SYSTEM SIMULATION MODELING ”
. OF A BEEF CATTLE ENTERPRISE
: ‘TO INVESTIGATE MANAGEMENT

‘ 7 ‘ DECISION MAKING STRATEGIES '

 

; Dissertation for'thiei Degree'of Ph.‘-D,;ffi* ‘

’MICHIGANVTSTATE} UNIVERSITY? i -  V; 7
{TMICHAEL RAYMOND IASKE
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thesis entitled , ". '- A
System Simulation Modeling of
a Beef Cattle Enterprise
to Investigate Management Decision
Making Strategies
presented by

Michael Raymond Jaske

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Ph. D. degree in Systems Science

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0X9 ABSTRACT

KIA SYSTEMS SIMULATION MODELING OF A BEEF CATTLE ENTERPRISE

To INVESTIGATE MANAGEMENT DECISION MAKING STRATEGIES
By

Michael Raymond Jaske

Management decision making can be greatly improved by provision
of better information about alternative choices to the decision maker.
The complexity of agricultural systems, and livestock ones in partic—
ular, has resulted in considerable neglect in early model building
efforts to supply better information. Simulation models have the
capability of surmounting many of the problems of modeling complica—
ted dynamic system behavior. This thesis develops a simulation model

of a general beef cattle enterprise to allow investigation of alter—

 

native management decision making strategies.

The model simulates the behavior of the major physical and
financial variables of the enterprise through time. Although the
model is intended for general use, attention has been concentrated on
modeling of the land extensive cow/calf range operation. The model
consists of five major components and several secondary components.
MajOr components are (1) cattle demography, (2) forage growth, (3)
feed stock accounting, (4) nutrient impacts on growth and reproduction,
and (5) management decision making. The financial component is the
most important component of the secondary group. Land allocation
among alternative uses and crop production are not modeled and are

arbitrarily specified by the user. A large FORTRAN computer program

 

 

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Michael Raymond Jaske
and subroutines accomplish this system simulation.

A highly disaggregated herd population model allows full explor—
ation of population dynamics. Using TDN as the basic feed quality
descriptor, and net energy for growth and maintenance where possible,
the nutrient impact component predicts rates of weight gain and repro—
ductive dynamics as a result of feed intake. Forage growth is modeled
as a function of the exogenous weather variables of solar radiation,
temperature, and rainfall. The financial component determines revenue
and cost as a result of physical events and these determine the effect
on profit, cash flow, depreciation, taxation, and debt levels.

The management component has been developed to provide for the
needs of managers in ongoing operating decisions as well as investment
planning. Detailed control variables allow realistic simulation of
events of interest to managers. The interactive structure of the com—
ponent, with straight forward decisions made endogenously following
standard economic criteria and more complex decisions made exogenOusly
by the model user, is implemented in a batch mode to allow creation
of files storing the model's values at decision points where user
control is required. A decision tree of alternative courses of action
can be developed by cataloging the files created at each encounter of
a decision point.

Three examples of management strategies are evaluated to demon—
strate the capability of the model to assist decision makers. These
are (1) early versus late calf weaning, (2) the rate of cattle herd
development in investment projects, and (3) general profit maximiza—

tion. These examples are discussed in terms of financial criteria.

 

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Michael Raymond Jaske
The thesis concludes with a summary of the accomplishments that
have been realized, conclusions about the worth of the model and the
demonstration examples presented, and a discussion of the current
state of validation of the model along with improvements and extensions

which appear to be helpful.

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SYSTEM SIMULATION MODELING OF A BEEF CATTLE ENTERPRISE
TO INVESTIGATE MANAGEMENT DECISION MAKING STRATEGIES
By

Michael Raymond Jaske

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Electrical Engineering and Systems Science

1976

 

ACKNOWLEDGEMENTS

This thesis has been completed with the help of many people.
My major advisor, Dr. Thomas J. Manetsch, has been most helpful in
reviewing various drafts, but most importantly he gave me the oppor-
tunity to find my own direction and to develop as a professional.
Dr. R. J. Deans and his student Margaret Schuette are responsible
for initiating this project and the cooperative effort among us
has been very beneficial. Dr. G. E. Rossmiller has provided advice
on economic matters and potential uses of the simulation model in
economic development. Other members of my committee——Dr. G. L.
Park, Dr. R. A. Schlueter, and Dr. J. S. Frame—-have provided me
with advice and encouragement. My wife, Marsha, has been most
patient and supportive during the years of my graduate education.

The financial support of the Department of Electrical Engin—
eering and Systems Science, and the Korean Agricultural Sector
Simulation Project, funded by AID contract csd-2975, is grate-
fully acknowledged. This thesis could not have been completed

without this support.

ii

 

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LIST OF

IIST 0F

Chapter

 

 

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

Chapter

I.

II.

III.

IV.

INTRODUCTION
GENERAL CONCEPTS

11.1 Systems Concepts

11.2 Modeling

11.3 Simulation

11.4 Use of Simulation Models

THE PROBLEM STATEMENT

111.1 General Review of the Problem

111.2 Previous Approaches and Review of the
Literature

111.3 Rationale for Selecting Simulation

111.4 Detailed Problem Statement

GENERAL DESCRIPTION OF THE MODEL

1V.l Overall Model Organization
IV.2 Specific Components

1V.3 Simulation Model Operation
IV.4 Summary

DETAILED DESCRIPTION OF THE MODEL

V 1 Cattle Demography Component

V 2 Forage Growth Component

V.3 Feed Stock Component

V 4 Nutrient Impact Component

V 5 Management Decision Making Component

Exogenous Decision Making
Endogenous Decision Making
6 Secondary Model Components
7 Simulation Model Calling Structure
.8 Summary
9 Glossary of Variables

l7
19

25
25

27
31
32

39
39.

70
75

79

79'

97
112
115
122

127
144
160
195
197
198

 

 

 

Ill.

VIII.

IPPEII

BIBLI

VI. MODEL TESTING AND VALIDATION

V1.1 Approaches to Validation
V1.2 Validation Tests

Logical Consistency
Tracking Historical Data
Expert "Eyeballing"
Prediction

V1.3 Summary

VII. MANAGEMENT STRATEGIES

V11.l Strategic Decision Making
V11.2 Illustration of Strategy Investigations
V11.3 Summary

VIII. SUMMARY AND CONCLUSIONS
VIII.1 SUmmary
V111.2 Conclusions
V111.3 Extensions to the Model
V111.4 Implementation

APPENDIX SYSTEMS SCIENCE REFERENCES

BIBLIOGRAPHY

iv

208

208
212

212
242
245
256
256

258
258
259
288
290
290
294
296
303
304

305

 

 

 

 

 

 

Table 5
Table 5

Table 5

Table I

Table

Table
Table
Table

Table

Tabl

Tab:

TaT

Table 4.1

Table 5.1
Table 5.2

Table 5.3

Table 6.1

Table 6.2

Table 6.3
Table 6.4
Table 6.5

Table 6.6

Table 6.7

Table 6.8

Table 6.9

Table 6.10

Table 6.11

Table 7.1

LIST OF TABLES

Age and Sex Description of the Cattle Herd
Cohorts

Definition of Crop and Cattle Expense Variables
Definition of Resource Variables

Parameter Values and Definitions for the Production
Cost Element of the Financial Component

Total Herd Population at Selected Points in Time
Versus DT Step Size

Comparison of Computed(Corrected) and Theoretical
Herd Deaths Over Time

Feed Stock Allocations
Feed Stock Values Compared Over Time
Sample Run of Feed Stock Use and Desired Allocation

Selected Financial Variables Over a Simulated Time
Horizon of One Year

Comparison of Calculated and Simulated Values of
Financial Variables

Forage Digestibility Factors Investigated to Obtain
an Improved Digestibility Range

Weather Effects on Forage Growth and Forage
Digestibility

Sensitivity Testing of the Parameters of the Forage
Growth Model

Effect of Grazing and Harvesting Policies on Forage
Growth and Obtainability

Results of Sample Runs Investigating the Effects of
Early Versus Late Weaning of Calves

 

46
172

174

185

215

217
220
222

223

226

234

237

248

266

 

Table 1.2
Table 7.1

Table I.

Table I.

Table 7

 

 

Table

Table

Table

Table

Table

Change in Net Worth Over Time
Breeding Method Cost Comparison

Financial Effects of Weaned Calf Retention
Policies

Financial Effects of Alternative Feeding Plans

Mature Breeding Cow Conditioning Effects from
Alternative Feeding Plans

vi

 

Page
275

279

280

282

286

 

 

Figure 2.

Figure 2
Figure 2

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Figure 2.1
Figure 2.2
Figure 2.3

Figure 2.4

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4
Figure 4.5
Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 5.1

LIST OF FIGURES

Page
General system diagram 9
System diagram illustrating multiple components 9
Block diagram symbols for mathematical operations 16
Relation between simulation step size and
simulation error 18
General system diagram for a beef cattle enterprise 40
Graphical illustration of the response Y(t), to an
input, X(t), for a distributed delay process 49
Graphical illustration of the response, Y(t), to an
input, X(t), for a discrete delay process 50
The accumulated calving fraction versus time 58
Decision mechanism for slaughter cohort sales 63
Decision mechanism for forage harvesting 64
Decision mechanism for feed stock sales and purchases
to obtain wintering nutrient requirement 65
Decision mechanism for herd feeding allocations 66
Blowup of the general system diagram to show
functional details of the management decision
making component 67
Flow diagram of the management decision making
component in relation to the simulation model 71
"Decision Tree" of alternative strategies using
the simulation model's restart capability 74
Enterprise system diagram illustrating physical
and information flows between components 77
Calling sequence of the simulation model components
to simulate the beef cattle enterprise through time 78
Decomposition of a kth order distributed delay
into a series of k first order delays 80

 

 

 

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Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure
Figure

Figure

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Kth order distributed delay with losses 81
Block diagram of subroutine HDMOG4 87
Determination of the annualized birth rate by

numerical approximation of the deriviative of the

accumulated births curve 90

Determination of BFRAC. values from the breeding
history of each cohort subpopulation 92

Determination of the photosynthetically active
quantity of plant material per unit area 99

Plot of points determining the temperature quality
index, TPF(t), from the average temperature 99

Plot of points determining the soil moisture

quality index, SMF(t), from the soil moisture 100
Plot of points determining the soil nutrient

quality index, SNFn(t), from the soil nutrient 100
value

Relationship between the grazing waste factor,
AWFn(t), and the stocking rate, STOCKLn(t) 103

The intermediate digestibility, BASEDGn(t), as
a function of pseudo—age, PINDEXn(t) 106

The growth quality factor,FRQUAL(t), as a function
of the integral of the temperature index over the
growth season 107

Plot of forage density digestibility factor against

per animal density 103
Block diagram of the forage growth component 111
Block diagram of the feed stock component 114
Block diagram of the nutrient impact component 121

Flow chart of subroutine INQUIR of the management
component 125

Flow chart of subroutine RESPNS of the management
component 128

 

 

 

 

Figure 5.1

Figure 5.

Figure 5.

Figure 5

 

Figure

Figure

 

 

 

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Figure 5.24

Figure 5.25

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Page
Subpopulation values from the female calf cohort
prior to weaning action by management 133
Subpopulation values from the replacement heifer
cohort following weaning action by management 133
Graph of culling rates for each subpopulation of
the mature cow cohort using accumulated calving
rates as a guide 139

Printed message at the spring growth onset decision
point requesting values for specified control
variables 145

Yearly pattern of crop harvests as exogenously
specified 161

Linear interpolation between exogenously specified
annual rainfall data points to obtain the current

rainfall value 162
Expected cattle prices over time 164
Base digestibility values versus an age index 231
Seasonal digestibility factor versus season 231
Plant densities over the growing season 241

Rate of weight gain of male calf animals versus age 245

Forage densities over time as a result of basic
climatic variables and grazing policies 251

Forage densities over time as a result of basic
climatic variables and grazing policies 252

Forage densities over time as a result of basic
climatic variables and grazing policies 253

Forage densities over time as a result of basic
climatic variables and grazing policies 254

Forage densities over time as a result of grazing
and harvesting policies 255

 

 

 

 

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7.5

7.6

Annual pattern of cyclic cattle prices
used in demonstration runs

Annual pattern of cyclic crop prices
used in demonstration runs

Annual pattern of solar radiation
incident on the enterprise site

Mature cow cohort populations through
time for the three investment patterns

Annual cash flow patterns through time
for three investment cases

Pattern of cash floWS through time over
the three-year time horizon of the
investigations for Cases 1, 2, and 3

Plot of the rankings of runs 6, 7, and 8
according to financial ranking and condition
ranking

Enterprise system diagram illustrating physical
and information flows between components

 

262

263

270

274

287

292

 

 

 

 

 

 

 

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CHAPTER I

INTRODUCTION

This thesis discusses the development of a simulation model of a
beef cattle enterprise and the use of this model as a tool to investi-
gate alternative management strategies available to the operator of that
enterprise. Although a general model of an individual enterprise has
been developed the emphasis of this thesis lies in the land extensive
cow/calf operation. Coordination of this thesis with work in the
Department of Animal Husbandry by Schuette has allowed incorporation of
that work in the nutrient impact component allowing considerable detail
in investigation of questions of nutrient feed intake on cattle growth
and reproduction. An interactive management decision making component
allows the user of this model to control the decisions made which affect
the long range behavior of the enterprise.

Chapter II discusses general concepts of systems, modeling, simula—
tion and uses of simulation models. These ideas are the foundation
upon which this thesis is based. Chapter III presents the general scope
of the problem, reviews the relevant literature and previous approaches,
and finally gives the detailed problem statement. Chapter IV gives a
description of the model and its components without extensive use of
mathematics. Chapter V presents the model and its components, both
minor and major, in detail and lists all variable definitions in an
appendix. The mathematical models used, the major assumptions made,
and the exact equations upon which the computer programs are based
are presented in this chapter. Chapter VI reviews the validation

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procedures used to develop evidence that the model and its components
properly represent their real world processes. Sensitivity testing of
some model parameters is also presented to assist in identification
of those capable of significantly altering the system's behavior.
Chapter VII reviews the results of several demonstration examples of
the capability of the simulation model to assist in various decision
making evaluations. Chapter VIII presents the conclusions drawn from
the construction and use of the model, reviews the results of the
demonstration examples, and discusses areas of improvement and exten—
sion of the model.

It is anticipated that this thesis will be read by three distinct
groups of persons-—systems science professionals, animal husbandry
specialists, and management personnel. Because of the widely varying
backgrounds of these three groups in terms of mathematical expertise
and familiarity with computer simulation studies, not all of the mater—
ial presented here is readily understandable by all readers. Specific
chapter groupings will be recommended for each potential audience in
order to facilitate understanding. Systems science professionals
should read chapters 3, 4, 5, 6, 7, and 8. Animal husbandry special—
ists should read chapters 2, 3, 4, 6, 7, and 8, while management per-
sonnel should read chapters 2, 3, 4, 6, 7, and 8. An Appendix is
provided which lists background references of particular interest to
readers not familiar with systems science who wish to become acquaint—

ed with it in more detail.

 

 

 

 

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CHAPTER II

GENERAL CONCEPTS

This chapter is written as an aid in understanding for those
readers who do not have experience in systems studies or in the devel—
opment and use of simulation models. Four important topics will be
covered. First, some essential systems concepts will be presented;
these form the basis for the entire approach used in this thesis.
Second, modeling will be discussed in terms of the steps in model
development, alternative modeling approaches, and useful diagrammatic
conventions. Third, the idea of simulation will be briefly explained.
Finally, simulation models will be examined from the point of view of
the limitations and capabilities of different uses. This chapter will
not be necessary for those having a systems background, or those with
previous experience in simulation modeling.

What is the rationale for using the "systems approach" in studying
a beef cattle enterprise? The systems approach to problem solving is
a general technique of analyzing needs to determine goals and evaluating
alternative ways of achieving the desired goals. It offers the manager
of an enterprise an opportunity to test management decisions to
increase profitability, as well as the initial planning on which an
investment is based. Although systems as an organized science is
relatively new, the techniques and methods are drawn from the basic
engineering disciplines. Systems studies and methods were first used
in the aerospace industry because of the very complex problems typically
encountered: the Apollo project is a notable example. During the

19603 business applications started as manufacturers realized that

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complicated production and inventory problems could be analyzed and
solved using a systems approach. In more recent years the scope of
systems studies has broadened rapidly. Extensions to economic and
socio—economic systems, especially in large aggregate models, have
become common. Systems studies are also being applied to smaller
scale systems such as pest management and river ecology; these can
become extremely complex when the myriad of details formerly neglected
are included. The remainder of this chapter is devoted to building
the basic foundation for the systems analysis application of this

thesis.
II.1 Systems Concepts

This section will present some basic ideas and concepts of the
systems approach to problem solving. These are the philosophy on
which the methodology is based, the terminology most frequently used,
and common graphical methods of representing the behavior of the
system being analyzed. The Appendix to this thesis consists of a
specialized bibliography that should be consulted for a thorough

treatment of the material presented in this chapter.

 

The methodology of the systems approach is based on a philosophy
that views a problem globally, i.e., from the broadest possible
perspective. The problem can be either one of design of a new system
or of control of an existing system. To solve a problem one must first
define it, but defining a problem requires knowledge of what one is

attempting to accomplish. The desired goals of the problem must be

 

 

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translated into specific objectives that are to be accomplished.
Knowledge of these objectives is vitally important to successful
solution of the problem. These are found via a needs analysis
involving all participants in the problem. If there appear to be
several feasible ways to accomplish some of these objectives, then
one must select from among the alternatives. Tradeoffs among various
objectives must be resolved when they are in conflict. The designer,
the manager, and the ultimate user should all have an opportunity to
participate in assigning weights to the different objectives of the
problem. This definition and selection process is highly iterative.
The intent is to discover the solution which best meets the objectives,
not merely to find a solution. The systems approach to problem
solving is an organized methodology for developing specific problem
objectives from the desired goals, and using these objectives to
evaluate and select possible alternative solutions

Clarification of the terminology used in any discussion greatly
assists in the communication process. A number of words and phrases
have meanings specialized to systems science; these are defined below

along with an example in the context of a beef cattle enterprise.

1. System——a collection of components with some form of regular
interaction.
example——the beef cattle enterprise itself
2.

Causality—-the concept of identifying the cause and its
resulting effect, a cause precedes its effect in the
time sequence of events

 

 

 

10.

 

6

example-—a decrease in rainfall (the cause) resulting in a
slowdown in forage growth rates (the effect)

Input variables—-variable consciously brought into the system
to affect its behavior

example—~feed crop purchases for use as cattle feed

Output variables——those variables which represent the
result of the system's operation and of the input
variables.

example--animal sales to the market

Component—~an identifiable grouping of relationships between
input and output variables.

example——forage growth and removal through grazing

Controllable inputs—~inputs to the system that are con-
trollable by some policy action.

example—-purchases of feed grains

Uncontrollable inputs—~those desired inputs to a system
which cannot be controlled.

example-~amount of water naturally available on a pasture

Exogenous inputs-—those inputs to the system as a result of
the system operating within an environment with
influences on the system.

example——cattle prices

System parameters-—particular values affecting the operation
of the system through its structure.

example—-basic photosynthetic efficiency of forage species
Transient—~the time behavior of the outputs which result

from zero level control inputs, commonly transient
behavior decays toward zero with time.

example—~changing age distribution of the breeding herd when
culling is stopped

 

 

 

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ll. Steady state—~the output variable behavior after all transient
effects have died away

example-—the final age distribution of the breeding herd
after changing effects are eliminated.

12. Asymptote-—the limiting value toward which a sequence of
numbers approaches.

example-—the total births of a calving season toward which
the accumulated number of births approaches over time

13. Stochastic variable--a family of random variables, the
elements of which are functions of some other variable,
commonly time.

example—-month1y rainfall as a function of time of year
This list of terms is by no means exhaustive, but it does cover the
major terminology that will be encountered in this thesis.

Graphical representations are frequently more easily understood
than verbal descriptions. Systems diagrams take advantage of this
perceptual characteristic of humans to present very concise systems
representations. The following diagrams are general ones outlining

in diagrammatic form the terms defined above.

11.2 Modeling

Modeling is the process of developing a mathematical description
0f the interrelationships between the input and output variables of
the system. The model is the resulting description. To model an
Object or a process, whatever its nature, requires one to specify the
most important of that which is known about it. Not uncommonly,

several variables are known to be important, but the exact relationships

 

 

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are unclear. The modeling process can be very helpful simply by forcing
oneself to be specific about ideas not usually articulated clearly.

Much greater understanding of a process can be gained by those who
attempt to model it because they are required to integrate together

all known features. This section will present steps of model develop-
ment, validation of the model, various approaches to modeling itself,

and some diagrammatic conventions. Only models using mathematical
equations will be included in this discussion because that is the type
used in this thesis.

An all important first step in model development is concept
selection. What is the concept we wish to model? Different concepts
of the same object or process are possible depending upon the view
point of the modeler. For example, consider the process of forage
Plant growth. All concepts of this process must interrelate the
exogenous inputs of weather to the outputs of plant growth. One
concept of this process could take a mass and energy balance approach
using the requirements of growth: solar radiation, carbon dioxide,
water, and soil nutrients. This would require development of math—
ematical relationships for root uptake of fluids, photosynthesis,
resPiration, and transpiration. Another concept could take a less
fundamental view by using experimental observations to allocate the
energy intake from solar radiation to growth depending upon the relative
"productive quality" of water, temperature, and soil conditions. A

model based on the first of these concepts would be able to examine

 

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certain aspects better than the second, but by being more comprehensive
it would be harder to develop. It would be more likely to run up
against the unknown in the biochemistry of growth. These two concepts
of plant growth would be used for different types of investigations
requiring different levels of detail of the process. If a highly
detailed model is desired, but the data to provide parameter values
and variable relationships is unavailable, then the structure of the
detailed model can be developed using crude working guesses until
better information can be incorporated into the model. Selection of
the concept, then, is important for it should be compatible with the
use of the overall model one is developing.

Once the concept has been selected, then the model itself must
be developed. Here one must be careful to include variables and
relationships which are relevant; one should exclude variables and
relationships which are irrelevant. Both are equally important. The
reason for this is simply that time and energy can be saved by excluding
variables and relationships which have no direct bearing on the process
being modeled. For example, in a model of the forage growth process,
solar radiation, temperature, rainfall, and soil nutrients are important.
Relative humidity has some effect on transpiration, but in the overall
process of growth it is relatively unimportant and may be excluded.
Relative humidity is irrelevant in this case. Variables and relation—

ships which are pertinent should be included; in general, those not

Pertinent should be excluded from a model.

 

 

 

 

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A common discovery in models composed of a number of components
is that the individual components may be known rather precisely, but
the interactions between them are indistinct. This is partly a result
of increasing specialization in research, and partly from an inability
of human beings to grasp the whole picture of what is happening in a
large and complicated process. Fortunately, the use of the systems
approach in multidisciplinary applications has alerted a number of
people to this tendency in research, and one can hope that these gaps
are soon eliminated.

A basic decision to be made early in the model development
process is whether the model will be broken up into components or
developed in its totality. From a mathematical and computational
viewpoint it would be better for the entire model to be developed at
once. This is not the usual method. Most frequently a model can be,
and is, divided into separate components with each component developed
separately. The component model interactions can be remembered easily
with the aid of diagrams such as Figure 2.2. An advantage to component
development is that concept selection is easier for a less comprehensive
process. Other advantages are the ability to use component models
developed elsewhere, and the ability to test the model much sooner than
if the entire model were developed at once. The last reason is
particularly important in validation of the model. The model developed
in this thesis follows the component organization pattern.

Validation of the completed model is one of the most important

steps in its development. Validation is the basic process of verifying

 

 

that the
describe
correct,
Federal
logical
able tc

data in

 

be gal
iaiorn
oi the
as th
regal
when

the ‘

iii

 

 

 

12

that the model correctly represents the real world it attempts to
describe. One can never be fully satisfied that the model is totally
correct, but use and experience with the model can bring confidence.
Generally validation can be assured by checking that the model is
logically consistent, follows intuitively obvious patterns, and is

able to track historical data. In many instances there is no historical
data to track, however, and confidence in a model's validity can only

be gained with use. When the model is of an existing system of which
information can be gathered, then a model can be validated by prediction

of the future. This approach works well in business management models

 

as the system--the business-~is monitored frequently, and data is

regularly collected. Confidence in the validity of the model is gained

when the model and the real world agree. When they do not agree then

the model can be improved by using this newly recorded historical

information. Only when a model has passed the validation stage should

it be considered an adequate description of the system it represents.

Two final steps in the model development process are sensitivity

testing and stability analysis. In some senses these are both means

of checking the validity of a model, but they go beyond merely that. /
Stability analysis and sensitivity testing are procedures whereby l
individual and groups of model parameters are adjusted and the model

outputs observed. Sensitivity of a parameter is said to exist when
small changes in the parameter are followed by large changes in the

output variables. In the sense of validity testing the model behavior

 

    

 

should mad
world is ‘
taooot he
very used
heusitiv
ol the s
parameto
of a mo
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the

 

13
should match the real world. In many cases, the parameter in the real
world is unknown, so the knowledge that it is sensitive in the model
cannot be used to validate the model directly. This information is
very useful, however, in directing the research going on in this area.
Sensitivity of a parameter indicates its importance in the operation
of the system; if past and present research have overlooked this
parameter, then redirection of efforts should be beneficial. Stability
of a model or a particular parameter set is said to exist if transient
fluctuations induced by sudden input changes diminish, so the model
outputs adjust to a steady state. This aspect is particularly important
in designing systems or in determining policies for controlling
existing systems; undamped oscillations are usually very undesirable
behavior. As an example, excessive seasonal fluctuations in herd size
would be undesirable. As with formal validity testing, the information
gained in sensitivity testing and stability analysis is used to verify
that the model is correct or to improve the model.

There are several approaches to modeling that can be selected by
the modeler depending upon the system and the intended use of the model.
A major characterization of a model is whether it is static or dynamic.
A static model is one in which time plays no role; the model only
describes variable interrelationships at one instant in time. For
example, a static model is the optimization of crop sales and purchases
for feeding uses at crop harvest time. A dynamic model includes time;
variables may change their values from one instant to another. Even the

relations between variables can change with passing time. An example

 

 

 

 

i
[ of a W

. . and new

i.
o
l a
a

for mode
essentie
of the ‘
variahl
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the e
the a

rep:

seal

 

 

 

14
of a dynamic model is the relation between quantity of feed consumed
and amount of weight gained in growing cattle. Another classification
for models is "black box" versus structural. "Black box" models
essentially deal with input and output variables; the inner workings
of the real world process are useful only as a guide in selection of
variables to use. This approach can only work if historical data are
available from which input/output relationships can be determined, for
example by regression analysis. Structural modeling derives its name
from models which incorporate the structure of the real world. Structural
modeling is more complex than "black box" modeling, because frequently
the exact structure is unknown. Nevertheless, structural modeling is
the approach used when feasible because greater confidence in the model's
representation of the real world exists.

No model will ever be perfectly representative of the process it
seeks to describe. Man's knowledge of the world is too limited for
that to occur. Even the totality of man's understanding may not, and
probably will not, be included in a model. There is simply too much
information to use, and the relation of the parts to the whole are
indistinct. One must always work with models that are imperfect in
some way. As human understanding grows and is incorporated into
models, they will perform better and have fewer shortcomings. Even
imperfect models are still valuable because they are so much better
than no model at all. This last point bears repeating; generally

models are so much better than no model that the imperfections are

 

 

 

 

 

15

gladly tolerated. Decisions based on use of a model will be very
useful and correct provided the limitations and imperfections of the
model are recognized.

Decision making is a process which involves uncertainty. This
uncertainty arises from lack of understanding of the process in
question, sampling errors in the data collected to represent the real
world, and the presence of stochastic variables. Imperfect models
are a result of this lack of understanding of the process, or perhaps
conscious exclusion of factors thought to be irrelevant. Proper
qualification of the predictions of models, and experience in using a
model should reduce the uncertainty due to model imperfection. This
still leaves the basic sources of uncertainty in decision making.
These can be partially overcome by certain statistical methods (Monte
Carlo usage of modelsl), but never completely eliminated. In short,
decision making will remain risky.

Modeling is greatly assisted by graphical aids that present
concise visual representations of the interrelationships among

variables. The human eye can readily discern the multiple interactions

 

between variables in graphical form; whereas it is much more difficult
to observe these relationships in a series of mathematical equations.

M

l. Hahn, G.J., "Sample Sizes for Monte Carlo Simulation", IEEE
Transactions on Systems, Man, and Cybernetics, No. 1972, pp. 678—680.

 

 

I|\

 

 

——§D—*

(l)

(1)

[dt

.2.
dt

(1) + (3)
+
(2)
(l) (3)
Th
(2)
(1) (3)
d
(2)

(2)

(2)

l6

 

add quantity (1) to quantity
(2) to get quantity (3)

multiply quantity (1) by
quantity (2) to get (3)

divide the numerator (l) by
the denominator (2) to get
quantity (3)

integrate quantity (1) to
get quantity (2)

differentiate quantity (1)
to get quantity (2)

take the value of quantity
(1) to use at location A

Figure 2.3 Block diagram symbols for mathematical operations

ll.l Simulat

Develops:
is an extrenn
first step.
step. is tl

in finding :

 

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17

11.3 Simulation
Development of a model as a mathematical description of a system
is an extremely useful and beneficial undertaking, but it is only the
first step. Solving the equations that make up the model is the next
step. As the size and complexity of models increase, the difficulties
in finding a solution become greater. While several possible methods
are theoretically available for determining a solution, the one se—
lected is nearly always closely related to the size of the problem.
Models that are amenable to analytic solution are generally very
small; for this reason modeling was not a very well-developed study
before the introduction of the modern digital computer. Simulation
is a particular method of solution for a model which employs the
computer.

A simulation model is a further abstraction from the real world,
beyond a mathematical model, because certain approximations have to
be made to make the mathematical model solvable. The most important
approximation is one dealing with the time dynamics of a model. The
infinite number of points lying between the starting and stopping
times would present an impossible task if each were to be solved. A
simulation model uses discrete time instances to approximate the con—
tinuous time which actually exists. Using discrete instances in time
makes the number of points where the model is to be solved finite,
and thus open to reasonable computation. Simulation, because of its
ability to easily handle time dynamics, is the method of model
solution frequently chosen when a model includes time.

The use of discrete time in place of continuous time is an

approximation that inevitably introduces error into the solution that

 

 

 

 

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of deenea
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as is ea:
tnadeoif
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lllus

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18

is obtained. The size of this error is generally a decreasing function

of decreasing step size (the interval between time points used). The
mmmer of steps required is inversely proportional to the step size,

as is easily shown. The modeler is then confronted with a classic
tradeoff; a tradeoff between simulation error and cost of running the
model. There is no best step size to use, as a widespread rule of
thumb calls for the smallest step size the project budget can afford.
Another criterion frequently used employs the information obtained
from running the model with successively smaller step sizes until an
asymptote is reached for an important output variable. By assuming
that the asymptote value is correct, one can choose the step size
giving a value within the desired range of error. The following figure

illustrates this idea.

 

 

 

ouigut range of permitted
variable error
value __________-____-_______
J metote
~----°——o—-—--—-—--—--——-'---

o o ‘

| O

| O

I o

I O

I

I

l

i

l

l

l

I

I

l

maximum Simulation Step Size
step size

Figure 2.4 Relation between simulation step size and simulation
error

 

 

 

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dump a
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l9

Simulation offers an advantage as a method of model solution
because it is able to utilize the organization pattern of computer
programming. A program is the main section of instructions directing
the computer to perform specific operations. A subroutine is a sec—
ondary section called from the main program. Simulation can be
handled as a program with subroutines as components. Changes in
component models then mean changes in the subroutine simulation
models. A model can be made operational rather quickly by inserting
dummy subroutines that have the proper interaction and connections,
but which may not actually perform any calculations or have a mean—
ingful effect. Debugging of each individual subroutine is much easier

than would be debugging for one single program model. This advantage
is another practical reason that the model development process uses
component models more often than large integrated models.

Simulation is then, first of all, a method of determining a
solution to the mathematical model. In practice, a simulation model
is a further abstraction from reality because it makes approximations
that need not be made in the mathematical model. There are tradeoffs
to be evaluated and made, mainly between simulation—induced error
and cost of running the model. The advantages of component models
in reducing the debugging time required are an asset to simulation.
Finally, simulation is an extremely valuable technique for developing

solutions to models possessing time dynamics.

II.4 Uses of Simulation Models
Simulation models can be used in a wide variety of ways.

Important among them are testing specific cases, running "best versus

 

 

 

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Emotions.
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20

worst” cases, Monte Carlo applications, and optimization of objective
functions. The goals of the user, the available budget, and the char—
acteristics of a particular use are all important elements in selection
from among these. This section will discuss alternative uses, the
decision criteria for choosing among them and the limitations, capa-
bilities, and costs of each. Costs will be viewed primarily in terms
of the number of simulation runs required for that use.

A fundamental use of simulation models is testing alternative
parameter and input variable values to determine the outcome. This
use allows a very creative interaction between decision makers and
the model as they are able to test various ideas and intuitions. A
major benefit that occurs is the learning experience on the part of
the decision maker as he gains a better feeling for how the system
works. The ability to interact with the model, learn from previous
trials, and try new values not previously felt helpful is very valu—
able. In this use the simulation model functions as a tool of the

decision maker, extending his ability to evaluate the outcome of

 

particular policies.
An example of this use of simulation models can be found in a

model of cattle grazing on natural pasture. A management policy over

 

stocking rates is necessary to maximize the effective use of forage
growth. A ranch manager can experiment with different stocking rates,
and evaluate their effectiveness by using the weight gain of the cattle
at the end of the season as the desired output variable. The manager
can gain a better understanding of the grazing process by using the
simulation model to test his intuition and the traditional methods of

grazing control.

 

This
he cost 1'
case. A 1
says very
nandononen
rated in
not soil
on cont
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that
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in t’
the

151

 

 

21

This first use of simulation models is extremely easy to organize.
The cost is quite low, since only one run is required for each test
case. A limitation is that a single run of a deterministic model
says very little about the likelihood of that outcome if there is any
randomness in the real world system. If randomness has been incorpo—
rated into the model to reflect the real world, then a single run is
not sufficient to allow choice between alternative values of parameters
or control variables. An additional limitation is that one may be
uncertain how to go about modifying the choice of control variables
to improve upon the outcomes of a previous run.

Perhaps the easiest way of dealing with aspects of randomness
in a simulation model is to devise the worst and best cases of inputs
that could be encountered. By running the model with these two cases,
one can determine bounds on the outcomes that should not be exceeded
in the real world system. All other outcomes will be contained within
the "envelope" determined by the best and worst cases. This method
is only slightly more difficult to use than the first. A limitation
is that ”best and worst" cases may be difficult to determine, espe-
cially when there are multiple sources of randomness in the real world

system. Another limitation is that one still does not know the most

 

likely outcome, only the bounds on the outcomes. Costs are quite low
for this use of simulation models, since only two runs are required
to evaluate each parameter or input variable desired.

A much better method of dealing with randomness in the model is
using the simulation model in a Monte Carlo mode. This requires that
the probability distributions of each source of randomness be known;

Perhaps a difficult requirement to meet. A run of the simulation model

 

 

 

ls nade oi
each stool
corded.
again did
liter a
tisties
naniaoc
he used
on part
tion on
sequin
cost

iteqn

SW

VET

 

22

is made with particular values drawn from properly random sources for
each stochastic variable. All output variables of interest are re-
corded. Another run is made with a new set of random variables,
again drawn from the proper distributions, and the outputs recorded.
After a sufficiently large number of runs have been made, the sta—
tistics of the outcomes can be computed with confidence. Mean and
variance would be the most important. These computed statistics can
be used to develOp the confidence intervals of the ponicy variable
or parameter under study. The major difficulty with using a simula—
tion model in a Monte Carlo mode is the large number of simulations
required to properly determine the statistics of the outcome. The
cost of Monte Carlo analysis for very large simulation models is
frequently so high as to be prohibitive.

The final category of simulation rodel use is optimization of
specified parameters or control variables. This method can provide
very beneficial results when an objective function can be specified
for minimization or maximization. Optimization is very important in
design of new systems. In problems of management policy or control
optimization of those policies, the optimized values should result
in the best system operation possible. A major difficulty with
optimization of simulation models is the large number of simulation
runs required: the same difficulty with Monte Carlo analysis. The
cost of the required runs may preclude use of optimization. Another
limitation of optimization in simulation models involves models that
have unspecified or arbitrary exogenous inputs. Specification of that

input allows optimization to be performed, but the values obtained

 

 

 

 

as optimal
mother v1
optimal a
The
in decid
let us I
ohjecti‘
pith a
nainial
the co
and ti

study

about
cons
and
the

lion

23

as optimal are conditional on the specific exogenous input used. If
another value is encountered, then the "optimal policies" may not be
optimal at all.

The objectives of the system study are the most important aspect
in deciding which way a simulation model is to be used. For example,
let us reconsider the cattle ranch possessing natural pasture. One
objective could be to determine the most likely weight gain of cattle,
with a specified stocking rate subject to the stochastic variables of
rainfall and temperature which influence plant growth. A third objec-
tive could be to optimize total revenue by controlling stocking rate
and timing of animal sales. Each of these three objectives of a
study w0uld use the same simulation model, but in different ways.

Cost is an important factor to consider when making the decision
about the way a simulation model is to be used. It should also be
considered from the start of the entire modeling process, as the form
and content of the model should be guided by the ultimate goals of
the system study. If an objective can only be achieved by use of
Monte Carlo analysis, for example, and the budget is tight, then the
content of the model, or sometimes its depth, can be altered. An idea
to keep in mind throughout is the relationship between the cost of the

entire system study and the benefits obtained from it.

11.5 Summary

This chapter has discussed the systems approach to problem
solving, some topics of systems science, and simulation models. A
review of the systems approach is, once again, an organized methodology

of problem solving that seeks to achieve the ultimate problem goal by

 

 

 

 

 

selection
from the
objects n
ships am
soteessl
sion mal
problem
approan
develo
result
tions

tech

and
read
det

50lll

24

selection of a solution which best meets specific objectives derived
from the goal. A systems approach works best where the process and
objects under study are well enough known that mathematical relation-
ships among variables can be specified. Another requirement for
successful application of the systems approach is that adequate deci—
sion making power exist to carry out the solution, whether it is a
problem of planning (design) or of management (control). The systems
approach utilizing simulation models is not perfect. The models
developed for the system under study can never be made perfect. The
results they predict must be viewed with an eye to their imperfec—
tions. On balance, however, the systems approach is a valuable
technique for analyzing problems and developing solutions to them.

By necessity the coverage of this chapter has been very rapid
and it has only touched upon the high points of these topics. If the
reader is interested in pursuing these subject areas in greater
detail, then the references listed in the Appendix are an excellent

source of introductory information.

 

 

e

lots

stun
l

ranch

M
T

ol the p
of the 5
Ill 1

 

 

CHAPTER III

THE PROBLEM STATEMENT

This chapter will present four topics: the general description
of the problem, a review of the literature, a rationale for selection

of the simulation method, and the detailed problem statement.

III.1 General Description of the Problem

This thesis is a study of a beef cattle enterprise: a farm or
ranch operation involving the breeding, growing, and selling of
cattle for slaughter. There has been a steady historical progression
of specialization in the industry to either breeding or fattening.
Moreover, the availability of low—cost grains, chiefly corn, has led
the fattening operation to lose its requirement of a land base. Feed
lots are the result. Management of such feed lots has been extensively
studied in recent years. The cow/calf operation, which is important
in the production of feeder calves, has received little attention.
The exception to this rule has been better weight gaining charac—
teristics. The current depression in the beef cattle industry, due
to both low cattle prices and the world food supply problem, is caus—
ing rethinking about the organization and methods of operation of
the entire cattle industry.

This thesis concentrates its attention on a specific type of
beef cattle enterprise: one which is characterized by a land—

extensive cow/calf organization. Further, this operation is

25

 

 

 

 

to he small en
its purchases
he scale of
methods of 51
individual e
lot this ope
This t?
nanagementd
received es
individual
ilcieucy h
thesis vii
tion of 1
0r produc
this the:
bleeding
Pat

is so a
dition;
Pledie
alumina

0f the

hunth

 

 

26

to be small enough to have no market effect from either its sales or
its purchases. That is, prices remain unchanged by its activities.
The scale of operation is sufficiently large, however, that the
methods of systems and simulation can be profitably applied to this
individual enterprise. Rough bounds on the number of breeding cows
for this operation might be 50 to 1,000 animals.

This thesis also concentrates on particular questions of
management of therenterprise. Management is an area that has not
received extensive study at the scale of the overall system operation.
Individual aspects of production and certain forms of production ef-
ficiency have received the bulk of the analysis here to date. This
thesis will not make any analysis in the areas of genetics, alloca—
tion of land to alternative uses, by—product or destination marketing,
or production of crops (except grazing forages). The emphasis of
this thesis is on Study of management policy in the areas of grazing,
breeding, timing of sales, and general herd management.

Part of the reason why study of the management of this enterprise
is so attractive is the general low level of mathematics used in trar
ditional practices. A major problem in the past has been a lack of
Predictive capability. Extrapolation of past trends has been a
dominant method employed. This is not sufficient when the dynamics
of the beef production process have delays approaching two years.
Another problem has been uncoordinated analysis of "separate" aspects
0f Production, rather than an integrated analysis of the whole. This

tendency has lead to dominance of certain types of emphasis, such as

 

 

 

 

 

 

genetic ma
of husbanr‘
tore typir
are pastt
'rrg leve‘
rrrket c
of these

perform

111.2

 

27

genetic manipulation. A general characteristic has been the dominance
of husbandry practices and recommendations over economic considerations.
Some typical problems unanswered by traditional management practices

are pasture management to maximize efficient forage use, proper feed-
ing levels to improve net profit, and the proper response to changing
market conditions. This thesis seeks to contribute to the solution

of these past problems and to increase the level of management

performance.

