
AMJ OND
Figure 4.2 Production Activity: Native Pasture
36
Iii Wheal for Grain Only Data Sheet ~I!IUiJIl3
Value
G
9.75
9.6
12
1.GB
4.08
1.24
1
65
.8
1

14
34
.5 '
Price Quantity
6 I
.15
12 _.JI
12 
.12.1
.1,2
2.48
Operating Inputs Units
Wheat Seed: Bu.
Anhydrous Ammon: Lbs.
18460 Fert Cwt.
Custom HaNest Acre
Misc. Expense: Bu.
Custom Hauling: Bu.
Insecticide: Acre
Machinery Fuel. Lube. Repairs: Dol.
56.86
Annual Operating Capital: Dol. 24.7~ 2.2293
Machinery Labor/Season: Hrs. 1.237 8.0405
JFM JAS
AMJ OND
Production
Wheat: Bu. 119
Figure 4.3 Production Activity: Wheat for Grain Only
37
.... Wheat fOf Forage and Gfain Only IMIiiI lt3
Operating Inputs
heat Seed:
nhydrous Ammon:
Custom HaNest
Misc. Expense:
Custom Hauling:
Machinery Fuel, Lube.Repairs:
Price
6  _.
12
2.48
.15
12 J
.12
.12
~Quantity I
1.25 
.8
.5
90
1
8
28
7.5
9.6
1.24
13.5
12
.96
3.36
o
60.67
1.35765
8.0405
98
~um
nnual Operating Capital:
Labor/Season:
Figure 4.4 Production Activity: Wheat for Grain and Forage
38
Figure 4.5 Production Activity: Grain GrazeOut
39
 ~~~    IIIi Oals (iifrT1i3
Operating Inputs Units Price Quantity Value
Oat Seed: Bu. 5.32 3 15.96

18160 Fert 0Nt. 112 .5 6
Anhydrous Ammon: Lbs. .15 60 9
Custom Harvest Acre 13 1 13
Custom Hauling: Bu. .12 55 6.6
Misc. Expense: Bu. .12 35 4.2
Machinery Fuel. Lube. Repairs: Dol. J11.84 ;
66.6
Annual Operating Capital: Dol. .09 21.68 1.9512
Machinery Labor/Season: Hr. 6.5 _ ...J 1.04 6.76
p
Hours Hours
......' JFM 0 JAS .37 I
AMJ OND
..
.21 I .45
Production
Oats: Bu. ,J 1.6 55 11 B8
It
Figure 4.6 Production Activity: Oats
40
; Cow_Call    ~             ~rI fE:i
63.375
102 OND 3.32!
97.2822
.44
.3
.1 i
.01
.02
Operating Inputs Units
4145% Prot Sup.: Lbs.
1920% Pro. Feed: Lbs.
Selt .Minerals: Lbs.
Vet Service: Hd.
Ve1MDSupplies: Hd.
Marketing Expense: OM.
PersoneJ Taxes' Hd.
Herd Bulls: CWL
Hauling: OM.
Mechinery Fuel. lube. Repairs: Dol.
EquipmentFuel. lube. Repairs: Dol.
Annuol Operating Capital: Dol.
Labor/8eMon: Hr.
JFM
Posture/SeMon: Aums
JFM
Production Units
Stf Colves(45): OM.
Hlr Colves(45}: Cwt.
CommercieJ Cows: Cwt.
Aged Bulls: CWt
Heifers(60o700): CWt
Price
1.13
.08
.08
2.8
14.65. 
1.75
15.3
B5 .J
.35
94
79 ~
42
49
74
Quan1i1y
299
367
30
1 I
1
4.32
1
.121
4.32
4.37 ;

4.22 I
8.73
13.58
605 I
Value
38.97
29.36
2.4
2.8
14.65
7.56
5.3
10.285
1512
TOTAL:
145.977
2.28
Volue
1.9228 190.7432
1.266 100.014
.873 36.666
.1358 6.6542
.121 9.954
Figure 4.7 Production Activity: Cow_Calf
41
lit SlockerSleels ~~~~~   ~ JifrT1t.':J
Operating Inputs
SlSItJ.iinerels.