III.2 Review of the Literature

An extensive literature discussing the beef cattle enterprise
exists. Much of it is characterized as non-quantitative explanations
of various subprocesses and reports of experimental observations. To
a large degree, this literature is spread among variOus specialized
disciplines such as animal nutrition, genetics, crop sciences, agri—
cultural economics, and physiology. Relatively few studies have
viewed the beef cattle enterprise as a system and rigorously ana—
lyzed it from the systems science point of view. The quantitative
studies which do exist have taken three broadly distinct approaches;
namely, analytics, optimizing, and simulation. Of these, only a
minority use the simulation approach; the one seeming to offer the
most potential for significant gain in this complicated, involved
Process of beef production by individual enterprises.

The remainder of this section will review the previous work
in the area of mathematical representation of, and management control

over, beef cattle enterprises. The three approaches of analytics,

 

 

 

 

 

optimizati

unit, alt}

M
iii?
studies
limited
some at
trtoriz

ships 1

new tr
respo
procr
rati
fror
exa

rat

28
optimization, and simulation will each be discussed as a separate

unit, although there is some overlap between them.

The Analytic Approach

While a strict definition for analytic would include all of the
studies referenced here, the term is used to describe those which are
limited to functional representations between variables. There are
some areas in which the analytic approach has been most prevalent:
tutorial papers, analysis of data to determine values for relation—
ships between variables, and attempts to offer advice to management.

Representative of tutorial papers designed to present material
new to the readership are development of general crop and livestock
response functions[12], traditional descriptions of the cattle growth
process[5], and the use of marginal analysis to optimize feedlot
rations[4]. Uses of analytics to develop mathematical relationships
from experimental data are too numerous to mention in detail. Several
examples will serve as illustrations: algebraic growth models from
cattle age-weight data[6], comparison of calving performance between
drylot and pasture[37], and comparison of traditional versus modern
range practices in Argentina[l3]. Carpenter's paper[9], developing
an algebraic growth model, is typical of analytic means of offering
advice to management over questions in the production process.

The simple analytic approach to studies of the production process
is inadequate for such complicated systems as this enterprise. While
the analytic approach is not used appropriately in studies of the
overall enterprise, it does continue to have value in determining the

relationships between variables from experimental data.

Mali}
is 3 1

[or the la
red uoulir
he usual
detemini
return ir
used a s
ruu size
Suhuablt
uf resu
Th

have er
method
ire d

be 1i
tiue.
prov

dung

tiu

the

 

29

The Optimization Approach

As a general technique, optimization has been extensively used
for the last three decades. Linear programming, dynamic programming,
and nonlinear programming are some important methods of optimization.
The usual agricultural application of these techniques has been in
determining the best combination of feed inputs to maximize economic

return in beef cattle feedlots[29,53]. Long, et al.,[33,34,35] have

 

used a simulation model in an optimizing mode to study the effect of
cow size on productive efficiency in drylot and pasture operations.

Schwab[49] has used linear programming to optimize the entire range

of resources used in a cow/calf operation.

The majority of applications of optimization in beef production
have employed linear programming as the optimization technique. This
method has certain restrictions which limit its usefulness in study-
ing dynamic processes. Linear programming requires that the variables
be linearly related, and that the relationships not be functions of
time. A model that can be optimized using linear programming cannot
provide an adequate description of the population and reproduction
dynamics of a breeding cattle herd.

All optimization algorithms possess some type of objective func—
tion that is either maximized or minimized. While there is no doubt
that the optimized variables are optimal for that objective function,
there is doubt that the objective function correctly specifies what
an enterprise manager wants optimized. For example, an important
characteristic to some managers might be a flexibility of operation
Which allows some room to maneuver if expected conditions do not mater-

ialize. An objective function cannot measure an operations flexibility.

 

 

 

hdirionall
hat are at
huot a m

problems i

he Simul

Sim
rudeis.
is ireqr
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tart]

 

30

Additionally, the usual methods have trouble with exogenous variables
that are arbitrary or stochastic. For these reasons, optimization
is not a method of analysis which provides a way of solving all of the

problems facing an enterprise manager.

The Simulation Approach

Simulation is a method for developing solutions to mathematical
models. Because of its ability to handle time dynamics, simulation
is frequently used where time is an explicit part of the problem.
The majority of uses of the simulation approach in beef cattle studies
have been macroeconomic in scale. Initiation of economic development
by using the cattle industry[26,3l,42,43] and government policy anal—
ysis in the agricultural sector are well represented in the literature.
The World Bank has used this approach for several years in evaluating
the potential value of economic development projects concerning the
cattle industry[10].

Simulation of beef cattle at the enterprise level is beginning
to appear more frequently in the literature. A pioneering work by
Halter and Dean[23,24] studying management in an integrated range/
feedlot operation appeared in 1965. Cartwright and Long of Texas A&M
University have participated in a number of works which concentrate
0n questions of cow phenotype optimization using a simulation model
of cattle energy requirements[28,33,34,361. Witz[54] has applied
Simulation to the feedlot ration optimization problem, while Afzal[l]
has studied inventory modeling to respond to drought conditions. Many
more references could be cited, but these serve as illustrations of

the aspects of a beef cattle enterprise that been studied using the

 

 

 

simulation

purrogrart

111.3 Rat
This
abeef ca
the great
process ;
acterist
the sion

in the
tion tr
hot on

a turd
intake

Feed

ture

a up

of e‘

the

the

31

simulation approach. Joandetl has recently published an extensive

bibliography of simulation applications involving beef cattle production.

III.3 Rationale for Selecting the System Simulation Approach

This thesis will use the system simulation approach in analyzing
a beef cattle enterprise. Simulation was selected because it offers
the greatest potential for understanding and solving the model of the
process as involved as production of beef cattle. What are the char-
acteristics of the enterprise that are so troublesome as to require
the simulation approach? Most important are the time delays inherent
in the growth process. In the U. S. the time required from concep—
tion to marketing for slaughter animals may range from 11-30 months.
Not only are time delays present, but the length of these delays is
a variable which is partially under the control of management. Feed
intake rates are an important control variable affecting growth rates.
Feed intake also governs the reproductive characteristics of both ma-
ture cows and grOWing heifer replacements. Reproduction, then, is also

a dynamic process. In short, the entire herd population is in a state

 

of dynamic flux. Herd population dynamics is a major complexity of
the beef cattle enterprise requiring the power of the simulation approach.

A similar source of complexity is the decision making that controls

 

the enterprise's sales and purchases. Decisions involving breeding,
because of the delay length in the growth process, will not affect

sales revenue for nearly a year. The proper price to use in decision
________________________'___

lJoandet, G. E., and T. C. Cartwright, "Modeling Beef Production
Systems," Journal of Animal Science, Vol. 41, No. 4, 1975, pp.1238—46.

 

 

“king is that
hmagememt der
hat are to 0
tipated saleE
decision makl
his implies
the beef prr
is another
Other
tions of it
into more ‘
gregated t
applicable
ies of th
times are
thermore
“limit
section

“'11 st

111.4

an em
breed

POrtj

emti

 

32

making is that which will be in force when the product is sold.
Management decisions are conditional on the stream of expected prices
that are to occur over the interval between the present and the anti—
cipated sales date. To further add to the trouble of the enterprise
decision maker is the well known volatility of agricultural prices.
This implies that price expectations change rapidly. Control over
the beef production process is very complicated and uncertain; this
is another powerful impetus toward using the simulation approach.
Other studies of beef cattle have developed partial representa-
tions of the production process as a way of decomposing the system
into more manageable pieces. These studies cannot, however, be ag-
gregated together to form proper recommendations that are generally
applicable. While simulation of the production and management dynam—
ics of the enterprise is possible, it is not easy. Very long lead
times are required to model and then simulate these processes. Fur-
thermore, simulation models can never be perfect because of the
approximations necessary to determine the solution. The following
section will describe in detail the exact problem that this thesis

will study.

III.4 Detailed Problem Statement

The system to be analyzed here is a beef cattle enterprise. Such
an enterprise can be characterized as being land extensive, involving
breeding of cows for calf production, and producing a significant pro—
portion of the nutrient requirements of the herd through forage growth.
It is of such a scale that it can be treated as an atomistic economic

entity.

 

 

 

 

The prr
distinct gr
his thesis
itself. T1
spsten: ca
rndnutrie
managemen
mamagemer

prior in

manager
of exogn
tapabil

and in

are de
thhtrn

grege

the
act
tie

tin

33

The problem addressed by this thesis is the construction of two
distinct groups of components of this beef cattle enterprise. First,
this thesis develops a dynamic simulation model of the enterprise
itself. This includes models for the f0ur major components of the
system: cattle demographics, forage growth, feed stock accounting,
and nutrient impacts. Second, this thesis develops an interactive
management algorithm which allows the user to investigate very detailed
management control policies for ongoing operational decision making
or for investment planning. This algorithm is structured so that the
manager can evaluate alternative strategies to cope with the effects
of exogenous variables on the enterprise. Three examples of the
capability of the model to assist decision making for ongoing decisions
and investment planning are presented.

The simulation models of the four components of the enterprise
are designed to be useful in analyzing various management policies to
control the cattle herd and related processes. This requires disag—
gregation to a level such that the herd can be controlled as discrete—
ly by the user as could the manager himself. This also requires that
the control variables of the model be devised so that a manager's
actions can be simulated. Since a major weakness of previous simula-
tion models of beef production enterprises has been a lack of popula—
tion dynamicsz, and since these are required to correctly evaluate
some herd control policies, the demographic model fully develops herd
Population dynamics. Introduction of herd population dynamics requires
that cattle nutrition and reproduction dynamics3 be included to
————__.____~____i____.___

2Ibid., p. 1243.

Developed by Margaret Schuette in partial fulfillment of M. S.
requirements, Department of Animal Husbandry, Michigan State University.

 

 

attentively a“
promth and fee
magement con
sent decision
represent an
enterprise tn
time. Sever
nun-physical
component t
and other e
The no
stem from
cesses oi
ponemt mo
lanp cont
thereby
This Tar
variable
because

them, 3‘

 

This in
renal
been
an in
l Waj
“hit

the

 

 

34

effectively and correctly describe births and deaths. The forage

growth and feed stock components are constructed with the appropriate
management control variables to allow the entire spectrum of manage-
ment decision making to be exercised. These four component models
represent an adequate description of the physical processes of the
enterprise to allow realistic simulation of the system behavior through
time. Several secondary components are developed to accomodate the
non-physical aspects of the enterprise; an example is the financial
component that determines the financial effect of purchases, sales,

and other activities.

The management algorithm has certain unusual requirements which
stem from the nature of the simulation models of the physical pro—
cesses of the enterprise. As an example, the cattle demography cone
ponent model maintains populations on a very disaggregated basis.
Many control variables must have the same level of aggregation,
thereby requiring many values to actually control herd populations.
This large number of effective control elements among a number of
variables has the effect of eliminating all optimization techniques
because of the extremely high cost of their use. Management control,
then, is exercised exogenously when certain decisions are required.
This necessitates an interactive control algorithm, but since the
usual source for computer interaction--the teletype--is ruled out
because of the large number of control elements that must be inputed,
an interactive batch mode of operation of the model has been devised.
A way to control the model's simulation thr0ugh time is developed
which allows stops and restarts of the simulation whenever required.

A beneficial feature of this interactive management algorithm is

 

 

 

 

was—ea...“ we .. .

that multil)1e
used as the b
algorithm reE
runs, inputir

decision to

The to
heel cattle
common to 1
model is t
puirement
trol varir
iluence t

minimum
aggregat
in theh
Specifi.
this sy
Tl
brieil

lust c

The

 

 

35

that multiple management policies can be evaluated, and the "best"
used as the base from which the simulation is restarted. Use of this
algorithm results in a time simulation which is a series of short
runs, inputing control variable values as required by the particular

decision to be made.

Specific Component Requirements

The four components representing the physical processes of the
beef cattle enterprise must meet certain requirements. A requirement
common to all is that each be dynamic, because a major element of the
model is the inclusion of time in an explicit manner. A second re—
quirement common to all is that the component models contain the con-
trol variables that allow the manager‘s decisions to direct and in—
fluence the physical processes of the components. A third common
requirement is that each model be constructed in a sufficiently dis—

aggregated faShion that a real manager's decisions can be simulated

 

in the behavior of the model. These general requirements and the
specific requirements outlined below must be met if the objectives of
this system simulation are to be realized.

The individual requirements of the component models will be
briefly summarized by listing the processes that each compenent model
must contain. The cattle demography component must contain:

(1) age, sex, and function disaggregation of the cattle herd,

(2) births, deaths, and transfers of herd members,

(3) birth rates a function of breeding activities,
(4) weights for each herd subpopulation grouping.
The forage growth component must include:

(1) plant growth as a function of exogenous weather variables,

 

 

 

(2) quart
whicl

(3) graz
(h) mach
(5) star
he nutrient

(1) del

The fun
deriven
that 1

realis

heats

Dome

cesr

 

36

(2) quantity and quality of forage disaggregated by land areas
which are homogeneous,

(3) grazing as a means of forage removal,
(A) mechanical harvesting as a means of forage removal,
(5) grazing consumption and wastage a function of stocking rates.

The nutrient impact component must include:

(1) determination of weight gains for herd subpopulations based
on the difference between energy consumption and maintenance
energy requirements,

(2) determination of the onset of estrOus cycling in young heifers
as influenced by nutrition from birth,

(3) dynamic energy requirements for mature cows as related to
reproductive condition, i.e., lactating, breeding, and
stage of gestation,

(4) determination of energy intake of cattle from multiple feed
sources with individual TDN characteristics.

The feed stock accounting component must include:

(1) accounting for current feed stock levels as a function of
purchases, sales, production, cattle feeding, and waste,

(2) feed stock losses from such sources as spoilage, handling,
waste, and pest contamination,

(3) determiantion of the feed stock TDN value for individual
feed stocks with particular rates of TDN decline over time.

The four physical components' requirements, as outlined above, are
derived from the basic intent of this thesis to develop a system model
that includes population dynamics, and that is capable of offering
realistic simulations that are useful to enterprise managers.

The management decision making component has two general require—
ments in addition to numerous specific ones. First, the decision
making algorithm must itself be dynamic to control the physical come
Ponent models which have included the dynamic elements of their pro-

cesses. Second, the component must include the correct control

 

variables to .
actual olerat
of the nuanagE
(1) timr
(l) sep

(3) tin
fen

These reqn
intent of
to invest
Changes :
The
infumat
Pauses
be email
(1
l

have

ramp

 

37

 

variables to allow evaluation of realistic strategies to cope with
actual operating conditions. The specific decision elements required
of the management algorithm are:

(l) timing and quantities of cattle sales and purchases,

(2) separate feeding rates for each herd subgrOup,

(3) timing and level of feed stock sales, purchases, cattle
feeding, and production,

(4) control over stocking rates in the individual land parcels,
(5) control over stocking rates for the individual herd subgroups,
(6) timing and level of mechanical harvesting of forage,

(7) control over the timing and degree of breeding, culling,
and weaning.

These requirements, both general and specific, stem from the stated

 

intent of this thesis to develop a simulation model that can be used
to investigate alternative strategies of management response to
changes in the environment in which the enterprise operates.

The decision maker must make specific decisions based on the
information that is known to him at the time. When the simulation
pauses for exogenous control inputs, the following criteria should
be available along with useful state variable values:

(1

V

accumulated cash flow to date,

(2

V

accumulated net profit to date,

(3

v

current levels of short and long term debt,

(4

V

current level of working capital on hand,

 

(5) production efficiency measures, such as the ratio of the
weight of cattle sold over the weight of feed used.

In addition to the requirements of each of the components that
have been discussed, the system model must accept certain exogenous

variables that have strong influence on the system. Three weather

 

 

variables-
nhst he 8‘
the produ
enterpris
to plant
vested n
tattle,
an mg
of unce
nanaget

aimed

ants
Chant
nat'n

the

38

variables~—solar radiation, average daily temperature, and rainfall-—
must be accepted because of their importance to forage growth. Since
the production and use of feed stocks is important in beef cattle
enterprises—-yet this modeling effort dOes not include the decision
to plant and harvest crops——the amount and quality of feed stocks har—
vested must be accepted as exogenous variables. Expected prices of
cattle, production resources needed, and feed stocks must be from

an exogenous source. These exogenous variables are the major source
of uncertainty in the operating environment of the enterprise; the
management strategies that the model will be able to evaluate are
aimed at perfecting responses to fluctuations in these variables.

The following chapter will describe in general terms the compon-
ents developed to meet the stated requirements of this chapter.
Chapter V will discuss these same components, but in the full mathe—
matical detail needed to completely understand how they operate and

the basis for their structure.

 

 

 

.1 an 0 .V l n. nu D. m . am pr.
3 TL t e l. at m I“ «l.
W D: 1 a 0
A» 2 mu. m m 9.
Wm. B» d 1 s
t m m h

 

 

CHAPTER IV

GENERAL DESCRIPTION OF THE MODEL

This chapter will provide a general description of the model
that was constructed to meet the requirements of the problem statement.
The processes that have been modeled and the variables used in the
model will be discussed for each of the components. The general orga—
nization of the model will also be reviewed. Chapter V will cover the
same material but in more explicit detail, by developing the mathe—
matical relationships that are implemented in the computer programs.
The present chapter will be limited to discussion of the modeling of

components in verbal terms.

IV.1 General Organization

Chapter III enumerated the four components of the system model
that represent the physical processes involved in a beef cattle enter—
prise; these are the cattle demography component, the forage growth
component, the feed stock component, and the nutrient impact component.
Further, the management decision making that controls the enterprise
constitutes another component. These are the five major components
of the enterprise system that will be covered in this thesis. A land
component, which would be required to fully investigate the entire
spectrum of possible enterprise operations, is not included here.

Figure 4.1 is a general system diagram illustrating the major physical

39

 

 

 

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41

and information flows among components. If also shows the transfers
of information and material across the system boundary.
The component with the most central impact is cattle demographics.
Three major processes are represented within this component. The
first is the birth of calves. This is a function of the breeding
policy of the manager, the age distribution of the mature cow herd,
and the nutrient intake of breedable females. The second major pro-
cess is the death of animals. Deaths are attributed to old age or to
premature events, such as disease or accident. The final process
that this component includes is maturation of animals within the herd.
Maturation will be described using the variables of age and weight.
Another important component is that of forage growth. This
Component must represent the growth and harvest of forages on a
dynamic basis; i.e., over the growing season. Plant growth is a
response to the exogenous variables of weather-—solar radiation,
average temperature, and rainfall. More important than actual rain-
fall is the level of soil moisture that is available for the root
SyStem to transport up to the leaf structure of the plant. Soil
moisture must be determined through the influence of evaporation and
Percolation of water down beyond an effective depth reachable by roots.
Digestibility of forage is another important factor in determining the
nutritional impact of grazing. Grazing and mechanical harvesting are

the methods of forage removal that are included in this forage growth

COmponent model.

Another component of the enterprise model includes feed stocks.

This aspect of the model is less complicated than any of the others,

 

 

 

hetanse re
various ft
determine
Feed sto<
ailocati
anong th
this met
this pa
ievei (
detern
stock.
syste-

this

on t
aniv
gro

nut

 

42

because relatively little is involved other than accounting for
various feed stock activities. Feed stock purchases and sales are
determined exogenously through the interactive management component.
Feed stocks used as cattle feed are a result of the level of feed
allocation to the herd and of the distribution of that allocation
among the possible crops. Feed stock losses are also determined in
this model. Crop production, although exogenously determined in

this particular system study, is also a factor affecting the overall
level of feed stocks. The last element of this component model is
determination of the total digestible nutrient (TDN) value of the feed
stock. TDN is used as the index of nutrient value because it is a
system of measurement which has been widely accepted for many years.
This long tenure means information in TDN is abundant.

The nutrient impact component develops the effects of feed inputs
on the cattle herd. The major processes included here are growth of
animals through weight gain and reproduction resulting in births. The
growth process is highly influenced by the quantity of digestible

nutrients consumed by cattle. The requirements of body maintenance

and of growth are met differently by the same feed input; this requires
that the energy values for Weight maintenance and weight gain be avail—

able for each feed stock consumed. When the requirements of body

maintenance are fulfilled, any excess energy intake can be applied

toward growth or toward other production processes. Reproduction is

quite responsive to energy levels available to the breeding females,

eSpecially in young heifers being brought into the breeding herd for

replacements.

The physical processes of estrous cycling in females,

 

 

 

 

 

 

huth nature 4
productive u
the control
selected to
Manage
this enterr
riding a n
rent is vc
of the he
the quest
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delays i
reprodu
and (3:

the re
exogev

ever

make

cont

Prov

val

 

 

43

th mature and immature, are determined in this component.1 The
oductive use of the reproductive condition of the herd is under

e control of the herd manager through the breeding policy that is
lected for use.

Management decision making constitutes the last component of

 

is enterprise model. Because this thesis is oriented toward pro-

ding a manager with a tool to improve his decisions, this compo—

nt is very important. The component is constructed as an expression
f the belief that optimization is not an appropriate approach for

he questions that this study attempts to address. The reasons for
his belief can be briefly summarized as follows: (1) the decisions
ontrolling the breeding action are highly dependent on the long time
klays before productive revenue is possible (2) herd management of
:eproductive animals is highly dependent on the future prices expected,
and (3) animal prices are unstable and highly volatile (especially in
the recent past). The substitute for optimization of decisions is
exogenous supply of control variable values. This means that when-
ever straightforward economic criteria cannot be explicity used to
make a decision, that the management component requires an input of
control values. The values used are up to the user. This technique
prevides an opportunity for the user to explore alternative control
values based on his intuition and knowledge of the behavior of the

system.

 

1Developed by Margaret Schuette in partial fulfillment of the
M. 8. requirements, Department of Animal Husbandry, Michigan State
University.

 

 

 

 

 

This
the enter}
live coup
physical
ration, T
cperatio

to prov:
discuss
variahi

of the

ill

svstr

the

devc

m

This section has briefly discussed the general organization of

e enterprise simulation model. The major processes modeled by the
ve components of the system model have been reviewed. The four
ysical components have been shown to involve cattle growth and matu—
tion, plant growth, feed value energetics, and feed crop usage. The
eration of the management component involves interaction of the user

provide control variable values. The following section will again
iscuss each component, but in a more formal sense, setting forth the
ariables used in the mathematical model of the component. The use

if these variables in the models will be explained.

IV.2 Specific components

This section will provide a description of the content of each
system component as it has been modeled. The major variables used,
the physical basis for the model, and the assumptions made in

developing the model will be discussed for each component model.

Cattle Demography Component

Development of the cattle demography component has been heavily
influenced by the requirement that population be maintained in a way
that disaggregates on the basis of sex, age, and function. This has
led the model to be constructed using nine cohorts to describe the
members of the herd. These are: (l) mature females, (2) replacement
heifers, (3) bred heifers, (4) mature bulls, (5) young bulls, (6)
steers, (7) male calves, (8) female calves, and (9) slaughter heifers.
Table 4.1 provides a more detailed explanation of the exact age/sex/

function disaggregation of these nine herd cohorts. The variable

 

 

 

 

 

 

not nea‘

with re

gregat:
number
at sut
cisio
descr
heifv
larg
in v

N
W

i

ii).

 

 

i(t) is the total population of cohort i. While this level of
ording herd population may seem quite detailed, in reality it is
nearly fine enough, as these groups do not behave homogeneously

h respect to growth and reproduction. Accordingly, further disag—

gation is provided by the variable SUBPOPi (t), which records the

j

er of animals in the jth subpopulation of cohort i. The number
subpopulations for each cohort varies with the homogeneity pre—
ion required. For example, the replacement heifer cohort must be
cribed rather exactly, since the onset of first estrous in these
ifers is an indicator of reproductive maturity. This requires a
rger number of subpopulations than does the slaughter heifer cohort
.which estrous cycling is of no interest. The variable KKi is the
fiber of subpopulations used for cohort i.

KK

i
IPi(t) = 3'21 SUBPOPij(t) (4.2.1)

Each subpopulation of a cohort assumes that the level of maturity
5 homogeneous for that group. Age and maturity are rather highly
arrelated in the typical operation in the U. S., but some variation
oes exist. This variation leads to characterization of maturation
s a distributed parameter process. The ages of individual members of
group having the same level of maturity are distributed around a
can. Some individuals are older than the mean, and some are younger.

"young"

e total length of time required for individuals to pass from
ature cows to "old" mature cows no longer breedable is also a dis—

ributed value. Thus, for mature cows (and for all the herd cohorts),

 

 

 

 

 

 

46

Table 4.1 Age and Sex Description of the

Cattle
Herd Cohorts

Cohort

male, 0—6

 

male 6—24

 

male, 24 month

(a) male animals

 

emale 0—6

6—2

 

24month x

 

(b) female animals

 

the n

vith

CESS

pron

equ

 

be delay time is a distributed parameter process. DELAYi(t) describes
he average length of time for individuals to pass through the range
f maturity that is represented by cohort i.

Flow rates of animals per year is a desirable way to describe
he movement of animals through the various cohorts and subpopulations
ithin cohorts. Inputs to delay processes and outputs from delay pro‘
cesses are easily visualized in this description. A distributed delay

process may be represented mathematically by a kCh order differential

equation:

k k-l
a 9_Xl£l + a 9———Z££l + ... + a y(t) = x(t) (4-2-2)
k dtk k-l dtk-l 0

where:
x(t) = the input rate
y(t) = the output rate
a1, a2, 33, ..., ak = constants.
The order of the equation, k, determines the nature of the response

for a particular delay time. The higher the value of k, the more

 

tightly clustered will be the distribution of individual delay times.
The value of k is a modeling parameter that is specified to most
closely simulate the actual parameter distribution as recorded by
experimental observation. Figure 4.2 illustrates the change in re—
‘sponse of different values of k in a distributed delay process.

Figure 4.3 illustrates, for purposes of comparison, the behavior of

a discrete delay process where all individuals have a common delay
time.

The variable Wij(t) describes the average weight of members of

SUBPOPij(t). Weight gain as a result of energy intake above the

   

 

 

7A... lg.

minimum r
rich the
that Still

class of

common
these
cohort
breed
equat
enter
vari
beca
encr
dev

PU

48

nimum metabolic requirement is represented by the variable DGAINij(t),

th the subscripts again referring to the subpopulation of the herd
at SUBPOPij(t) counts. The average slaughter grade or slaughter

.ass of cattle described by SUBPOPij(t) is the value of the variable

rADEij(t) .

Births and deaths are the final processes of the demography

>mponent that remain. BRi(t) and DRi(t) are variables representing

rese processes, respectively, on the basis of an annual rate. Only

)horts l, 2, and 3 have BRi(t) values because these are the only

reedable female cohorts. The simple distributed delay model of

quation 4.2.2 is flow conserving; that is, all of the flow which

nters the delay subsequently leaves the delay through the output

ariable. This does not appear to fit the case of cattle maturation,

ecause deaths and sales before final maturity are commonplace occur—

nces in cattle enterprises. This problem will be solved in the

evelopment of the exact mathematical equations for the maturation

mocess in Chapter V.

Forage Growth Component

Plant growth as a response to energy and nutrient inputs is the

*UbjeCt of this component model. The biological growth process is

exceedingly complex. Solar radiation——SOLAR(t), average temperature—-

5‘V(3Tl'fl’(t), and rainfall——RAIN(t), are the exogenous variables driving

this Process. The model developed here is to some extent a modifica-

tion of a grasslands model developed by Patton and Marshall [40]-

While much more detailed models of this growth process could be

 

 

49

 

V

  

 

Time

——-—.—_._._———~——-———_—~_———_—~—.—_——_

_.. —... __—_—.__—_———___——————q-_-_-.-

   

 

 

t t Time

gure 4.2 Graphical illustration of the response, Y(t), to an
input, x(t), for a distributed delay process

 

 

 

50

K(t)

 

 

 

 

 

 

 

 

 

Time

Y(t)

...—-..—..-__...___._..__l.__-.__.__-_.__._-

 

“l

n

tI = the delay length

0

 

 

n .—......____

H
0

Time

Figure 4.3 Graphical illustration of the response, Y(t), to an
input, x(t), for a discrete delay process

 

 

 

develop

of this

A1

this 111
tion.
impor
is in
into
ing,
gree
pro‘

nut

51

:loped, the present effort is felt to be adequate for the needs
:his thesis.

Animal consumption is the primary end use for the forage growth
3 model describes, whether grazed or harvested for later consump—
n. Since the nutrient value of animal feed inputs is of great
ortance, the digestibility, DIGEST(t), and energy value of forages
included in this model. The model divides the biotic component
,0 two materials, green plant material~-GRN(t)--suitable for graz-
;, and root storage——ROOTS(t). Grazing is strictly limited to
sen material. The abiotic component consists of soil with two
)perties of interest; these are soil moisture, SM(t), and soil
trients, SNUT(t). SNUT(t) is a composite of all of the nutrients
portant to plant growth: nitrogen, phosphorus, potassium, and trace
tals. SM(t) is determined as a result of three variables interact-
g over time; these are rainfall—~RAIN(t), percolation of soil mois—
re—~PERC(t), beyond the depth that roots can reach, and evaporation——
AP(t). Because grazing management is an area that will be of im—
rtance to evaluation of enterprise decision—making, the model is
nstructed so that different land parcels are available for varying
=es. The size of these parcels, LAND“, is arbitrary, but it is
‘sumed that they are each homogeneous with respect to all variables
:ed in this model. The subscripts n on the variables of this com—
lnent model refer to values for the nth land parcel; NLANDS is the
ital number of these land parcels.

The growth process within an individual land parcel begins with

Le fundamental exogenous input—-SOLAR(t). Solar radiation does not

 

 

 

affect 2
between
in shad
amount
When p
is tn
radia
energ
pera

prec'

of

em

ct all green plant material equally. A major distinction is made

een those areas of the plant that are in direct sunlight and those
shade. This model approximates that distinction by limiting the
unt of plant material available for photosynthesis per unit area.
n plant density is higher than a specified threshold, the excess
treated as being photosynthetically inactive. The input of solar
iation on the active plant material determines a net photosynthetic
rgy conversion——PHOTO(t). The relative quality of the ambient tem—
ature, soil moisture, and soil nutrients are used to reduce this
dicted quantity whenever these conditions are less than ideal.

This net photosynthetic energy is available for growth in either
two places—~forage greenery or root storage. The partition of this
ergy is a function of the relative proportion between greenery and
ot storage which already exists. A transfer of energy from root
orage to greenery takes place according to the proportion of green—
'y and root storage quantities. Gross greenery growth rates,
mDOTn(t), and net root storage growth rates, ROOTDTn(t), for the nth
ind parcel are the result of the interplay between the partition of
iotosynthetic energy and the transfer of energy from root storage to
rage greenery.

The net greenery growth rate, dGRNn(t)/dt, for land parcel n is
etermined from PRODOTn(t) by subtracting the amounts representing
nimal and mechanical harvesting. AHRn(t) and MHRn(t) are the model
ariables for these latter two activities, respectively. The actual

arvest, either by cattle or machine, has a greater effect on the

 

 

 

 

quantity 0
occurs in
to determ'
from the
waste fac
rate wit
waste fa
waste f:
green p
ment oi

QUITE“

age 1
this

acct

bri

1e:

53

ntity of plant material than the amounts harvested indicate. Waste
urs in each of these activities; therefore, a waste factor is used
determine a higher (and more accurate) amount of greenery removed

m the land by both mechanical harvesting and grazing means. The

to factor for grazing is modeled as a function of the stocking

e within a particular land parcel; high stocking rates have higher
te factors than do medium stocking rates, which in turn have higher
te factors than do low stocking rates. The net growth rate of

een plant material, dGRNn(t)/dt, is integrated over the time incre—

t of the simulation to determine the quantity of GRNn(t) for the
rrent period of time.

The final mechanism of this component model is the determination

5 current digestibility, DIGESTn(t), of the green plant material in
ind parcel n. This is computed through use of an index of the aver—
;e growing time to generate the forage existing at present. The higher
iis value, the longer it would take at the current growth rate to
:cumulate the present quantity of greenery. The digestibility of
stage is aSSumed to decline with age. This assumption attempts to
ing to the model the age dependent shifts in the proportion of plant
eaf area, stem, etc. without having to actually model forage using
ese different plant parts. An additional factor affecting digesti—
ilities is the density of green plant material per animal grazing in
particular land parcel. This density is determined by dividing
urrent greenery by current stocking rate times days per simulation
ime increment for the entire land parcel. When high forage densi—

ies exist then the digestibility of the forage is assumed to be

 

 

unchangEd
are low ti
to accoun
that is i
Forage d:
the cur

grazing
Feed St-

Ti
curren-
feed 5
cannot
quant

peric
chan
and

and
of

0W

54

nged from the value determined previously; however, when densities
ow then the previously determined forage digestibility is reduced
,count for the fact that animals will be forced to eat material

is included in GRNn(t), but which is of very poor quality.

ge digestibility is then modeled as a function of current quantity,
:urrent growth rate, season, and the current density of forage per

ing animal.

     

Stock Com onent

The main function of the feed stock component is to provide a
ent value for feed stocks on hand and the TDN value of each of these
stocks. This model is quite simple in comparison to the other
onent models. FSTOCKn(t) is the variable used to describe the
atity of feed stock n on hand at the beginning of the current time
.od. FQUALn(t) gives the TDN value of feed stock n. FSTOCKn(t)
lges value through sales-—CSALESn(t), and purchases-—STKPURn(t),
crop production-—CROPnl(t), quantities fed to cattle—-STKFEDn(t),
through loss from pests and waste—~STKLOSn(t). Except for losses
stocks, each of these variables are calculated elsewhere in the
:all system model. For example, STKFEDn(t) is determined in the
:ient impact component model as a result of the allocations of feed
each cohort, and the distribution of the allocations among the
sible feed stocks on hand. STKLOSn(t) is computed in the feed stock
:1 by multiplying an annual fractional loss rate for the nth feed
:k, FRCLOSn(t), by the current quantity of feed stock n on hand.
The change in quality of feed stocks is highly influenced by

rate of turnover of the stock itself. The variable SPOILn(t) is

 

 

 

 

used to dete
stock It. Ti
user in the
the new ave
each of the
time petio
from the s
the cure
This

the mock
tepresen

growth 5
tuttiett

he
went t:
detail
(inalit
descr
tine
vain.
iewe
trot
wal
anf

0n

55

to determine the annual rate of decline in TDN values for feed
L n. The particular values used are read in as data by the model
in the initialization phase of the program. Each time period
new average TDN value is determined by accounting for the TDN from
of the following sources: carryover from the previous simulation
period, new purchases, and crop production. The average amount
‘the sum of these three sources is the value used in FQUALn(t) for
current time period.

This component handles one other minor accounting task by totaling
production of crops to get annual production to date. CROPGn(t)

:esents the total amount of crop n harvested to this point in the

nth season.

Eight Impact Component
Development of this component model has been guided by the require-
t to describe reproductive links with nutrient intake in considerable
ail. The model uses four variables to describe the quantity and
lity of the nutrient allocation for each herd cohort. CNCALi(t)
cribes the quantity of concentrates allocated to cohort i for one
e period. TDNCi(t) describes the average total digestible (TDN)
ue of the allocation to the ith cohort. FEEDALi(t) describes the
el of roughages allocated to the ith cohort for one time period
m voluntary feeding by management. TDNRi(t) represents the TDN
ue of the roughage allocation. The nutrient requirements for
mals of a particular cohort for weight maintenance are predicted

the basis of the animals‘ metabolic weights. The feed consumption

 

 

 

 

of anion
the dif
the ens
energy
Resear
nine 1

cohor

to ti
heif

int

56

ls is predicted to be a specified fraction of their weights.

   
    
   
 

fference between the energy value of the nutrients consumed and
ergy required for weight maintenance, and other requirements, is
available for weight gain. The model uses the standard National
ch Council2 relationships between energy and weight gain to deter—
he rate of weight gain, DGAINij(t), for the jth subpopulation of
i.

eproductive considerations in the component model are restricted
ee herd cohorts: mature cows, replacement heifers, and bred

3. Reproductive requirements for bulls are assumed to be zero
‘5 model. The energy requirements of mature cows vary depending
age of the calf they are nursing, their current state in the
tion period, and their breeding status. A beef cow has certain
ological priorities which cause differential impacts if the over—
energy intake is smaller than required, and the ability to be

d is not the highest priority activity. Replacement and bred

rs come into puberty as a function of age, weight, and rate of

t gain; following puberty they have reproductive cycling just as
'e cows cycle. All three of these herd cohorts have the charac-
tic that the success of breeding is a function of both current
>rior feed energy intake rates.

Breeding is the major event that the model uses to bring repro—

;ve dynamics into herd population dynamics. TBRDi and DURBi

2

National Research Council, Nutrient Requirements Of Domestic,
als: Number 4——Nutrient Requirements of Beef Cattle, 4th Revised
Lon, 1970.

 

 

 

 

describe t
represents
the time :
Ci’hTijk r
ith serwi
SUBPOP ii I
In
proporti
from the
Similar:
by time
the owe
season
the Cu
each f
the we
Subpot
latio
down
other
rate

tiat

con

57

be the onset and duration of breeding for the ith cohort. lNBij
tents the number of servicings for SUBPOPij(t). CTlMijk gives

Lme of calving that corresponds to the kth servicing of SUBPOPij(t).
ik represents the predicted accumulated calving rate after the
:rvicing. Figure 4.4 depicts the expected calving pattern for
?ij(t) as a result of its breeding activity.

in Figure 4.4 the first point (subscripted ij,l) describes the
rtion of cows giving birth to calves during the interval of time
the beginning of the calving period to time point CTIMij,l'
arily, the second point describes the cow proportion giving birth

me p01nt CTIMij,2'

The final point (subscripted ij,5) describes
verall proportion of cows giving birth over the entire calving
n. BEGCAV(t) and ENDCAV(t) describe the beginning and ending of
urrent calving season, respectively. A pattern of calving for
female cohort capable of reproducing is determined by computing
eighted average of the entire cohort using the number within each
pulation of that cohort as the weight for the individual subpopu—
n pattern. An adjustment factor, PADJST, can be used to scale
the entire calving curve to reflect the incidence of disease and

factors affecting breeding, if desired. The instantaneous birth
at any point in time is determined for the cohort by differen—
ng the cohort calving pattern.

For details concerning the model for this component one should

It Schuette[48].

 

 

 

'h

iccun
Calw:
Fra

58

umulated
ving
.tion

 

I

 

 

 

|
I
I
I
___________ | I
P I
C ATij ’2 I l :
I I |
I I
I ' I
I | I
I I |
———————— o-———o | .
CPAT.. I I I I
13,1 I I |
I I | |
I I ,
I I I
| I l I
| I I I
I : I I
I . I I
I . | I
I I I L I .
I T
I I I I
| CTIMij ,1 : CTIMij ,3 ' CTIMij,5 : Time
I I I I
BEGCAV CTIM .
13 ’ 2 CTIMi j ,4 ENDCAV

igure 4.4 The accumulated calving fraction versus time

me

at the
to the
produr
both
high]
tact:
catt
per:
aho

do

   
 

59

ement Decision Makin Com onent

   

Management decision making is a very complex process, especially
he detailed level used in this model. A factor that contributes
he complexity of the decisions is the lengthy time delays of the
uction process. Management must make decisions on the basis of

h current and expected prices. This makes decisions of the manager
hly conditional on the expected prices he has used. An additional
tor is the well known volatility of agricultural prices, including
tle prices. Since the expectations of the manager are apt to change
iodically, the decisions be made under the previous assumptions

ut future price behavior are likely to diverge from what he would

 

under his current expectations. An additional factor is the mul—
le desired goals of the manager which cannot be readily reduced to
single objective function. Thus, the decision making of a beef
:tle enterprise manager is not well suited to optimization proce-
:es for these reasons.

What information is necessary for the decision maker to use as
a basis for his decisions? Certainly expected prices of cattle,
Ips, and production resources are important. The time horizon over
.ch these are needed is different for each type of decision. For
ample, breeding is an activity based on decisions which use prices
far forward in time as the likely date of sales of the resulting
’spring, on the order of two years. The decision of what stocking
:es to use in various land parcels is likely to require only a few
Iths of expected prices. The states of this system are a vitally

tortant category of information. Current cohort populations,

 

current
parcel,
system
catego:
crop 9
over I
the c

endog

requ
the
Thi
gen

lat

60

  
  
  
 

rent feed stock levels, current quantities of forage in each land
cel, and current financial conditions are examples of states of the
tem which are important to decision making. The last important
egory of information is expectations about future events. What

p production is expected? What is the average forage production

r the growing season? All of this information is needed to describe
conditions under which decisions are made, whether they are made
ogenously or exogenously.

This component has been developed with regard to the general
uirement that the control variables of the model be able to simulate
decisions made by an actual enterprise manager operating a ranch.

's has meant that very detailed control variables are needed; in
eral, much more detailed than have been used in agricultural simu—
tion models in the past. The major decisions that the manager must
ke to control his enterprise include:

(1) timing and level of sales and purchases of cattle,

(2) timing and level of sales and purchases of feed stocks,

(3) feeding rates and types of feed for each cattle cohort,

(4) stocking rates during the forage growth season,

(5) timing and level of mechanical harvest of forage,

(6) timing and extent of breeding, culling, and weaning.
e following control variables are included in the simulation model

carry out the above list of operating decisions.

(1) ADDRT.(t) = the net annual rate of additions to the iFh
1 herd cohort

(2) AGEMIN = the minimum age of calves to be weaned

(3) CSALESn(t) = quantity of feed stock n sold this period

 

61

(4) CATTIN. (t) = the quantity of TDN of feed type m fed to
ink
a member of cohort i per day during the
period of the 2th feeding plan

 

(5) CNCFRC. (t) = the fraction of the concentrate TDN allocation
in
to be derived from feed stock n
(6) CULFRC.(t) = the fraction of the population of the jth
J subpopulation of cohort l to be culled
(7) DURBi(t) = the duration of the breeding period for cohort i
(8) FPLANS (t) = the time at which the 2th feeding plan ends
(9) MHRn(t) = the rate of forage harvest from land parcel n

(10) PADJST

calving rate adjustment factor

(11) PDSTRBin(t) = fraction of the population of cohort i that
is to graze in land parcel n

(12) REMOVL(t) = fraction of the forage to be harvested

 

(13) RHGFRCi (t) = the fraction of the roughage TDN allocation
n to be derived from feed stock n

(14) TBRDi(t) = time of breeding onset for cohort i
(15) TCULL(t) = time of mature cow culling
(l6) TFRAC. (t) = the fraction of the weaned female calves from
31 the jth subpopulation transferred to cohort i
(17) TMHRk(t) = time of the kth forage harvest
(18) TWEAN(t) = time of weaning for calves
(19) STKPURn(t) = quantity of feed stock n purchased this period.

Decision making in this component model, as has been previously
lained, is performed both endogenously and exogenously. When a
ision can be made without recourse to exogenous input, it is so
e. Such endogenous decisions include: (1) timings and quantities
sales of the two slaughter cohorts—~steers and heifers, (2) the
ision to harvest forage as guided by preseason planning, (3) sales

purchases of feed stocks to obtain the winter feed base, and

 

(I) the actu
the herd as
quantity pr<
I.8 indicat
of the four
The re
ting contr<
(l) determ
its which
cohorts,
of animal
its tome
types of
events;
and wean
four eve
iahles i
calls f
events
the cut
fallin
the g!
ments
Which
com

the r

62

the actual feed allocations of concentrates and roughages fed to
herd as guided by the feeding plans and adjusted to meet forage
ntity problems as well as feed stock shortages. Figures 4.5 through

indicate the decision mechanisms and the variables used in each
the four endogenous decisions.

The remaining herd decisions are determined by the user by input—

ig control variable values exogenously. These decisions include:

> determining stocking rates for herd cohorts, (2) breeding activ—
y which includes timing, duration, and type, (3) weaning of the calf
horts, (4) sales from or additions to the herd cohorts, (5) movement
animals through the cohort structure following maturation beyond
:5 former range, and (6) culling of the mature cows. Four of these
rpes of decisions are clearly associated with particular physical
Jents; these are the onset of spring forage growth, breeding, culling,
1d weaning. The component model has been developed so that these

ur events, termed "decision points", are recognized and control var—
bles are sought upon recognition. A fifth "decision point" also

11$ for exogenous input of control variable values when any of three
ents occurs; these are (l) the quantity of feed stocks is less than

e current rate of feeding times two periods, (2) working capital
lling below $2000, and (3) the quantity of feed stocks at the end of
e growth season being significantly different from the feed require—
ents for the wintering season. Figure 4.9 is a blow up of Figure 4.1
hich shows the mechanism whereby the management decision making
omponent recognizes that a decision point exists and acts to achieve

he needed input of control variable values by the model user.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

63
I Weights or Hard Legend:
Subpopulation
® -- from Subroutine Weight.
@ -- exogenous to the model
® -- decision variable
Gain ® -- to financial accounting
L 7 ‘ ‘- ism
eding
vols
Weight
Gains
I
Costs
3 and
Revenue
r‘op Prices
- Expected
Net Fri 6
Revenue c s
Management
Sale
Decision-making
Cohort
Animal
Sales

igure 4.5 Decision mechanism for slaughter cohort sales

   

 

Stock
tat/as

64

   
   
    
  

Specified
Harvest
Tires

® -- exogenous to the model
® -- Forage Component
6)) -- decision variable

-- from the main model

poking
;es

 

 

Forage Harvest

Decision Making < > 3:35

 

 

 

Herve st
Rates

 

'gure 4.6 Decision mechanism for forage harvesting

 

 

 

 

 

 

 

 

65
D Anticipated Legend:
Net Sales
(9 -- decision variable
® -- Feed Stock Component
(9 -— exogenous to the model
@ —- from the main model
Feed Stock
E Sales and Purchases
>'—"_ ' ' Decision Making ement
Time
Time of Year
Crop
Purchases
‘
F Crop
Sales

Figure 4.7 Decision mechanism for feed stock sales and purchases

to obtain wintering nutrient requirement

 

\'\

Basin
Rough
Ratio

Dee

1131

F1

66

       
 

 

 

 

> resired Population legend:
Roughage
Rations (::> -- Population Component
(::) -- decision variable
61) -- Nutrient Impact
Component
(::) -- from the main model
® -- Forage Component
) Desired
Concentrate
Rations

Requirements

 

 

 

 

 

Rates
Grazing
Forage
Shortage
7 Current
Roughage and Ti
Concentrate

Allocation
Decision-Making C > F°rag°

Quality
’ Forage
Quantity
oughage Concentrate
llocation Allocation

Lgure 4.8 Decision mechanism for herd feeding allocations

 

 

 

 

 

 

 

        

  

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67

 

 

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.----_..-__..---.._-..-...._.‘

 

Figu
making c0
decision
to see i:
values f
passes t
conditi<
shown 1‘
model 5
is prir

at his
result
which
the c:
contr
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insu'.

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68

Figure 4.9 illustrates the operation of the management decision
king component with the two elements-—exogenous and endogenous
:cision making——logically related. The component constantly checks
3 see if any condition requires the use of exogenous control variable
alues from the model user; if none is required, then logical control

asses to the endogenous decision making element. When an event or

 

ondition does trigger recognition of a decision point, then the steps
:hown in the exogenous decision making element are followed. The
mdel simulation is stopped after current state variable information
is printed; this pause allows the user to study the current situation
at his leisure and input control variable values to implement his
resulting decisions. The model is restarted from the exact point at
which it stopped and continues the simulation as before, except that
the controlling actions of the user are substituted for any previous
control decisions or decision making criteria. This sequence of
events is followed in every time increment of the time simulation to
insure that decision points requiring human decision making are

recognized when they exist.

Secondary System Components

In order to simulate the beef cattle enterprise in the way that
:he problem statement requires, several secondary components are also
needed. A component performs the task if determining the proper value
vf the exogenous variables—~crop production, prices, and weather—~for
he current time. The main program reads in as data an entire year

f exogenous variable values in its initialization phase; a subroutine

 

iscalled
the appro
The
inportan
requires
the none
nation :
process
current
Second,
reache
and in
are or

“(ICES

Price
In t'
stre
Done

to.

fuI

pa

69

3 called at the beginning of each time iteration which determines
he appropriate exogenous values to use.

The financial effects of alternative policies are the most
important outputs to use in choosing among the policies. This

requires that a financial component be included that accounts for

the monetary effects of sales, purchases, and payments. This infor—

mation is used in two different ways. First, the ongoing management

process requires information about present, immediate past, and
current values of such variables as yearly net profit to date.
Second, when the final time horizon of the simulation has been
reached, the user wants summary information to help him to analyze
and interpret what has OCCurred during the simulation. These tasks
are carried out by a package of subroutines which perform all
necessary financial accounting and analysis.

The last secondary component is one which manages the expected
prices that the manager uses as the basis for his decision making.
In the initial program start and at each decision point, the future
stream of expected prices for cattle and crops changes. This com-
ponent reads in this new information as needed. A second task is
to adjust the future expectations to account for the passage of time.
As simulated time is incremented forward, this component shifts the
future expectations toward the present and records the most recent
past value in the pst expectations variable. It gives the decision
maker the opportunity to know what price he expected to encounter

at times that have come and gone.

 

1V.3 Sin
Opel
interact
initial
prise tr
enterpr
At this
hrpm
sions
tion t
procer
run h
the r

compr

been
Pris
sub
cat
cl:

hi

70

.3 Simulation Model Operation

Operation of this simulation model is heavily influenced by the
teractive management component. Initially, the user reads in the
Litial conditions and system parameters for the particular enter-
:ise to be studied. The model will automatically simulate the
nterprise behavior through time until a decision point is reached.
t this point the model requires the user to input specific values
or particular control variables. These values implement the deci—
Lions that the user has made. The model then continues its simula-
:ion through time until the next decision point is reached. The
)rocedure is repeated until the final time horizon of the simulation
sun has been reached. Figure 4.10 illustrates the organization of
the management component and its relation to the other system
components in the simulation loop.

When the management component detects that a decision point has
aeen reached, a detailed printout of the current status of the enter—
prise is made. This printout typically includes the current herd
subpopulation breakdown, current feed stock quantities, the expected
cattle and crop prices over a future time horizon, and current finan-
:ial status. The user must carefully study this information to make
118 decision about what is to be done at this point in time. The user
Imy be investigating the effects of a particualr decision rule; he
muld input control variable values to follow that decision rule.
he user also inputs new expectations about future prices and events.

At the true that the management component completes printing of

he decision assistance information, it prints all variable values

 

 

 

 

Figure 4.10

 

 

 

 

 

 

 

 

 

 

   
   
 
 

  

  

 

 

 

 

 

 

 

 

  

 
     

 

 

 

 

 

 

71

Enterprise
Model

...... ._____________________1
I I
I
. Model Variables I
Recognition UIdated I
of a I
Standard :
Decision Point I
Decision Maker I
In-uts Controls :
NO I
I
I
I
‘ I
I
Model Variables l
Recognition Updated I
of a l
Special |
Decision Point I
Decision Maker :
NO In.uts Controls I
|
I
I
‘ I
I
I
I
Endogenous I
De C is ion S THE I
MANAGEMENT '
COMPONENT :
.J

 

Flow diagram of the management decision making
component in relation to the simulation model

 

into a p
to be re
tions 3:
making
to read
with tI
ables
E_nte_r;
to cm
chara
to re
new I
po'm
can
PIOI
per-
4.1
can
is

As

72

  
  
  
  
  
  
  
  

' to a permanent file in the computer. This file enables the model
0 be restarted at exactly the same point and under the same condi—
ions as when it stopped. When the user restarts the model after
king his choice of decision variable values, the first action is
to read from the permanent file to reestablish all model variables
ith the proper value, the second step is to read the control vari-

ables (using the formats given in the User's Guide to the Beef Cattle

 

Enterprise Simulation Model), and finally to implement these values

 

to control the enterprise simulation model. An extremely valuable
characteristic of this interactive management component is the ability
to return to a decision point that has already been passed by, input
Inew control variable values, and continue the simulation from that
point. At each decision point any number of control variable sets
can be used by restarting the model with the desired control values,
proceeding to the next decision point, printing all values into a
permanent file, and returning to the original decision point. Figure
4.11 illustrates the decision tree of alternative control sets that
can be evaluated. The key to this ability is the permanent file that
is created to "freeze” the simulation as it was at a decision point.
As long as the user does not dispose of these permanent files, he
retains the option of returning to any one and proceeding forward
in time with any control values that are desired.

This evaluation of alternative strategies method of use will be
employed later in this thesis to explore some management strategies
for (1) age of weaning, (2) rate of herd development projects, and

(3) general profit maximization.

 

Use of the I
The si
evaluating
Certain acI
plex decis
the user a
evaluate I
model wit‘
feed stoc
etc. In
to the 5‘
time. I
mod\el, I
reilfl
deviate
t0 invv
Revisi
the re
to re;
latio‘
etc.
entev

the I

thrv

   
  
  
  
  
  
  
 

se of the Simulation Model

The simulation model is a tool for the user to employ in
valuating specific alternatives confronting his own operation.
ertain activities, such as breeding, weaning, etc., are highly com—
lex decision and quite dependent on future prices and events. When

he user approaches Such events in real time, he wants to begin to

 

valuate his possible courses of action. He would then start up the
odel with the current states of his cattle herd, forage in the field,
eed stocks on hand, expected crop production, financial condition,
tc. In effect, he initializes the simulation model to correspond

to the states of his own enterprise. Then the model is used to explore

 

the future consequences of his decision options through simulated

 

 

time. After having explored the alternatives using the simulation
model, the decision maker is in a much better position to make his

real world decisions. At any time that conditions in the real world

 

deviate from the user's previous expectations, he can use the model
to investigate the effect of these differences on his enterprise.
Revision of previously made decisions is possible on the basis of
the results of these investigations. The user of the model is alerted
to real thme events that require investigation through use of the simu—
lation model by his own awareness of weather, prices, political events,
etc. The simulation model is an assist to the manager of a beef cattle
enterprise, not a substitution for the experience and intuition of
the manager.

The simulation model has simulated the dynamics of the enterprise

through time but in ways that are not completely accurate. Two

 

LEGEND

0 resta

0 rests

74

GEND

 

restart file selected

restart file not selected

decision decision
point point
one two

I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

current
real time

 

decision
point
three

Figure 4.11 ”Decision Tree" of alternative strategies investigated
using the simulation model's restart capability

 

sources
between
in the
errors
tion t
of ina
do n0‘
reaso
the s
poin‘
mode
vari
beeI
age

his

1V

75

 

sources of inaccuracy provide the bulk of the reason for the divergence
between real and simulated values. The first of these is inaccuracy
in the simulation model formulation itself; this is due to modeling
errors and approximations that simulation makes to develop a solu-
tion to the mathematical model of the enterprise. The second source
of inaccuracy is management decisions in the real world system that

do not conform to those made in the simulation. For these and other

 

reasons, the simulated enterprise behavior will never follow exactly
the same path as the behavior Of the real world enterprise. At each

point in real time requiring alternative decision explorations, the

 

model should be reinitialized with the Current states of the model
variables used to describe the enterprise. The simulation model has
been constructed so as to be available for use by an enterprise man-
ager at any time and to be as flexible as possible to accommodate

his needs.

IV.4 Summary

This chapter has provided a general description of the simulation

 

model that this thesis has developed. Five major and three secondary
components of the model have been reviewed. The operation of the
model by the user has been discussed. In the aggregate these com-
ponents constitute the model that will be used to investigate stra-
tegies of management decision making by this author and other users.
Figure 4.12 provides an overview of the major components and the key
control points that provide the means of implementing the decisions

made endogenously by the management algorithm and exogenously by the

 

user. Figure
sequence of t
horizon. Th!
equations th

computer prc

76

user. Figure 4.13 provides a pictorial description of the calling
sequence of the model as it simulates the system over a desired time
horizon. The following chapter will present the detailed mathematical
equations that form the mathematical models that are simulated in the

computer programs.

 

 

 

 

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78

 

 

Exogenous Inputs
Component

 

 

 

 

I

Expected Prices
Component

 

 

 

 

 

Livestock System
Components

 

 

 

I

Management
Decision Making
Component

 

 

 

 

 

 

 

Financial
Component

 

 

 

 

Figure 4.13 Calling sequence of the simulation model components
to simulate the beef cattle enterprise through time

This
presented
in the prI
are the b
Each of t
separate

section,
A c
be found
volume
from ei

volume

I.l C

ulativ
is th
basis
aver;
ages
func
BIRI
pre

rat

CHAPTER V
DETAILED MODEL DESCRIPTION

This chapter will build upon the general description of the model
;ented in Chapter IV. This chapter will take the variables defined
:he previous chapter and develop the mathematical equations which

the basis for the computer subroutines of the simulation model.
1 of the five major system components will be discussed as a
arate section; the secondary components will constitute another
tion, and the final section will summarize the enterprise model.

A complete listing of the computer program and its subroutines can
found in User's Guide to the Beef Cattle Enterprise Model, a separate
ume from this thesis. Complete instructions for operating the model
m either the initialization or restart mode may be found in this

ume as well.
Cattle Demography Component

This component model uses four subroutines to provide the sim—
tion of the birth, death, and maturation processes. Subroutine HDMOG4
the major element; it maintains herd populations on a disaggregated
is by age, sex, and function. Subroutine WEIGHT determines the
rage weight of particular subpopulations as the herd matures and
s. Subroutine BIRTHZ computes an instantaneous birth rate as a
ction of prior nutritional status and breeding activity. Subroutine
AT is used by BIRTHZ to determine birth rates by combining the
dicted birth information about each female subpopulation into birth
as that apply to an entire cohort population.

79

 

The In
maturation i
Equation 4.2
it does not
not conserVI
and additio
covered by

the Laplace
Y(s',

whe

Upon solv
II
This form

as k 1st

decompos

><
A
w
v

FiguI

80

The key to the model of maturation is recognition that
ration is a process in which age is a distributed parameter.
.tion 4.2.2 provides the basis for the model of this process, but
oes not allow for cases in which flow is not conserved. Flow is
conserved in the maturation process because of deaths, sales,
additions to the herd. These occur throughout the range of age
red by the cohort delay. Following Manetsch [38] one applies

Laplace Transform to 4.2.2 to obtain

k
Y(s) n (Dis + 1) = X(s) (5.1.1)
i=1

where:
Y(s) = transform of the output time function
X(s) = transform of the input time function

.solving for Y(s), one obtains
k 1
Y(s) = H ———————— X(s) (5.1.2)
i=1 D s + l
1
:form suggests that the kth order distributed delay can be modeled

L lst order delays in a cascaded form. Figure 5.1 illustrates this

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mposition.
1 l
1 l 7 w...- —’q D + l——-—’
________ —» “"“' s
) DlS ‘I' 1 Rl(S‘ D25 + 1 R2(S) D38 + l R3(5) k Y(S)

 

 

gure 5.1 Decomposition of a kth order distributed delay into a
series of k first order delays

 

Each of the
as stages wi
Sino

is a loss f
of the stag
loss from I

losses fr0I

stages has

conventior

><
A
m

v

Iigm

81

of the individual first order delays of Figure 5.1 are referred
tages within the overall delay.

Since flow is not conserved in the case of maturation, there
.loss from the delay. In general there can be a loss from each
he stages of Figure 5.1, which in the aggregate sum to the total

from the entire delay. Figure 5.2 illustrates this idea of
es from individual stages. Notice that the numbering of the
;es has been reversed in this figure to conform with the usual

'ention [32, 38].

 

 

 

 

 

 

 

 

 

 

 

 

 

_____’. . ..__). .———>
' K ' K—1 1
R =Y

Rk Rk—l l (S)

L

Lk Lk—l 1

+
+ +

L = total loss rate

gure 5.2 Kth order distributed delay with losses

 

 

At any I
storage

the lam

Losse
sinpl

anal:

The

dif

in

be

de

82

I any moment the total number of individuals in the ith stage (the
;orage in stage i), Qi(t)’ is a function of the flow rate, Ri(t)’ and

1e length of the ith delay, Di(t). This gives
= *
._(t) Di(t) Ri(t) (5.1.3)

3 the total delay for the entire process, D(t), is spread uniformly

Ier all k stages, then 5.1.3 becomes

L(t) = Q(£)*Ri(t). (5.1.3a)

K
asses from this quantity can be individually specified, but as a
implyfying assumption, let a common proportional loss rate, PLR(t),
pply to all stages. Then the loss, Li(t)’ is

i(t) = PLR(t)*Qi(t). (5.1.4)

he net change in storage for the ith stage follows the following

ifferential equation,

(5.1.5)

 

Q (t) _
3t — Ri+1(t) — Ri(t) - Li(t)

ecause the rate of change in the quantity is the rate of input to the
elay minus the rate of output. Referring to Figure 5.2 gives the
nput rate to state i as Ri+l(t)’ while the output rate is the sum of

he output going to the next stage, Ri(t)’ and the loss, Li(t)-

dfferentiating 5.1.3 gives

 

Qi(t) = D(t)*dRi(t) + Ri(t)*dD(t) (5.1.5a)

 

IQUating the right hand sides of 5.1.5 and 5.1.5a and solving for

IRi(t)/dt gives the following,

 

 

This is
tribute
length.

SI
equativ
ith he
by equ

number

SUBPOI

The t

P0P“:

POP

prov

pub

[IOI

83

 

{.(t) = K R (t) — R (t) l + D(t)*PLR(t) + dD(t)
Elt— D(t) 1+1 1 K— ‘KdT- (5.1.6)

1is is the general expression for the ith stage of a kth order dis—
:ibuted delay with proportional loss rates and a time varying delay
angth.

Subroutine DLVDPL is used to simulate a delay process which follows
Juation 5.1.6. RINij(t) represents the jth stage flow rate for the
:h herd cohort. The storage for that stage, SUBPOPij(t), is determined

7 equation 5.1.3a using the cohort delay length, DELAYi(t), and the

Imber of stages in cohort i, namely KKi' Then
.13 = *
POPij(t) DELAYi(t) RINi.(t) (5.1.7)
KK.
1

1e total storage ofIthe ith delay process (cohort i) is simply the
ummation of the storage in each stage. This gives the total cohort

qulation as
KK.

1
)Pi(t) = 3'21 SUBPOPij(t) (5.1.8)

A distributed delay is an excellent way of modeling the physical
tocess of maturation. For some purposes, the actual age and weight
ly serve better. this is the case for prediction of the oneset of
merty in heifer calves. What is needed is a delay model that is
It distributed; the output rate is a uniform delay of a prior input
te. When proportional losses and the potential for a time—varying
lay length are required, the delay process becomes more complicated

an the simple illustration of Figure 4.3.

84

A simple discrete delay with no other characteristics can be
esented by

= X(t — d) (5.1.9)
re:

Y(t) = output rate at time t

X(t) = input rate at time t

d the time delay

the time delay, d, is an integer number of DT time increments, then
) = X(t - N*DT) (5.1.9a)
ice that this process can also be represented in terms of a cascade
single stage delays, with each stage corresponding to a delay of

: DT. Then,

:) = R10; — DT)

It) = R2(t - DT)

1(t) = [l - PLR(t)]*RN(t - DT) = X(t) (5.1.11)

n the delay length, d, changes, then the number of stages separating
input and output must change correspondingly, because the delay

igth for each stage is fixed as DT. If the delay length increases,

en there will be an interval with no output rate until the extra

mber of required stages of DT delay are completed. If the delay

ngth is decreased, then a large output rate will suddenly occur as

e storage of the excess number of stages leaves the delay model.

Subroutine DVDPLR has been developed to simulate this form of

screte delay with proportional losses and variable delay time.

 

 

 

Storage
5.1.7 I
corres

SUBPOI

using

(1150

 

 

PU

 

age in this discrete delay is computed in the same way as equation
7 computes storage for a distributed delay. Since each stage
esponds to a fixed delay of length DT,

OPij(t) = DT*RINij(t) (5.1.12)
For this simulation model cohorts l, 4, 5, 6, and 9 are modeled
ng distributed delays and cohorts 2, 3, 7, and 8 are modeled using

crete delays.
The proportional loss rate, PLRi(t), that applies to the ith
ort is made up of two loss factors. These are the death rate,
’(t), and the net rate of annual additions to the cohort, ADDRTi(t).
Ice this variable is not on a proportional basis as is DRi(t), it

divided by the current population of the cohort to obtain

‘ ADDRTi(t) “

{1(t) = DRi(t) - W (5.1.13)

is loss rate is on an annual basis; therefore, within the delay

)routines, the loss rate that applies for a single incremental

e period is PLRi(t)*DT. If POPi(t) is zero and ADDRTi(t) is
itive, a special mechanism adjusts the populations to reflect an
ition of animals through the ADDRTi(t) control variable. DRi(t)

r each of the nine herd cohorts is read into the model as data in

e initialization phase of the main program. It is assumed constant
er the entire length of the simulation. An improvement that could
made in the model would be to internalize some part of the death
te as a function of the weather variables,to simulate exposure,

6 asaafunction of the nutrient intake over time, to simulate

 

 

 

 

 

 

 

weakenin
constant
variablv
points '
PLRiIt)
Tr
repres
DVLDPI
the ar
happe'
as th
the I
to w
wean
ways
intl
coh

de<

86

ening from poor nutrition. Since the death rates are actually
tant, a more proper designation is DRi. ADDRTi(t) is a control
able that the user can specify as desired at any of the decision
ts which call for that as a variable for exogenous control.

(t) is used in the cohort delay models as explained above.

To reiterate, each of the nine cohorts of the cattle herd is
:esented by a delay process, either subroutine DVDPLR or soubroutine
)PL. The output flow rate from the ith delay, ROUTi(t), represents
annual flow rate of animals from that cohort at time t. What
pens to these animals? For example, what happens to female calves
they age beyond the delay length given by DELAY8(t)? Presumably
delay length is set to represent a natural weaning age which acts
wean all calves which get to that age and still have not been
ned. These weaned calves can be handled in a number of alternative
8: (l) entered into the replacement heifer cohort, (2) entered
o the bred heifer cohort, (3) entered into the slaughter heifer
ort, or (4) sold on the market as weaned calves. Management must
ide what fraction of these calves are used for each of the above
It uses. Three control variables act to carry out the manager's
:ision; these are C3, CS, and C9. In a similar fashion the manager
;t decide how the output from each of the nine herd cohorts will be
ad. Figure 5.3 is a block diagram of subroutine HDMOG4; in it are
Lustrated the possible flows among herd cohorts, the control vari-
Ies which direct those flows, and the general structure of the

nographic model.

 

87

 

 

 

  
   

H

Female Calves
Marketed

c_5

  
   
   
 
     

 

  

Heifers
mketed

 

 

 

 

Bir
Births 2
skim .
female

heifers

split I
CALVES

Cl der

IS thv

 

and t

 

5 are I
I'

i BIRTI
RPOP
a di
matl
tiov
hei

cob

88

Birth is the remaining process that this component model includes.
hs are generated in HDMOG4 by multiplying an annual birth rate,
t), by the reproductive population, RP0P1(t), for each of the three
le reproductive cohorts——mature cows, replacement heifers, and bred
ers. Total births, CALVES, is an annual input rate which must be
t between male and female calves.
3
ES = 2 BR.(t)*RPOP (c) (5.1.14)
i=1 1 i
enotes the proportion of births which are female, and 1.0 - Cl
he proportion which are male. The birth rate on an annual basis
the reproductive population in the three female reproducing cohorts

determined in subroutine BIRTHZ. The major function of subroutine

 

IHZ is to determine the value of BRi(t) and RPOPi(t) at time t.
Pi(t) is similar in definition to POPi(t) but is used ot maintain
istinction between heifers giving birth to their first calf and
ure cows who have calved at least once previously. This distinc-
n is not properly developed by the POPi(t) variable because some
fers in the reporduceable cohorts (numbers 2 and 3) leave those
orts and enter the mature cow cohort before the calving interval
been completed. Since the birth rate for the mature cow cohort
based on a population of mature cows, a distinction must be drawn
ween the two types of members residing in POP1(t). RPOP1(t) is
actual number of mature cows in POPl(t) which have calved pre-
usly. RPOP2(t) includes all members of cohort 2 which are preg-
t and all former members now in cohort 1. RPOP3(t) includes all
bers of cohort 3 which are pregnant and all former members now

cohort l.

 

 

LL
.m
e

oft

IIher

RPOI

bot

coI

 

89

The variables BEGCAV and ENDCAV mark the beginning and the
Iding of the calving interval. These are determined as a result
5 the previous breeding activity (roughly nine months in the past).
Ien t is within the interval (BEGCAV, ENDCAV) values of BRi(t) and
’OPi(t) are usually non-zero, Outside of this interval they are
>th zero.

Subroutine BIRTHZ computes the birth rate for each breedable
>hort by determining the derivative of the curve of accumulated
irths over the time interval of calving. The points which make up

113 curve, BFRACi l = l, ..., INTCAV, are determined in subroutine

1,
trat using the previous breeding activity. Figure 5.4 illustrates
)w the birth rate is numerically approximated from the accumulated
irth curve for cohort l.

Subroutine IBRAT is called at the beginning of the calving season

3 establish the values for BFRAC Three variables provide a record

11'
E the breeding history for each of the subpopulations of the repro-

mcing cohorts. INBi is the number of servicings for SUBPOPij over

3'
1e breeding interval. CTIMijm is the expected calving date for
UBPOPij(t) which results from the mth servicing; this time is the

ummation of the actual time of breeding and the average gestation

eriod. CPAT m is the accumulated fraction pregnant for SUBPOP (t)

ij ij
h

fter the mt servicing. The BFRAC11 curve for a cohort is determined
y these variables. The number of data points composing the BFRACil
urve is

= ENDCAV — BEGCAV

NT
CAV 0.025 (5.1.15)

 

 

 

 

 

 

90

cumulated Births

   

 

 

slope = BR1(t)
O O O
BFRACl,ll
I
I
I
I
I I
I I
l I
I I
l I
I I
I I
' I
. I I
5 ° . .
. I
, I
l I
I
I
l I
I I
I I
| I
I I
I I
. I |
: I
. I
I

I I
I l

L ABFRACl,1 I i 1

BEGCAV t-dt t ENDCAV

igure 5.4 Determination of the annualized birth rate by numerical

approximation of the deriviative of the accumulated
births curve

 

 

...“ ”an.
—_.. .

Q

Figure 5.5
for each c:
the accumu
tration‘, o
simulatior
been bred
tion, 3331

The cohor

weighted
Catt
By assmn]
ulation '.
average
determ:
change j
these a:
occurs
energy
Pass be
If the
the 3:11
then t'
do not
the Inc
Subjec

grade:

91
re 5.5 illustrates the way in which the predicted calving variables
each cohort subpopulation are used by subroutine BIRAT to determine
accumulated calving curve for the entire cohort. For ease of illus-
ion, only three subpopulations will be used whereas in a typical
lation model run there are apt to be 5—10 subpopulations that have
bred in each of the female cohorts. Again for ease of illustra-

, assume that the number of animals in each subpopulation is equal.
cohort average in Figure 5.5 is then simply the average of the
ijk values for the three subpopulations without needing to be
hted by the numbers of animals in each of the subpopulations.

Cattle weights are determined through use of subroutine WEIGHT.
ssumption, all animals represented by a particular cohort subpop-
ion have the same weight. This value is, loosely speaking, an
age weight of a fairly homogeneous group, but the value is not
rmined by actually averaging individual animal weights. Weights
ge in the cattle herd through two distinct but related processes;

e are growth and aging. Within an individual subpopulation growth

rs as a result of feed intake energy being in excess of maintenance
gy requirements. Due to the passage of time, however, individuals
between adjacent herd subpopulations, and even between herd cohorts.

he animal that has just arrived in a subpopulation does not have

same weight as the average of the subpopulation prior to its arrival
the average must be recomputed to reflect its arrival. Animals

ot continue to gain weight indefinitely; to account for this fact

model has a constraint on weight for each herd cohort. The final
ect of this submodel is price gradation of beef cattle. Fixed

es have been assigned to each herd cohort. These remain constant

 

 

 

Accumulat
of Cohort

1.0 '

 

 

 

 

 

 

 

 

 

 

 

0.5 '

 

 

 

 

 

 

 

 

 

0L

Figu

92

LEGEND
umulated Fraction

Cohort Calved —— subpopulation l

subpopulation 2

 

—- subpopulation 3

.CIDO
l
l

—— cohort average

   

O

 

4 . : 4+—
BEGCAV CTIMi32 ENDCAV

gure 5.5 Determination of BFRACi values from the breeding
history of each cohort subpopulation

 

r

unless the
daily gain
Then the e
diverted t
ulation.
proportio'
reflected
The
in the jl
is SUBPOI
mtpopul
cussed e

time acc

who)

If aniu
the ave
transfc
0f the
that s

ALPHAj

Where

Noti

93

;s the maximum weight constraint is reached and the projected

r gains would force weights higher yet but for the constraint.

the excess of energy that has been directed to weight gains is
rted to changing the price gradation of the cattle in that subpop—
ion. This mechanism is assumed to reflect the changing muscle/fat
artions that exist in cattle as weight increases and which are
acted in changing prices for different levels of fat in meat.

The variable Wij(t) represents the average weight of all animals
1e jth subpopulation of cohort i,i.e., those animals whose number
JBPOPij(t). The daily rate of weight gain for animals within this
opulation is DGAINij(t). If no aging (the maturation process dis—
ad earlier) were to take place, then weights would change over

according to

t

t) = Wij(t-dt) + J DGAINij(u)du (5.1.16)

t-dt
nimals aged, but did not change weight from changes in size, then
average weight of a subpopulation would be solely a function of the
sfer of animals between herd subpopulations. ALPHAi(t) is a measure
1e fraction of the animals in a subpopulation of cohort i that leave
subpopulation in a single time increment.

= *
Ai(t) DT KKi
DELAYi(t)

(5.1.17)
DELAYi(t) = the delay time of the ith herd cohort

KKi = the total number of subpopulations in the ith cohort

DT = the length of time of a simulation time increment.

ce that ALPHAi(t) is bounded between zero and one. Because the

 

 

 

,;
f

KK. and DI
1
particula:
of that c
j of coho
increment

given by

BETA..(t
1]

where:
C
This ap}
applied
namely
the eql
is a WI

these

Mt)

Equac
Y0ung
ferre
each
memb
intc
COhI

Cal

94

and DELAYi(t) variables are constant over all subpopulations of a
icular herd cohort, ALPHAi(t) is also uniform over all subpopulations
hat cohort. BETAij(t) is the fraction of animals in subpopulation

‘ cohort i that were in the same subpopulation in the previous time

'ement; therefore an approximation to the true BETAij(t) value is

 

:n by
.ij(t) = SUBPOPi.(t)*(1 — ALPHAi(t)) (5.1.18)
C
'e:
= * _ *
C SUBPOPij(t) (1 ALPHAi(t)) + SUBPOPi,j_l(t) ALPHAi(t).

. approximation allows the simple form of equation 5.1.16 to be

.ied to each of the two sources of animals in subpopulation j;

:ly animals from subpopulation j and subpopulation j-l. Therefore
equation for the weight of members of subpopulation j of cohort

l weighted sum of the weights and rates of weight gain from both of

;e sources.

t
't = BETA.. t * W.. t-dt + DGAIN.. d 5.1.19
I) 1J<)[ lJ( ) [Ht 13m T] < >

t

+ (1 — BETAij(t))*[ Wi’j_1(t-dt) + I DGAINi,j_l(T)dT

t-dt
ition 5.1.19 applies to all subpopulations of cohort i except the
Igest; the youngest is different because it involves animals trans—
red between cohorts. The weight of the youngest subpopulation of

l cohort,e.g. Wil(t), is determined from the weight of the previous
ters of that subpopulation and the weight of the animals transferred
I it from another cohort. An example of this transfer between

Irts is the movement of heifers into the mature cow cohort. The

f cohorts use a fixed birth weight for male calves, and another

 

 

‘h

fixed'
to net

COW C(

ble W
impac
herd

of d

DGA

 

95

weight for female calves. An improvement to the model would be
ke these birth weights a function of the nutrient intake of the
ohort through time, especially during gestation.

Weight constraints for each herd cohort are imposed by the varia—
STMAXi(t). The rate of weight gain determined in the nutrient

t component is checked to see how it affects the weight of the
subpopulations. This check results in the following redefinition

e rate of daily gains based on the values obtained from NUTRN.

 

f
DGAINij(t),
{t
if Wij(t—dt) + J DGAINij(r)dr< WGTMAXi
t—dt
0,
ij(t) = 1 if Wij(t-dt) s WGTMAXi (5.1.20)
*
FRAC DGAINij(t),
if Wij(t—dt) < WGTMAXi,
t
and Wij(t—dt) + I DGAINij(r)dr > WGTMAXi
t—dt
K
WGTMAX. — W..(t—dt)
FRAC = __t.___1__._1_3_.__ (5.1.21)
DGAIN..(r)dT
Jt—dt: 13

Grading of beef cattle is a complicated procedure that heavily

ves subjective gradations of differences by human beings. Many of

bjective measures used, moreover, are such cattle descriptors as
size, height, etc. Since the gradation process and the objective
3 on which it is based are missing from this model the determina—
of grades will quite arbitrary. An attempt will be made to relate

yes in grade from those initial values entered as data by the user

 

 

 

\\

to 0(

the 1

for

five

sep

nee

 

 

96
isions when the projected rate of weight gain conflicts with
Kimum weight constraint. Individual price grades are specified
2h subpopulation of each cohort,i.e., GRADEij(t). There are
iscrete steps of grades and associated with each of them is a
te cattle price; this price structure is the reason for the
or cattle grading. Over the entire five grades there might be

:e difference of 100%. Grades are determined as follows,

if wij(t—dt) = WGTMAXi (5.1.22)

GRADEij(t—dt),

{ t

GRADE .(t-dt) + [ DGAIN..(T)dr*FATFAC,

13 t-dt 13

Q.(t) =
t if Wij(t—dt) < WGTMAXi

FATFAC = a parameter relating predicted rates of weight gains
at maximum allowed weight to changes in price grade
through the mechanism of muscle/fat proportions

GRADEi.(t) = an integer value (from 1 to 5) indicating the
J proper price grade characterizing any animals in
the jth subpopulation of cohort i; highest prices
are for grade 1, and lowest prices for grade 5.

 

 

v.2

dif

CE]

as

 

 

97

orage Growth Component

‘he grazing process is a complicating factor in the already
:ult problem of modeling plant growth. The interaction of cattle
-ants is not yet well understood. Cattle have preferences for
in species of forages over others, but these preferences are dynamic
a composition and digestibility of each plant species change over
rowing season. To fully explore the dynamics of the grazing process
e1 must include the following factors:
(1) growth and maturation of individual species as determined
by exogenous weather variables and field conditions of
canopy height, competition, slope, soil type, etc.
(2) digestibilities and consumption preferences for the major
plant components——stem, leaf, new shoots, and seed
(3) impact of grazing on growth, regrowth, reproduction, and
regeneration of plant species.
ly the above task is beyond the scope of this thesis. The model
oped to meet the requirements of the forage growth component, as
d in the problem statement section of Chapter III, is only an
al step on the road toward a complete grazing model.
The growth model developed for this thesis is an adaptation of
sslands model of Parton and Marshall[40]. Net photosynthetic
y conversion to plant material is a product of a transfer coef—
nt per unit of material times the amount of effective material
the level of incoming solar radiation times the minimum of three
h quality condition indices. These indices measure the relative

ty of temperature, soil moisture, and soil nutrients in terms of

 

98

,imal growth conditions. The net growth predicted by the basic energy
[version equation is partitioned into growth of greenery and increases
root storage by a function of the prior quantities of these values.

The amount of plant material that can effectively convert solar
iiation to plant growth is limited due to shading. This constraint
approximated by imposing a plant density limit on the quantity of
ant greenery per unit area which can convert solar radiation. Figure
6 illustrates the determination of the photosynthetically active
ount of plant greenery, ACTIVEn(t), per unit area.

Three quality indices are used to describe the relative quality
factors of plant growth other than solar radiation. The factors are
:mperature, soil moisture, and soil nutrients. The index variables
:scribing these are TPF(t), SMF(t), and SNFn(t), respectively. Use of
Iese indices implies the assumption that certain levels of these vari—
Iles are better for plant growth than others, regardless of the level
5 solar radiation. Figures 5.7 through 5.9 illustrate the relationship
:tween each of these variables and its corresponding index value. The
1ta points for each of the four figures, 5.6-5.9, are derived from
1rton and Marshall[40] and Sauer[47]. Better values could be determined
trough experimental study of weather conditions and plant growth at a
Irticular enterprise location. The values of the three quality indices
7e determined by use of the table interpolation function TABLIE[32].
1e value of the variable is the argument and the index value is the
:sult of the interpolation between data points.

The net growth rate of total plant material in any land parcel,

[0T0n(t), is determined through the following equation,

 

 

..—

ACTIV

1800

Fig

99

IVEn(t)

 

.—._._—— —-——_ _——————.—_———_

 

 

0 1800 GRNn(t)/LANDn
(kg/heC)

ure 5.6 Determination of the photosynthetically active quantity
of plant material per unit area

 

 

 

(t)

~ 0

O
. o
O
. O
O

o 10 20 3o 40 50 60 7o AVGTMP (t)

(° C)
Ire 5.7 Plot of points determining the temperature quality index,
TPF(t), from the average temperature

 

.75

.50

 

100

 

 

 

[th)
O O O O
5
O
O
0 P O
O
O
5 .
0 O
’ . . - . . . 1 . 1, .
0 2 4 6 8 10 12 14 16 18 20 22 SM(t)
(cm)
.gure 5.8 Plot of points determining the soil moisture quality
index, SMF(t), from the soil moisture
[F (t)
r O O O O 0
0
,ST
0
0 '
O
5 _
O
O
0 20 40 60 80 100 SNUTn(t)
gure 5.9 Plot of points determining the soil nutrient quality

index, SNFn(t), from the soil nutrient value

 

 

 

 

101

HOT0n(t) = ACTIVEn(t)*PHOMAX*SOLAR(t)*MIN (5.2.1)
here:

PHOT0n(t) = total plant growth rate in land parcel n-—kg/hec/day

ACTIVEn(t) = active plant material in land parcel n—-kg/hec

PHOMAX = conversion factor, 0.0004 kg/kg/langley/day

SOLAR(t) = solar radiation in langley/day

MIN = minimum value of TPF(t), SMF(t), and SNFn(t).
his rate must be partitioned into the proportion going to greenery
rowth and the proportion going to root storage. Since the quantity
f greenery and indirectly the amount in root storage in each land parcel
s a function of the previous grazing and harvesting activity, the pro—
ortioning factor ZX3n(t) is determined separately for each land parcel.
X3n(t) = PAR3 + PAR4*(1.0 - e‘PAR5*GRNn(t)/LANDn) (5.2.2)
here:

ZX3n(t) = proportion of PHOT0n(t) going to root storage

GRNn(t) = quantity of greenery in land parcel n——kg

PAR3, PAR4, PARS are constant parameters.

transfer of growth from root storage to greenery occurs at a rate

hat is largely controlled by the proportions of the total plant material
hat are in root storage and greenery. This accounts for the spurt of

rowth observed after a field has been heavily cropped as new shoots

ppear from the crowns of the roots.
- PAR2*LAND
n(t) = PAR1*ROOTn(t)*e GRNn(t)/ n (5.2.3)
here:
F (t) = rate of material transfer from root storage to greenery
n
——kg/hectare/day

LANDn = area of land parcel n in hectares

 

 

 

 

102

ROOTn(t) = quantity of root storage per hectare—-kg/hectare
PARl, PARZ are constant parameters.
he net growth rates of greenery and root storage in a pure growth

ituation are determined by equations 5.2.1 ~ 5.2.3; these result in

 

GRN (t)

—-‘i—— = (PHOTOn(t)*(1.0 « ZX3n(t)) + Fn(t))*LANDn (5.2.4)
dt

ROOT (t)

——n—— = PHOTOn(t)*ZX3n(t) - Fn(t). (5.2.5)
dt

This component model is not directly concerned with these pure
rowth equations. It is, however, the base on which consumption by
nimals and harvest by machine can be built. AHRn(t) describes the rate
f consumption of greenery in land parcel n by grazing animals, while
HRn(t) describes the rate of greenery removal through harvesting. Both
f these variables have units of kilograms per day. Neither grazing nor
arvesting is a pure consumption process; there is waste from trampling,
eces, dropping of cuttings, etc. A waste factor is used to model this
ccurence. MWF is a mechanical waste factor, with value 1.10, that is
onsidered constant for all levels of forage harvesting. AWFn(t) is a

aste factor for the grazing process; its value is a function of the

 

tocking rate in a particular land parcel n. Stocking rates represent

he number of animals per unit area of land. This model uses the control
ariable, PDSTRBni(t), to describe the proportion of the population of
ohort i grazing in land parcel n. Equation 5.3.6 determines the

tocking rate for land parcel n.