Merketing Expense:
Vet Service:
Vet Medicine:
Custom Hauling:
Machinery Fuel. Lube. Repairs:
Equipment Fuel. Lube. Repairs:
Units Price
Lbs. .08
Cwt 1.75
Hd. 9
Hd. 7
Owt. .35
Dol.
Dol.
QuClOtitY
.
9.11
6.79 J
1
1
11.15 I
Value
7288
118B25
9
7
3.!Kl25
10.69
.79
1.74, JAS 0
o J ONO .79
Weight NoJStr. Quantity Value
66542 558.9528
43.9938
17.2503
409.84
19.5
Hours
o
1.65
45.54
Aums
191.67
4.36
3
Aums
Houre
.09
94 ~
6.5
Dol.
Owt.
Hr.
Aums
JFM
AMJ
Units Price
Owt.
Production
Streers(60D700):
Pasture/Season:
Annual Operating Capital:
Steer CeJves(45):
labor/Season:
Figure 4.8 Production Activity: Stocker Steers
42
... StockerSleer·G~~       ~rlii:)
Operating Inputs Units Price Quantity Value
Salt _MineroJs: Lbs.
Marketing Expense: OM.
Vet Service: Hd.
Vet Medicine: Hd.
Custom Hauling: OM.
Machinery Fuel Lube. Repairs: Dol.
Equipment Fuel. Lube. Repairs: Dol.
.08
1.75
9
.~
7
.35 
1273
7.8
12.17
1.0184
13.65
9
7
4.2595
14.26
.79
Annual Operating Capital:
Steer Calvas(45):
Le.bor/Season:
Dol.
OM.
Hr.
.08
94
6.5 .J
279.24
4.37 I
1.825
49.9778
22.3392
410.79
11.8625
Hours Hours
Pasture/Season: Aums
Aums Aums
JFM JAS
AMJ OND
Production Units Price Weight No./Streer Quantity Value
Streer(70oaOO): Cwl 7.644 588.588
Figure 4.9 Production Activity: Stocker Steers GrazeOut
43
Operating Inputs Units Price Quantrty Value
Vet Medicine: Hd. 4 4
Mixed Feed: Lbs. ,048 2500 120
Lot Chorge: Days ,05 130 6.5
Toxes: Days ,004 130 52
Trucking: Cwl 15 7,5 11.25
Order Buyer: OM. .35 7,5 2.625
Sick Pen Change: Days ,015 130 195
Beef Check Off: Dol. 1 l
147.945
Annual Operating Capital: Dol. ,088 232,31 20.44328
Ste8r8(700800): OM. 77 7,8 600.6
Production: Units Price Weight NO./Steer Quantity Value
Slaughter Stresrs: Cwl /65 111,8 'I 1·99 I 11.682 759.33
Figure 4.10 Production Activity: Slaughter Steers
44
... The lalm Planning Model
      
Rrt~
lValue IRHS ICow ISStr ISGO ISlSlr IW G IW FG INP 1011 IGO IHJ~ lHAM./ IHJAS IHOND 245 3999 0 0 573 7 22\;3 GOO 0 0 3227 0 0 9609
ODliMl 77164.3 0 ·145977 ·439939..·499779 ·147945.5686 60.67 ·369 ·666 ·49226 ·65 ·65 ·65 ·65
Lancl'T GOO GOO 0 0 0 0 0 _0__1_ 0 0 0 0 0 0
latdP  riiJ  0  '0 '0  BOO 0 0 1 1 0 1 1 0 0 0 0
lBJFM 449.94 450 3.99 1 37 1 4 0 oa .00 0 0 oa ·9 0 0 0
LBAMJ 276.26 450 1.49 0 77 0 21 .21 12 21 21 0 ·.9 0 0
LBJAS 449.99 450 1.02 0 0 0 37 .94 0 37 94 0 0 ·9 0
lBOND 449.89 450 3.32 165 165 0 57 0 .12 45 0 0 0 0 ·9
CaoUI 9990.36 l00J0 139.19 191.67 279.24 232.31 24.77 15.005 .22 21.69 1959 2 2 2 2
M...eOl 90000 90000 0 0 0 0 0 0 0 0 0 0 0 0 0
PTJAoI '.1 0 1 71 1 74 213 0 0 ·1.74 32 0 ·2.23 ,0 0 0 0
PTAM.! ·05 0 339 0 77 0 0 0 ·36 0 ·77 0 0 0 0
PTJAS .1 0 416 0 0 0 0 0 ·36 0 0 0 0 0 0
PTOND 13
.  ..   0 229 79 79 0 0 ·.79 ·34 0  79 0 0 0 0
SI437Bl .1
.
0
 .
·19229 436 4.37 0 0 0 0 0 0 0 0 0 0
H(422Bl 02 0 1.266 0 0 0 0 0 0 0 0 0 0 0 0 i
CmCll¥I8l 01 0 973 0 0 0 0 0 0 0 0 0 0 0 0 ~
~~l .03 0 ·1359 0 0 0 0 0 0 0 0 0 0 0 0
Hf605Bl ~04 0 ·121 0 0 0 0 0 0 0 0 0 0 0 0
St665Bl 17 0 0 ·679 0 0 0 0 0 0 0 0 0 0 0
St11Ji5Bl 0 0 0 0 0 11.692 0 0 0 0 0 0 0 0 0
IWIiBl .1 0 0 0 0 0 34 ·29 0 0 0 0 0 0 0
O~l 0 0 0 0 0 0 0 0 0 55 0 0 0 0 0
St764Bl 0'0 0 0 7644 79 0 0 0 0 0 0 0 0 0
... The lalm Planning Model 1Ilirt It:'f
21.4 3.3
·09 94 42 49 94 74 94 77 77 65
0 0 0 0 0 0 0 0 0 0
0 0 0 0 '0 0 0 0 0 0
0 0 0 0 !O 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 ,0 0 0 0
0 0 0 0 0 0 0 0 0 0
·1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 1 0 0 ·1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 1 0
Figure 4.11 The Solution of the Farm Planning Problem (in Matrix form)
45
... AepollfofSolullon  ~  ~~    ~[i11f3
Stocker steer on grazeout is:(head
aughter steer is:(nead)
e for grain on~ is:(bu.)
Wheat for grain and forage is; bU.)
lYe pasture [s:(aums)
Oats is:(bu.)
Hire labor In 1sf season Is~hrs)
Pasture transfer 1st2nd season is:(aums
Pasture transfer 2rrd3rd season is:(aums
Figure 4.12 The Solution Report ofthe Farm Planning Problem ( in Plain Text)
46
       
... Sensitivity RepOltl ~[ii]It:!
Name IherrC I~. lhand IbOlW 111$45 111145 Isicow  IdbU Ib$l.45 Isll67 tFinalValue 0 .10   • _86_0_,8_4_ 08_9__9•9•9,991 0 31.05 ,21,41 3.33 1692.19 I~97 Reduced Cost ·7.23 •. TO'  r0  ·2.75 0 0 0 0 0
Obiective Coelficiert 6.5 [·6.5 ·6.5 '·09 94 r9 42 49 ·94 74
Anowable IllClease 7.23 2,75 10.17 .200000 0 6,9 '10.01 64.33 0 !72.19 '.
Anowable DeClease 1(+3it'llE+30 . 22.84 ' 1E+30 lE+30 64.75 193.9 603.67 1.8 677.51
I~:~~:~~~;::::::::~:~ :~«~:~"'=~ ~::&~:::):~::::':·:"N;J>::jI :t.;:;.:..:,:...~;::.:~::~:< . . ~.v~ll·:~:;A>":"';:::&X""':::::::'*:>:Z:::~~~
I~
.... Sensitivity Reportl      ~1iiIlt:J
N.ame ~ di6GS Idi764 Ibsl780 1$1.1114 Islw Isloat 11II1 s IDIt I IDlll 11IIf I
FlIlaiValue 2708,75 0 0 0 2584226! 0 0 132.86 22027 187.92
ReducedCo$l. 0 0 0 0 0 0 ·4.81 0 0 '0
Objective CoeIlicienl 84 77 ·77 65 3.5 16 0 0 0 0 ,
., AlowClble lno_ 13.57 0 0 6.32 25.03 .69 4.81 4.81 461 4.76
Alowable Deaease 191 r lE+30 3.57 1E+30 55 1E+30 1E+30 2.58 1.27 117
..... ....... .. .  ..