 

9
rocmna) = “13m * 2 PDSTRBni(t)*POPi(t) (5.2.6)
n i=1

5

103

 

:e:
STOCKLn(t) = the stocking rate of grazing animals in land
parcel n —— #/hectare
PDSTRBni(t) = the proportion of the population of cohort i
which is grazing in land parcel n
POPi(t) = the population of cohort i
LANDn = size of land parcel n —- hectares.

ire 5.10 illustrates the relationship between stocking rates and
grazing waste factor, AWFn(t). As the stocking rate increases,

waste factor is also increased reflecting greater impacts of cattle

 

 

 

:he land.
AWFn(t)
.5- O
O
O
O
O
.0” .
5 D
0 l. 2. 3. 4. 5. STOCKLn(t)

(animals/bee)

'igure 5.10 Relationship between grazing waste factor, AWFn(t),
and the stocking rates, STOCKLn(t)

104

.roduction of these sources of greenery consumption and their
;pective waste factors concludes the factors which affect the

tnge of greenery in pasture. This gives the net growth rate

:d in the model,

[lg—(L) = (memo (t)*(1.0 — 2x3 m) + F (Mum) - AWF (t>*AHR (c)
. K n n n J n n n

— MWF*MHRn(t) (5.2.7)

The quantity and the quality of forage growth consumed by animals
1 equally important. DIGESTn(t) describes the quality of forage in
1d parcel n in terms of total digestible nutrients (TDN) on a dry
sis. Digestibility is a dynamic variable that reflects time changes
average plant composition and in actual changes in the energy value
the individual parts. Since this model does not maintain forage
intities on the basis of constituent parts, a less rigorous approach

digestibility must be used. Digestibility is modeled as a function

 

three factors: relative age of green material, time of season,
1 density of greenery per animal grazing. The base digestibility
.ue (in terms of Z TDN on a dry matter basis) is determined by

a relative age of green material in a particular land parcel. This

 

lel formulation assumes that the major element in the change of

rage digestibility over time is a process of decline associated

:h the length of time since growth first started. Time in the

iwing season and greenery density per grazing animal are Viewed as

:ondary factors modifying the base digestibility value. Mathemati-

.ly, forage digestibility is described by

iESTn(t) = BASEDGn(t)*FRQUAL(t)*FDENSEn(t) (5.2-8)

105

re:

DIGESTn(t) = forage digestibility of green plant material
in land parcel n as Z TDN

BASEDGn(t) = base forage digestibility determined from the
relative age of forage greenery in land parcel n

FRQUAL(t) = seasonal digestibility factor modifying the base
digestibility value BASEDGn(t)

FDENSEn(t) = forage density digestibility factor modifying
the base digestibility value BASEDGn(t).

The base digestibility of forage in any land parcel is deter—
sd by linear interpolation between data values representing digesti—
Lty versus relative age. The argument used to obtain the resultant
ige digestibility value is the variable PINDEXn(t). This variable
In index representing the amount of time that would be required
the current forage quantity in a land parcel to be grown at the

:ent rate of growth existing within that land parcel. Mathemati—

Ly,
_ GRN (t)
)EXn(t) — n (5.2.9)
dGRNn(t)
dt

: index is able to represent the major situations in plant growth
Ising the ratio of current quantity over the rate of change of

: quantity. Figure 5.11 graphically plots the relationship between
and digestibility which is the key to this model of plant quality.
:an be seen from the graph, the plot is a monotonic decline in

Lge quality with increasing relative age. This formulation in
unction with equation 5.2.9 is able to correctly represent the
,ity of forage over time. For example, if during a period of high

'th mechanical harvest were to severely reduce the quantity on hand,

 

 

\\

106

 

 

BASEDGn(t)
1.0
.75»
O
O
O
I
O
O
I
.50' . Q
.25'
0 A I A A l A A 1 I A
o 10 20 3o 40 50 PINDEXn(t)

Figure 5.11 The intermediate digestibility, BASEDG (t), as a function
of pseudo—age, PINDEXn(t) n

an the relative age determined by equation 5.2.9 would be quite

v. Using the plot of Figure 5.11 gives the correct fact of relative-

high forage quality. Others cases encountered in forage growth

:uations are also handled by this model of forage digestibility

well. Although the relative age of forage is important in determin—

; digestibility, it is not sufficient. There are qualitative differ-

:es in the new growth over the length of the growing season and in the

rticular growing conditions encountered. This factor is incorporated

:o the model through use of a multiplicative forage quality factor

EUAL(t). FRQUAL(t) is determined by integrating the value of TPF(t)

tr the length of the growing season and using that integral value

determine an index of the degree of plant maturity attained.

 

,1
5‘

107

 

 

FRQUALn(t)
1.01L A
A A A
A
A A ‘
A A
.75 '
.50 .
.25 h
0 a A A A # L l A A A
0 50 100 150 200 250 SUMTPF(t)

igure 5.12 The growth quality factor, FRQUAL(t), as a function of
the integral of the temperature index over the growth
season

TPF(t) = TPF(T)dr (5.2 10)

4TSPRNG

SUMTPF(t) = the integral of the temperature quality factor over
the growth season to current time t

TPF(t) = the temperature quality factor as determined from
use of Figure 5.7 and the average temperature

TSPRNG = time at which spring growth begins.
TPF(t) is used as the argument for another use of the table func—
1 TABLIE[23] to determine the value of FRQUAL(t). Figure 5.12 indi—

as the relationship between SUMTPF(t) and FRQUAL(t) graphically.

 

 

 

108
FDENSEn(t)
1.0t
O O D
O
C
.75-
o
.50'
.25’
0 5 10 15 20 25 30 GRNDENn(t)

Figure 5.13 Plot of the forage density digestibility factor
against per animal density

The final factor modifying the base digestibility value is
NSEn(t)-—the influence of the current amount of forage per animal
digestibility. The value of this density factor——GRNDENn(t)—-is
d as the arguement to obtain FDENSEn(t) by linear interpolation

ween data values as represented in Figure 5.13.

GRN (t) 2
DENn(t) = _.__n_____ (5. .11)
STOCKLn(t)*LANDn*DAYS
re

STOCKLn(t) = animals grazing in land parcel n—-#/hectare
LANDn = number of hectares in land parcel n
GRNn(t) = greenery in land parcel n——kg

GRNDENn(t) = forage density per grazing animal—-kg/anima1.

\\

 

 

109

This development concludes the description of the model for
etermination of forage digestibilities; three factors have been
hown to be important to this modeling effort: relative age of
orage in land parcels, season of the year, and the density of
orage available for grazing in each land parcel.

Two state variables remain to be defined before this component
vodel's description is complete. SM(t) is a variable describing the
mount of soil moisture. SNUTn(t) is a variable describing the amount
f soil nutrients. The rate of change of soil moisture is dependent
n three factors:

SM(t)

dt = RAIN(t) — EVAP(t) — PERC(t) (5.2.12)

 

here:

SM(t) = soil moisture at its current level—-cm in effective root
depth

RAIN(t) = rainfall in cm/day
EVAP(t) = evaporation in cm/day
= a*AVGTMP(t)2

PERC(t) = percolation beyond root depth in cm/day
—SM(t)/c

II

b* 1.0 —e
a, b, c are constant parameters.

'he rate of change of soil nutrients is a function of the rate of

hotosynthetic energy conversion and of fertilizer application to the

oil. This implies that the greater the growth rate, the larger is

.he withdrawal of nutrients from the soil.

iSNUTn(t)

= — *PHOTO t (5.2 13)
dt SPFERT B n( )

 

 

110

SNUTn(t) = current level of soil nutrients in land parcel n
SPFERT = rate of applicatin of fertilizer per unit of land

PHOTOn(t) = rate of photosynthetic energy conversion in land
parcel n

B = a constant parameter.

This forage growth component model is relatively crude. It
Jides the basic elements needed to evaluate realistic grazing
agement strategies but could be improved considerably. This model
also very empirical, as is evidenced by the extensive use of TABLIE
Look up interpolations between data values. The data values used
uld, and could, be tuned to a particular location. Figure 5.14
a block diagram of the entire component model. This figure is a
venient way to trace the interconnection of the model variables

they have been described in this section.

 

lll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

..TElE
some
, L
f(GRN,TEMP,SOIAR,SM£IQr
PHOTO
I
‘ H 1.0
+
zr3 - Z M /
Home) I
H
STOCKL
+
f(GRN,ROOTS) + 2 _ 11 £213.
F _
GRNDOT
H Elli
5““ MWF
GRN

 

 

 

 

 

 

 

 

 

 

 

 

 

r %,GRNDOT,TEMP ,STOCKL)

'igure 5.14 Block diagram of the forage growth component

112
Feed Stock Component

The feed stock component consists of basic accounting for the
.ous activities involving feed stocks. Chapter IV, section 2,
:ribed these activities. Subroutine FEEDS performs this accounting
:he enterprise simulation model.
Quantities of feed stocks are represented by the variable FSTOCKn(t).
equation determining current feed stock levels uses the previous
:1, the amounts bought and sold, the amounts fed to cattle, and the
Int lost through waste and pests. Thus

)CKn(t) = FSTOCKh(t—dt) + STKPURn(t-dt) + CROPn(t—dt)

CSALESn(t—dt) - STKFEDn(t—dt)

FRCLOSn*FSTOCKn(t~dt)*DT (5.3.1)

FSTOCKn(t) = current quantity of feed stock n —- kg
STKPURn(t) = quantity of feed stock n purchased —— kg
CROPn(t) = quantity of feed stock n produced —— kg
CSALESn(t) = quantity of feed stock n sold —- kg
STKFEDn(t) = quantity of feed stock n fed to cattle —— kg
FRCLOSn = annual rate of loss of feed stock n
DT = length of simulation time increment —— years.
of the sources of increase or decrease for FSTOCKn(t) except losses
determined in other model components. FRCLOSn is a constant frac—
al loss rate assumed to be uniform over the entire year.
The digestibility of feed stocks in terms of a TDN value are
lied by FQUALn(t). Changes in quality are a result of purchases,

production, and spoilage. Spoilage is assumed to mean that the

 

113

:y of the crop declines over time. SPOILn is an annual frac—
l decline in quality of crop n; like FRCLOSn it is assumed to
nstant over time. FQUALn(t) is determined by

.n(t) = FQUAN*FQUALn(t—dt)*SPOILn*DT
Fsmocxnu)

 

+ PRQUAL7n (t) * STKPURn (t) + CROPn (t ) *CROPQLn (t)
FSTOCKn(t)

 

(5.3.2)

FQUAN = FSTOCKn(t-dt) - CSALESn(t—dt) — STKFEDn(t—dt)
PRQUALn(t) = the TDN value of feed stock n purchases
CROPQLn(t) = the TDN value of feed stock production.

The final variable determined in this component is the total
Ial crop production of feed stock n, namely CROPGn(t). This
re gives a running total of the production to date and could be
>ared with XCPRODn(t) to obtain an estimate of the quantity of
1 stock n that might yet be harvested in this growing season.

?Gn(t) = CROPn(T)dT (5.3.3)

I t
TSPRNG
‘ Figure 5.15 is a block diagram illustrating the total inter—

ationship between variables that are included in this component

31 of feed stocks.

 

114

  
   

 

we

 

CROPQL CROP

FRCLOS

 

 

 

Z
+ FSTOCK
+

 

 

 

 

STKPUR
PR UAL SPOIL
’d
n
1 ~ m
+ RT.
FQUAL

Figure 5.15 Block diagram of the feed stock component.

 

 

115

I Nutrient Impact Component

The model for this component develops the impacts of nutrient
take in two areas: reproduction and growth. The nutrient impacts
.at are modeled are those related to energy; protein requirements
I well as vitamins and trace minerals are assumed to be available in
ifficient quantities that energy is the predominant variable of in—
erest. The majority of this component is contained in subroutine
UTRN, and is described in Schuette[48]. This thesis will not present
hose results except as they interact with the remainder of the system
Iodel.

Feed quantities and qualities are a prime concern of this compon-
ent. Feed is described in terms of four variables for each herd cohort:
(l) CNCALi(t)——the quantity of concentrates allocated to cohort i,

(2) RHGALi(t)——the quantity of roughages allocated to cohort i, (3)
IDNCi(t)——the average TDN value of the concentrates allocated, and

(4) TDNRi(t)—-the average TDN value of the roughages allocated to
"ohort 1. These variables are inputs to subroutine NUTRN which then
determines the impact of these feed inputs. NUTRN returns several
variable values: TDMICi(t)—-quantity of concentrates actually consumed
by cohort i, TDMIRi(t)——quantity of roughages actually consumed by
cohort i, and DGAINij(t)—-the rate of daily gain by the jth subpopula-
tion of cohort i as a result of the interaction of its feed intakes

of energy and requirements for energy.

Total roughage allocation to any cohort is composed of feeds from
grazing as well as those from feed stock allocations. Usually these

sources are disjoint, but there are some conditions under which grazing

vould be supplimented by feed stocks. The procedure used here is to

 

 

 

116

nine the roughage allocation as a result of the grazing distri—
n of the herd, and add to it the voluntary feed allocations. The

. grazing roughage allocation for the ith cohort is then

 

* *
NLANDS PDSTRBni(t) POPi(t) GRNn(t)

iL (t) =
i n21

 

(5.4.1)

9
Z PDSTRB
n

it
1:1 POP (t)

l

 

FORGALi(t) = current forage available to the ith cohort as a
result of its distribution over the land parcels
.. kg

GRNn(t) = total quantity of greenery in land parcel n —- kg

PDSTRBni(t) = fraction of the population of cohort i which is
grazing in land parcel n

POPi(t) = current population of cohort i.
digestibility of this allocation in terms of TDN is a function of
forage digestibilities in each land parcel.

NLANDS IPDSTRBni(t)*POPi(t)*GRNn(t)*DIGESTn(t)I

TDNi(t) = 2 9
‘ n=1 2 PDSTRBn2(t)*POPl(t)*GRNn(t)
r=1

re:

 

(5.4.2)

FORTDNi(t) = digestibility of the FORGALi(t) allocation in TDN

DIGESTn(t) = the TDN digestibility value of the forage in land
parcel n.

Addition of the roughage from grazing and the voluntary allocation
es the total roughage allocation to cohort i,
ALi(t) = FORTDNi(t) + FEEDALi(t) (5.4.3)
ch has a digestibility value determined by the weighted average of

different sources of the roughage.

 

 

 

117

= *
(t) FEDTDNi(t) FEEDALi(t) + FORTDNi(t)*FORGALi(t) (5.4.4)

 

FEEDALi(t) + FORGALi(t)

FEDTDNi(t) = the average TDN value of the roughage voluntarily
allocated to cohort i

FEEDALi(t) = the roughage allocation voluntarily given to herd
cohort i —— kg/DT.

Determination of the value of FEDTDNi(t) and TDNCi(t) requires
; the allocation of TDN from roughage and of TDN from concentrates
:elated to the actual physical quantities of feed stocks that are

This results in

 

 

* *
. (t) = CATTINli£(t) POPi(t) DAYS (5.4.5)
1 CNCALi(t)
CATTIN . (t)*POP (t)*DAYS
TDNi(t) = 212 1 (5.4.6)
FEEDALi(t)
re:

TDNCi(t) = average TDN value for the concentrate allocation
to cohort i

FEDTDNi(t) = average TDN value of the roughage allocation to
cohort i

CATTINl.£(t) = quantity of TDN allocated to each member of
l cohort 1 per day from concentrates under plan 2

= quantity of TDN allocated to each member of

CATTIN
cohort i per day from roughages under plan 0

212(5)

CNCAL (t) = physical quantity of concentrates allocated to the
i .
ith cohort —— kg/DT

FEEDALi(t) = physical quantity of roughages allocated to the
ith cohort -— kg/DT

DAYS = number of days in a simulation time increment.

units of the variables FEDTDNi(t) and TDNCi(t) are kg TDN/kg feed,

 

 

 

118

lowing directly from their definition as the average TDN value of
uantity of feed stocks fed to cattle.
Determination of the actual quantity of feed stocks fed to cattle
each time increment of the simulation requires knowledge of the
ired distribution of the TDN allocations over the possible feed stocks
sting. The control variables CNCFRCin(t) and RHGFRCin(t) are used
management to distribute the cohort allocations of concentrates and
ghages over the range of available feed stocks. STKFEDn(t) is the
iable used to represent the actual quantity of feed stock n used for
tle feeding in the current time increment of the simulation. This
iable is not a rate but a quantity, as are all variables affecting
current quantity of feed stock n on hand——FSTOCKn(t). Since the
d stock variables include both roughages and concentrates in a single
ting, the following equation determines the amount of feed stock n

d for cattle consumption in this time increment.

9 ...-
_. *
.FEDn(t) — DAYS*iEl POPi(t)* CATTIN1i (t) CNCFRCin(t)
- " 1
*-——————- 5.4.7
+ CATTIN2i (t)*RHGFRCin(t) FQUALn(t) ( )
re

STKFED (t) = quantity of feed stock n fed to cattle in this DT
n

CNCFRC. (t) = fraction of the TDN allocation of concentrates to
in cohort 1 derived from feed stock n

RHGFRC. (t) = fraction of the TDN allocation of roughages to
In cohort i derived from feed stock n

FQUALn(t) = current TDN value of feed stock n

POPi(t) = current population of cohort i.

Equation 5.4.7 brings together the actual quantities of feed

Icks that have been used to feed cattle. It combines the consumption

roughages and concentrates in one single equation, but Since this

 

isa

proi

str'

men

mat

41“
{I555

 

119

a mutually exclusive description there is no overlap to cause
)blems. Therefore, the matrices CNCFRC(t) and RHGFRC(t) are con—
ructed so that when the inth element of one is nonzero, the inthele—
it of the other is zero. Additionally, the rows of both of these
trices must sum to one if any allocation is to be made. This require-
nt exists because either a row of CNCFRC(t) or RHGFRC(t) represents
e fraction of the cohort allocation that is drawn from each of the
ed stocks. A final note concerning the use of the feed stocks for
nsumption——this model assumes that the entire amount of the feed
ock allocated for consumption is used. Any quantities allocated to
e herd or a specific cohort which are not consumed are assumed to be
mpletely wasted.

The consumption characteristics of the herd cohorts determine
ether the allocations to the herd are completely consumed or not.
en the herd is not grazing, any excess allocation over consumption is
tally wasted. When the herd is grazing, however, a differentiation
st be made between nutrient intakes from grazing and from voluntary
eding. The following priority of cattle consumption preferences is

sumed to hold: (1) cattle prefer concentrates to roughages, and (2)

Lttle prefer feed stock roughages to grazed roughages. Differential

feferences among feed stocks are assumed to be negligible, although

Iey do in fact exist. The consumption of roughages by the herd which

7e not covered by voluntary roughage allocations comes from grazing.

Iis grazing removal of forage must also be distributed across the

Lfferent land parcels being grazed. The variable PDSTRBni(t), which

is used to obtain the stocking rates in the land parcels, is used here

3 distribute the forage removal by grazing over the land parcels.

 

2‘
fl

120

5
HR (t) =
n i=1

[PDSTRBin(t)*(TDMIRi(t) — FRAC*FEEDALi(t))] (5.4.8)
here:
TDMIRi(t) = actual roughage consumption of cohort i

AHRn(t) = grazing removal of forage from land parcel n

FRAC = proportion of roughages consumed that are from voluntary
feed sources

 

SPLIT, if RHGALi(t) > FEEDALi(t)
1.0, otherwise
SPLIT = a parameter based on cattle preferences.

Variables internal to subroutine NUTRN maintain the reproductive
ondition of each subpopulation of the breedable female cohorts. See
chuette[48] for a complete discussion of this model. Reproductive
ffects on male breeding cohorts have been ignored up to this point in
he model's development. When breeding activity occurs, the variables

PATijk and CTIMi. describe the resulting pattern of pregnancy rate

jk
nd timing for the jth subpopulation of cohort i from its kth servicing.

ne variables are used in Subroutine BIRAT of the population demography

omponent to develop overall cohort birth curves.

The simulation model of this component is the subroutine CONSUM.
1e subroutine develops values for STKFEDn(t), AHRn(t), DGAINij(t), and
eproductive impacts reflected in the values of CTIMijk and CPATijk
ien breeding occurs. Figure 5.16 represents a block diagram of the

1broutine CONSUM.

 

 

CATTINl

 

 

 

 

H H n n
llll I'll lqg F UAL

 

 

 

 

 

 

 

 

 

 

 

 

 

n
d TDNC
.FORTDN
d
EEEAL FORGAL
+
+
f(FEEDAL,RHGAL)
FRAC
I I 7
SUBROUTINE
NUTRN
- o
" TDMIR +
DGAIN
reproductive AHR
TDMIC effects

CATTINZ

lllll

—————4
POP

11

.-

FEDTDN

FEEDAL

Figure 5.16 Block diagram of the nutrient impact component.

 

  

   

 

PDSTRB

 

 

.5 Management Decision Making Component

This section will provide the full details of the model of the
‘ nagement component. As outlined previously, management decisions
[:ve been separated into two discrete groups; those decisions which
fan be determined endogenously using standard economic criteria and
:hose whose nature is not so obviously solvable. This latter group
If decisions is acted on by the user of the model through exogenous
supply of control variable values. The purpose of this section is
:o explain the details about how decision points-—times when exogenous
:ontrol is exercised-—are recognized, to give the form of the equa—
:ions for carrying out specific decisions, and to review the criteria
for endogenous decision making.

Four of the five decision points are organized around physical
:vents; these are the onset of spring growth, breeding, weaning,
Ind culling. These will usually occur in the order listed above, but
not necessarily so. The fifth decision point is the occurrence of an
:vent requiring the attention of the model user. These are fall feed
:tock supplies unsynchronized with feeding plans, feed stocks unable
:o carry the herd for two DT time increments, and working capital
falling below acceptable levels.

One characteristic which makes decision making difficult at
:hese five points is the fact that the prices the manager expects
Ilay a key role in the action he takes. An additional complication
,s the uncertainty in knowing how to act with regard to husbandry

rctivities such as weaning, culling, and breeding. The very long

 

 

 

123

time delays involved in the production of marketable cattle (at
whatever stage of maturity) and in the introduction of replacement
breeding animals imply that the manager must guess the future market
and hope he does so correctly. The response of many managers is to
go with the current price as a guide for future desired production.
This results in wide industry supply fluctuations (and thereby price
fluctuations) over a multi-year cycle. This cyclical behavior exists
to some extent in all livestock products and is partly a result of
the uncertainty (due to the delay lengths) that long production

lead times bring to decision making. This component model is there—
fore organized to recognize decision points, to allow the user to
make his own judgmental decision, and to determine all other decisions
internally using standard economic criteria.

Organization of this component model can be easily understood
through review of Figure 4.9. In every time increment of the simu-
lation model subroutine INQUIR attempts to determine whether any
of the five forms of decision point currently exist. Figure 5.17
illustrates the construction of INQUIR. In each DT simulation time
increment the current time value is checked against each of the five
possible time points that constitute decision points-—TSPRNG, TBRD(1),
TBRD(Z), TWEAN, and TCULL. Additionally, the three criteria that call
for a special decision point are checked. If any of them are true,
then the special decision point is called by setting IFLAG equal to
2, while IFLAG is set to 1 at any of the regular decision points. If
the IFLAG variable value is not equal to zero at the conclusion of

the decision point checks, then INQUIR creates a permanent file of

 

 

 

 

 

124

Ill values that are needed to preserve the simulation in its current
;tate. This permanent file is available for access at any time to
:estart the time simulation exactly where it left off. If the IFLAG
value is still zero (as it was set as the initial action in the sub—
:outine) at the end of all decision point checks, then control skips
from subroutine INQUIR to subroutine NORMAL.

Subroutine INQUIR is constructed (again see Figure 5.17) so that
each decision point is checked every DT increment of simulated time
so that multiple decision points at any one time can be detected.
in example of this is the event of weaning and culling occurring
at the same time. INQUIR will have gotten all the way thrOugh its
structure to the point of checking whether time is equal to TWEAN;
since this is true, the if statement branches to YES, IFLAG is set
equal to one, and the detailed states of the model and any other
information that the decision maker might need to make a decision are
printed onto the output file for the user to observe. Following the
Logic of INQUIR, the checking of time for equality to TCULL is the next
operation. The if statement check is true, then the logic path of YES
is followed. This logic branch results in additional printing of
state variable and other decision information, but the printing for
each decision point is tailored for that decision point resulting
in some new information being made accessible to the decision-maker.
In practice the values of TBRD(1) and TBRD(2) are also likely to be
equal; that is why the logic of INQUIR bypasses part of the YES

branch of the TBRD(2) if statement check when time has already been

 

 

125

IFLAG = 0 START

 

YES PRINT
= TSPRNG IFLAG=1 .
1. price expectations

4. financial status

 

 

 

 

PRINT
IF ————‘

N0 T = TBRD(1) IFLAG=1

price expectations
herd populations
subpopulation weights
feed stockl ml
financial status

WL‘WNH

 

 

 

A T

 

 

PRINT
IF IF “-——

T = TBRD(1)

price expectations
herd populations
subpopulation weights
feed stock levels

. financial status

T = TBRD(2)

IFLAG=1

mpmmb—a

 

 

 

 

m

...

. price expectations

. calf cohort numbers
and weights for each
subpopulation

. financial status

N

La

 

 

 

J

 

 

PRINT

 

H

price expectations

. mature cow cohort
numbers and weight
for cat ch of the
subpopulations

. financial status

n
T = TCULL YES IFLAG=1

N

1...)

N0

 

 

 

Figure 5.17 Flow chart of subroutine INQUIR of the management
component

 

 

 

126

      

gRINT

 

  

. price expectations

NH

. financial status

4‘ T
v

COMPUTE

 

 

 

 

 

FLEVEL (t): the

e n
in this increment

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

IF PRINT
1. rice ex ectations
LEVEL>FSTOCK IFLAG =2 2. herd numgers and wghts
2 .
for all subpopulations
3. feed stock levels
4 feed requirements
N0 5 crop expectations
6 financial status
YES COMPUTE
FWLONG : the win-
N0
1.price expectations
2.herd numbers and ugh:
for all subpopulations
3.feed stock levels
4.winteting feed needs
5.crop expectations
6.financial status
= irLAG=2
WRITE
NO CREATE THE RESTARTFILE—>.
BY SUFFERING OUT ALL
VARIABLE VALUES WHICH
ARE NEEDED TO RESTART
THE SIMULATION AT THIS
YES EXACT POINT

 

 

 

Figure 5. l7 (cont 'd.)

 

 

 

 

 

127

recognized as equal to TBRD(1), thus setting the value of IFLAG to

one. The logic of INQUIR has been developed so that multiple decision
points existing at a particular point in simulated time can be detected
and acted upon. Subroutine RESPNS, which reads in control variable

values, has a parallel structure to subroutine INQUIR.
Exogenous Decision Making

When a decision point has been detected, the decision information
printed, the permanent file constructed, and the simulation stopped,
the user makes his decisions based on any decision rule or intuitive
feeling that he desires. Once he has made his decisions for a partic-
ular decision point and the data cards for the control values are pre—
pared, the user restarts the simulation by reading from the permanent
file to fix all model variable values just as they were when the deci—
sion point(s) was detected. The next step is to read the control vari-
able values; subroutine RESPNS accomplishes this action. Figure 5.18
is a flow chart illustrating the construction of subroutine RESPNS.

Subroutine RESPNS is constructed parallel to the structure of
subroutine INQUIR; the control variables that are read in to direct the
enterprise's operation at each decision point follow the input formats

in User's Guide to the Beef Cattle Enterprise Simulation Model. When

 

current time is equal to a decision point time, or when the value of
IFLAG is two, then the logic path follows the YES branch from the if
statement. The first action is to read the control variable values
which apply for that decision point from the user supplied data cards;
the second action is to perform any execution statements that are
peculiar to that decision point. An example of such specialized exe—

cution statements is the action to wean the calf cohorts; here the

 

 

 

 

 

    
 
     
     
 
  
 
 
  

READ

 

expected prices
grazing controls
expected growth
forage harvest time
harvest controls

 
 

UIbHNH

 

 

 

READ

 

expected prices
breeding duration
feeding plans
TWEAN, TCULL

b~u N H

 

 

 

 

 

READ
. expected prices
. breeding duration
. feeding plans
. TWEAN, TCULL

#1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
  

 

     
 

READ COMPUTE
YES 1. expected prices 1. weaned calves
‘2. weaning controls 1. transfers to
3. minimum age heifer coh.
4. CULL 3 record time
and ages and
weights t
No ean n
A. weaning costs
READ COMPUTE
YES 1. expected prices . cull nature
2. culling pattern ____.. cow cohort
2' :::§ agiitions 2. determine
' s s culling costs

  

 

 

 

 

 
   
    
     
 

READ

 

. expected prices

. herd transfers
. feed stock actions
. feeding plans

  
 

 

 

@

Figure 5.18 Flow chart of subroutine RESPNS of the management
component

 

[‘

 

 

 

129

control variable TFRAC£i(twean ) is used to transfer a fraction of the
2th female calf subpopulation to the ith heifer cohort. Similar exe-
cution statements are required to cull the mature cow cohort using the
control variable CULFRCj(tcull). When any necessary execution state—
ments have been completed for a particular time related decision point,
the logic path proceeds with the determination of the existence of
other decision points in this simulation time increment. If a special
decision point has been detected by subroutine INQUIR, then the value
of IFLAG is two. If IFLAG has a value of two, then subroutine RESPNS
branches to the YES side of the final if statement check, reads in any
control variable values required, and performs any needed execution
statements. At the conclusion of this step, the YES branch logic path
rejoins the main flow within the subroutine; the last action is then
to exit from the subroutine and proceed with the normal logic flow of
the overall simulation model.

The final element in the management component is subroutine
NORMAL; this element will be discussed in considerable detail in the
last part of this section under the subtitle "Endogenous Decision
Making." Control is transferred to NORMAL from two points; first, from
subroutine INQUIR if no decision points have been encountered in the
current time increment. The second referral point for subroutine
NORMAL is after subroutine RESPNS has completed its reading of control
variable values and executed any statements carrying out the user's
decisions.

Spring growth onset and breeding decision points require the user

to specify the value of various expectation and control values that will

have long term effect on the enterprise's behavior. At the time spring

 

 

.. I'llA
.[Illllllfl

 

 

130

growth begins the user must specify several control variables that will
influence the use of forage and its growth over time. PDSTRBni(t) con—
trols the stocking rates on each of the land parcels through specifi-
cation of the fraction of the population of cohort i that grazes on

land parcel n. Equation 5.2.6 illustrates this effect. TMHRk specifies
the times at which forage is to be mechanically harvested, while REMOVL
controls the amount harvested. XCPRODn and XCQUALn provide information
to the model about the expected amount and quality (TDN) of crop n that
will be harvested in this growing season. This includes forage growth
as well as feed crops.

Breeding is the activity of the enterprise that is most affected
by the uncertainties of cattle and feed stock prices. At this time the
manager must decide how his reproductive females will be bred, the
duration of the breeding period, and which animals are to be bred.
These decisions are very complex since they are ultimately conditional
on the prices that will occur in the market for cattle and for feed
stocks in the interval between the beginning of this breeding period
and the soonest date for calf sales. Moreover, the relationships
between feed stock intake rates over time and the success of breeding,
and between feed stock intake rates and weight gains of growing cattle
are so complicated that only use of a simulation model of the herd is
likely to correctly develop the impacts of breeding and feeding policies
on calf numbers and weights. Knowledge of the physical outcomes of
different feeding and breeding policies would then be combined with
expected prices to obtain predictions of financial outcome conditional
on the prices used. This simulation model can accomplish this invest—

igation through use of the decision point mechanism developed to permit

 

 

 

 

131

just this sort of evaluation of control strategy alternatives.

When the breeding decision point is reached, the management com—
ponent recognizes this fact and creates the restart file of simulation
variable values. It has also printed current state variable values to
allow the user to have a complete picture of the current condition of
the enterprise. The user makes the decisions about breeding and feed-
ing policies he wishes to follow and restarts the model to determine
the results of his decisions over time. When the next decision point
of the simulation is reached this procedure is repeated. The user
proceeds in this manner until the final time horizon has been reached
for evaluation of the breeding and feeding policies he is investigating.
He can then return to the restart file from which he started and repeated
this entire procedure using a different set of control variable values
representing a different breeding policy. By utilizing this sort of
procedure to investigate the alternative breeding and feeding policies
the user should be able to select one that is best for the price expec—
tations and other assumptions he is using. Figure 4.11 illustrates the
sort of alternative routes that can be developed using the decision
point mechanism.

The control variables that the user enters at the breeding deci-
sion point are (l) DURBi(t)——the duration of the breeding interval for
the ith female cohort, (2) FPLANSz(t)——the times at which the feeding

plans for the herd end, (3) CATTIN (t)--the feeding rates for the

ikl
cohorts under the different feeding plans, and (4) DISTFDin£(t)-—the
proportions of the desired TDN feeding levels to come from specific

feed stocks under the alternative feeding plans.

 

 

 

 

 

132

Weaning is an event which requires extensive calculation to carry
out the user's decisions. At the time of weaning, the population of
calves (both male and female) will be spread among numerous sub—
populations of cohorts 7 and 8. The user specifies how he wants these
calves used through the variables AGEMIN and TFRACzi(t). AGEMIN is
the minimum age that is to be weaned. This variable is included to
allow control over weaning in extended calving seasons, where calves
may be present in the entire range of subpopulations of the calf cohorts.
TFRAC£i(t) is the fraction of female calves in subpopulation 2 that are
to be transferred to cohort i. In all cases the index Q refers to
the 2th subpopulation older than the minimum weaning age, and 1
refers to cohorts 2 or 3——the replacement heifer and bred heifer
cohorts.

An important consideration in the mechanics of weaning is to
preserve the age distribution that has been maintained in the calf
cohorts following transfer to the heifer cohorts. This age distri-
bution is important to future determination of puberty in heifers,
which is largely a function of age and weight. Discrete delays are
used in the calf and reproductive heifer cohorts to allow the
population to be recorded strictly on the basis of age, not on the
basis of relative maturity as is done in the other herd cohorts. The
individual stage delay length for the delay models of the calf and
replacement heifer cohorts are equal so as to keep the same level
of fineness of the age distribution. Figures 5.19 and 5.20 illustrate
the way in which the variables AGEMIN and TFRACi(t) can select from

the female calf cohort to create the new entries in the replacement

 

 

 

 

 

 

igBPFP8j(twean)
20 ' o 9
l .
‘ :
AGEMIN 9 : I o
I l | I l
I | . I I
' I I ‘ :
1o ' : . l i .
, I I ' I
I I
: : l : :
i 9 1 i : I o
' ' I I I : '
I t ‘ I l '
' ' I I ' 3 I
0 l n n 4 l L n L L
2 4 10 12 14 16 18

Figure 5.19 Subpopulation values from the female calf
to weaning action by management

 

j index

cohort prior

 

gngpP2j(twean)
TFRAC12(twean) 0
TFRAC22(twean) 0
TFRAC32(twean) = 0.5
20 ' TFRAC42(twean) = 0.5
TFRAC52(twean) = 1.0
Q TFRAC62(twean) = 1.0
2
U
10 ' O O : O
I I I
I I : z
: : ' :
l I '
: : i :
I I I I
O A. -
4 6 8 10 12 14 16 18

Figure 5.20

j index

Subpopulation values from the replacement heifer cohort
following weaning action

 

 

 

134

heifer and bred heifer cohorts. Figure 5.19 depicts a female calf
cohort with six subpopulations older than the minimum age for weaning,
AGEMIN. The table of values listed for TFRAC£2(t), £= l,...,6 indicate
the fraction of the subpopulation indexed in the 1th position greater
than the index corresponding to AGEMIN that are transferred to the
replacement cohort. The result of the initial female calf cohort
subpopulation distribution, and the indicated values of AGEMIN and
TFRAC22(tL is the replacement heifer cohort subpopulation distribution
given by Figure 5.20. Mathematically,

SUBPOP (t) = SUBPOP (t)*TFRAC (t) (5.5.1)

22 £2

8,m+£
where:

SUBPOP ij(t) = the population of the jth subgrouping of cohort i

TFRAC£ 2(t) = the fraction of the m+£ subpopulation of cohort eight
transferred through weaning to the replacement heifer
cohort

m = the subpopulation index corresponding to the oldest sub—
population younger than age AGEMIN.

Similarily for the females calves weaned and sent to the bred heifer

 

cohort,

= * 5.5.2
SUBPOP3£(t) SUBPOPS’m+£(t) TFRAC£3(t) ( )

where:

TFRAC£3(t) = the fraction of the m+£ subpopulation of cohort
eight transferred through weaning to the
bred heifer cohort.
The remaining calves in the female calf cohort older than AGEMIN are

sold on the market, as are all male calves not retained for bull replace-

ment S o

135

Sales of cattle is partially accomplished through use of the
cohort delay output variable ROUT1(t). Subroutine RESPNS makes use
of this variable when carrying out sales of the weaned animals not
saved for the reproductive or fattening cohorts. The current value
of ROUTi(t) has been computed in subroutine HOMOG4 in the demography
component. Subroutine RESPNS redefines this value to include sales
animals from the entire cohort rather than only those leaving the

cohort due to satisfying the required discrete delay time. Then

1 m7
R0UT7(t) = [-—J E SUBPOP7 (t) (5.5.3)
DT j=m j
ROUT ( ) — i “:8 SUBPOP (t)*[l - TFRAC (c) — (5 5 4)
8 t ' DT , 8j j+l—m,2 ' '
J=m
TFRACj+l_m’3(t)]

where:
ROUTi(t) = annual rate of output from the ith cohort delay process

TFRAC£i(t) = fraction of the female calf subpopulation indexed
m+£ transferred to the ith heifer cohort

m = the subpopulation index corresponding to the oldest sub-
population which is younger than AGEMIN

DT = time increment of the simulation——fraction of a year.
ROUTi(t), as redefined above, is used to transfer cattle between
cohorts using the control variables C2, C3, C4, C5, C6, C9, C10, and
C11. These equations have aggregated together many animals of different
ages, and hence weights; the weight of the final subpopulation of the

calf cohorts must be redefined to reflect this aggregation. Therefore

 

 

 

136

 

 

KK7
*
jgm SUBPOP7j (t) w7j (t)
W7,KK7(t) = (5-5-5)
27 SUBPOP7j(t)
j=m
8
w _ _ *
E SUBPOP8j(t) [1 TFRACj+1-m,2(t) TFRACj+1vm,3(t)] W8j(t)
W8 K (c) = 3"“
3 8 m8
* _ _
E SUBPOP8j(t) [1 TFRACj+1_m,2(t) TFRACj+1_m,3(t)] (5.5.6)
j=m
where:
wij(t) = average weight of the jth subpopulation of cohort i.
SUBPOPi (t) = the number of animals in the jth subpopulation

ij of cohort i
KKi = the number of subpopulations in the ith cohort

TFRAC£ i(t) = fraction of the female calf cohort subpopulation
indexed nH£transferred to the ith cohort.

Equation 5.5.5 is simply the weighted average of weights of male calves
weaned. Equation 5.5.6 is the weighted average of female calves weaned,
but which are not selected for transfer to either of the reproductive
heifer cohorts. Using the variable TFRAC£1(t), the simulation model
user can be selective about what calves are retained for use as replace—
ment animals. A common strategy of enterprise operators is to choose
the oldest calves for such replacements to maximize the likelihood of
successful initial breeding.

The final action of these special execution statements at calf
weaning is to set all SUBPOP7j(t) and SUBP0P8j(t) values to zero (for
j subpopulations older than AGEMIN) to reflect the fact that these

calves have been weaned and are gone.

 

137

Culling is a relatively simple process mechanically, but it has
wide ranging implications on future herd reproductive characteristics.
CULFRCj(t) is the fraction of the jth subpopulation of the mature cow
cohort that is to be culled. This control variable allows very detailed
control over culling-—control that can be used to remove cows which are

not reproductively useful from the herd. The following equation imple—

ments culling for each subpopulation individually,

SUBPOP1j(t) = SUBPOPlj(t)*(l-CULFRCj(t)) (5.5.7)
where:
SUBPOPlj(t) = the number of animals in the jth subpopulation

of the mature cow cohort
CULFRCj(t) = the fraction of the jth subpopulation culled.
In a fashion similar to 5.5.3, the output rate of the mature cow delay

is used as a vehicle for funneling the culled cows through the financial

mechanism.
1 “I
ROUT (t) = ROUT (t) + -—- Z SUBPOP (t)*CULFRC (t) (5.5.8)
1 1 _ lj j
DT j—l
where:

ROUTl(t) = the annual rate of output of animals from the mature
cow delay process

CULFRCj(t) = fraction of the jth subpopulation culled

DT = the time increment of the simulation~—fraction of a year.
Equation 5.5.8 differs slightly in form from 5.5.3 and 5.5.4 in that
the previous value of ROUT1(t) is retained, with the culled cows being
added to the former value. The reason for this difference is that in
the case of culling, the cows culled are in addition to those which

are leaving the delay process through old age. Weaning is an action

 

 

 

138

which is all inclusive, so that the animals exiting the calf cohort
(if any) when weaning takes place are counted in the equations 5.5.3
and 5.5.4, where they would be counted twice if the form of 5.5.8 was
followed.

Since the mature cow cohort is assumed to have relatively small
weight differences among the various subpopulations there is no need
to compute a psuedo average weight for the output rate as is done in

equations 5.5.5 and 5.5.6. The weight W

l,KK1(t) is assumed to be a

sufficiently accurate value.

Figure 5.21 illustrates an example of this culling process guided
by the input of control values by the model user. Solid square points
represent the overall calving rate achieved by the various subpopulations
of the mature cow cohort during the previous calving season. Circular
points represent a particular culling fraction to be applied against
that subpopulation. This example culling pattern is guided by the
desire to eliminate cows from the herd which have not calved in the
previous year. The likelihood of cows failing to calve increases with
previous calving failures, so elimination of such animals from the
herd should raise the overall herd calving fraction. The reason for
desiring a higher calving fraction is the simple goal of reducing
feeding costs to achieve the same physical output. Other strategies
can, of course, be followed by model users. The culling fraction for
the youngest subpopulation is lower than the value indicated by the
above strategy to reflect the fact that these animals were not yet

mature at their first calving experience.

 

 

 

139

Accumulated Birth Rate
or
Culling Rate

 

 

1.0 -
I I I
I I
0.8- I
' I
0.6 ' I
I
0.4 - .
O O
0.2 - 0
o 0 o
‘ o o
0 L n 1 . J
2 4 6 8 10
j index
. —— accumulated birth rate for jth subpopulation

. -— culling rate for jth subpopulation

Figure 5.21 Graph of culling rates for each subpopulation of the
mature cow cohort using accumulated birth rates as
a guide

 

 

140

The manager could also be interested in adding to his herd, as
well as culling some or all of it. The control variables ASELLi(t)
and C2, C3, C4, C5, C6, C9, C10, and Cll are available to the user at
the culling decision point to carry out any herd changes desired, whether
positive or negative. Figure 5.3 illustrates how the herd maturation
flow variables CZ, ..., C11 affect the herd. ASELLi(t) is the pro—
portion of the current herd population of cohort i that is to be sold

in this time increment. Then

-ASELLi(t)*POPi(t)*(l-DRi(t)*DT)

 

ADDRTi(t) = (5.5.9)

DT

where:
ADDRTi = the annual rate of additions to cohort i
P0P1(t) = the current cohort 1 population
DRi(t) = the annual cohort 1 death rate

DT = the simulation time increment

ASELLi(t) = proportion of the population of cohort i that is
to be sold in this time increment.

"Special decision point" is the term used to designate three events
that require the interactive attention of the model user. The first
of these is post-harvest feed stock levels imcompatible with the
planned feeding rate through the end of the wintering season. The
second of these is feed stocks insufficient to meet the planned
feeding over a short interval into the future, eg. one to two simulation
time periods. Finally, the third decision point testing criteria is
that working capital falls below $2000.00. Each of these criteria

is checked every time increment of the simulation just as the Current

 

 

 

141

time is checked for equality with one of the time related regular
decision points.

In the first simulation time increment following the completion
of fall harvesting, subroutine INQUIR determines the requirements
for each feed stock by using the current cohort populations and the
current values of the time based feeding plans. This results in a
value of ACTEDln(t)—-the total quantity of feed stock n required by
feeding plans from the present through the end of the wintering
season. ACTED1n(t) is determined in much the same way as STKFEDn(t)
is determined except that ACTEDln(t) is integrated over time in order

to obtain the entire wintering requirements. This gives

FPLAst—l l 9
ACTED (t) = f —-—-—————-* 2 POP (t )*[CATTIN, _ (t)*
In tfall FQUALn(t) i=1 i fall 11% 1
*
CNCFRCin(t) + CATTIN12£_l(t) RHGFRCin(t)] dt
tspring l 9
+-f -————————- Z POP (t )*[CATTIN (t)*
FPLANS£~1 FQUALn(t) i=1 1 fall 112

*RHGFRC t dt
CNCFRCin(t) + CATTIN122(t) in( )1
where: (5.5.10)

ACTEDl (t) = the season long requirements for feed stock n based
n on the present feeding rates and feed distribution

planned
CATTIN. £(t) = quantity of TDN fed to individual members of cohort
11 1 per day from concentrates under feed plan 2
CATTIN12£(t) = quantity of TDN fed to individual members of cohort

i per day from roughages under feed plan 1

CNCFRC. (t) = fraction of the concentrate allocation of TDN to
in cohort 1 derived from feed stock n

 

142

= DISTFDin£(t), if LABEL1?n = 1

0, if LABELFn = 2

RHGFRC, (t) = fraction of the roughage allocation of TDN to
1n cohort 1 derived from feed stock n

= DISTEDin2(t), 1f LABELFn = 2

= 0, if LABELFn = 1
FQUALn(t) = fraction of TDN per kg feed for feed stock n

POP(t ) = the population of the ith herd cohort at t

fall fall
FPLANS£ = time when the 1th feed plan ends and the 2+1 plan begins

1, if t < FPLANS

1
2, if FPLANSl : t < FPLANSZ
z ' 3, if FPLANSZ : t < FPLANS3
4, if FPLANS3 : t < FPLANS4.

When the values of ACTED1n(t) have been computed, the following
equation is the criteria used for deciding that a special decision point
is needed to allow the user to adjust feed stock levels and planned

feeding patterns to be compatible. A special decision point is required

 

if
FSTOCK (t ) - ACTED (t )
FTOLl < n fall In fall (5.5.11)
ACTEDln(tfall)
where:

FTOL1 = fraction feed stocks can differ from the computed feed
stock requirements implied by the feeding plans

FSTOCKn(t) = the current quantity for feed stock n on hand

ACTED1n(t) = feed stock n requirements of the present feed plans.

The second special decision point criteria is checked each time
increment that feeding is taking place. A special decision point is

required if

 

 

 

 

143

FINFLT*ACTED2n(t) > FSTOCKn(t) — STKLOSn(t) (5.5.12)
where:

ACTED2n(t) = feed stock requirement for feeding cattle during the
present time increment for feed stock n

FSTOCKn(t) = current quantity of feed stock n on hand

STKLOSn(t) = quantity of feed stock n lost thrOugh spoilage in
the current increment of time

FINFLT = 2.0, factor by which the feed stock requirement of the
current time increment is inflated as a safety
margin.

ACTEDzn(t) is determined in the same manner as is STKFEDn(t) in sub—

routine CONSUM (described in section 4). Then,

9
DAYS —
_—_ ____.___ * * * *
ACTED2n(t) FQU n(t) iglPOPj-(t) LCATTINiu(t) DISTFDin£(t) 1N1
* *
+ CATTINi 2(t) DISTFDin £(t) 1112] (55.13)
where:

ACTED2 n(t) = the quantity of feed stock n required by the current
feeding plan for this time increment

POPi(t) = current population of cohort i
FQUALn(t) = fraction of TDN per kg feed for feed stock n

DISTFDin(t) = fraction of the feed allocation to cohort i
derived from feed stock n
CATTINil(t) = quantity of TDN allocated to cohort i from concen—
trates per day under feed plan £
CATTIN. (t) = quantity of TDN allocated to cohort i from
12
roughages per day under feed plan 2

INl = indicator of type of feed

[I

1, if LABELFn = 1

II

= 0, if LABELFn 2

 

 

144

IN = an indicator of roughage feed

1, if LABELFn = 2

0, if LABELFn = 1
DAYS = number of days in a simulation time increment.
If the level of working capital falls below the arbitrary value
of $2000, the model also signals a special decision point. This event
is indicative that large cash outflows have drained the enterprise of
working capital. A possible solution is short—term borrowing.
When any of these events signal a special decision point, the

model follows the normal decision point procedure and awaits a restart
with control variable values. Since the problem is not fully specified
by events leading to a Special decision point, the entire range of con-
trol variables is available to the user for inputting new values.
Even if relatively little adjustment is made, the user is required to
input all control variables; the values are left to user discretion.
The User's Guide to the Beef Cattle Enterprise Simulation Model
specifies the exact format of the data cards containing control varia—
ble values required for each decision point. Figure 5.22 is a typical

message printed by the computer at a decision point indicating the

control variables which are required to restart the simulation.

Endogenous Decision Making

The management component model is constructed so that if none of
the five decision points is encountered, then logical control shifts to
subroutine NORMAL. This subroutine carries out all endogenous deci-
Four categories of decisions

sion making within the component model.

comprise the contents of this subroutine; these are:

 

All.”

145

EXOGENOUS INPUT REQUIREMENTS IN ORDER
APFUTR(5,20)
BPFUTR(8,10)
CPFUTR(NSTOCK,10)
PDSTRB(NLANDS,9)
XCPROD(NSTOCK)
XCQUAL(NSTOCK)
CFINAL REMOVL
TBRD(1),TBRD(2),TWEAN,TCULL

TMHR(5)

SEE THE USER GUIDE FOR INPUT FORMATS

Figure 5.22 Printed message at the spring growth decision
point requesting values for specified control
variables

 

 

146

l

V

timing of slaughter cohort cattle sales,

2

V

fall crop sales and purchases to obtain wintering feeding
requirements,

3) mechanical harvesting of forage growth, and

4

v

concentrate and roughage cohort allocations.

These decisions are obviously more routine than those which must be
made at each of the decision points. The criteria upon which some of
these areas of endogenous decision making are based are standard
economic ones; e.g., selling if the marginal cost of holding exceeds
the marginal revenue. Some of the parameters used here are supplied
at decision points for use over an extended time period.

Mechanical harvest of forage growth is an example of using
exogenously supplied parameters over an extended period of simulated
time. Three key variables are inputted into the model at the spring
growth onset decision point; these are TMHRk, REMOVL, and CFINAL.
TMHRk specifies certain simulated times at which the forage growth
then existing in various land parcels should be harvested. REMOVL
specifies a fraction of the "excess" over and above current herd
needs that is to be harvested at each of these harvest times. CFINAL
specifies the fraction of the standing quantity of forage that is to
be harvested at TFALL-—the end of the growth season. MHRn(t) is the

daily rate of forage removal from land parcel n. It is determined by:

0, if t {[TMHRk, k=l, ..., 5]

MHRn(t) = 0, if GRNnt) < FLEVELn(t) (5.5.14)
REMOVL
__._.* .—
DEYS [GRNn(t) FLEVELn(t)]

 

 

 

147

where:
GRNn(t) = the quantity of forage material in land parcel n
DAYS = the number of days in the time increment UT
9
FLEVELn(t) = LOW*DAYS* X PDSTRBni(t)*POPi(t) (5.5.15)
i=1
= a minimum quantity of forage needed to supply
the animals grazing in land parcel n for one

time increment

PDSTRBni(t) = fraction of the population of cohort i grazing
in land parcel n

LOW = 5.0, a minimum daily quantity of forage intake
POPi(t) = current population of cohort 1.
When the end of the growth season arrives (t = TFALL), then the
manager controls the final forage harvest through CFINAL.

GRNn(t)*CFINAL
DAYS

(5.5.16)

MHR (t) = daily rate of mechanical harvest of forage from land
n parcel n

 

GRNn(t) = quantity of forage available in land parcel n

CFINAL = fraction of the forage in land parcel n to be harvested
at the end of the growth season

DAYS = number of days in a simulation time increment.

Another end—of—growth-season activity is sales of the crop
production that is produced by the enterprise. The predicted sales
amounts have been determined at a breeding decision point; and if
no extraordinary crop price changes have occurred that were not
foreseen, then the predicted quantities are either sold or purchased.

The resulting feed stock levels should be adequate to meet the desired

 

 

148

feeding rates that the manager has also specified at a breeding

decision point.

CSALESn(t) = - REACTDn, if REACTDn < 0 (5.5.17)
STKPURn(t) = REACTDn, if REACTDn > 0 (5.5.18)
where:

CSALESn(t) = quantity of feed stock n sold this period
STKPURn(t) = quantity of feed stock n purchased this period
REACTDn = the predicted net purchases of feed stock n.
REACTDn is controlled by the user at the various decision points which
are appropriate for such feed stock predictions.

An extremely important decision in a cattle enterprise is timing
of animal sales. This decision is complicated by the reproductive inr
plications of most sales; the uncertainties of the future market make
decisions in this area quite complex. Two herd cohorts--steers and
slaughter heifers--do not share this general difficulty. These cohorts
have already been designated as sales animals only; the near term
market condition and the weight gaining characteristics of these animals
are the major considerations of the decision maker. The approach taken
in this model is to determine whether or not the expected marginal
revenue of retaining these cattle for one time increment exceeds the
expected marginal costs. When net marginal revenue is positive no
sales are made; the entire cohort population is sold when net marginal
revenue is negative. A further check over a future interval of cattle
prices is made before a decision to sell on the first griterion 15
actually carried out.

A key element in determination of expected marginal revenue is

the weight gain expected from the input of feed to the animal. The

 

149

method used here parallels the development of Schuette[48] in the
nutrient impact subroutine NUTRN. The quantity and quality of feed
fed to each slaughter cohort animal is the primary determinant of the
weight gain of that animal. A constraint on cattle intake of feeds
allocated is the capacity of the animal to consume the feed; this is

modeled as a maximum fraction of the animal's body weight. Then

_ 0.75
DMIij(t) — min[ a*wij(t) . ALLOCi(t) 1 (5.5.19)
where:

DMIi.(t) = the daily consumption of feed of members of the
J jth subpopulation of cohort 1 (dry matter basis)

Wij(t) = weight of members of the jth subpopulation of cohort i

 

ALLOCi(t) = CNCALi(t) + RHGALi(t) (5.5.193)
POPi(t)*DAYS
= the total allocation of feeds to members of herd
cohort i

a = parameter based on the body weight of the cattle
CNCALi(t) = concentrate allocation to cohort i —— kg/DT
RHGALi(t) = roughage allocation to cohort i —- kg/DT
POPi(t) = population of cohort 1
DAYS = number of days in a DT time increment.
Equation 5.5.19 has fixed the quantity of feed that is available for
digestion by a member of a particular weight animal, while equation

5.5.20 determines the average TDN value of this quantity.

DMITDNij(t) = CNCALi(t)*TDNCi(t) + [DMIij(t) - CNCALi(t)]*TDNRi(t)

 

DMIij(t) (5.5.20)
where:
DMITDN (t) = the average TDN value of the feed consumed by a
ij member of the jth subpopulation of cohort i

 

 

 

150

TDNCi(t) = average TDN value of the concentrate allocation
to cohort i

TDNRi(t) = average TDN value of the roughage allocation to
cohort i.

This equation assumes that the concentrates are consumed in their
entirety before any roughages are consumed.

Once DMITDNij(t) is determined it may be used as the basis for
computing the energy values of the DMIij(t) feed consumption for two
purposes, i.e., energy used for maintenance of body processes and
energy used for weight gains. EGAIN represents the energy value of
the feed consumed in terms of mcal energy for gain/kg feed, while
EMAIN represents the energy value of the feed consumed in terms of
meal energy for maintenance/kg feed. These values are determined from

DMITDNi (t) using Subroutine CNVRT, which uses a method of conversion

5!
between these different systems of units authorized by the National
Research Council.

The amount of energy used for weight gains is that which remains
after the animal's maintenance requirements have been subtracted from
its energy intake. Since there are two energy values per feed intake

(one for body maintenance and one for weight gains) the determination

of the energy available for weight gains must be determined from the

 

quantity of feed used for maintenance purposes. This results in

EFORGij(t) = EGAIN*[ DMI

where:

0.75
ij(t) — 0‘077*wij(t) /EMAIN ] (5.5.21)

EFORG. (t) = energy available for weight gains for an animal
lj in the jth subpopulation of cohort i —— mcal
EGAIN = gain energy value of the feed intake -- meal/kg

EMAIN = maintenance energy value of the feed intake -— mcal/kg.

 

 

 

151

Having the value for EFORGij(t) is the next to the last step for
determining the actual rate of weight gain for animals in the jth

subpopulation of cohort i. DGAINij(t) is computed by the following

    

equation
a. : b.*EFORG..(t)
DGAIN1'(t) = i _l_ 1 _1___0_1_;5_ - ci (5.5.22)
3 d. w..(:) ‘
1 1:]
where:

DGAINi.(t) = the rate of weight gain for members of the jth
J subpopulation of cohort i —— kg/day

ai, bi’ Ci’ di = constants for the ith herd cohort.

The upper signs are used when EFORGij(t) is positive, and the lower
Signs are used when it is negative. This equation, then, gives posi—
tive weight gains for positive energy for gain values, and negative
weight gains for negative energy for gain values.

Determination of the rate of weight gain that will result from
the planned quantity and quality of feed allocation allows the margin-
al revenue of that weight gain to be calculated. This value is an
expected revenue gained from feeding the animal to obtain the weight

gain computed by equation 5.5.22.

KK

FREVi= Xi DGAINij(t)*DAYS*SUBPOPij(t)*XPECTAk(t+dt) (5.5.23)
i=1

where:
FREVi = expected marginal revenue from the ith cohort —— $

DGAIN..(t) = the rate of weight gain for the animals in the
13 jth subpopulation of cohort 1 ~- kg/day

SUBPOPi (t) = population of the jth subpopulalation of cohort i

j
XPECTAk(t+dt) = expected price of cattle of grade k at time
t+dt -- $/kg

k = GRADEij(t) = price grade of animals within SUBPOPij(t)

 

 

 

 

 

 

1. .1. 1.11.7”. EJAfiJY‘WWE

.4‘... ‘1.

152

KKi = the number of subpopulation within cohort i
DAYS = the number of days in a DT time increment.

Once the expected marginal revenue of the weight gain has been
determined the remaining factor is the marginal cost of the weight
gain. Here, however, the marginal cost of maintaining the animal
another DT time increment is more than just the cost of the feed used
for weight gain. To be precise, the marginal cost is the cost of all
of the feed fed to the animal, the costs of delivery of that feed, and
any other costs associated with retaining the animal. The model for
marginal costs used here breaks costs down into two factors, cost of
the feed allocated, and cost of delivery of that feed. Other factors
are assumed to be negligible in comparison to these two factors.

NSTOCK CPRICEn(t)

FCOST. = POP (t)*DAYS* Z -—————*[ CATTIN. (t)*
1,feed 1 n=1 FQUALn(t) ill
*
CNCFRCin(t) + CATTIN12£(t) RHGFRCin(t)] (5.5.24a)
where:
FCOST. f d = the cost of the feed stocks fed to members of
1’ ee cohort i in the current time increment —- $

CPRICEn(t) = current price of feed stock n —- $/kg

CATTINil£(t) = allocation of TDN from concentrates per animal
per day to members of cohort 1 under feeding
plan 2 -— kg TDN/day

CATTIN12£(t) = allocation of TDN from roughages per animal per

day to members of cohort 1 under feeding plan 1
—— kg TDN/day

CNCFRC1 (t) = DISTFD.n£(t), proportion of the feed from con—
n centrafes delivered to cohort 1 derived from
feed stock n

RHGFRCin(t) = DISTFDi (t), proportion of the feed from rough—
ages deTivered to cohort 1 derived from feed
stock n

 

 

 

 

 

 

 

IL

 

 

153

FQUALn(t) = the average TDN value of the nth feed stock.

The cost of feeding these quantities of feeds is given by

FCOSTi,feeding

= [ CNCALi(t) + FEEDALi(t) ]*HRFED1*BPRICEl(t) (5.5.24b)
where:

= cost of feeding cohort i for one DT time
increment from labor use -- $

FCOSTi,feeding

CNCALi(t) = quantity of concentrates fed to cohort i —— kg/DT
RHGALi(t) = quantity of roughages fed to cohort i -— kg/DT
HRFEDl = hours of labor for feeding cattle -— hours/kg
BPRICEl(t) = cost of labor -- $/hour.
The total marginal cost of retaining the ith cohort of the herd for
another DT time increment is then the summation of the two factors

explained above——the feed itself and the labor to feed it. Then

FCOSTi = FCOSTi,feed + FCOSTi,feeding (5.5.24c)

where:

FCOSTi = the total marginal costs of retaining cohort i for
another DT time increment -— $.

When the expected marginal revenue is discounted apprOpriately,
and then still exceeds the expected marginal costs, then no members of
the cohort will be sold in the current time increment. Discounting
the expected marginal revenue reflects the uncertainty that exists
in the future cattle price values. If marginal revenue happens to be
smaller than marginal costs, then expected cattle prices are searched
over some interval into the future in an attempt to discover the
highest price within this time interval. The period of time into the
future searched by subroutine NORMAL is a control variable set by the

model user. If the highest value of cattle prices within the interval

 

 

 

 

 

 

 

 

154

[t, t+RANGE) falls within the interval [t, t+dt) then the entire
cohort population should be sold. The revenue gained from sales will
be highest if the animals are sold immediately, rather than retaining
them for the future. The control variable ADDRTi(t) is used to carry
out this sales action; therefore

_ 7‘: _ *
POPi(t) (1 DRi DT)

ADDRTi(t) = -—-——-—Efir———-——-- (5.5.25)

where:
POPi(t) = population of cohort 1

DR = death rate of cohort i in fraction per year

i
ADDRTi(t) = annual rate of additions of animals to cohort i f
-— animals/year
DT = the basic simulation time increment -— years.

If the highest price occurs at a time exceeding t + dt then no sales
are made in this period, because more revenue can be gained by waiting
for this higher price before selling.

The endogenous decision mechaniSm for selling the slaughter cohorts
has utilized the idea of marginal net revenue to guide the decision
to sell or to retain animals. When marginal revenue (net) is positive
then the proper decision should be retention of the cattle since the
costs of holding are exceeded by the anticipated revenue of holding.
Alternatively, when marginal net revenue is negative, the proper deci—
sion is to sell immediately. This mechanism is a straightforward
application of standard economic theory.

The last area that is included in this model of endogenous deci-
sion making is the allocation of feed stocks to the herd cohorts. This

also includes the distribution of the allocation among specific feed

 

 

 

 

155

stocks using the control variables CNCFRCin(t) and RHGFRCin(t).
Feed stocks are allocated to the herd under two separate circum-
stances: during the wintering period and during the growing season
if the quantity or quality of forage falls too low. The alternative
feeding plans used by the manager of this enterprise are modeled
using the variables FPLANS, CATTINik(t), and DISTFDin(t); these are
the times when feeding plans change, the quantity of TDN allocated
to members of herd cohorts per day, and the distribution of the TDN
allocation among feed stocks, respectively. The allocations of con-
centrate and roughage to each cohort is determined by the allocation

to each animal, the distribution of the allocation among the feed

stocks, and the TDN value of each feed stock. This results in

NSTOCK
= * it
CNCALi(t) “Z CNCFRCin(t)/FQUALn(t) CATTINill(t) POPi(t)*DAYS
(5.5.26)
[NSTOCK
= * * *
FEEDALi(t) 1 E1 RHGFRCin(t)/FQUALn(t) CATTINi2£(t) POPi(t) DAYS
(5.5.27)

where:

CNCALi(t) = the quantity of concentrates allocated to cohort i
for one DT time increment——kg conc./DT

FEEDALi(t) = the quantity of roughages allocated to cohort i
for one DT time increment—~kg/DT

= allocation of TDN from concentrates per day to

CATTIN11£(t)
members of cohort i under feed plan 1

CATTIN.2£(t) = allocation of TDN from roughages per day to
1 members of cohort i under feed plan 2

POPi(t) = current population of cohort i

DAYS = the number of days in a DT time increment

 

 

 

 

 

 

156

FQUALn(t) = the current average TDN value of feed stock n

DISTFDinl(t)’ if LABELFn = l

CNCFRCin(t) =
0, if LABELFn = 2
(DISTFD. (t), if LABELF = 2
1n£ n
RHGFRCin(t) =
0, if LABELFn = 1

(1, if 0 j_t < FPLANSl(t)

2, if FPLANSl(t) j_t < FPLANSZ(t)

3, if FPLANSz(t) §_t < FPLANS3(t)

4, if FPLANS3(t) j,t < FPLANSA(t)
The nutrient impact component subroutine CONSUM uses the variables
CNCALi(t), CATTINil£(t), FEEDALi(t), CATTIN12£(t), and RHGFRCin(t)
to determine the average TDN value of concentrates, TDNC1(t), and of
roughages, TDNRi(t). This is more fully explained in section V.4.

During the grazing season there may be instances where
supplementary feeding is necessary to provide nutrients that grazing
alone cannot deliver. Drought, with extremely low growth rates or
none at all, is an example. Subroutine NORMAL checks for such don-
ditions by determining the quantity and quality of forage available.
Normally the feed allocations to all cohorts are zero; i.e., CNCALi(t)
= FEEDALi(t) = 0.0, i=1, ..., 9. A minimum herd feeding rate,
RGRAZE(t), is computed to compare against forage stocks, with

NLANDS
RGRAZE(t) = MIN*DAYS* Z STOCKLn(t)*LANDn (5.5.28)
n=l

where:

RGRAZE(t) = a minimum quantity of forage necessary to Sustain
the grazing herd over one DT time increment—-kg/DT

 

 

 

 

 

 

157

STOCKLn(t) = the stocking rate in land parcel n—-#/hec
LANDn = area of land parcel n--hectares
MIN = a minimum daily ration of forage per animal--kg/day
DAYS = the number of days in a DT time increment.

The quantity of forage available, TGREEN(t), and the associated

average TDN value of that forage, VGREEN(t), are given by

NLANDS
TGREEN(t)= X sauna) (5.5.29)
n=1
1 NLANDS
VGREEN(t) = m * Z GRNn(t)*DIGESTn(t) (5.5.30)
n=l

where:

GRNn(t) = quantity of forage in land parcel n

DIGESTn(t) = quality of forage in land parcel n.
If TGREEN : RGRAZE(t) and VGREEN(t) 3 0.40 then no supplemental
allocation is made; otherwise, the following roughage allocation is
made
FEEDALi(t) = RAL*DAYS*POPi(t), i=1, ..., 9 (5.5.31)
where:

FEEDALi(t) = quantity of roughage allocated to herd cohort i——
kg/DT

POPi(t) = current population of cohort i

RAL = 5.0, a minimal supplementary feeding level to assist an
individual animal--kg/day.

The entire allocation of supplement must come from stored forage
retained from the previous wintering season, or perhaps from forage
already harvested and stored this growth season. RHGFRCil(t) = 1.0

for all herd cohorts.

 

 

158

Summary

The management decision making component model has been constructed
to meet the requirements specified in the problem statement (Chapter
111). Because the complexity of many decisions makes them extremely
difficult to reduce to computationally solvable forms, the model has
been developed to seek some control values exogenously. Such deci-
sions have been termed decision points and usually are associated with
specific herd actions; e.g., breeding, weaning, culling, and starting
grazing. Some less complex decisions can be determined endogenously
within the model using standard economic criteria. Examples are the
decision to sell slaughter cohort animals, forage harvesting, and feed
allocations to the herd. The mechanical process of seeking exogenous
values for some control variables involves using the simulation model
interactively in a batch mode. The user studies the simulation rec-
ord over time and the specific information printed at each decision
point to provide a basis for action. Evaluation of multiple decision
strategies at a particular decision point is possible through the use
of permanent files which "freeze" the simulation as it is at a decision
point. The user can review the results at his leisure and then con-
tinue the simulation by simply attaching the appropriate permanent
file once he has made his selection. This feature makes exploration
of intuitive feelings and alternative exogenous variable assumptions
quite feasible.

The decision making component has been developed to be realistic

in its treatment of actions taken by operating managers of ranchs.

 

 

 

 

 

 

The fine level of control variables makes many different types of
strategy evaluation possible. Annual decision patterns, such as
culling and weaning, can be investigated, as can investment planning
projects. In short, the decision making component has been con-
structed to be as flexible as possible in meeting the potential de—
sires of managers interested in evaluating the consequences of

alternative decisions.

 

 

 

 

160

v.6 Secondary Component Models

Chapter IV, section 2, provided a brief introduction to the three
secondary components of this system; these are exogenous variable
determination, management of expected prices, and enterprise financial
accounting. This section will review the purpose and detailed con-

struction of each of these components' model.

Exogenous Variable Component

 

The simulation model has three types of exogenous variables which
influence the physical variables and management decision making. These
are crop and animal prices, climatic factors-~temperature, solar radia-
tion, and rainfall, and feed crop production. Although a totally
comprehensive model of a beef cattle enterprise would endogenously
determine the crops to be planted as a function of prices and available
resources, this modeling effort is restricted to exogenous specification
of feed crop production. A year long stream of crop production is
specified with uniform spacing of values. This process is illustrated
graphically in Figure 5.23. The subroutine EXOG determines crop product—
ion for each possible feed crop in the interval ( t — dt/2, t + dt/2 )
by comparing the current simulated time T to the specified harvest time
of each crop. The effect of this structure is an impulse whose height
is the amount harvested in the interval. CROPn1(t) is the variable name
used for this quantity harvested in the time interval. CROPQLn1(t)
gives the TDN value of this quantity, CR0Pn2(t) specifies the quantity
of crop n residue that is harvested, while CROPQLn2(t) gives the TDN

value of that residue.

 

 

 

 

161
CROPnl(t)

40,000
35,000
30,000
25,000
20,000

15,000

5,000

0

 

 

‘
10,000 ‘
I

 

.]

llTll
0.0 .65 .7 .75 1.0 time

Figure 5.23 Yearly pattern of crop harvest as exogenously specified

Current prices and the current weather variables are also determined

by subroutine EXOG. These are treated somewhat differently than crop

production because both prices and weather are continuous variables,

while crop production is not. Instead of searching the input values for

a match between current time and some specified time point to get an
associated data value, prices and the weather variables are determined
through linear interpolation to compute the proper value.

function TABLIEl is used to accomplish this interpolation.

The utility

Figure 5.24

shows how this procedure works for the weather variable RAIN(t). The

following exogenous variables are determined in Similarily: SOLAR(t),

AVGTMP(t), APRICEk(t), k=1,...,5 and CPRICEn(t), n=l,...,NSTOCK.

 

l. Llewellyn, R.,FORDYN: A Industrial Dynamics Simulator, privately

published, Raleigh, N. C., 1965, p. 4—20.

 

 

 

 

 

 

 

 

 

 

162
Rainfall
(cm/day)
. O
O .\
RAIN(t) ‘3
\. I
. O
O
O
p
C
O
o o
t Time

Figure 5.24 Linear interpolation between exogenously specified
annual rainfall data points to obtain the current
rainfall value

 

Currently the model assumes that the weather and crop variables
are spaced uniformly with an interval of 0.05 years between values.
Further, the model assumes that the weather variables are repeated
year after year with no change. This assumption requires that one
view the weather variables as long run averages rather than specific
values from a stochastic process. A change in the component model
to actually use stochastic processes to represent the three weather
variables would be quite simple, but since at this time the entire
model uses deterministic variables rather than stochastic ones, this
change will not be made. Other spacings between the Specified annual

pattern would also be quite easy to implement, even non—uniform ones.

 

 

 

 

 

 

163

Expggted Prices Component

Expected prices are an important base for the decision making of
the enterprise manager. These prices are also characterized by their
volatility as the agricultural sector of the economy; and the beef
cattle industry, in particular, reacts to economic and political events
throughout the world. The subroutine RESPNS has provisions for reading
in up to two years' expected prices for cattle and up to one year's
expected prices for crops at each decision point.

During routine operation of the overall model as it simulates the
passage of time, subroutine GENERT acts to make available the proper
stream of future expected prices from the current point in time. Re—
call that at each decision point the model user is asked to respecify
the stream of prices for the feed stocks and for all five cattle
slaughter grades through the future. The array CPFUTRn(t) holds the
stream of future prices for feed stock n spaced in intervals of 2DT's
from the present, to, through simulated time t + 20DT's.

O
APFUTRk(t) holds the stream of future prices for cattle grade k spaced

The array

in intervals of 2DT's from the present,to, through simulated time t +

0
In an effort to make this specified set of prices available to

ODT's.
the model as simulated time progresses forward from the time at which
the values were specified, GENERT advances the entries in the arrays
CPFUTRn(t) and APFUTRk(t) on alternate DT increments of simulated
time. Figure 5.25 provides an example of this procedure using the
variable APFUTR3(t). In Figure 5.25a the points specify the expecta—

tions of prices for cattle of grade 3 for a time span of 24DTs. The

labelled points p , p , p specify grade 3 cattle prices at times
1 2 3

 

 

 

 

 

 

 

 

164
APFUTR3(t)
0.80
0.70 .
. o
o

0601; . .pl .pz .133 . o I . .

g - t1 1 94k . A n . . . L

to t0+2DT' to+6DT t0+20DT TIME

Figure 5.25a Expected cattle prices over time starting from t0

 

 

 

APFUTR3(t)
0.80 ,
0.70 _
. o
o
0 o
0.60 1:5 p O
c
1 2 p3 . . O

I

/

t1 tl+2DT tl+6DT tl+20DT TIME

Figure 5.25b Expected cattle prices over time starting from t1

 

 

 

165

t + 4DT, to + 6DT, and t0 + 8DT, respectively. The point to

0
represents the current value of simulated time while pl, p2, and

p3 are specified distances of time into the future (from the point
of view of simulated time). When simulated time advances as the simu—
lation proceeds, the stream of points needs to be shifted to the left
to bring the proper value of expected price into correlation with the
present value of simulated time. Lets suppose that simulated time
has advanced 4DTs from to; this is the value t1. Figure 5.25b de—
picts the proper positioning of value of APFUTR3(t) with tl being
the present simulated time. The curve given by data points in Figure
5.24s has been shifted 4DTs to the left as it should to preserve the
relationship between pl, p2, and p3. Notice that the price values
p2 and p3 are still the proper 2DTs and 4DTs into the future of simulated
time from tl in Figure 5.24s as they were in Figure 5.24a. Subroutine
GENERT maintains this price positioning for all five cattle price
grades, and for all NSTOCK feed stock prices.

Subroutine CBOX[23] is used in subroutine GENERT to perform this
shifting of price array entries 0n alternate DT time increments.
CBOX also cycles the price value being removed to the furthest most
array location meaning that a price cycle of duration 4ODTs is assumed
for cattle prices, and a price cycle of 20DTs is assumed for feed
stock prices. Of course the model user has the opportunity to respecify
the entire stream of prices at each decision point, so the price cycle
assumption implied by using CBOX is quite weak.

The major reason for this complex movement of price values as
simulated time advances is the ease with which current prices and future

expected prices from the current time may be determined. The three

 

 

 

 

 

 

 

166

functions XPECTA(k,T), XPECTB(1,T), and XPECTC(n,T) are used to
determine the expected price at time T for grade k cattle, resource 1,
and feed stock n, respectively. Each of these function subprograms
are designed to linearly interpolate between array entries to deter-
mine the correct price at any desired time point within the range of
times for which price expectations are valid. Current prices are
determined from these function subprograms by using the current

time as the argument of the function; this gives APRICEk(t) =
XPECTA(k,t), BPRICEl(t) = XPECTB(1,t), and CPRICEn(t) = XPECTC(n,t).
The function subprogram TABLIE(from Llewelyn) is used within each of

the expectation functions to perform the linear interpolation required.

Financial Accounting Component

This component performs two tasks: first, accounting for all
purchases, sales, repayments, and taxes which occur during simulated
time; and second, computing present values of certain variables at
the end of a multiyear simulation run. Subroutine FINANC is the main
element of this component, others are subroutines REVENU, PRCOST,
CAPTAL and TAXSUB. The name of each of these subroutines is il-
lustrative of the function it performs. This component will be
explained in terms of four types of variables: revenues earned,
costs incurred, interest on debt and debt repayment, and taxes.

Subroutine REVENU determines the revenue earned from sales of
cattle and crops. Physical amounts sold times the market price equals
the revenue incoming to the enterprise. Because crops are assumed to

be homogeneous, crop revenues are much easier to determine than cattle

revenue .

 

 

 

 

 

 

 

 

167

Then
CREVn(t) = CPRICEn(t)*CSALESn(t) (5.6.1)
where:

CREVn(t) = revenue from sales of crop n —- $/DT

CPRICEn(t) = market price of crop n —— S/kg
CSALESn(t) = quantity of crop n sold —- kg/DT.

Total crop revenue i8 the summation of each crop's revenue giving

V (t) = NCROPS

NCROPS + 1 Z CREVn(t) (5.6.2)
n=1

CRE

where:

CREVNCROPS + 1(t) = total crop revenue earned in this time

increment--$/DT

CREVn(t) - crop revenue earned from sales of crop n in this
time increment—~S/DT

NCROPS = the total number of possible crops.

Determination of cattle revenue is complicated by the fact that
not all sales animals have the same weight or the same price grade.
Quantities of cattle sold from each of the nine herd cohorts are
given by two variables, ROUTi(t) and ADDRTi(t) represents the annual
output rate of cohort i, while ADDRTi(t) represents the annual rate
of additions to the herd (which can be either positive or negative).
When ADDRTi(t) < 0, then there is a negative addition to the cohort;
i.e., sales. These additions are assumed to affect each cohort
subpopulation as a uniform percentage of its current subpopulation.
Section 1 explains this process more completely. Certainly not all
of the animals leaving cohort i are sold-—some are only being trans—
ferred from one cohort to another. An example is the output from
the replacement heifer cohort; here virtually all of the output

is being transferred to the mature cow cohort and not being sold.

 

 

 

 

 

 

 

168

 

Figure 5.3 illustrated the structure of the herd demographic model and
the use of the control variables CZ, C3, C4, C5, C6, C9, 010, and C
to direct the flows of cattle leaving each cohort. The variable CONi(t)
represents the proportion of the output flow rate, ROUTi(t), that is
sold. Study of Figure 5.3 will show that

C0N1(t) = 1.0 (5.6.3)

CON2(t) = 1.0 P C10

 

CON3(t) = C11

CON4(t) = 1.0

CON5(t) = C6

CON6(t) = 1.0

CON7(t) = C4

CON8(t) = C9

CON9(t) = 1.0

Combining the sales resulting from negative "cohort additions,"
and exits from the herd due to satisfaction of individual cohort delay
times, gives the total animal sales in the current time increment as
ASALESi(t) = DT*[ROUTi(t)*CONi(t) + Ui(t)] (5.6.4)
where:

ASALESi(t) = number of animals sold from cohort i in this time
period~—#/DT

DT = length of the simulation time increment in years
ROUTi(t) = cohort i delay output rate——#/year

CONi(t) = proportion of ith cohort output rate sold

 

Ui(t) = 0, if ADDRTi(t) 3 0

= —ADDRTi(t), if ADDRTi(t) < 0

   

 

 

 

169

ADDRTi(t) = annual rate of additions to cohort i-—#/year.
Since cattle prices are in terms of $/kg, the above expression is not
yet sufficient for determination of revenue. The weight of each of the
cohort sale quantities must yet be determined. Additionally, there are
five cattle price grades; this requires that the average grade for
each cohort's sale animals also be determined. The variables AVGWi
(t)and AVGGRDi(t) specify the average cohort sales weight and average
price grade, respectively.

DT*ROUTi(t)*CONi(t)*wi,KKi(t)

AVGW, = +
1“) ASALESi(t)

 

[ASALESi(t) — DT*ROUTi(t)*CONi(t)]*ALWTi(t) (5.6.5)
ASALESi(t)

 

where:

.th .
Wi.(t) = the average weight of cattle in the j subpopulation of
J cohort i

ALWTi(t) = the average weight of the ith herd cohort —- kg/animal

KK.
*
£1 Wij(t) SUBPOPij(t) (5.6.5a)
j=1 POPi(t)
where:
KK. = the number of stages in the delay model of cohort i

.th .
SUBPOP..(t) = number of animals in the j subpopulation of
13 cohort i

POPi(t) = total population of cohort i.
The average grade of cattle sold from cohort i is
*
DT*ROUTi(t)*CONi(t) GRADE1,KK,(t) (5 6 6)
AVGGRD.(t) = 1 + . .
1 ASALESi(t)

[ASALESi(t) — DT*ROUTi(t)*CONi(t)]*ALGDi(t)
ASALESi(t)

 

 

 

 

 

if j
170

where:

GRADEi.(t) = the price grade of animals in the jth subpopulation
J of cohort i

ALCDi(t) = the average grade of animals in cohort i

KKi GRADE..(t)*SUBPOP..(t)
13 11

z (5.6.6a)
J=l POPij(t)

 

 

ROUTi(t) = the output rate of the ith cohort delay model——#/year

ASALESi(t) = the number of cattle from cohort i sold in this time
period——#/DT

CONi(t) = the fraction of the output rate of cohort i sold
SUBPOPij(t) = the population of the jth subpopulation of cohort i

POPi(t) = population of cohort i

DT = the time increment of the simulation—~fraction of a year.
AVGGRDi(t) is further constrained to be an integer, since there are
specific price grades, not a continuum of prices based on slight
physical differences. The revenue earned from cattle sales, AREVi(t),
is then

AREVi(t) = ASALEsi(t)*AVGwi(t)*APRICEAVGGRDi(t)(t) (5.6.7)

where:

AREV.(t) = revenue earned from sales of cattle from cohort i in
1 the current time increment——$/DT

 

ASALESi(t) = the number of animals sold from cohort i in the
current time period——#/DT

AVGWi(t) = the average weight of cattle sold from cohort i——kg
APRICEk(t) = the current price for cattle of grade k——$/kg

AVGGRD.(t) = the average price grade of cattle sold from cohort
1 i in this time increment.