• _ ...~.~. • • • ',. •• ~f1 '. pO'.. ,... • .....
"
Figure 4.13 The Solution of the Sensitivity Analysis
47
The Following Gives the Ranges of Objective Coefficients that the Optimal Solution Remains
o limal Value: 7n&4.3
ell Slaughter Steer:
ell Heifer eatves (4~)
ell COmmercial COws
Buy Steer CaJv.es (7=8).
Sell Aged Bulls'
Figure 4.14 The Solution Report of the Sensitivity Analysis ( in Plain Text)
48
CHAPTER V
SUMMARY AND CONCLUSION
Farm Planning Model has been a topic of farm and agribusiness management for
many years. It is used to determine optimal aUocation of a farm s limited resources such
as land, labor and capital among alternative crop and livestock enterprises. It helps
farmers to decide what and how much will be produced to make the optimal returns from
available resources. Agricultural economists have developed several software systems to
solve the Farm Planning Model in the past. There are also other software systems
available to solve the farm Planning problem. Since the algorithm behind the Farm
Planning Model is linear programming, all of these software systems are relatively
complex and require certain levels of computer skills and knowledge of linear algebra and
agricultural economics background. This kind of inconvenience prevents farmers from
using these systems. This study is to develop a windowsbased easytouse software
system for the farmers to solve farm planning problem themselves. The system is called
Farm Planning Model System.
The Farm Planning Model System developed in this study includes four parts: the
farm planning data sheets, the farm planning model, the farm planning solvcr and the
sensitivity analysis. The farm planning data sheets allow the users to enter the relevant
information of the farm planning problem (such as the amounts of resources and the
49
prices of products and so on). The farm planning model generates the objective function
and the constraint matrix for the farm planning problem automatically from the
infonnation the users enter in the farm planning data sheets. The farm planning solver
solves the farm planning problem to return the optimal solution back to the same
constraint matrix generated in the part of the farm planning model. The optimal solution
provides the users with the optimal value for the farm planning problem and its
associated allocation of the products produced and the resources used. The sensitivity
analysis gives the ranges of variation of these coefficients for which the optimal solution
remains optimal. The farm planning model system is implemented using Visual Basic
5.0 under the Windows 95 environment.
The Farm Planning Model System is applied to a real Farm Planning problem.
The solution of the System is compared to those of MUSAH86 and Microsoft Excel
linear programming module, and the results are the same.
The Farm Planning Model System has the following advantages:
(I) Easytouse. Any farmer with basic Windows skill can use this system.
(2) Cost efficiency. The software requirements are only Windows 95 and Visual
Basic 5.0.
An extension of the sensitivity analysis is expected in the future work of this farm
planning model system.
so
....
REFERENCES
[Barnard79] Barnard, C.S. and 1.S. Nix. 1979. Farm Planning and Control. 2"d ed.
Cambridge University, Cambridge, UK.
[Castle72] Castle, E.N., M.H. Becker, and FJ. Smith. ]972. Farm Business Managemenl.'
The DecisionMaking Process. 2nd ed. Macmillan Publishing, New Yark, New
York.
[Childress74] Robert L. Childress. 1974. Sets, Matrices, and Linear Programming
PrenticeHall, Englewood Cliffs, New Jersey.
[Doye88a] Damona G. Doye and Raleigh Jobes. 1988. The OSU Livestock Enterprise
Budget. OSU Extension Facts. No. 779. Oklahoma State University, Stillwater,
Oklahoma.