The total revenue earned from cattle sales in the current time period :

171

is the summation of the revenue earned from sales in each cohort,
giving

9
AREVlO(t) = 121 AREVi(t) (5.6.8)

where:

AREV (t) = total revenue earned from sales of cattle in this
10
time increment -— $/DT

AREVi(t) = revenue earned from sales of cattle from cohort i
in this time increment -- $/DT.

Subroutine PRCOST determines the costs of production for cattle
and for crops. Cattle production costs are determined by valuation of
the quantities of eight production resources used for various activi—
ties associated with the cattle herd. Examples of such activities are
breeding, weaning, culling, feeding the herd, etc. Nine categories of
production cost are used to allow realism in this model. A list of the
nine categories of cattle production cost along with the variable name
and the units used is given in Table 5.1. Crop production costs are
determined in a much less rigorous manner since crop production is not
modeled as such in this simulation model. Crop production costs are
basically determined by assuming that the cost of production to the
enterprise is a fixed proportion of the market price at harvest time.
This costing mechanism is recognized as being unrealistic, but it is
tolerable here because of the place crop production assumes in the
overall priority of this project. ACOSTk(t) and CCOSTk(t) are the
variables which are used to represent specific categories of cost for

cattle and crops, respectively. Table 5.1 defines these variables.

 

172

 

 

 

Table 5.1 Definition of Crop and Cattle Expense Variables
Variable Definition Units
ACOSTl(t) Labor expenses $/DT
ACOST2(t) Repair expenses $/DT
ACOST3(t) Utility expenses $/DT
ACOST4(t) Veterinary and breeding expenses $/DT
ACOST5(t) Fertilizer and seed expenses $/DT
ACOST6(t) Leased land expenses $/DT
ACOST7(t) Animal feeding expenses $/DT
ACOST8(t) Cattle purchase costs $/DT
ACOST9(t) Miscellaneous, overhead, etc. $/DT
.CCOST;(t)I—Feed.Ergp—pfoduction.expenses ———————— $7DT-_'—-_
CCOST2(t) Mechanical harvesting of forage costs $/DT
Feed stock purchase expenses $/DT

CCOST3(t)

 

 

 

 

 

 

 

 

173

Crop costs are determined directly from crop Production and feed

stock purchases. Since all crops except forage are exogenously speci—

fied by the user, determination of costs is quite difficult. The

method used here is to simply deflate the current market price to
get a hypothetical production cost. Then

NSTOCK
CCOST (t) = 2 CROP (t)*CPRICE (t)*DEFLAT (5.6.9)
1 “:2 nl n

NLANDS ]
CCOST2(t) = DAYS* X MHRn(t) *[HRHARV*BPRICE1(t)
n=1 J
+ SPHARV*BPRICE3 (t) ] (5.6.10)
where:
CCOST1(t) = production of the current feed crop costs

CCOST2(t) = current costs of harvesting forage

CROPnl(t) = current production of crop n -— kg/DT

 

BPRICEl(t) = current price per unit of production resource 1
HRHARV = hours of labor per kg forage harvested

SPHARV = units of utilities required to harvest forage
-— units/kg

MHRn(t) = daily rate of forage harvest from land parcel n
DAYS = number of days in a DT time increment
CPRICEn(t) = current market price of feed stock n —— $/kg

DEFLAT = scaling factor to determine crop production costs in
terms of current price.

Costs of crop purchases are simply the summation of the quantities
purchased times their current price, giving
NSTOCK

CCOST3(t)= Z STKPURn(t)*CPRICEn(t) (5.6.11)
n=1

 

 

174

where:

STKPURn(t) = quantity of crop n purchased this time period

CCOST3(t) = cost of feed stock purchases in the current period

CPRICEn(t) = current price of crop n-—$/kg.
Total crop costs in this period (feed stock costs) is the summation
of each of these individual cost factors; CCOST2(t) is excluded

from this summation because the forage production costs will be

added into the animal production costing. This is done simply to

keep all animal—related factors together.

CCOST4(t) = CCOSTl(t) + CCOST3(t) (5.6.11a)
where:
CCOST4(t) = the total crop-related production costs in this

time period.

Table 5.2 Definition of Resource Variables

 

VARIABLE I DEFINITION
RESORCl(t) Hours of labor

RESORC2(t) I Units of veterinary supplies
RESORC3(t) Units of utilities
RESORC4(t) Kgs of fertilizer
RESORC5(t) Kgs of seed

RESORC6(t) Hectares of land leased
RESORC7(t) Units of breeding supplies
RESORC8(t) Units of repair materials

 

The quantities of each resource variable, RESORCl(t), used in
each time increment of the simulation are a function of the differ-

ent events and activities which have taken place within that DT time

 

 

175

period. To write conventional equations listing the total amount
of each resource used would require as many equation sets as there
are combinations of events and activities. To avoid this difficult
task, the quantity of resources required for each event or activity
will be defined separately for each event or activity which exists.
The total quantity of each of the eight resources used in any par-
ticular DT time increment is determined by the particular set of
events which has occurred within that time increment. This means
that the sense of each of the equations used here is
RESORCl(t) = RESORC1(t) + a specific event—related amount.

In the simulation model this organization is quite natural because
of the ease with which IF statements can be used to shunt the logi-
cal path of flow through series of equations which apply only for
specific events or specific times of the year. When an equation
of form 5.6.12 through 5.6.25 is encountered, the quantity calcu-
lated is simply added to whatever sum already existed for that
variable. The only requirement needed to perform this addition
is initialization of resource quantity used to zero at the beginning
of each DT increment of the simulation.

Feeding is a major activity requiring the use of resources,

primarily labor. The amount of labor used for feeding is

NSTOCK
1215501201“) =HRFEDl* Z STKFEDn(t) (5.6.12)
n=1
where:
RESORCl(t) = hours of labor required to feed cattle this time
increment——hr/DT

STKFEDn(t) = quantity of feed stock n fed to cattle—~kg/DT
HRFEDI = hours of labor per kg of feed stocks fed.

 

176

Another major source of production costs is breeding, especially

if artificial insemination is used. This activity requires labor

as well as breeding supplied, Furthermore, breeding is not a single
event but an activity covering an extended period of time; i.e.,
DURBi(t) for the ith cohort. The number of hours of labor required
for breeding is modelled as a function of the number of servicings
experienced by each herd cohort subpopulation. The variables DT

and DURBi(t) act to spread the quantity of labor hours required
uniformly over the interval DURBi(t), i=1, ..., 3. They act simi—

larly in spreading breeding supply resources used uniformly as well.
KK

 

 

 

3 1 INBij(t)*SUBPOPi,(t)*DT
RESORC1(t) = HRBRED* Z DURB (t) J (5.6.l3a)
i=1 j=l 1
KK.
. 3 1 INBij(t)*SUBPOPi.(t)*DT
RESORC7(t) = SPBRED* Z Z J (5.6.13b)

i=1 j=l DURBi(t)

where:

RESORCl(t) = hours of labor used for breeding in this time
increment——hours/DT

RESORC7(t) = units of breeding supplies used for breeding in
this time increment—-units/DT

INBi.(t) = number of breedings for the jth subpopulation of
J cohort i

DURBi(t) = duration of cohort i breeding
HRBRED = hours of labor required per servicing
SPBRED = number of units of breeding supplied per servicing

SUBPOPij(t) = number of cattle in the jth subpopulation of

cohort i.
Calving costs are modeled as using labor exclusively; equation

5.6.14 determines the number of hours of labor used in a DT time

 

 

177

increment by summing the number of newly born male and female
calves and multiplying by.the labor resource parameter HRCALV.

Then

RESORCl(t) = HRCALV*[SUBPOP7l(t) + SUBPOP81(t)] (5.6.14)

where:

RESORCl(t) = hours of labor required for calving assistance
in the current time period

SUBPOP7l(t) = number of newly born male calves

SUBPOP81(t) = number of newly born female calves

HRCALV = hours of labor required per calf born.

When calves reach a specified age, all calves are vaccinated

and most male calves are castrated. These events are modeled as

using labor and vaccination supplies, giving
RESORCl(t) = HRCAST*(1 - C2)*P0P7(t) + HRVACC*[POP7(t) + P0P8(t)]
(5.6.15)

RESORC2(t) = SPVACC*[POP7(t) + POP8(t)] (5.6.16)

where:

RESORC1(t) = hours of labor required in the current DT time
increment to perform castration of male calves
and vaccination of both male and female calves-—

hours/DT

RESORC2(t) = units of veterinary supplies used for vaccination
in this DT time increment-—#/DT

 

SPVACC = quantity of veterinary supplies used per calf vaccinated

POPi(t) = total population of the ith cattle cohort

C2 = fraction of male calves cohort output being retained for
bull replacement

HRCAST = hours of labor per calf castrated

HRVACC = hours of labor per calf vaccinated.

 

178

Weaning and culling are herd management activities which only

require labor. Weaning labor requirements are:

KK7 KK8 ‘
RESORCl(t) = HRWEAN* X SUPBOP7j(t) + X SUBPOP8.(t)
j=IAMIN j=IAMIN 3

(5.6.17)
where:

RESORCl(t) = the number of hours of labor required to wean
calves and transfer them to desired uses—-hours/DT

SUBPOP7j(t) = population of the jth subgroup of male calves

SUBPOP8j(t) = population of the jth subgroup of female calves

KKi = the number of subpopulations of the ith herd cohort

HRWEAN = number of hours of labor required per calf weaned——
hr/calf

IAMIN = the subpopulation index of the calf cohorts which is
the smallest index greater than the age represented
by AGEMIN.

Culling is another herd management procedure which can be

modeled as utilizing labor resources exclusively. The quantity

of labor required for culling is directly proportional to the number

of cows culled; this gives
KK

RESORCl(t) = HRCULL* Z SUBPOPl,(t)*CULFRC.(t) (5.6.17a)
j=1 J J

where:

RESORCl(t) = the number of hours of labor required for culling
of the mature cow herd

th .
SUBPOPl.(t) = the number of cows in the j subpopulation of
J the mature cow cohort

CULFRC.(t) = fraction of subpopulation j of the mature cow
J cohort culled

HRCULL = hours of labor per cow culled.

 

179

Reseeding and fertilizing pasture lands is one way that a

manager can increase forage production. The costs of this activity

are in the use of labor to perform the activity and in the physical

supplies used.

NLANDS
RESORCl(t) = (HRSEED + HRFERT)* X LANDn (5.6.18)
n=1
NLANDS
RESORCS(t) = SPSEED* Z LANDn (5.6.19)
n=1
NLANDS
RESORC4(t) = SPFERT* Z LANDn (5.6.20)
n=1
where: 1
RESORCl(t) = hours of labor used in reseeding and fertilizing
of herd grazing lands—~hours/DT
RESORC5(t) = quantity of seed used in reseeding grazing lands——
kg/DT
RESORC4(t) = quantity of fertilizer used in fertilizing grazing

lands of the herd—~kg/DT

LANDn = area of land parcel n--hectares

NLANDS = number of distinct land parcels

HRSEED = hours of labor to seed per hectare

HRFERT = hours of labor to fertilize per hectare

SPSEED = units of seed applied per hectare

SPFERT = units of fertilizer applied per hectare.

Another event highly land oriented is harvesting of forage

growth through mechanical means.

or for cash sale.

This would be either for storage

Harvesting requires labor and utility usage, since

fuel is an element of the composite resource ”utilities."

180

NLANDS
RESORCl(t) = HRHARV*DAYS* Z MI-IR (t) (5.6.21)
n=1 n
NLANDS
RESORC3(t) = SPHARV*DAYS* Z MHR (t) (5.6.22)
n=1 n
where:

MHRn(t) = mechanical harvest rate from land parcel n--kg/day

DAYS = the number of days in a DT time increment

HRHARV = hours of labor per kg forage harvested--hour/kg
SPHARV = units of utilities per kg forage harvested-~units/kg
RESORCl(t) = hours of labor required for forage harvesting in

this time increment--hour/DT

RESORC3(t) = units of utilities used in forage harvesting in
this time increment--units/DT.

RESORC6(t) is the quantity of land which is leased, either for
grazing or crop production. HLEASE is this quantity; it is assumed
to be constant over a single year.

Two activities are assumed to take place on an ongoing basis

throughout the year. Repair of buildings, equipment, and land

improvement, ie. fencing, is one. A second is the use of utilities

to warm buildings and provide power for lights, ventilation, etc.
The amount of utilities required is certainly a function of the
time of year and of the activities that are seasonal because of

climatic variations.

9 NSTOCK

RESORC3(t) = UNIT*[SPUTL1* Z POPi(t) + SPUTL2* ): FSTOCKn(t)
i=1 n=1 )

(5.6.23a)

if t < TSPRNG, or t > TFALL

181

9 NSTOCK ‘
RESORCB(t) = UNIT* SPUTL3* Z POPi(t) + SPUTL4* ' X FSTOCK (t)
i=1 n=1 n
(5.6.23b)
if TSPRNG : t _<_ TFALL

where:

RESORC3(t) = quantity of utilities used in this time increment
to provide heat, power, lights, etc.--units/DT

POPi(t) = current cohort i population
FSTOCKn(t) = current feed stock n quantity--kgs

TSPRNG, TFALL = the onset and stoppage of plant growth, respectively

SPUTLl = units of utilities per animal per month—-units/
animal/month

SPUTL2 = units of utilities per kg of feed stock per month—-
units/animal/month

SEUTL3 = units of utilities per animal per month—~units/animal/
month

SPUTL4 ? units of utilities per kg of feed stock per month--

units/animal/month

UNIT = DT/.O83333.
Equations 5.6.23a, b represent the quantity of utilities needed to
provide power for a DT time increment to buildings during wintering
and grazing periods, respectively. SPUTLl, SPUTL2, SPUTL3, and SPUTL4
are monthly time-based parameters; the variable UNIT is a scaling
factor to adjust the use of utilities to the time interval DT that
has been used.

Repairs are also an ongoing activity that must be adjusted to
get a quantity of resources used per DT time increment. Labor and

repair materials are the only resources that are used in the equation

modeling these repairs.

182

[ 9 NSTOCK
RESORCl(t) = UNIT* HREQIP* Z POP.(t) + HRFCAP* Z FSTOCK (t)
l i=1 1 n=1 n
NLANDS
+ HRMAIN" 2 LAND (5.6.24)
n=1 n
[ 9 NSTOCK
RESORC8(t) = UNIT* SPREP1* X POP.(t) + SPREP2* Z FSTOCK (t)
l ._ 1 n
1-1 n=1
NLANDS 1
+SPREP3* X LANDSn (5.6.25)
n=1
where:
RESORCl(t) = quantity of labor used for repairs this time
increment--hours/DT
RESORC8(t) = quantity of repair material used in this time

increment--units/DT

LANDn = area of land parcel n--hectares

HREQIP = hours of labor per animal per month--hour/anima1/month

HRFCAP = hours of labor per kg of feed stock per month--hour/
animal/month

HRMAIN = hours of labor per hectare per m0nth—-hour/hectare/
month

SPREPl = units of repair material per animal per month/units/
animal/month

SPREPZ = units of repair material per feed stock per month-—
units/kg/month

SPREP3 = units of repair material per hectare per month--units/

hec/month
POPi(t) = current pepulation of herd cohort 1
These two equations model repair resource consumption as functions

of the number of cattle, the quantity of feed stocks on hand, and

the amount of land area in use.

183

Determination of animal production costs is completed by costing
out the quantity of resources used in each DT time increment of the
simulation. RESORC£(t), 2 = l, ..., 8 gives the quantity of each of
the resources used. BPRICE£(t), R = l, ..., 8 gives the price per
unit of resource as the resource variables RESORC(t) were defined
in Table 5.2. Multiplication of the quantity of physical resource
used by its current price is the cost of supplying that resource
quantity in the current time increment. The production cost vari—
ables ACOST£(t) give the costs of animal production in the current
time increment by appropriately grouping the production resources.

This gives the production costs as defined in Table 5.1 as

ACOSTl(t) = RESORCl(t)*BPRICE1(t) (5.6.26)
ACOST2(t) = RESORC8(t)*BPRICE8(t) (5.6.27)
ACOST3(t) = RESORC3(t)*BPRICE3(t) (5.6.28)

ACOST4(t) = RESORC2(t)*BPRICE2(t) + RESORC7(t)*BPRICE7(t) (5.6.29)

ACOST5(t) = RESORC4(t)*BPRICE4(t) + RESORC5(t) (5.6.30)
ACOST6(t) = RESORC6(t)*BPRICE6(t)*DT (5.6.31)
NSTOCK
ACOST7(t) = 2: STKFEDn(t)*CPRICEn(t) (5.6.32)
n=1
9 6
_ i: . .
ACOST8(t) — DT*iE1ADDi(t)*APRICEPGRADEi(t)(t) PAWATEi(t) (5 33)
ACOST9(t) = OVHEAD*DT (5.6.34)
where:

ACOSTk(t) = production cost in category k in the current time
increment--$/DT

PAWATE.(t) = average weight of animals purchased and added
1 to cohort i in this period-—kg

 

184

BPRICE£(t) the current price per unit of RESORC (t)--$/unit

the quantity of resource used in the current time
increment of the simulation as determined from
all events and activities which have occurred in
the DT increment--units/DT.

RESORC£(t)

DT = the simulation time increment in fraction of a year

NSTOCK = the number of feed stocks in use by the enterprise

STKFEDn(t) = quantity of feed stock n fed to cattle in the
current time interval--kg./DT
CPRICEn(t) = current price of feed stock n——$/kg.

APRICEk(t) = current price of grade k cattle——$/kg.

PGRADEi(t) = grade of cattle purchased as a addition for
cohort i
OVHEAD = annual miscellaneous production costs——$/yr

ADDi(t) = annual rate of herd additions

0, if ADDRTi(t) 5 0

ADDRTi(t), if ADDRTi(t) > 0.

Total animal production costs for this time increment are

ACOST10(t) = .E ACOSTi(t)

iii
ACOST7(t) values are excluded from this total because they are
counted in CCOST3(t) where the purchases of feed crops are itemized.
Double counting of expenses would occur if ACOST7(t) were included
as a part of the total running operating costs of the enterprise.
ACOST7(t) is useful, however, because the current value of feed
stocks fed to the herd is a valuable item of status information for
management.

Table 5.3 itemizes the entire parameter list used in deter-

mining production costs and presents a sample value. Other values

185

 

 

Table 5.3 Parameter Values and Definitions for the
Production Cost Element of the Financial
Component
Parameter Value Definition
OVHEAD 5000. annual overhead and miscellaneous costs--$
DEFLAT 0.91 ratio of crOp production costs to prices
SPBRED 0.5 units of breeding supplies per cow servicing
SPVACC 1.0 unlts of vaccination supplies per calf
HRCALV 0.05 hours of labor per calf born
HRFEDl .00047 hours of labor per kg. feed fed
HRBRED .25 hours of labor per cow servicing
HRVACC 0.05 hours of labor per calf vaccinated
HRWEAN 1.75 hours of labor per calf weaned
HRCULL 0.2 hours of labor per cow culled
NRCAST 0.2 hours of labor per male calf castrated
HRSEED 0.04 hours of labor per hectare of land seeded
HRFERT 0.04 hours of labor per hectare of land fertilizer
HRHARV .0021 hours of labor per kg. forage harvested
HREQIP 0.03 hours of labor for equipment repair per
animal per month
HRFCAP .00002 hours of labor for repair per kg. feed
stocks per month
HRMAIN 00475 hours of labor for repair per hectare of land
per month
SPUTLl 2.5 units of utilities per animal per month
during wintering
SPUTL2 .0001 units of utilities per kg. feed stock per
month during winter
SPUTL3 0. unlts of utilities per animal per month
during grazing
SPUTL4 .00001 units of utilities per kg. teed stOCK per
month during grazing
SPUTL5 0.02 units of utilities per kg. forage harvested
SPSEED 0.0 units of seeds used per hectare sowr
SPFERT 0.0 units of fertillzer per hectare fertslized
SPREPl 0.10 units of repair material per animal per month
SPREPZ .000013 units of repair material per kg. feed stock
per month
SPREP3 0.01 unlts of repair material per hectare of land
per month

HLEASE

 

 

hectares of leased land per year

 

 

186

can, of course, be used by reading in any desired value during
program initialization and start up. Detailed cost examination
of individual enterprise records and operation should serve to
obtain better values than these given. A final note--OVHEAD repre—
sents miscellaneous costs and the salary that a manager would obtain
that is separate from hours of physical labor that he might perform.
Debt of the enterprise has been divided into the arbitrary
classifications of short-term and long-term. This has been done to
draw the needed distinction between borrowing for land purchases,
e.g., mortgages, and borrowing for operating capital. Long-term
debt is assumed to only decrease or remain constant during individual
runs of the model. Short—term debt can be increased by borrowing at
special decision points, the interest rate and repayment schedule
can also be renegotiated, whereas these are fixed for long-term

debt. Long-term debt is therefore handled by the following equations.

CAPTL1(t) = CAPTL1(t-dt) — PMONTH(t) (5.6.36)
PINTER(t) = CAPTL1(t)*CAPTL3*DT (5.6.37)
where:

CAPTL1(t) = current long—term debt——$

CAPTL contracted monthly repayment of long-term debt—-$/month

2

CAPTL3 = annual interest rate for long-term debt

PINTER(t) payment of interest on long-term debt in this

time increment--$/DT

repayment of principal on long—term debt in
time increment—-$/DT

PMDNTH(t)

0, if CAPTL1(t) = 0
CAPTL1(t), if CAPTLl(t) f CAPTL2(t)

CAPTL2(t), if CAPTL1(t) > CAPTL2(t).

187

Short-term debt is handled analogously except that additional loans
can be obtained, and the interest rate and repayment variables are

functions of time.

SDEBT(t) = SDEBT(t-dt) — SMONTH(t) + SLOAN(t) (5.6.38)
SINTER(t) = SDEBT(t)*SDEBTR(t)*DT (5.6.39)
where:

SDEBT(t) = current short-term debt-—$
SDEBTR(t) = current annual interest rate on short—term debt

SLOAN(t) = short-term debt incurred this time period--$/DT

SINTER(t) = payment of interest on short-term debt--$/DT
SREPAY(t) = monthly repayment of short-term debt--$/month
SMDNTH(t) = repayment of principal on short-term debt--$/DT

0, if SDEBT(t) = 0

SDEBT(t), if SDEBT(t) f SREPAY(t)

SREPAY(t), if SDEBT(t) > SREPAY(t).
The total payments of principal and interest, both long— and short-
term, are aggregated into CAPTL5(t).
CAPTL5(t) = PMONTH(t) + PINTER(t) +~SMONTH(t) + SINTER(t) (5.6.40)
Inclusion of debt in its various forms and the required repayment of
debt in an important aspect of this model, because of its significant
contribution to negative cash flows. Debt repayment on common terms
is a constant cash outflow, whereas cash inflow is highly concentrated
and seasonal. This leads to the common occurence of negative cash
flows during the bulk of a year interrupted by singular periods of
heavy cash inflow. Short-term debt is a key feature allowing oper—

ating capital to remain positive, thus permitting continued enterprise

operation.

 

 

 

188

The final financial element included in this model of enterprise
finances is taxation. Taxes take two forms—~income taxes on the gross

profits of the enterprise, and property taxes on its real property.

 

 

 

Since taxation is a highly localized process, the model developed
here is rather basic and should be made more specific for actual
operation in a fixed environment. Income taxes are assumed due in
one payment on April 1 for gross income earned in the preceding
calendar year. Property taxes are paid twice yearly, on January 1,
and on July 1. Depreciation is taken on depreciable assets (assumed
to have a cemmon tax life) at the time of tax payment and is computed
using sum of the digits. Thus taxable income is accumulated from

January 1 using

TAXINC(t) = TAXINC(t-dt) + TPGRP(t) - CAPTL4(t) (5.6.41)
where:
TAXINC(t) = accumulated yearly taxable income—-$

CAPTL4(t) = annual depreciation--$

 

TPGRP(t) gross profit in this time period--$/DT.
Equation 5.6.41 is used to determine the current contribution to
taxable income from the gross profits of the current simulation time
increment. Taxable income is an accumulated variable which begins
with an initial value of zero on January 1 of each year; in simula-
tion runs which last longer than a single year, the variable TAXINC(t)

is reset to zero when the simulated time equals January 1. At this

 

time two actions occur: TAXLIB(t) is set equal to the current value
of TAXINC(t), and TAXINC(t) is set equal to zero. TAXLIB(t) repre~

sents the taxable income from the previous year which is subject to

   

 

189

represents the average depreciation lifetime of these assets. The
sum-of-the digits method of depreciation is used to determine the

actual depreciation charge that can be made in each tax year. This

 

 

 

computation is made by the model on April 1 of each simulated year
and is subtracted from taxable income at that point. CAPTL4(t) is
the variable name used to represent this depreciation variable; it

is determined by equation 5.6.42 to be

 

TLIFE — INT(t-t0)
.-.- *
CAPTL4(t) LIFE LVALUE (5.6.42)
2 INT(t—t )
0
t=tO

 

where:

CAPTL4(t) = current amount depreciated in this time
increment--$

LIFE = the depreciable lifetime allowed by tax law--years

INT(S)

a function which integerizes the value 3

LVALUE the original purchase price being depreciated//$.

 

CAPTL4(t) is equal to zero at all times other than April 1 of each
year.

Property taxes are paid on the actual real estate actually
owned. The variables LANDn, giving the area of the nth land parcel,
are not necessarily owned; seme could be leased. The true area

subject to tax is the difference between total land and leased

 

land.
HLANDS )

TAx(t) = 0,50*pR0TAx* t Z LANDn — HLEASE (5.6.43)
n=1

if t = January 1, or July 1

   

 

 

 

 

190

income tax in the current year. As long as income taxes have not
yet been paid, the variable TAXLIB(t) remains at the value that it
was set to on January 1. On April 1 tax is paid at the current rate
payable by corporate farms; TAX(t) is the income tax paid. Then

0.0, if t t April 1, January 1, July 1
TAXCt) =

TRATE*TAXLIB(t), if t = April 1

where:

TAX(t) = the dollars in taxes paid this time increment
of the simulation--$/DT

TRATE = 0.5, the tax rate on gross taxable income

TAXLIB(t) = the gross taxable income from the previous
tax year--$.

A significant factor involved in determination of taxable income
is depreciation-any allowable depreciation is subtracted off of gross
profits when computing taxable income. Depreciation is itself a
complex subject which is highly controlled by rules and regulations
of various tax authorities. Additionally, it is completely specific
to the individual enterprise being studied since the heart of depre—
ciation is the quantities of depreciable assets owned by the enter-
prise and the allowable depreciable lifetime. This financial model
makes a very modest effort to include depreciation primarily because
of its potential significance in causing differences in the dynamic
computation of cash flow and net profit.

The model of depreciation adopted here employs the general idea
of an average purchase value of assets owned and a corresponding
average depreciable lifetime. LVALUE represents the total purchase

prices of all depreciable assets owned by the enterprise, while LIFE

 

 

 

 

 

 

 

 

 

 

where:

PROTAX = annual tax on land--$/hectare—year
LANDn = area of land parcel n —— hectares
HLEASE = area of land leased -— hectares.

The combination of taxes on property and on income is handled by
the variable TAX(t). TAX(t) is zero at all times of the year
except for the dates January 1, April 1, and July 1.

Subroutine FINANC provides the overall organization of the
financial component by calling the above simulation models of the
various financial elements. Gross profits in the current time

increment is the difference between revenues and payments.

TPGRP(t) = AREV10(t) + CREVNCROPS+ft) — ACOST10(t)
- CCOST4(t) - CAPTL5(t) (5.6.44)
where:
TPGRP(t) = current period's gross profit-~$/DT

AREV (t) = total animal revenue earned in this
10 .
per10d——$/DT

CREVNCROP 3+1 ('3)

= total crop revenue earned in this
period--$/DT

ACOST10(t) = total animal production costs in this
period--$/DT

CCOST (t) = total crop production costs in this
4 .
per10d—-$/DT
CAPTL5(t) = total debt payments in this period—-$/DT.

Cash flow in this period is the difference between gross profits and
tax payments, if any.

CASH(t) = TPGRP(t) — TAX(t) (5.6.45)
where:

CASH(t) = current time increment cash flow——$/DT

 

 

 

 

 

 

 

192

TAX(t) = taxes paid in this time increment, either income
or property——S/DT

TPGRP(t) gross profits of the enterprise in this time

increment--$/DT.

Cash flow is an important management decision-making variable because
it reflects the actual transfer of cash into and out of the enter-
prise. As explained earlier, beef cattle enterprises are character-
ized by steady net cash outlfows during most of the year, interrupted
by heavy cash inflows when products are sold. These seasonal sales
products are, of course, weaned calves and excess forage and crop
production. Finally, net profit in the period is the difference
between cash flow and depreciation, giving
TPNP(t) = CASH(t) — CAPTL4(t) (5.6.46)
where:

TPNP(t) = net profit in this time increment--$/DT

CAPTL = depreciation taken in this time increment-~$/DT.

4

Operating capital of the enterprise is, of course, affected

 

by cash flow and borrowing, giving

WCAPT(t) = WCAPT(t-dt) + SLOAN(t) + CASH(t) (5.6.47)
where:
WCAPT(t) = current level of operating capital-—$

short-term loans incurred in this time
increment-—$.

SLOAN(t)

Yearly accumulated profits, both gross and net, and cash flows

 

are important variables in analyzing the overall operation of this
enterprise. The subroutine FINANC determines such annual variables

by summing the individual incremental values for each calendar year.

   

 

 

 

193

This gives

TAGRPm(t) = TAGRPm(t-dt) + TPGRP(t) (5.6.48a)
TANPm(t) = TANPm(t-dt) + TPNP(t) (5.6.48b)
TACASHm(t) = TACASHm(t-dt) + CASH(t) (5.6.48c)
where:

TAGRPm(t) = accumulated gross profits to date in the mth year
of operation—-$

TANPm(t) = accumulated net profits to date in the mth year of
operation—-$

TACASHm(t) = accumulated cash flow to date in the mth year of
operation-—$

m = index of the year of operation since the beginning of the
simulation

1, if 0 ft~<1

2,if1_<_t.<2

DUR, if DUer f t < DUR

DUR = time specified as the final time horizon of model time
simulation.

Computation of present discounted values of these three annual
variables is extremely helpful in evaluating the impact of specific
management policies over time. Undiscounted values can be quite
misleading since the time value of money and the impact of inflation
are net accounted for. When the simulation has reached the final

time horizon (t = DUR) the following values are computed for a

variety of discount rates.

M TAGRPm(t) (5.6.49a)

 

m=1 (1 + DFLATRi)m

194

 

 

6
M TANP (t)
PRV21 = 2 1“ (5.6.49b)
m=1 (1 + DFLATR1)m
M TACASH (t)
PRV3i = X m (5.6.49c)
m=l (1 + DFLATRi)m
where:
PRV11 = present discounted value of annual gross profits using
discount rate 1
PRV21 = present discounted value of annual net profits using

discount rate 1

PRV3i

present discounted value of annual cash flows using
discount rate i

DFLATRi = discount rate 1
M = the integer number of years of the simulation run.

The financial component is an important part of the simulation
model of the enterprise; it is central to evaluation of alternative
management strategies because it reduces physical events and activi—
ties to dollars and cents. Most applications using the model will be
interested in the financial aspects of management strategies rather
than the specifics of the physical events that have occurred as a
result of the strategy. The financial model developed in this section
is certainly adequate for the purposes of this thesis, but in use by
specific enterprises there will need to be certain changes to tune
the financial model to the Specific enterprise operating environment.
Tax rates and the parameters listed in Table 5.3 are the main means
of tuning the model; these are entered during the initialization of
the computer program. The details of this initialization can be

found in the User's Guide to the Beef Cattle Enterprise Simulation

Model, Chapter Three.

 

 

195

V.7 Simulation Model Calling Structure

The previous sections of this chapter have defined the mathemat-
ical models that describe the various processes of the system. The
simulation models that implement these equations are written in FORTRAN,

and can be found in the User's Guide ..., Chapter Four. Figure 4.13

 

and others have referred the reader to the general calling structure
of the simulation model. This section will indicate the exact sub-
routine calling structure used, noting calls to subroutines from within

other subroutines by indentations to the right.

MAIN . . . . . . . . . . the main program
GENERT
EXOG
HDMOG4 . . . . . . . . population demography

*
BIRTHZ . . . . . . birth rates

BIRAT
DVDPLR
DLVDPL
DDPLR
WEIGHT . . . . . . . . cattle weights

FEEDS . . . . . . . . feed stock accounting

FORAGE . . . . . . . . forage growth

INQUIR . . . . recognition of decision
points

RESPNS# . . . . . . . . reading control inputs

NORMAL . . . . . . . . endogenous decision making

 

* developed by Margaret Schuette[48]

# called only when a decision point is encountered by INQUIR

 

 

196

MAIN, continued

CONSUM . . . . . . . . nutrient impacts

NUTRN . . . . . . shell for Schuette

* subroutines
COWCYC
*
ALAC
*
GROFEM
*
GROMAL
FINANC . . . . . . . . financial accounting
REVENU
PRCOST
CAPTAL
TAXSUB
PRINTR . . . . . . . . intermediate simulation

increment printing.

This listing of subroutine calls is only a brief reference to the
organization of the computer program and its subroutines which actually
simulate the system behavior. The full and complete details of the
FORTRAN programming can be found in Chapter 4, User's Guide to the Reef

Cattle Enterprise Simulation Model.

 

 

 

 

 

 

 

v.8 Summary

This chapter has developed the mathematical models upon which the
simulation model is based. These models meet the requirements of the
problem statement, but considerable room for improvement and exten—
sion remain. The four physical system components--cattle demography,
forage growth, feed stock accounting, and nutrient impacts--provide
the model user with the necessary detail to be useful in investiga-
ting management decision making strategies. The management decision
making component itself has been shown to involve both endogenous
decisions made by the model and exogenous decisions made by the model
user. Several secondary components have been explained in terms of
handling necessary details such as correct selection of exogenous
input variables and financial accounting. The following chapter will
outline various means used to validate the model, that is, to verify

that it properly describes the beef cattle enterprise.

 

 

 

198

v.9 Glossary of Variables

The following alphabetical listing of variables includes all variable

names used in the preceding sections of this chapter. These same names are

used whenever feasible in the computer program and subroutines, as listed

in Appendix 1.

Parameter names are not included here, but may be found

in the text as they are used.

1.

10.

ll.

12.

l3.

l4.

ACOSTm(t) =
ACTEDkn(t)
ACTIVEn(t)
ADDRTi(t) =

AGEMIN =

AHRn(t) =

ALGDi(t) =

ALLOCi(t) =

ALWTi(t) =

APFUTRmk(t) =

APRICEk(t)

AREVi(t) =
ASALESi(t)

ASELLi(t) =

the produEfiion cost in the current DT time increment
for the m cost subdivision--$/DT

quantity of feed stock n required for feeding in the
current DT(k=2), or the winter season (k=1)--kg

forage density photosynthetically active in the nth

land parce1--kg/hectare

the annual rate of addition of animals to herd cohort
i—-#/yr

the minimum age of calves weaned--years

the rate of forage harvest by grazing in land parcel n—-
kg/day

the average price grade of cattle in cohort i currently

total quantity of feed allocated to individuals in
cohort 1 per day--kg/day

the current average weight of cattle in cohort i--kg

current expectation of the value of the kth grade
cattle price m DT's into the future--$/kg

the current market price of cattle of grade k—-$/kg

revenue earned in the current time increment from
sales of cattle from cohort i--$/DT

the number of cattle sold in the current time increment
from cohort i--#/DT

the proportion of the current pOpulation of cohort i
that is to be sold in this time increment

 

 

199

 

15. AVGGRDi(t) = the average price grade of cattle sold in this time
increment from cohort i

16. AVGTMP(t) = the average temperature in the current DT time
increment--°C

l7. AVGWi(t) = the average weight of cattle sold in this time increment
from cohort i--kg

l8. AWFn(t) = the animal harvest wastage factor in the current time
increment for land parcel n

 

l9. BASEDGn(t) = the basic digestibility factor in the current time
increment for land parcel n

20. BEGCAV = the time in the year at which cows begin to calve

21. BFRACil = the 1th point in the curve describing the accumulated
calving pattern for cohort i

22. BPFUTle(t) = the current expectation of the value of the 1th
production resource price m DT's into the future——
$/unit

23. BPRICE1(t) = the current market price for the 1th resource of
production--$/unit

24. BR (t) = th current birth rate on an annual basis for the

1 E

i herd cohort--#/yr

25. CAPTLm(t) = the current value of the mph financial variable

26. CASHl(t) = current cash flow in this time increment—-$/DT

27. CATTINik1(t) = the quantity of TDN allocated to members of herd

cohort i per.day from concentrates (kel), or
roughages (k=2), under feed plan 1

28. CCOST1(t) the crOp pfioduction cost in the current time increment

for the l crop cost subdivision-—$/DT

29. CFINAL = the proportion of the existing forage in each land
parcel that is to be harvested at the end of the
growth season (TFALL)

30. CNCALi(t)

the quantity of concentrates allocated to cohort i
for the current time increment-~kg/DT

31. CNCFRCin(t) = the fraction of the concentrate TDN allocation to
cohort i to be obtained from feed stock n
32. CPATijk = the fraction of the jth subpopulation of cohort i

to have calved by CTIM..
13k

 

 

 

 

 

 

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

CPFUTR (t) =
mn

CPRICEn(t)

CREVn(t) =

CROPnl(t)

CROPGn(t)

CRQUALn1(t)
CSALESn(t)

CTIMijk(t)

CULFRCj(t)
C2 =
C3 =

C4

C5

C6

C9

C10

C11 =

DAYS =

11

200

the current expectation of the value of the nth feed
stock price 2m DT's into the future--$/kg

the current market price of feed stock n--$/kg

the revenue earned from sales of feed stock n in
the current time increment-—$/DT

crop production in the current time increment for
feed stock n--kg/DT

annual crop production to date of feed stock n——kg

the TDN value of the current quantity of feed stock
n being harvested this time increment

the quantity of feed stock n sold in the current
time increment--kg/DT

the time of year that calves will be born of female
animals from subpopulation j of the ith cohort as
a result of the kth servicing--years

the fraction of the jth subpopulation of the mature
cow cohort that is to be culled at TCULL

fraction of the output of the male calf cohort trans-
ferred to the young bull cohort after weaning

fraction of the output of the female calf cohort
transferred to the slaughter heifer cohort

fraction of the output of the male calf cohort sold
on the market as weaned calves

fraction of the output of the female calf cohort
transferred to the replacement heifer cohort

fraction of the output of the male calf cohort sold
on the market after weaning

fraction of the output of the female calf cohort
sold on the market as weaned calves

fraction of the output of the replacement heifer
cohort transferred to the mature cow cohort

fraction of the output of the bred heifer cohort
sold on the market

the number of days in the DT time increment

 

 

 

 

 

 

 

 

51.

52"

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

DELAYi(t) =

DFLATRi(t)

DGAINij(t)

DIGESTn(t)

DISTFDin1(t)

DMIij(t) =
DMITDNij(t) =
DR. =

1

DT =

DUR =
DURBi(t) =

EFORGij(t) =

EGAINi(t)

EMAINi(t)

ENDCAV =

EVAP =

201

the current length of time required for the average
member of cohort i to pass through the maturity
interval modeled by that cohort——yr

the ith discount rate used to compute the discounted
present values of financial variables at the end of
the simulation run

the rate of weight gain for the jth subpopulation of
cohort i—-kg/day

the TDN value of the forage in land parcel n at the
current time

the fraction of the cohort i allocation of concentrates
(if n is a feed concentrate), or of roughages (if n

is a feed roughage) to come from feed stock n under
feed plan 1

the dry matter intake per day of a member of subpopulation
j of cohort i--kg/day

the average TDN y lue of the dry matter intake of
members of the j subpopulation of cohort i

the annual death rate for herd cohort i members--
fraction/year

the time increment used in the simulationn-year

the time horizon over which the simulation is to be
run--years

the duration of the breeding season for members of
cohort i——years

quantity of energy available for weight gain after
maintenance needs satisfied-~mcal

energy value of the feed intake in terms of growth

for cohort i__mca1 gain energy
kg feed

energy value of the feed intake in terms of maintenance

for cohort i__mcal maint. energy
kg feed

 

the time at which the calving season is complete-—year

the equivalent height of water evaporated per day—~cm/day

 

 

 

 

 

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

82.

83.

84.

85.

Fn(t) =

FATFAC =

FCOSTi(t) =

FDENSEn(t) =
FEDTDNi(t) =
FEEDALi(t) =
FLEVELn(t) =
FORGALi(t) =
FORTDNi(t) =

FPLANSl(t) =

FQUALn(t)

FQUANn(t)

FRCLOSn(t) =

FREVi(t) =
FRQUAL(t) =

FSTOCKn(t) =

FTOLl =

GRADE1 (t) =

J

GRNn(t) =

202

the rate of transfer of growth from roots to greenery
in land parcel n—-kg/hectare/day

parameter relating predicted dailygains for cattle at
their cohort weight maximum into price grade increases

the cost of retaining the p0pulation ofcohort i for
an additional time increment at the planned feeding
schedule--$

forage digestibility factor based on forage density
per animal in land parcel n

the average TDN value of the roughage fed to cohort i
from feed stock sources

the quantity of roughage allocated to cohort i for the
current increment of time--kg/DT

the minimuquuantity of forage needed to sustain animals
grazing in land parcel n per DT time increment--kg

the quantity of roughage allocated to cohort i as a
result of grazing policy-~kg/DT

the TDN value of the forage from roughage allocation
to cohort i

the time at which the 1th feed plan for the herd is
completed——year

the current TDN value of the nth feed stock

the quantity of feed stock n in the current time
increment which is carried over from the previous

period's stocks-~kg
the annual loss rate of feed stock n—-fraction/year

expected marginal revenue gained from retention of
cohort 1 animals an additional DT time increment--$

forage digestibility factor relating current forage
digestibility to time in the growth season

the current level of feed stock n supplies--kg

the absolute fractional deviation between current

feed stock levels and seasonal requirementsallowed
. . .th

the current price grade of cattle in the 3

subp0pulation of cohort i

the current quantity of forage existing within
land parcel n—-kg

 

 

 

 

 

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

100.

101.

102.

103.

 

GRNDENn(t) =

IFLAG =
INB.. =
13

INTCAV =

min) =
LAND =
n

LIFE =
LVALUE =
MHRn(t) =

MWF =

NCROPS =

NLANDS =

NSTOCK

PDSTRBni(t) =

PERC(t) =

PGRADEi(t) =

PHOT0n(t) =

P =
INDEXn(t)

203

the quantity of forage greenery available per animal
per day in land parcel n——kg/animal/day

an indicator flag describing the existence of regular
and special decision points

the number of servicifigs during the breeding season
for animals in the j subpopulation of cohort i

the number of intervals of length one-half month
within the calving interval

the number of subpopulations within cohort i
the area of land parcel n--hectares

the average depreciable life of the mix of depreciable
assets owned-—years

the purchase price in total of the depreciable assets
owned—-$

the rate of mechanical harvest of forage growth in
land parcel n—-kg/day

the wastage factor in mechanical harvest of forage

the number of feed stocks potentially used by the
enterprise

the number of land parcels

the number of feed stocks potentially used by the
enterprise

the fraction of the population of cohort i grazing in
land parcel n

the equivalent height of water percolating down below
effective root depth--cm/day

the average grade of animals purchased and added to
cohort i

the net growth rate of forage in land parcel from
photosynthetic energy conversion——kg/day

relative age of forage existing in land parcel n-—days

 

 

 

 

 

104.

105.

106.

107.

108.

109.

110.

111.

112.

113.

114.

115.

116.

117.

118.

119.

120.

PINTER(t) =

PMONTH(t) =

POPi(t) =

PROTAX =

PRQUALn(t) =

PRmG =

RAIN(t) =

REACTDn(t) =
REMOVL(t) =
RESORCl(t) =

RGRAZE(t)

RHGALi(t) =

RHGFRCin(t)

RINij(t) =

ROOTn(t)
ROUTi(t) =

RPOPi(t) =

204

payments of interest in the current time increment
on long—term debt-—$/DT

payments on principal in this time increment for long—
term debt--$/DT

the current population of cohort i

the current property tax rate on an annual basis--
$/hectare/year

the TDN value of feed stock n purchases

the discounted present value of the annual values of
gross profit (m = 1), net profit (m=2), or cash flow
(m=3), using discount rate k

the current rate of rainfall-~cm/day

the current intentions of feed stock n net purchases
at the end of the growth season (TFALL)—-kg

the current fraction of the existing forage in each
land parcel to be harvested at each harvest time

the quantity of production resource 1 used in the
current time increment-~units

the minimum quantity of forage required to maintain
the cattle herd grazing in the current time increment——
kg/DT

the overall roughage allocation to herd cohort i in
this time increment--kg/DT

the fraction of the roughage TDN allocation (from
feed stocks) to cohort i to be obtained from feed
stock n

the intermediate output rate in the delay model of
cohort 1 corresponding to subpopulation j

the current density of roots in land parcel n-—
kg/hectare

the current output rate of animals from herd cohort
i--#/year

the population of cohort i which is reproductively
characteristic of cohort i behavior

 

 

 

 

121.

122.

123.

124.

125.

126.

127.

128.

129.

130.

131.

132.

133.

134.

SDEBT(t) =

ll

SDEBTR(t)
SINTER(t) =
SLOAN(t) =
SM(t) =

SMF(t) =

SMONTH(t) =

SNF(t) =

SNUTn(t) =

SOLAR(t)

SPLIT =

SPOILn(t) =

SREPAY(t)

STKFEDn(t)

STKPURn(t)

STOCKLn(t)

SUBPOPij(t) =

the current level of short—term debt-—$

the annual interest rate required for short—term
debt

payments of interest made in the current time increment
for short—term debt--$/DT

current quantity of short—term debt acquired this time
increment-—$/DT

the current level of soil miosture within an effective
root depth-—cm

the current value of the soil moisture quality index

the current repayments of principal of short~term
debt——$/DT

the current value of the soil nutrients quality index

the current level of soil nutrients in land parcel
n—-units

the current average daytime rate of incoming solar
radiation-~langleys/day

the fraction of roughage consumption derived from
feed stock roughages when an excess roughage allocation
has been made

the annual rate of TDN decline in storage for feed
stock n

the current monthly payment to principal required
for the outstanding short—term debt-—$/month

the quantity of feed stock n allocated to herd
consumption in the current time increment--kg/DT

the current quantity of feed stock n purchased in
this time increment-—kg/DT

the stocking level of grazing cattle in land parcel
n—~#/hectare

. . .th _
the current number of animals in the j subpopulation
of cohort i

 

206

 

138. SUMTPF(t) = the current value of the integral of the temperature
quality index (TPF)-—units

139. TACASHm(t) = the annual cash flow in year m of the enterprise
simulation--$/year

140. TAGRPm(t) = the annual gross profit in year m of the enterprise
simulation—-$/Year

141. TANPm(t) = the annual net profit in year m of the enterprise
simulation——$/year

142. TAX(t) = the number of dollars of taxes paid in this time
increment to all authorities—-$/DT

143. TAXINC(t) = taxable income in the current calendar year to date-—$

144. TAXLIB(t) = income from the previous calendar year liable for income
taxes currently--$

145. TBRDi(t) = the current value of the date on which breeding of
cohort i is to commence-—year .

146. TCULL(t) = the current time at which culling of the mature cow
cohort is to occur—~year

147. TDMICi(t) = the quantity of concentrates consumed by herd cohort
i in the current time increment—-kg/DT

148. TDMIR_(t) = the quantity of roughage consumed by herd cohort i
1 in the current time increment—-kg/DT

149. TDNCi(t)

the average TDN value of the concentrate allocation
to herd cohort i

150. TDNRi(t) = the average TDN value of the roughage allocation to
herd cohort i

151. TFALL = the time at which the growth season staps——year

152. TFRACmi = the fraction of the weaned female calves in the mth

cohort subpopulation older than the youngest subpopu—
lation weaned which is transferred to cohort i

153. TGREEN(t) = the total quantity of greenery available for grazing
by cattle at time t--kg

 

154. TMHRl(t) = the time at which the 1th mechanical harvest of forages
is to occur——year

   

 

 

155.

156.

157.
158.

159.

160.

161.

162.

163.

164.

165.

166.

167.

168.

169.

TPF(t) =

TPGRP(t)

TRATE =
TSPRNG =

TWEAN(t) =
VGREEN(t) =
Wij(t) =

WCAPT(t) =

WGTMAXi =
XCPRODn(t)
XCQUALn(t)
XPECTAk(t)
XPECTBl(t)

XPECTCn(t)

zx3n(t) =

207

the current value of the temperature quality index

total dollars of gross profit earned in the current
time period——$/DT

the rate of taxation for_businesses on taxable income
the time at which the growth season is begun-—year

the time at which the calf cohorts are to be weaned——
year

the average TDN value of the total forage currently
available for grazing

the average weight of members of the jth subpopulation
of cohort i--kg

the current level of working capital on hand-—$

the maximum weight that members of cohort i can
achieve—-kg

the expected production of feed stock n during the growth
season--kg

the expected TDN value of the production of feed stock
n expected

the expected price of cattle of grade k at time t-—
$/kg

h
the expected price of the It resource of production
at time t--$/unit

the expected price for the nth feed stock at time t~—
$/kg

the fraction of the photosynthetically converted
energy growth rate used for root growth

 

 

 

 

 

CHAPTER VI

MODEL TESTING AND VALIDATION

Validation is, in its essence, a process of verifying that a
model correctly represents the real world process that it is supposed
to represent. Model validation is an essential step in model devel—
opment because use of an invalid model c0uld easily be worse than no
model at all. Validation of simulation models is more difficult to
achieve than validation of other model forms, because of the great
complexity that simulation models are commonly used to portray dy-
namically. This chapter will seek to review some approaches to model
validation in general, present evidence to demonstrate the simulation
model's validity, and summarize more sophisticated procedures for

developing user confidence in this model.

V1.1 Approaches to Validation

In some respects the process of validating a model is a search
for truth. What is desired is that the model truly represent the
real system. Unfortunately, demonstration of truth has been subordi—
nated to questions about truth and truthfulness themselves in the
literature. Philosophers through the ages have failed to resolve
these questions in any generally acceptable manner. In the realm of

economic models there are three approaches to establishment of model

208

 

 

 

 

 

209

truthfulness about the real world.1 Robbins [44] espouses the
thinking that models must be ultimately based on unverifiable basic
assumptions that have to be accepted or rejected on their own merits.
The model should correctly evolve from them, but the basic assump—
tions themselves are not testable. Hutchinson [27] totally rejects
this approach and maintains that nothing is proved true until it can
be empirically tested. This includes the basic model assumptions;
they are suspect where assumptions cannot be supported by data.
Freidman [17] represents the Positive Economics school of thinking,
which would find truth if a model correctly predicts behavior. Some
question this line of thinking by stating that it leads to use of
models which may predict behavior correctly, but which are based on
obviously false assumptions. Some also draw a distinction between
positive and normative models,2 but this beef cattle enterprise
simulation model contains both positive and normative characteristics.
We are led to the conclusion that this model must produce the proper
behavior but must also be developed according to realistic and valid
assumptions.

In a practical sense validation is a two—phase process for

simulation models. First, there is the problem of validating, or

 

1T. H. Naylor, J. L. Balintfy, D. S. Burdick, and K. Chu,

Computer Simulation Techniques (New York: Wiley, c. 1966),

Chapter 8.

2Definitions frOm Gilmour [18], Chapter 1:
Positive~—a model which must show reasonable correspondence to the
real system
Normative——a model which indicates a desirable level of operation
for the real system which may or may not be currently
achieved.

 

 

210

verifying, that the simulation model correctly represents the
mathematical model. Here the major difficulty is debugging com-
puter programs and checking that approximations made to achieve a
solution are giving acceptably low errors. Second, there is the more
difficult problem of verifying that the mathematical model really
does represent the real world system. The less well understood the
real world system is the greater the difficulty in validating the
model.

A common occurrence in development of simulation models is
discovery of areas that have been ignored by conventional researchers,
even though strong understanding is needed to develop a model of an
entire system. This uneven level of understanding of parts of a
system leads to difficulties in validation, because it is the entire
system behavior that is of interest. The "weak links" which exist,
because the necessary exploratory research has not been done, inhibit
generation of confidence in a system model. A beneficial result of
development of simulation models is the discovery of these poorly
understood areas, if then resources for research can be reallocated
to these problem areas.

Several specific proposals for validating simulation models have
been developed. These borrow from one another rather heavily, and
perhaps this is due to the type of problem that the developer was
familiar with at the time he proposed his procedure. Gilmour [18]

proposes the following steps:

 

 

 

211

1. determination of face validity
2. determination of output validity through
a. analysis of stability
b. historical comparison
c. comparative analysis of output after making
assumption changes.
Popper [41] suggests that the goal of such exercises is increasing
confirmation in the truthfulness of the model. Therefore the proper
procedure is to make tests of the model; the more tests the model

passes, the greater the degree of confirmation in its truthfulness.

A procedure which seems generally applicable to many situations

 

proposes a hierarChy of testing stages. The procedure is to work
from easy to difficult as confidence in the model's validity is
developed. These validation steps, in order of increasing difficulty,
are:

l. logical consistency

2. tracking historical data

3. satisfaction of expert eyeballing

4. prediction of the future.
One accomplishes these steps through study of model output over time
by varying parameters to observe the direction of output changes, by
determining that the parameter sensitivities reflect real system

sensitivities, and in general by immersing oneself in the model for

 

lengthy periods to understand how the simulation behaves. Satisfac-
tion of experts in apprOpriate areas is an excellent indication of
validation. This satisfaction can be achieved, in all likelihood,

only after an iterative series of presentation reviews, criticism,

 

 

 

 

 

212

and model changes. Prediction is the final test of model validity,
to be confirmed or rejected by real events.

Complete certainty in model validity is never possible; this
means that models are used with less than perfect confidence in their
predictions. Model use and continuing refinement should be linked
together to insure that the model increases in validity as time
passes. Chapter 8 of this dissertation will suggest several areas
wherein greater sophistication in the component models would prove
beneficial to both generation of confidence and usefulness to model

users 0

V1.2 Validation Tests

This section will define and present examples of validation tests
for the four steps reviewed in section one: logical consistency,
tracking historical data, satisfaction of expert eyeballing, and pre—
diction of the future. It should be understood that validation testing

has not been limited to examples presented here.

Logical Consistency

Logical consistency is the requirement that the model satisfy
elementary system characteristics. Among these are satisfaction of
system identities, variables uniquely defined, consistency with known
laws, etc. Also classified here are basic tests to insure that behave
ioral modes of the model correspond with real world behavior. Identi—
ties that exist in the real system must be modeled and simulated as

identities. If the change of a parameter in a real system would change

 

 

 

 

 

 

213

an output variable, then the same direction of change should occur
in the simulation model. If the real world system is stable under
certain conditions, then the simulation model must be stable as well.
Varying model parameters to generate alternative output dynamics,
sensitivity testing of parameters, multiple input condition sets, and
hand calculation are all means of determining logical consistency in
a simulation model.

Examples illustrating logical consistency in six areas will be
described here. These will concern:

1. stability of the simulation approximations by tests of DT
size

2. verification of population identities

3. verification of feed allocation and feed stock consumption
identities

4. verification of financial identities

5. exploration of parameter values controlling forage
digestibility

6. exploration of parameter values controlling forage growth.
These examples will constitute partial evidence of the validity of
the simulation model developed to describe a beef cattle enterprise.

An important characteristic of the simulation model is stability
with respect to the DT step size used in the time simulation. The
following section of this chapter will present the results of two tests
of the simulation model's stability with respect to DT size. The ap-
proximations that are made in the differential equations of the popu-
lation model to make them solvable in the computer via difference
equations are directly related to the size of the DT step increment

selected. Theory indicates that the errors of approximation should

 

 

 

 

 

 

214

tend toward zero as DT tends toward zero. First, during the early
deve10pment of the demographic model five different step sizes were
investigated to use in selecting the most appropriate DT step. Sec-
ond, an exhaustive comparison of two runs of the most recent version
of the simulation models was made using different DT sizes. These two
examples will demonstrate that the DT step size selected for use is
sufficiently accurate and need not be reduced to attempt greater
accuracy.

An early version of the demography component HDMOG4, referred
to as HDMOG3, was tested with five DT step sizes; the sizes tested
were 0.01, 0.02, 0-03, 0.04, and 0.05 years. Three points in the
simulated time output printing were selected for analysis; these
times were 0.15, 0.50, and 1.0 years. Time equal to 0.15 corre-
sponds to the most common value printed before the run using a DT
value of 0.01 was prematurely aborted. Time equal to 0.50 corre-
sponds to the point in the simulation horizon where maximum population
was achieved. Time equal to 1.0 corresponds to the final time value.
Table 6.1 presents the results of these simulation runs in terms of

the total herd population at these three specified times for the

 

five DT sizes investigated. Examination of these results shows that
there is very little difference in the pepulation values obtained for
any of the DT sizes investigated. Therefore, to economize in the use

of computer execution time, the size of 0.05 years was selected for

use in this simulation model.

 

 

 

215

Table 6.1 Total Herd Population at Selected Points
in Time Versus DT Step Size

 

 

DT size T = 0.15 T = 0.50 T = 1.00
0.05 215.17 349.43 243.31
0.04 216.15 347.94 242.65
0.03 215.17 349.35 243.40
0.02 216.30 352.01 244.98
0.01 215.17 -- --

 

 

 

An attempt at validation of the population demography component
is important because of the central position held by this part of the
model. An identity exists in the demographic equations which will be
exploited in this section to verify that the demographic component
does perform correctly. By definition,
net population change = births - deaths — sales + purchases (6.2.1)
over any time interval, where each of these are quantities not rates.
This equation may be solved for the variable, deaths, and this new
equation used to compute deaths in each time interval. These death
values computed from computer run output printing will be compared
with the death values computed using the theoretical death rates
assumed to apply over time.

Equation 6.2.1 can be solved for the variable, deaths, and
transferred into the proper variable names as given in section v.9,

with the following result:

 

 

 

216

t+dt 9
deaths = SUBPOP71(t+DT) + SUBPOP81(t+dt) + X APURi(t+dt)
t i=1

9 9
— Z ASALESi(t+dt) + Z [POP.(t) — POP.(t+dt)] (6.2.2)
. 1 1
1=1 i=1
where:
t+dt
deaths = total herd deaths over the time interval (t,t+dt)
t
SUBPOP7l(t+dt) = male calf births over the interval (t,t+dt)
SUBPOP81(t+dt) = female calf births over the interval (t,t+dt)
0, if ADDRTi(t) : o
APURi(t+dt) =
ADDRTi(t)*DT, otherwise

= animals purchased for cohort i during the time
interval (t,t+dt)

ASALESi(t) = animals sold from cohort 1 during the time interval
POPi(t) = population of the ith cohort at time t.
The theoretical deaths that should occur over the time interval
(t,t+dt) are determined by the individual cohort death rates and the
cohort populations at time t. The death rates are constant over time
and are specified as data entries in the simulation model initiali—

zation phase. Therefore, deaths should follow the following theoreti—

cal relationship:

t+dt 9
deaths = DT* E POP (t)*DR. (6.2.3)
1 1
t i=1
where:
t+d t
deaths = total herd deaths over the time interval (t,t+dt)
t

DRi = annual death rate for cohort i.

 

 

 

217

These two equations will be used to compute the simulated value and

the theoretical value of deaths compared for a typical run of simula—

tion model over the interval (0,0.35) in DT increments of 0.05 in

Table 6.2.

Table 6.2 Comparison of Computed(Corrected) and

Theoretical Herd Deaths Over Time

 

t+dt

 

 

 

 

 

 

 

 

t+dt
t sim. deaths theo . deaths error
t t t
l
0.00 0.424 (0.325) 0.325 0.099 (0.000)
0.05 0.419 (0.320) 0.308 0.111 (0.012)
0.10 0.422 (0.323) 0.297 0.125 (0.026)
0.15 0.844 (0.745) 0.692 0.152 (0.053)
0.20 1.020 (0.921) 0.886 0.134 (0.035)
0.25 1.089 (0.990) 0.921 0.168 (0.069)
0.30 1.063 (0.964) 0.956 0.107 (0.003)
0.35 1.083 (0.984) 0.953 0.130 (0.031)
1
interval totals 6.364 (5.562) 5.336 1.028 (0.226)\
interval error ——— -~- 19% (4%)

 

The results presented in Table 6.2 indicate a consistently high

estimation of death rates by the death rate equation 6.2.2, as com—

pared to the theoretical values computed using equation 6.2.3.

Since

equation 6.2.2 is subject to errors from many sources, it is not sur—

prising that there is some error present.

A factor contributing to

 

 

218

these consistently high estimates is the way in which the variable
ASALESi(t) is computed. This variable is the number of cattle sold

in the time increment (t-dt, t) from cohort i. As explained in section
V.6, this variable is integerized so as to give even integer numbers

of animals sold from each herd cohort. This integerization process
loses the true value, but the rationale is that the errors of inte—
gerizing will sum to zero over the entire herd. In the results ana—
lyzed in Table 6.2, the ASALES4(t) value is always zero, but it is
zero because the integerizing process makes it zero. Without such
integerizing there w0uld be a small positive value for each ASALESA(t)
through time. When this factor is included in the error deternfination,
the resulting percentage of error in accumulated deaths over the time
span (0,.35) drops from 19% to 4%. In table 6.2 the values in paren-
theses indicate the value of simulated deaths and the error of this
value, taking into account the integerization SOurce of error.

The sample output analyzed here verifies that the demographic
component is performing as it should. The population identity
relating births, deaths, sales, and purchases has been shown to be
simulated quite closely to the theoretical values. When the errors
are viewed in terms of their magnitude compared to the total herd
population at any time, then such errors are extremely small (on
the order of 0.2%). The only significant effect of the error is a
very slightly smaller herd population than w0u1d be predicted if
the theoretical death rates held true. A slight error is made in
the financial component by using this integerization process, but

it is not significant.

 

 

 

 

219

A second area where identities may be used to determine proper
functioning of the model is in feed allocations and feed stock con—
sumption. Management allocates feed to the cohorts on the basis of
specified desired levels of TDN to be delivered per animal per day.
Depending on the current TDN value of each feed stock and the desired
proportion of the TDN allocation to come from each feed stock, the
physical quantities allocated are determined. CNCALi(t) and FEEDALi(t)
are the quantities of concentrate and roughage allocated to cohort i,
respectively. These allocations are in units of kg/DT. Equation
6.2.4 represents the total feed (in kg/DT) allocated to the herd.

9
ALLOCATIONl = i§l[CNCALi(t) + FEEDALi(t)] (6.2.4)

The mix of the TDN allocation to each cohort from feed stock n and

 

the population of each cohort reSult in the quantity of feed stock n
fed in the current time increment—-STKFEDn(t). Equation 6.2.5 repre—
sents the total quantity of feed stocks allocated to the herd.
NSTOCK
ALLOCATION2 = z STKFEDn(t) (6.2.5)
n=1

Logical consistency requires that these allocations be equal to one
another; that is, the allocation in terms of cohort allocations must
be the same as the allocation in terms of feed stocks used for feeding.

A typical model run from initialization (t=0.0) to the spring
decision point (t=.25) was selected for analysis to veryify this feed
stock identity. Table 6.3 presents the results of output printing

over a time interval of 4 DT's. The allocations according to

 

 

 

220

equations 6.2.4 and 6.2.5 are given along with the difference between
them. Even cursory examination will show excellent agreement between

these two forms of feed stock allocations.

Table 6.3 Feed Stock Allocations

 

 

 

 

 

 

t ALLOCATIONl ALLOCATION2 DIFFERENCE1_2
0.05 54,037.3 54,039 ~1.7 I
0.10 54,552.4 54,555 —2.6 \
0.15 54,742.0 54,742 —-- \
0.20 61,192.3 61,192 0.3 J

 

Source: Computer Printout Number MV57864

A second feed stock identity used to verify that the accounting
process of subroutine FEEDS works properly is the basic individual
feed stock balance equation.

FSTOCKn(t) = FSTOCKn(t-dt) — CSALESn(t) - STKFEDn(t) - STKLOSn(t)

+ CROPn1(t) + STKPURn(t) (6.2.6)
Briefly stated, present feed stock level equals former feed stock
level minus sales, quantity fed to cattle, losses and plus crop pro-
duction and stock purchases. Detailed explanation can be found in
section V.3. This equation must be followed for the feed stock
component of the simulation model to be working correctly.

By drawing on the same printout used above, the validity of the

feed stock component can be demonstrated. A single feed stock was

 

221

selected for study and followed through the same time interval used
above; i.e., (0.0,0.25). Table 6.4 presents the results of the come
puter printout and the calculated value of FSTOCKn(t) using equation
6.2.6. FSTOCKp represents the simulated value printed, while FSTOCKC
represents the calculated value. Excellent agreement was found
between these two values at each time point. The simulation model
component FEEDS does work properly.

A third testing point for logical consistency in the feed
allocation and feed stock consumption area involves comparison of
the desired TDN to be fed to the herd and the TDN actually fed. Allo-
cation of TDN is controlled by the user through the values of
CATTINil£(t), CATTIN12£(t), and FPLANSR. These are the kg TDN to
be delivered to each member of cohort i from concentrates per day,
the kg TDN to be delivered to each member of cohort i from roughage
per day, and the times at which feed plan f is to be completed,
respectively. Desired TDN delivery is then

9

DESIRED TDN = DAYS*iZlPOPi(t)*[CATTIN11£(t) + CATTIN12£(t)] (6.2.7)
Actual TDN delivered to the herd is simply the product of each feed

stock delivered times its TDN value, summed over all feed stocks.

This gives
NSTOCK
ACTUAL TDN = Z FQUALn(t)*STKFEDn(t) (6.2.8)
n=1
An example run for a single DT time increment is presented in

Table 6.5; this is the same run analyzed previously. There the popu-

lation and desired feed levels are reported for each herd cohort as

 

 

222

 

womnm>z can Hounaaoollmouoom

 

 

 

 

 

 

 

 

 

 

o H o H o -- a-uuosuo

maesmfi Nausea assess «chaos omkmmm .. ueuoeme
-- em as mos Has omNN monasm
-- o o o o 6 some
.. momma amass amass enema o amaaem
-- o o o o o mameem
.. o o o o o mmuamo

wowemfi assess assess fleeces omsNNN OOOmNN axooeme

mN.o oa.o mH.o on.o mo.o oo.o 6

oEHH Ho>o poummfiou mosam> xuoum boom «.0 oHan

 

 

223

Table 6.5 Sample Run of Feed Stock Use and
Desired Allocation

 

 

 

 

 

 

 

 

i/n POPi(t) CATTINill(t) CATTINi21(t) FQUALn(t) STKFEDn(t)
1 228.800 5.0 1.0 0.49 15,937

2 39.939 4.0 1.0 0.76 7,425
3 ——— 4.0 1.0 0.83 ———

4 19.837 6.0 2.0 0.46 16,977
5 ——— 5.0 1.0 0.76 13,700
6 ——— 5.0 1-0 ——— ——-

7 --- ___ ___

3 --- ___ ---

9 --- 4.0 1.0

 

Source: Computer Run MV57864

DESIRED TDN = 31,594.3 kg/DT

ACTUAL TDN = 31,673.5 kg/DT

error = +0.25%

 

 

224

well as the quantity fed and quality of each feed stock. Only a
very slight difference exists between actual and desired TDN; this
further indicates logical consistency.

A final area where logical consistency can be verified through
identities is within the financial component. Variable values are
computed within four subroutines specialized in a particular area,
such as production costs, and are brought together to form higher
level variable values, such as gross profit, in subroutine FINANC.
Three equations will be used to verify that the financial component
is properly bringing costs, revenues, depreciation, debt repayment,
and taxes into computation of gross profit per period, annual gross
profit, and discounted gross profit at final project termination
correctly.

The fundamental equation of interest is that one determining gross
profit per DT time period. This is
(t) - CCOST

TPGRP(t) = AREVlO(t) + CREV4(t) — ACOST (t)

NACOST+1 NCCOST+1
— CAPTL5(t) (6.2.9)
In this equation gross profits in the current time increment are the
animal and crop revenues minus the animal and crop production costs
minus debt servicing. This gross profit figure contributes to tax~
able income for the current year, as do depreciation charges. This
rationale gives a second equation:
TAXINC(t) = TAXINC(t—dt) + TPGRP(t) — CAPTL4(t) (6.2.10)
where TAXINC(t) is the taxable income earned in the calendar year to

date. Finally, at the conclusion of the simulation time horizon,

the discounted annual gross profit figures are used to compute the

 

225

discounted present value of this profit stream over time. Thus

TAGRPm(t) = TAGRPm(t) + TPGRP(t) ‘ (6.2.11)
MYEAR TAGRP

PRVUL: Z ———m—m (6.2.12)
m=l (1+DISC2)

For a detailed explanation of these equations and individual variable

definitions, see sections 6 and 9 of Chapter V.

A test case used to analyze whether the financial component is
working properly is represented in tabular form in Table 6.6. A
non—interactive management algorithm was used in this run to speed
up the simulation process; this allowed a run over a one—year time
horizon in a single model run. A DT time increment of 0.03846 (two
weeks) gives 26 time increments over the time interval (0.0,l.0).
Table 6.6 lists all financial variables needed to compute equations
6.2.9—12 by hand.

Computing TPGRP(t), as given by equation 6.2.9, and comparing
it with the simulated values given in Table 6.6, reveals no instances
where the computed value and the simulated value differ by more than
one cent. This excellent agreement indicates that TPGRP(t) is simu-
lated correctly from the constituent elements of equation 6.2.9.
Table 6.7 summarizes the comparison of the simulated and calculated

values of TAGRPm(t), TAXINC(t), and PRV through PRV

1i 16'

Examination of Table 6.7 will reveal excellent agreement between
the printed values obtained from the simulation and the calculated
values determined from the elements of the equations. Again, the

conclusion is reached that the financial component is properly

 

226

 

 

00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00 000 000.0
00.00000- 00 0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000- 00 0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000- 00.0000- 00.00000 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000.0
00.0000- 00.0000- 00.0 00.0000 00.0 00 000 00.0 00.000 000 0
00.0000- 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.0000- 00.0000- 00.0 00.0000 00.0 00 000 00.0 00.000 000.0
00.0000- 00.0000- 00.0 00.0000 00.0 00.000 00.0 00 000 000 0
00.0000- 00.0000- 00.0 00.0000 00.0 00 000 00.0 00.000 000.0
00.0000- 00 0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000 0

3 V

0 0 w o 0 00

000000 00000 00000 00000 s w >000 >000 0200

NL NI

3 V

D 3

0 O

S S

l L

+ +

T. .L

 

 

 

 

 

 

 

 

 

umww one we cou0uom mafia
COHuQHDEHm m Hm>o moanmflum> Hmfionmnflm vmuooaom 0.0 @0300

 

 

 

227

 

 

 

00.00000 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000 0
00.00000 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000 00.0000- 00.0 00.0000 00.0 00.000 00.0 00 000 000 0
00.00000 00.00000 00.0 00.0000 00.000 00.0000 00.00000 00.000 000.0
00.00000- 00.0000 00.0 00.0000 00.000 00 000 00.0 00.0000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.000 00.0 00.000 000.0
00.00000. 00.00000 00.0 00.0000 00.0000 00.000 00.0 00.00000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000 0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000.0
00.00000- 00.0000- 00.0 00.0000 00.0 00.0000 00.0 00.000 000.0
3 V
0 3
0 0 w w 0 00

osz<H mmome 09m<o AHm<o L l >mmo >mm< 0509

m m

D 3

0 0

m m

+ +

I I

 

 

 

 

 

 

 

 

 

U.ucoo 0.0 mafimH

 

 

228

Table 6.7 Comparison of Calculated and Simulated

Values of Financial Variables

 

 

 

 

Variable Cgmguted I Simulated Difference
TAXINC(tf) $48729.08 348729.07 $—0.0l
TAGRPl 59479.08 59479.07 —0.0l
PRVll* 59479.08 59479.08 -0.01
PRV12 58312.82 58312.82 0
PRVl3 57191.42 57191.42 0
PRV14 56112.34 56112.33 —0.01
PRV15 55073.22 55073.22 0

 

 

1

 

 

 

%

the discount rates used for PRV

11

through PRV

15 are

0.0, 0.02, 0.04, 0.06, and 0.08, respectively

 

 

 

 

 

229

simulating the revenues and costs involved in the enterprise's
operation.

A final note concerning validation of the financial component
directs the reader's attention to Table 6.6. The typical pattern
of highly irregular cash flows from cattle and crop sales are well
illustrated in this run. The effect on gross profit in each time
increment is just as mentioned previously in this thesis——a cattle
enterprise is characterized by negative cash inflows, punctuated
occasionally by very heavy positive inflows. Even though the overall
profit earned in this model run is positive, there are only three
DT time increments where positive cash inflows have occurred. These
times are 0.692, 0.769, and 0.808. These times correspond to sales
of weaned calves, sales of culled cows, and sales of forage harvested
beyond projected herd needs for the winter. The animal production

costs reported in the ACOST (t) column are indicative of the

NACOST+1
many different events occurring through the course of the year
requiring different levels of resource consumption and, hence,
overall production cost.

Proper determination of forage digestibilities is an important
aspect of the validation of the forage growth component, because of
the vital influence digestibilities have in the nutrient impact com-
ponent. The initial modeling attempt for this component, following
Anway [2], failed to properly predict forage digestibilities. Some

reasons for this failure are the lack of a factor relating forage

density in terms of quantity of forage per animal grazing to

 

 

 

 

 

 

230

digestibility and that the curves represented by the arrays BDGEST
and QUALTY were not well specified.

Digestibility of forage in each land parcel is determined bv
equation 6.2.13. It is the product of the basic digestibility, the
seasonal adjustment factor, and the forage density adjustment factor.
DIGESTn(t) = BASEDGn(t)*FRQUAL(t)*FDENSEn(t) (6.2.13)
Each of these three factors is determined by linear interpolation
between data values to obtain the proper factor value corresponding
to the argument value. A complete discussion of this formulation and
the determination of the function value corresponding to the input
argument can be found in section V.2.

Figures 6.1 and 6.2 depict several trial sets of values for the
elements of the arrays BDGEST and QUALTY used in the determination
of BASEDGn(t) and FRQUAL(t), respectively. Table 6.8 lists the re—
sults of nine runs investigating the effect of alternative trial
shapes of the curves defined by the elements of the arrays BDGEST
and QUALTY. Run 1 is the result of the original curves as taken
from Parton and Marshall [40], Sauer [47], and Anway [2]. Runs
2 through 6 investigate alternative shapes of these curves as pic—
tured in Figures 6.1 and 6.2. Runs 7 through 9 illustrate the effect
of alternative weather patterns on the original model (run 1) and
the best model (run 6). All runs have zero—level mechanical harvest-
ing and grazing to remove these influences from the range of digesti-

bilities produced by the natural response of the forage growth

component to climatic input factors.

 

 

 

231

1.0 BASEDGn(t)

 

 

 

o 3 10 15 20 25 3o

 

 

 

. . . . . PINDEXn(t)
35 40 45 50 55 (day)
Figure 6.1 Base digestibility values versus an age index.
1.0 FRQUAL(t)
.9_
.8_
n 7 ‘.~"..-‘-
' ‘\\ """ ‘ ““““ i «-... Run 2
\
.6_ \
\
\
‘\
.5, .
\
\
.4, \
\
\
.3 , 'L\
\
‘v0
\
.2 . ‘.‘
‘\
.1 ~‘.,Run 1
. l . . . 0 . 00. . L . SUMTPF(t)
O 25 50 75 100 125 150 175 200 225 250 275

Figure 6.2 Seasonal digestibility factor versus season.

 

 

 

232

Table 6.8 Forage Digestibility Factors Investigated
to Obtain an Improved Digestibility Range

 

 

 

 

 

 

 

 

Run Definition Digestibility Range

1 original 29 - 46 Z

2 first QUALTY set 32 — 46

3 first BDGEST set 35 - 51

4 both 2 and 3 38 - 51

5 second QUALTY set 38 - 51

6 both 3 and 5 45 — 54 \

7 1 and first of \
climate changes 28 — 53

8 6 and first of \
climate changes 45 — 56

9 6 and second of
climate changes J 45 — 51 X

 

 

Runs 2, 3, 4, and 5 represent intermediate improvements over

the base run. A better run than all of these is run 6, which incor—
porates the changes made in run 3 and run 5. Forage digestibilities
ranged from 45 to 54% TDN in this run. This range closely corresponds

to digestibilities of forage grasses obtained through field trials

 

and experimental observation in temperate climates [11, 14, 15]. If
the forage material is alfalfa or other high—energy plant species,
then this range in digestibilities is excessively small. A scaling
factor to adjust forage digestibility base levels might be adapted to
provide a more flexible tool for evaluating different grazing
environments. This improvement will be left for future development.

Runs 7, 8, and 9 represent an attempt to determine the
responsiveness of the forage growth model to alternative climatic
patterns. Logical consistency requires that forage growth and digest—
ibility have some degree of response to levels of solar radiation
and rainfall. Run 7 evaluates the effect of a first alternative
weather pattern on the "best" model, as determined in run 6. Run 9
evaluates yet a second alternative weather pattern on the "best"
model. Table 6.9 indicates the weather conditions, range of forage
digestibility, and forage production for runs 1, 6, 7, 8, and 9.
Runs 1 and 7 should be compared to each other, as should the group
of runs 6, 8, and 9.

Comparison of runs 1 and 7 in Table 6.9 reveals that under
conditions of reduced rainfall and reduced solar radiation that

forage production has dropped significantly from run 1 to run 7.

 

234

Table 6.9 Weather Effects on Forage Growth and
Forage Digestibility

 

run
variable 1 7 6 8 9

 

 

average solar
radiation(ly) 221 186 221 186 186

 

average rain—

fall(cm/day) 0.84 0.69 0.84 0.69 0.70

 

average tem-

_‘_.___—___

perature(°C) 8.5 8.5 8.5 8.5 8.5
digestibility
range(%) 29—51 28—53 45—54 45—56 45-51

total forage

production 4449 3813 4449 3813 4418
(kg)

 

 

 

 

 

 

 

 

235

The range of digestibilities has also broadened marginally. These
effects are what would be expected, since forage growth is primarily
related to solar radiation levels. In fact, the percentage of reduc—
tion in forage growth is roughly midway between the percentage of
reduction in solar radiation and the percentage of reduction in
rainfall.

Comparison of runs 6 and 8 in Table 6.9 reveals that the shift
from the standard climatic variable pattern shared by runs 1 through
6 to the climatic variable pattern shared by runs 7 and 8 has a very
similar effect to that reviewed above for runs 1 and 7. Again, the
range of forage digestibilities has broadened slightly. The same
drop in forage production has occurred, becaase the growth prediction
aspects of all nine of these runs are common.

Run 9 shares the same factors determining forage digestibility
with runs 6 and 8 but has yet a different weather pattern. The aver-
age values of the climatic patterns listed for runs 8 and 9 are
nearly the same, but the pattern across the year (and especially the
growing season) is different. This difference is all important, as
the results of run 9 indicate. Run 9 has only a slightly decreased
level of forage growth from run 6, whereas run 8 had quite a large
drop. Forage digestibilities have also decreased in the range ex-
perienced in run 9, compared to an increase in range in run 9, using

run 6 as the basis for comparison. This illustrates the obvious fact
that the distribution of rainfall is as important to plant growth as

is the overall level of annual rainfall.

 

 

 

 

 

 

 

 

 

 

 

236

Forage growth is sensitive to a number of parameters in the
growth model, as explained in section V.2. The original parameter
values result in a split between greenery and root storage, which
appears to favor storage excessively. The following paragraphs
will discuss some sensitivity studies of the forage.growth component
to obtain an improved proportioning of energy transformation between
greenery, growth, and root storage.

Five parameters, which are used in a total of two equations,
were tested singly and together in an effort to achieve a more real-
istic forage growth characteristic. Equation 6.2.14 indicates the
return flow rate of greenery growth from energy storage in the roots
to greenery.

-GRN (t) /PAR2*LAND
Fn(t) = PARl*ROOTn(t)*e n n (6.2.14)
Equation 6.2.15 determines the proportion of the overall plant growth
rate being apportioned to root storage, as opposed to greenery growth.

-PAR5*GRNn(t)/LANDn]
J (6.2.15)

ZX3n(t) = PAR3 + PAR4*[1.0 - e
Table 6.10 lists the results obtained from 14 runs testing various
parameter values in an attempt to achieve an increased proportion of
total growth directed to greenery instead of to root storage. The run
numbering used here continues that started in the runs listed in

Table 6.8.

Runs 10 through 22 represent changes in the noted parameter(s)

from.the base values listed for run 6. Run 6 is the same as the run

6 referred to in Table 6.8. It includes the original parameter values

 

 

 

 

 

 

237

Table 6.10 Sensitivity Testing of the Parameters
of the Forage Growth Mbdel

 

 

 

 

Run Description Forage(kg/hec) Roots(kg/hec)
6 base values 4449 3221
10 PAR5=0.0008 4595 3143
11 PAR5=0.0005 4926 2919
12 PAR5=0.0003 5280 2614
13 run 12, PAR4=.20 5463 2446
14 run 12, PAR4=.20 5651 2272
15 run 12, PAR4=.15 5844 2093
16 run 15, PAR1=.15 5915 2108
17 run 15, PAR1=.20 5956 2116
18 run 15, PAR2=400. 6033 2090
19* run 18, PAR1=.20 6402 2212
20 run 18, PAR3=.15 6452 1764
21 run 18, PAR3=.10 6886 1426
22* run 21, PAR1=.15 7035 1457

 

 

 

 

 

* an unstable parameter set which caused the quantity of
roots per hectare to approach zero

 

 

 

 

 

 

 

 

 

238

obtained from the first developers of this model form (Parton and
Marshall, Sauer, and Anway) and the improved digestibility factor
relationships described earlier in this chapter. The goal of these
investigations was to obtain improved parameter values, which would
decrease the quantity of root storage, while increasing the quantity
of greenery growth. The quantity of forage and root storage reported
in Table 6.10 are the average kilograms per hectare existing at the
conclusion of the growing season. No animal or mechanical harvesting
was allowed in these runs.