[Doye88b] Damona G. Doye and Raleigh Jobes. 1988. The OSU Crop Enterprise
Budget. OSU Extension Facts. No. 780. Oklahoma State University, Stillwater.
Oklahoma.
[Epplin97] Francis M. Epplin R. Joe Schatzer, and Joseph E. Williams. 1997. Use of
Spreadsheet Software to Solve Farm Planning Models. Unpublished manuscripl.
Oklahoma State University, Stillwater, Oklahoma.
[Herbst86] Herbst, 1.11. 1986. Farm Management.' Principles, Budgets. j)Iut7.\·. 7"" eel.
Stipes, Champaign, Illinois.
[Kay94] Kay, R.D. and W.M. Edwards. 1994. Farm Management. 3"<1 ed. McGrawHill,
New York, New York.
[Li85] Li, E.C. 1985. "Tutorial introduction to MUSAH86: A microcomputer program
for LP," Oklahoma State University Department of Agricultural Economics
Working Paper. Stillwater, Oklahoma.
[Locks74] M.O. Locks. 1974. Practical Linear Programming with Computer
Applications. Western Periodicals. California.
[Loomba64] Loomba, N.l'. 1964. Linear Programming. McGrawHill, New York. New
York.
51
[Murtagh81] Murtagh, B.A. 1981. Advanced Linear Programming: omputation and
Practice. McGrawHill New York, New York.
[Osburn83] Osburn, D.O. and K.C. Schneeberger. 1983. Modern Agricultural
Management: A Systems Approach to Farming. 2nd ed. Reston Publishing, Reston,
Virginia.
[Simonnard66] Michel Simonnare. 1966. Linear Programming. PrenticeHall, Inc.,
Englewood Cliffs, N.J.
52
Appendix 1
Installation Procedure for the Farm Planning Model System
1. Hardware and Software Requirements
Hardware: CPU with speed of 133 mhz or above.
CPU with Random Access Memory (RAM) of 16 MB or more.
CPU with spare disk space of at least 40 MB.
SVGA color minitor.
IBM compatible keyboard.
IBM compatible mouse.
Software: Windows 95 / 98 / NT operating system.
Microsoft Visual Basic 5.0 or above compiler.
2. Installation and Operating Procedure
The Farm Planning Model System is about 1.6MB and in two floppy disks.
Jnstallation Procedure:
Copy all files from Disk I and Disk 2 into the hard drive.
Operating Procedure:
Step l. Open the project file and run the program (just click the "~ " icon).
Step 2. Open data sheets (input data).
Step 3. Farm Planning Model (in Matrix Form) is generated automatically
after you input the data sheets.
Step 4. Click solver to solve the program.
Step 5. Solution Reports (Solution Report in Matrix Form and Solution
Report in Plain Text Form) are returned.
Step 6. In order to do sensitivity analysis, click the "Sensitivity Analysis"
in the menu, then click the "Adjustable cells", the Sensitivity Analysis
Reports (Sensitivity Analysis Report in Matrix Form and Sensitivity
Analysis Report in Plain Text Form) are Returned.
53
VITA
Wenhui Hua
Candidate for the Degree of
Master of Science
Thesis: APPLICATION OF THE REVISED SIMPLEXED METHOD TO TI IE FARM
PLANNING MODEL
Major Field: Computer Science
Biographical:
Personal Data: Born in Wuxi, Jiangsu Province, China, January 10, 1969, the
daughter of Zihua Zhou and Yongxiang Hua.
Eduction: Graduated in July, 1986 from Dingsu 2nd High School in Jiangsu.
China. Received Bachelor of Arts degree in Economics from Hangzhou
University, China in July, 1990. Completed the requirements for the
Master of Science degree with a major in Computer Science at Oklahoma
State University, Stillwater in December, 1999.
Experience: Document clerk from September 1990  March J993 in Yixing
Ceramics Import and Export Company, Jiangsu, 'hina. Teaching
Assistant from January 1998  present in the Computer Science
Department at Oklahoma State University, Stillwater, Oklahoma.
,.
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