Runs 10, 11, and 12 evaluated successively smaller values of
PARS from its base value of 0.001. The effect of this parameter is
to decrease the weight of the current greenery in the equation con-
trolling the split of growth going to root storage and growth going to
greenery. The observed effect was, in fact, successively higher
forage levels and lower root values.

Runs 13, 14, and 15 evaluated successively smaller levels of
PAR4 from its base value of 0.30. The effect of this parameter is
to control the maximum fraction of photosynthetically converted
growth which is directed toward root storage as opposed to greenery.
The result of these decreases in the value of PAR4 were increased
forage growth and decreased root storage, as predicted by the equa-
tions themselves. These three runs were performed while holding
PARS at the value of 0.003, so the base level of comparison for them
Erm2rmMrmmrm6.

Runs 16 and 17 are unprofitable attempts at departures from

run 15, with increased levels of parameter PARl. Rather than

 

 

 

 

 

239

decreased root storage, as might be expected, there were very slight
increases in the season end figures. Run 19 evaluated the addition

of PAR2 = 400, while retaining the other values of run 17. It results
in unacceptable behavior, in which root storage quantities drop from
their initial spring level to zero. All three of these runs are
actually unreasonable, since the average root storage quantity drops
nearly to zero in runs 16 and 17. Parameter PARl is quite sensitive
in early forage growth stages, and any levels higher than the base
level of 0.10 reSult in unrealistic model behavior. For this reason,
PARl = 0.10 will be retained as an element of all parameter sets.

Run 18 evaluates the effect of PAR2 increases on the best run
obtained so far; i.e., run 15. Increasing PAR2 from its base level
of 200 to 400, decreases the weight given to forage greenery levels
in predicting energy transfer from roots to greenery. As expected,
increased forage growth and decreased root storage result.

Runs 20 and 21 evaluate the effect of decreased levels of
parameter PAR3 from the basis of run 18. PAR3 controls the minimum
level of the proportion of photosynthetically predicted storage going
to roots. Decreases from 0.20 to 0.15 and 0.10 result in significantly
increased forage growth and decreased root storage.

Run 22 again attempts decreases in the value of parameter PARl,
with the same unstable results as in runs 16, 17, and 19. This rein-
forces the conclusion that paramter PARl should be maintained at a
value of 0.10, regardless of other parameter values. To do other—

wise allows excessively high transfer from roots to greenery,

 

 

 

240

resulting in the quantity of root storage being driven to zero.
This cannot be permitted to happen.

As a result of these investigations, the parameter set evaluated
in run 21 was adopted as the new basis set to be used in any subse—
quesnt use of the model. This set includes PARl = 1.10, PAR2 = 400,
PAR3 = 0.10, PAR4 = 0.15, PARS = 0.003, and PAR6 = 15.0. End-of-the*
growth—season forage quantities are 6,886 kg/hec, while root storage
quantities are 1,426 kg/hec. Figure 6.3 [ 3,20,40] plots the dynamic
growth path followed by forage greenery in run 21, along with several
wide-ranging indications of relative forage growth. Goudriaan [20]
reports two growth patterns very different from the growth path fol—
lowed by run 21. Simulation models were developed for each of these
curves, which duplicated the observed data quite closely. The range
of forage growth values reported by Parton and Marshall [40] repre~
sent outcomes of alternative climatic conditions for their grassland
model. Unfortunately, the weather variables they used were quite
different from those resulting in run 21; in fact, the seasonal rain-
fall was much less than that encountered in run 21, which is reflected
in the much slower growth levels experienced. The range of growth
values reported by Baker [3] are indicative of Venezuelan conditions.
This range completely brackets the result of run 21. The various
references cited here, while unable to verify that the forage growth
pattern is accurate, are indicative that the proper range of response

has been achieved with the parameter set used in run 21.

 

241

Forage Density

    
   
 

 

 

 

(kg/bee)
15000 '
Goudriaan 2
10000 '
Goudriaan l
5000-
Baker
simulated J
- Parton and
Marshall
0 I, A A ‘_ n l J 4
90 120 150 180 210 240 270 Time
(days)

Figure 6.3 Plant densities over the growing season

 

 

 

 

 

 

 

242

Tracking Historical Data

An important part of the validation process is the tracking
of historical data by the simulation model. This ability (on the
part of the model) is a significant achievement, which contributes
substantially to confidence in the simulation model. Demonstration
of the model's ability to track multiple historical time series is
further evidence (and of a higher order than logical consistency
tests) that the model really does represent the real system it is
supposed to represent. The following paragraphs will clarify the
process of tracking historical information, discuss some potential
problems and difficulties, explain the relationship between tracking
the past and predicting the future, and explain the historical
tracking performed here.

The purpose of having a model track historical time series is,
except for academic studies into past behavior, determination of the
model's valid representation of the structural relationships over the
period in question, with the common sense feeling that this validates
the model for the future as well. Obviously this linkage of the past
and the future supposes that the relationships between variables is
constant through time. In other words, the system has not changed.
We can see immediately that this supposition is questionable as a
general rule of behavior. We need, therefore, assurance that the
past and the future systems are the same, if we are to trust a
validated model of the past in the future.

When we are satisfied that tracking historical information is

a valuable thing to accomplish, how does one go about it? How many

 

 

 

 

 

243

time series should be used? What means of reconciling deviations
between simulated values and historical values should be used? How
closely must the simulation series track the historical series to
be proclaimed satisfactory? What criteria can be used to distinguish
between time series which are "important" and those which are "unim—
portant?" Of these many questions, little of a definitive nature can
be said. Current practice leans heavily to such measures as sum of
squares and total sum of squares of the deviations between historical
and simulated series as indicators of disagreement between data and
model.3 Gilmour [18] reviews many statistical techniques which can
be used in principle but offers little direction about criteria
for choosing among them for specific examples. This is an area
needing research and attention as simulation models become more
widely used and more important to decision—making at both the micro
and macro economic levels.

Supposing that one had available relevant time series and an
appropriate measure(s) of error, there remains the thorny problem
of fine tuning the model to reduce this error measure. In the compli-
cated simulation models now being constructed, there are extremely
large numbers of parameters which are candidates for change to make
the model perform better. No general advice is possible here, as
every model is unique at this point. It takes a deep familiarity with,

and intuition about, the model to select parameters for adjustment to

 

3G. L. Johnson, G. E. Rossmiller, and T. W. Carroll, "Problems
of Verification and Validation of Large—Scale Simulation Models,"
Statistics Seminar, Michigan State University, January 20, 1976.

 

 

 

 

improve the error measure. This is a time-consuming problem which
should be viewed in a long-term perspective as an ongoing process.

This brings one up to the point where one must realize that
models are rarely ever clearly right or wrong. They have gradations
of rightness and wrongness which can be changed over time through
improved parameters, improved data to track against, and improved
structural relationships. Models (in the positive sense) are built
to predict the future, not to duplicate the past. A model must be
installed and used and then trusted to greater degrees as its per-
formance improves. The "new" historical information recorded as time
passes becomes data which can be tracked against, even if there were
no "old" historical data in the first place. If the model structure
is adequate, the passage of time affords the user/developer the op-
portunity to track against valid time series to fine tune the model
parameters. The model will gradually improve, and confidence in its
predictions will then increase. Eventually good models will be
trusted and used because of their great ability; bad models will be
either made good or shelved.

The simulation model of a beef cattle enterprise developed in
this thesis has no historical data to track against. This is a weak—
ness which will inhibit verification and validation of the model,
but not fatally so. The very extensive work on logical consistency
reported earlier in this chapter is a partial substitute for this
lack of data. The use of experts to "eyeball" model results is an
additional step in the validation process which can be relied upon

to complete the determination of validation for this model.

 

 

 

 

245

Expert "Eyeballing"

As the third step in the hierarchy of validation procedures,
the satisfaction of expert "eyeballing" is more sophisticated than
logical consistency and tracking historical data. At the same time
this step is also less rigorous than the first two. It is quite
possible for a model to have cleared the first phases of validation
and still be found wanting by experts of the system's behavior. Logi—
cal consistency and tracking of historical data are levels of valida—
tion which do not require extensive knowledge of the system under
study. A model can still contain errors of significance which can
only be detected by having an expert review the model output for cer-
tain initial conditions and control modes. The intuitive knowledge
of the expert is highly useful at this point because it is this source
which can say, "This just doesn't look right!" More detailed study

of such problem areas can reveal whether the model is correctly simu-

 

lating the real system that it is supposed to represent. If found
wanting, then the model can be improved and returned to the expert
for appraisal; this iterative process of review may cycle several

times before an acceptable model emerges validated.

An example of expert "eyeballing" discovering modeling misbehavior
is the case of the rates of weight gain for calves. Well into the
validation process, the discovery was made (by an expert in animal
husbandry) that the predictions of male and female calf weight gains

were inconsistent with common experience. Figure 6.4 illustrates

 

 

Rate of weight gain

 

246

 

(kg/day)
1.2 >
1.0 '
Beltsville
0.8 .
simulated
0.6 .
four breed
average
0.4 _
0.21
0 - * ‘ Calf Age
0 05 .10 15 .20 .25 .30 (years)

Figure 6.4 Rate of weight gain of

 

male calf animals versus age

 

 

 

247

the pattern of weight gains produced by the model and two typical
weight gain patterns.4

Examination of Figure 6.4 shows that the modeling error is the
pattern of weight gains starting at excessively high levels for very
young calves and decreasing with age. The real behavior is to have
low rates of weight gain initially, with subsequent increases as the
calves grow older. Realization of this error resulted in a modifi-
cation to one of the routines imbedded within subroutine NUTRN.
Details of this final version can be found in Schuette[48].

A second example of the use of expert "eyeballing" of output
reSults to determine model validity is given by a series of simula—
tion runs exploring alternative grazing and harvesting policies for
their effect on forage growth. This series of runs explores timing
of forage harvest, intensity of grazing, and combined grazing/har—
vesting schemes for their effects on dynamic growth and total forage
available for harvest. Additionally, the effect of weather differ—
ences on the effect of these policies is evaluated through use of
second runs in many cases. Table 6.11 presents the results of 15 model
runs reporting total forage harvestable with the described management
action, and with no harvesting activity at all. The units reported
are are kg forage harvested and harvestable per hectare, and kg TDN
forage harvested and harvestable. The effects in terms of kg TDN/hec
are more crucial to the impact on the cattle herd because TDN values

change radically as new growth appears after harvesting actions.

 

4USDA, Beltsville Growth Standards for Holstein Cattle, Technical
Bulletin No. 1099, Washington, D. C., 1954, p. 5.

 

248

Table 6.11 Effect of Grazing and Harvesting Policies on Forage Growth and Obtainability

 

 

 

 

 

 

 

 

 

Forage Quantity (kg/hec) J- kg TDN/hec
I
Run Description Action No Action Difference Difference
l 80% harvest at T = 0.4 5,790.02 6,886.34 —l,096.32 —4S4.22
2 80% harvest at T = 0.5 6,251.11 6,886.34 —635.23 -205.67
3 80% harvest at T = 0 6 6,175.32 6,886.34 ~7ll.02 —298.79
4 80% harvest at T = 0.7 6,410.52 6,886.34 —475.82 -214.11
S 80% harvest at T = 0.4
anda tT= 0.7 5,357.11 6,886.34 -l,529.23 —649.03
6 80% harvested at T = 0.4,
= 0.5, T = 0.6, T = 0.7 2,863.26 6,886.34 -4,023.08 -l,672.55
7 80% harvested at T = 0.4
and at T = 0.7, w t
different weather from run 5 3,827.04 5,831.44 -2,004.40 -862.87
8 80% harvested at T = 0. 4,
T = 0.5, T = 0.6,T =0 7, with
different weather from run 6 2,016.39 5,831.44 —3,815.05 —l,651.83
9 Animal grazing removal of
500 + 2,000T kg/day This action is infeasible with season—long grazing.
10 Animal grazing removal of I
500 + 2,000T kg/day, with
different weather from run 9 This action is infeasible with season—long grazing.
ll Grazing 5.0 kg/hec—day 4,613.6 6,886.34 —2,272.74 —915.05
12 Grazing 5.0 kg/hec—day, with
different weather from run 11 4,674.20 5,831.44 —l,lS7.24 -430.43
13 Grazing 5.0 kg/hec—day + 80%
harvested at T = .4, with
different weather from the base This action is infeasible with season—long grazing.
l4 Grazing 5.0 kg/hec—day + 80% I
harvested at T = 0.5, with
different weather from the base 2,381.81 5,831.44 —3,502.63 —l,446.27
15 Grazing 5. 0 kg/hec—day + 80%
harvested at T = O. 7, th .
different weather from the base 3,649.10 5,831.44 -2,182.34 -887.17

 

 

 

 

 

 

249

Runs 1, 2, 3, and 4 explore the effect of a single harvest
removing 80% of the existing forage by weight at times 0.4, 0.5,

0.6, and 0.7, respectively. In terms of minimum effect on physical
quantity potential harvestable (amount actuallylharvested and final
forage value) run 4 is superior. In terms of TDN, run 2 is slightly
less harmful than is run 4. In all cases the effect of harvesting is
to reduce the quantity of potentially harvestable forage.

Runs 5 and 6 investigate multiple harvesting schemes, with the
result that two harvests is superior to four but that both are worse
than any of the single harvests evaluated in runs 1 through 4. Runs
7 and 8 duplicate the harvesting action of runs 5 and 6, respectively,
but under somewhat less favorable weather conditions. The overall
harvest possible using only a single end of the growth season harvest
(T=O.75) drops from 6,886 kg/hec to 5,831 kg/hec simply because of
weather differences. Run 7 turns out to be worse than run 5 in both
physical effect and TDN effects, while run 8 is superior to run 6
in both physical and TDN effects. The overall average rainfall,
average solar radiation, and average temperatures are important to
growth as well as the distribution lying behind such averages. Dis—
tributional effects are surely responsible for the improvement of
run 8 over run 6 in light of run 7 being inferior to run 5.

Runs 9 through 12 shift from forage harvest to cattle grazing.
Runs 9 and 10 explore the consequences of a heavy grazing pressure
on a land parcel of 100 hectares. In both the standard weather con—

ditions (run 9) and less favorable weather conditions (run 10), the

 

 

 

 

250

given rate of forage removal through grazing is untenable with season—
long grazing. The pressure is so great that all forage is consumed.
Figures 6.5 and 6.6 depict the dynamic forage levels which occur in
runs 9 and 10, respectively, with grazing and without, for comparison
purposes.

Runs 10 and 12 illustrate the effects of'a successful level of
grazing on forage production. Although this policy is successful in
terms of being possible over the grazing season, the net effect of
grazing is reduced forage production. This effect is quite sensitive
to weather, as the difference between runs 11 and 12 indicates. Run
12 has an overall growth reduction of 1,054.9 kg/hec from basic
weather conditions but a marginal increase in forage potential under
the grazing policy tested. Figures 6.7 and 6.8 illustrate the dynamic
pattern of forage growth in runs 11 and 12, respectively.

Runs l3, l4, and 15 illustrate the effects of combined grazing
and harvesting policies. The grazing intensity remains constant at
5.0 kg/hec/day, while the timing of 80% harvesting shifts from 0.4
to 0.7. Figure 6.9 illustrates the dynamic effect of those policies
on forage density. Run 13 is an untenable policy, as the early har~
vest combined with grazing pressure exhausts all plant material in
midsummer. Runs 14 and 15 are feasible, but neither would be par—
ticularly profitable, since the quantity harvested during the growth
season is not as large as the drop in the final density at T = 0.75.

The fifteen runs reported here present a picture of the current

operating characteristics of the forage growth component, with

 

 

 

251

Forage Density
(kg/hec)

4000 -

3000'

2000

     

1000 ' no grazing

grazing

 

A L Jr

0.20 0.30 0.40 0.50 0.60 0.70 Time
(years)

Figure 6.5 Forage densities over time as a result of basic climatic
variable inputs and grazing policies

 

252

Forage Density
(kg/hec)

4000,

 

3000.

2000

1000.

    

grazing

 

- l n A

0.20 0.30 0.40 0.50 0.60 0.70 Time
(years)

Figure 6.6 Forage densities over time as a result of basic climatic
variable inputs and grazing policies

 

 

 

 

 

253

Forage Density

  
  

 

   

 

 

(kg/heC)
4000 .
3000
no grazing

2000
1000

grazing ‘

O ” | l 1 A IL I
0.20 0.30 0.40 0.50 0.60 0.70 Time
(years)

Figure 6.7 Forage densities over time as a result of basic climatic 5

variable inputs and grazing policies

 

254

   
   

Forage Density

 

 

 

 

(kg/heC)
4000 f
3000 .
no grazing
2000 [
1000 _
grazing
0 4 I I l l I
II
0.20 0.30 0.40 0.50 0.60 0.70 Time

(years)

Figure 6.8 Forage densities over time as a result of basic climatic
variable inputs and grazing policies

 

 

255

Forage Density

      

 

 

(kg/bee)
4000
3000
climate induced
growth pattern
2000
run 15
1000
0 .
0.20 0.30 0.40 0.50 0.60 0.70 Time

(year)

Figure 6.9 Forage densities over time as a result of grazing
and harvesting policies

 

 

 

 

256

respect to grazing and mechanical harvesting policies. The effects
of the policies investigated here are conditional on the weather
patterns used in each run. Other weather patterns are, of course,
possible; and the results of the specific policies could change with
such different weather patterns. Finally, more exhaustive policy

tests would be certain to reveal superior policies yet.

Prediction

Section one of this chapter indicated that prediction is the
final step in model validation. Prediction is not attempted until
the model has passed through the preceding three steps in the vali-
dation process. Once the model is thought to be ready for use, it
is used, but on a tentative basis. The model will make time pre-
dictions that can be verified simply by waiting for real events to
catch up to simulated events. An extremely helpful action at this
point would be careful data collection oriented to the variables
used in this model and predicted by it. This allows tracking pro—
cedures to be used to identify time series which are not as well
modeled as others and, thereby, indicate areas where parameter changes
or new model structure is needed. This final stage of validation is
also a time when users can begin to develop confidence in the model
as they see it work and improve over time. Gradually the model will

be more and more reliable, and the validation effort can be concluded.

V1.3 Summary
This chapter has presented a hierarchy of validation steps which

a model must pass through before it can be considered verified or

 

 

 

 

 

 

 

257

validated. These steps are logical consistency, tracking historical
data, satisfaction of expert "eyeballing”, and prediction. A large
number of examples of logical consistency have been presented here

for the beef cattle enterprise model, as well as some discussion of

satisfaction of expert "eyeballing.' Tracking of historical data has
not been attempted simply for lack of suitable test cases. Predic—
tion must wait for an actual model user willing to devote the neces—
sary resources to this final step in the validation process. In

short, the model in its current state is well dowu the road of vali-

dation, but it has not yet completed the validation stage of model

development.

 

 

 

 

 

 

Chapter VII
MANAGEMENT STRATEGIES

This chapter will be the primary report of uses of the simulation
model to investigate management strategies of decision—making. Three
topics will be covered here: an orientation to management strategies as
used in the model, several illustrative demonstrations of the model and
its capability, and a summary of what has been learned from these sample
demonstrations.

VII.1 Strategies of Management Decision Making

Although this model contains many quite detailed control variables
to allow realistic simulation of an actual enterprise, its main useful—
ness lies in investigations of broader questions of management decision—

making. As used here the word strategy refers to an approach to manage-

 

ment or operation which embodies a multiple of individual decisions.

An example of a management strategy is the question of whether to sell
calves as they are weaned, or to retain them for sale later as yearlings.
A relatively fundamental difference exists between these two modes of
operation. Quite different cash flow patterns would be expected, as
well as rather different wintering feed requirements, etc. Detailed
decisions to be made within each of these strategies include how much
and what type of feed to allocate to the herd cohorts, how to effective—
ly use forage growth, and what sales date should be followed. The
simulation model accomodates these types of decisions through the
mechanism of decision points where the user has the choice of alter—
native actions to take to control the behavior of the enterprise. These

258

———__1

259

decision points occur as often as complex decision requiring the

input of a decision—maker are encountered.

VII.2 Demonstration Examples of Strategy Investigations

This section will discuss specific uses of the simulation model
in investigating alternative strategies of management decision—making.
Three different and distinct areas of management strategy will be
evaluated here:

(1) early versus late weaning of calves

(2) the rate of development appropriate in increasing
the steady state size of the breeding cow herd

 

(3

V

general profit maximization for a given breeding cow herd
size.

These three examples have been chosen as the means of illustrating
the capability of the simulation model because of the wide range of
decision-making that they encompass. The reader can think of numerous
other examples which might be just as appropriate as these. In order
to cover these three examples in the limited time and space available,
the testing will be under typical conditions but will not be exhaus—
tive or complete. The conclusions drawn here should be viewed as
tentative and preliminary and subject to further testing before
being confirmed.

The major criterion for comparing the strategies tested here

will be financial; this is in keeping with the subject being discussed

 

in this thesis—~a profit maximizing agricultural business. Other cri—
teria will be used when appropriate to reflect differences not handled
or poorly handled by financial considerations.

The three demonstration examples to be discussed in the remainder

of this chapter require numerous exogenous variable specifications

 

 

 

260

through time. These variables fall into four groups: expected prices,
climatic variables, crop production, and miscellaneous. Expected
prices over time are required for the five cattle price grades, the
eight production resources, and for each of the feed stocks. Climatic
variables required are the solar radiation, average daily temperature,
and rainfall patterns through time. Crop production specifications
include the timing and quantity harvested for each feed stock. The
miscellaneous category includes the quantity of grazing land and its
divisions into homogeneous parcels, the property tax rates, as well
as other initial conditions.

All three demonstrations will use an expected price pattern
which assumes an annual cycle of price fluctuations for cattle and
feed stocks. Expected prices for the eight production resources are
assumed to be constant through time. Figures 7.1 and 7.2 illustrate the
pattern and degree of fluctuation for expected prices of cattle of
grade 1 and feed stock 1 (forage), respectively. A pattern of constant
prices will be used in the weaning timing demonstration for comparison
with the cyclic prices usually assumed. Such prices will be roughly
midway between the highs and lows of the cyclic price pattern. Figure
7.3 illustrates the annual pattern of solar radiation incident to the
enterprise site. Forage harvesting will be performed at the end of
the growth season as well as within the growth season at T = 0.55.
Finally, the onset of spring growth and the end of the growing season
are assumed to be 0.25 and 0.80, respectively, throughout all runs for
these three examples. The many other initial conditions required to
operate the model will not be specifically mentioned; unless other~
wise noted such initial conditions are uniformly applicable over all

the model runs discussed.

 

 

 

 

 

 

 

 

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264

Early Versus Late Calf Weaning

The first illustrative example of the beef cattle enterprise
model will concern a relatively self contained policy issue——should
calves be weaned early or late? Beef producers face this decision on
an annual basis, so it is a question of concern. The effects of these
policy alternatives are largely confined to three areas, although second-
ary effects are numerous. These three areas are (1) overall profit
effects resulting from sales of either light or heavy calves to the
market, (2) total feed requirements with retention of calves into the
winter feeding season, and (3) effects on estrous cycling in calves
selected as replacements for the breeding herd.

The exogenous variables used in the runs to examine this policy
issue were largely as described earlier in this section. However, the
cyclic prices used most frequently throughout the runs discussed in this
chapter were augmented by a pattern of constant prices for purposes of
comparison. Feed stock production was assumed to be 45000 kg of shelled
corn at T = 0.65, 20000 kg of corn silage at T = 0.70, and 15000 kg of
rye grass at T = 0.75. 660 hectares of grazing land was divided into
five parcels of 200, 200, 100, 100, and 60 hectares. Property taxes
were assumed to be $50 per hectare per year.

Four runs of the model were made to investigate the major effects
listed above. The time horizon covered by these runs was from T = 0.0
through T = 1.25. An experiment involving two factors was performed,
with the first factor being age of weaning, and the second factor being
the annual pattern of prices expected. Age of weaning was tested in
two groupings, with the age of weaning ranging from 3 to 5 months in

the early weaning group, and from 5 to 7 months in the late weaning group.

 

 

 

 

265

Price patterns were also tested in two groups; the first group used
constant cattle, production resource, and feed stock expected prices,
while the second pattern had cattle prices cycling on an annual basis

as exemplified by Figure 7.1. Peak cattle prices in this second pattern
were in the spring with minimum prices in the fall corresponding to the
traditional weaning/culling time.

Table 7.1 reports the results of the four simulation runs which
evaluate the effect of weaning age on enterprise behavior. Early
weaning—~constant prices, early weaning-—cyclic prices, late weaning——
constant prices, and late weaning~—cyclic prices are the four runs
reported in this table. Five factors of primary importance are listed
for each run; these are annual cash flow, revenue earned from calf sales,
total purchased feed stocks consumed, replacement heifer estrous onset,
and bred heifer estrous onset. The first three of these factors are
obtained from the end of the year financial summary, while the last
two are obtained from the intermediate print statements at time T = 1.25.
This latter time happened to be the time at which the simulation model
determined the age of heifer estrous onset.

In Table 7.1 the run with the minimum cash outflow (all four have
negative cash inflows for the year) is run 3, i.e. late weaning with
constant prices. This is largely due to the fact that it is also the
run with the largest revenue earned from calf sales. Even with cyclic
prices, however, late Weaning is financially superior to early weaning
as is demonstrated by run 4. The higher calf weights at a later time
of weaning are responsible for this superior financial performance.

Late weaning also resulted in a slightly smaller total feed con—

sumption (of purchased feed stocks) than early weaning. This was due

 

 

 

 

 

266

 

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267

to the fact that calf nutrients could be partially supplied by grazing
during the early fall period, but were mainly supplied by lactating
cows which themselves were grazing and therefore not consuming feeds
which are counted in the quantity listed in Table 7.1.

Additionally, the ages of the heifers at first estrous, both for
replacement heifers and bred heifers, were younger for late weaned
calves than for the early weaned calves. In both late and early weaning
the oldest group of female calves were selected for replacements, and
the second oldest were selected for bred heifers. All of the other
calves were sold on the market. The age difference between the oldest
and second oldest female calf groups selected accounts for the difference
in the ages of first estrous between replacement and bred heifers. The
age difference , for both replacements and bred heifers, between those
weaned early and those weaned late is only 0.0359 years, or approxi—
mately two weeks. This difference would have some effect on the rate
of pregnancy achieved for the two heifer groups during their first breed-
ing, but only in a marginal way.

The overall conclusion drawn from this set of four runs of the
model is that late weaning is to be preferred to early weaning even
under adverse price expectations. Only when the expected fall in prices
for cattle during the fall period is so severe so as to more than offset
the increase revenue from heavier animals should early weaning be con-
sidered. Even in this instance the consequences of additional purchased

feed consumption and delayed estrous onset should be carefully considered

before early weaning is adopted.

 

 

 

 

 

 

 

 

268

Rate of Development
This example of the capability of the enterprise model illustrates
the ability of the model to assist in project investment planning. The
three cases considered here are ones which would be considered among
the range of possible approaches to achievement of the goal. The pro-
ject to be investigated here is achievement of a steady-state breeding
cow herd of 200 animals within three years of project initiation. The
three cases tested are (1) purchase of 200 bred heifers and no other
animals, (2) purchase of 250 mature cows and no other animals, and
(3) purchase of an entire ongoing herd having a steady—state cow
population of 100 animals. Certainly other possible initial states
exist, but these three will be the ones tested in this model demonstration.
Each of the three runs discussed here shares the same common
exogenous variable environment. The standard weather pattern used in
the majority of the simulation runs of this thesis is again present
here. Figure 7.3 illustrates the solar radiation pattern of this
weather set over the calendar year. Annual cycle of cattle and crop

prices is expected with peak crop prices in the spring and minimum

 

prices in the fall. Similar timings of the cattle price fluctuations
are assumed. Figures 7.1 and 7.2 illustrate typical levels of price
fluctuation and the timing of these fluctuations. Production resource
prices are assumed constant throughout the three-year time interval
evaluated. All runs begin at T = 0.0 (corresponding to January 1 of
the calendar year), and spring calving was used for all three runs.
The grazing land parcels were identical to those of the weaning demon-

stration, as were the feed stock production quantities and timings.

 

 

 

 

 

269

Property taxes were again $50 per hectare per year and due in
Semi—annual installments.

Figure 7.4 indicates the convergence of the mature cow populations
of each of the three cases toward the target value. Case 1 population
increases rapidly from zero to 200 because the initial conditions were
200 bred heifers which quickly had their calves and became mature cows.
Subsequently this population drops below 200 because there are no
replacement animals to take the place of cows which die or are culled.
Only as replacements are generated from the first calf crop does the

population again approach the desired level of 200. Case 2 exhibits

 

a steady drop from the initial level of 250 cows that one would expect
because culls and deaths are not replaced with incoming heifers until
the first calf crop matures to replacement heifer age. Case 3 follows
a slow but steady path of population increase that is expected of a
herd which began at a level of 100 and which is growing solely through
retention of weaned female calves. Culling is at a very low rate in
this case to maximize cow population. All female calves are retained
for replacement heifers to minimize the time required to reach the
target population. By T = 3.0 Cases 1 and 2 are quite near the desired
population target, but Case 3 is still somewhat short of this goal.

Had the plot of Figure 7.4 been extended to T = 3.25, then all three
cases would have been slightly in excess of the target population.

The considerable rise in the Case 3 population would have been due to
the large number of replacement heifers (retained from previous calf
crops) which would be changing cohort designations as they become two

years old. All three cases can be considered to have reached the target.

i.e—

 

 

 

 

 

270

 

 

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Selection of a "best" rate of development from among a group of
alternatives is most likely to be made on the basis of financial return.
The selection of criteria to determine this return is a decision which
should be made quite carefully. Operating characteristics as well as
some measure of the change in value of property and assets should be
made. For this demonstration example the cash flow of the runs and the
change in net worth of assets other than land will be the criteria used
for selecting the best alternative. Cash flow will be discussed in
terms of overall accumulated flow, annual cash flow, and per period cash
flow. Net worth will be discussed in terms of long and short term debt,
change in value of feed stocks on hand, and change in value of the
cattle herd. Operating capital levels will also be included.

Figure 7.5 illustrates the cash flows on an annual basis for the
three cases under consideration. All of them share the characteristic
of being highly negative; this indicates the current poor condition of
the cattle industry faithfully. High feed prices and low cattle prices
are the cause of this situation. Case 1 is less negative than the
other two alternatives in years 2 and 3, but case 3 actually made money
in the first year. Case 3 then plunges down to the worst position of
the three for years 2 and 3. This drop can be attributed to low revenues
associated with retention of all female animals to maximize calf births
in the following years. A reason for the highly negative cash flows
of the three alternatives is the debt repayment made necessary by
borrowing to meet the needs of the enterprise during the long intervals
with negative cash flow. Typical loan conditions used here was repay—

ment within one year at 10% interest on the unpaid balance. These terms

 

 

 

 

 

 

272

 

 

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273

insure that the loans must be rolled over since the entire three year
interval produces no windfall of revenues to enable the enterprise to
eliminate them entirely. If more favorable terms could be arranged
then the cash flows would not be quite so bad, but then the debt
situation would not be as good.

More detail on the timing of cash inflows and outflows contribut—
ing to the annual patterns of Figure 7.5 are given by Figure 7.6.

Here the individual DT time increments of cash inflow have been
aggregated into values for intervals of 0.20 year. Cases 1 and 2 show
quite similar patterns of cash flow over the entire three year project
duration. Case 3 differs somewhat from the other two, but becomes more
similar as time approaches the end of the project. The working capital
requirements of the enterprise can be determined through integration

of the consecutive periods of cash outflow. Such outflows must be
covered by working capital on hand at the beginning of the outflow
interval, or by borrowing during the outflow interval with repayment

to be negotiated between the borrower and the lender.

The change in net worth of the enterprise is a function of the
change in herd composition and age structure, changes in the feed stock
inventory, changes in the level of working capital, and debt load. Table
7.2 illustrates the net worth changes which have occurred over the three
year time horizon of these investigations. The initial cattle herd
valuations are strictly a function of the composition of the herd at
T = 0.0, as initial feed stock valuations are solely determined from

the quantities of each feed stock on hand. All three cases shared a

 

 

 

 

 

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274

 

 

 

 

 

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r-
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(years)
- Case 3

 

Figure 7.6 Pattern of cash flows through time over the 3 year time
horizon of the investigations for Cases 1, 2, and 3

 

 

 

275

Table 7.2 Change In Net Worth Over Time

 

Financial Variable Case 1 Case 2 Case 3

Initial--T = 0.0

Value of cattle 32000 92500 64900
Value of feed stocks 21060 21060 21060
Working capital 45000 45000 45000
Long term debt 62100 122600 95000
Short term debt 0 0 0
Net Worth of liquid assets 35960 35960 35960

Final-—T = 3.0

Value of cattle 80200 83000 83050
Value of feed stocks 20400 18220 25070
Working capital 43370 13330 —7l60
Long term debt 0 50600 23000
Short term debt 41200 46400 29000
Net Worth of liquid assets 102770 17550 48960
Change in net worth +66810 —l7510 +13000

 

L

 

 

 

 

 

 

common level of net worth of assets and liabilities. The widely
varying herd valuations were offset by different debt levels which
would represent the borrowing necessary to acquire such herds. Overall
net worth at T = 0.0 was set at $35,960, exclusive of land related
indebtedness and valuation.

After three years, Cases 1 and 3 have increased net worth while
Case 2 has suffered a significant drop in net worth. Cattle and feed
stocks were valued at the appropriate prices in effect at T = 3.0 to
obtain these end of project figures. Due to the annual cattle and
crop price patterns used throughout this dissertation, the prices in
effect at T = 3.0 happen to be identical to those in effect at
T = 0.0. Case 1 had such a large increase in net worth because the
herd increased dramatically in value-~animals which were initially
valued as replacement heifers were valued at the conclusion of the
project as mature breeding cows. Overall debt shrank in all three
cases, but the rapid repayment of long term debt was offset by large
increase in short term debt. The short term debt levels are a result
of the negative cash flows which have had to be funded through borrowing.

An overall combination of cash flow and changes in net worth
gives a rather gloomy picture for all three development cases. Case
1 has an overall undiscounted present value of —$34,790, while Case 2's
value is —$l69,210 and Case 3’s is -$l30,200. Clearly Case 1 is the
best of the three tested by a wide margin. Therefore, these tests would
conclude that purchase of bred heifers is the best choice from among

these three. However, the fact remains that even Case 1 lost nearly

 

 

 

 

 

 

 

277

$35,000! Only land speculation or desires for tax losses to offset
other taxable income would induce an investor to make this investment

under the conditions tested with these runs.

Profit Maximization

The final demonstration of the capability of the simulation model
to evaluate and assist in decision making will be a search of selected
control values and strategies to maximize profits for a given breeding
herd size. Here the breeding cow population will fluctuate around 200
animals with appropriate replacements to maintain this herd size.
Three areas of potentially significant financial effects will be
investigated: use of artificial insemination versus natural breeding,
sales of weaned calves or retention for later sales as yearlings, and
herd feeding plans. Monetary considerations of alternatives will be
supplemented by other criteria when appropriate in selecting among
possible control value sets. Cattle and crop prices will be assumed
to fluctuate on an annual cycle as illustrated by Figures 7.1 and 7.2.
The weather variables will be assumed to follow the pattern given by
Figure 7.3——a plot of solar radiation levels over the calendar year.
Property taxes are assumed to be $20 per hectare per year, and due in
equal installments June 30 and December 31. Total land area allocated
to grazing is 660 hectares divided into five land parcels. No land is
leased. Small quantities of shelled corn, rye grass, and oat silage
are produced for winter consumption.

The decision to select either artificial insemination (AI) or

natural breeding over the other has elements of financial cost, breeding

 

 

 

 

 

 

278

cow conception rates, and genetic change involved. This enterprise
simulation model excludes genetic factors completely. Currently, the
overall conception rate from AI is the same as natural breeding as long
as the onset and duration of breeding are equal. This leaves the
direct financial costs as the only viable means of making comparisons
between these breeding methods. Two model runs were made to investigate
the financial effects of the method of breeding. One had a bull/cow
ratio of 1:20 with no AI used, while the other used AI exclusively with
zero bull population. Both runs covered the time interval from T = 0.0
through T = 1.0. Table 7.3 summarizes the results obtained.

Use of natural breeding is superior in terms of financial cost by
a margin of 4,900 dollars. AI supplies and labor are a large expense
which more than exceeds the feed costs and replacement costs of maintain—
ing a bull herd. AI supplies were assumed to be priced at $10 per
ampule, which is a typical value. In actual practice there might be
the additional factors of different cow and heifer conception rates
and genetic changes to modify these findings. However, the financial
costs of the two methods of breeding clearly favor natural breeding;
enterprise profit maximization implies the use of natural breeding.

Disposition of weaned calves is a question which cattle ranchers
face yearly. Should they be sold after weaning, or retained for sale
later as yearlings? Immediate sale had the advantage of lower winter
feed requirements, less labor in general animal care and feeding, and
a known current market price. Retention for later sale speculates

that the increased revenue of selling heavier animals will offset the

 

 

 

 

 

 

 

 

 

279

Table 7.3 Breeding Method Cost Comparison

 

 

 

Costs of Costs of
Factor AI Natural
Breeding Breeding
($) ($)
Labor and AI supplies 10,980 ———
Bull feed costs -—- 1,270
Bull replacements ——— 4,800
Total 10,980 6,070

 

 

 

 

 

costs of keeping these slaughter cohort animals. Three separate

runs were made to compare the overall financial effects of (1) sale
immediately following weaning, (2) retention of female heifers not
selected as breeding replacements, and (3) retention of all weaned

calves. All animals retained for later sale were sold at T=l.15

 

when yearly cattle prices Were at their peak; animals sold at that
time were from 10 to 12 months old.

Table 7.4 indicates the results of these three runs. Total
cash flow and net profit are reported for the period (0.0, 1.15).
Additionally the values of the feed stock inventories at T=l.20 have
been compared and the difference of the two retention runs from the
base given. Finally, total cash flow and net profit are adjusted to
include the feed stock inventory valuation differences. These adjusted

values are a true basis for comparison among the three runs. As the

 

 

 

 

280

values of adjusted cash flow make clear, the more weaned animals that
are retained the worse off the enterprise becomes. Under the feed
plans used, and the basic price cycle specified, the profit maximizing
operator would sell all weaned calves not retained for replacement of

breeding cows and save none for later sale.

Table 7.4 Financial Effects of Weaned Calf Retention

 

 

Policies
Factor Sell All Sell Males Sell None
($) ($) ($)
Total Cash Flow +4770 +2790 +100
Total Net Profit -5980 -7960 —10650
Feed Inventory Value 0 -3620 -1850
Total Adjusted Cash Flow +4770 -830 —1750
Total Adjusted Net Profit -5980 —11580 ~12500

 

 

 

 

 

 

 

 

 

The final aspect of profit maximization to be investigated in this
thesis is the area of cattle feeding plans. Feeding of cattle is a very
significant part of the overall cost of a cattle enterprise and offers
room for financial savings if feed reductions can be made. The simula—
tion model is well suited to these investigations because of the great
flexibility which exists in the quantity and quality of feed that can
be allocated to the individual herd cohorts over time. For example,
the model user can specify up to four different feeding plans through
time and control the time at which allocations shift from one to another.

Since these plans are changeable at most decision points the time interval

 

 

 

 

 

 

281

during which each feeding plan is in effect can be quite short.
Within a particular feeding plan the user can specify the quantity

of TDN he wishes allocated to each cohort's animals for both concen-
trates and roughages per day. The units of the control variables of
the feeding plan are kg TDN/animal/day. Further, the user can specify
what fraction of the roughage and the concentrate allocation is to be
obtained from what feed stock. This model organization gives the
model user nearly as much flexibility as an actual enterprise manager
in feeding cattle.

A series of eight simulation runs of one year's duration was
made, attempting to reduce feed allocations withOut hurting cattle
performance. The base run had a series of six feeding plans cover-
ing the entire one—year interval drawn from rough adherence to rec—
ommended guidelines. Two different sources caused misallocations
where improvement was obviously attainable. First, several instances
occurred in which the allocation to animals of a particular cohort
was more than they would consume. This excess is considered totally
wasted in the model (see section V.4 for details). Second, several
other instances occurred in which the allocation to animals of a
cohort gave a projected daily weight gain rate which conflicted with
the weight maximum constraining that cohort. In such instances any
daily gains exceeding the weight maximum are disallowed (see section
V.l for details). Thus, the immediate goal was to eliminate these
sources of excess feed consumption from the feeding plans.

Table 7.5 indicates the results of the eight model runs over

the time interval (0.00,1.25). Run 1 is the base from which improvements

 

 

 

 

282

 

 

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283

were to be made. Run 2 increased the mature cow allocations during
calving to attempt more rapid weight recovery, while also decreasing
allocations to replacement heifers and mature bulls. Both these latter
two cohorts were being allocated excessive feed quantities; heifers
were allocated more than they would consume, while bulls were fed so
much that the resulting daily gains took them beyond the weight
constraint of 600 kg. A small improvement in the overall financial
measure of Run 2 was shown——approximately 6.7% better than the base run
in terms of the combination of annual cash flow and the excess feed
inventory on hand.

Run 3 attempted to the correct the problems still remaining after
Run 2 by further decreasing replacement heifer feed allocations in the
early part of the year, and by reducing the allocations of concentrate
to bulls throughout the year. These changes resulted in another small
increase on overall profitability as total feed allocated was reduced.
An 11.7% improvement from the base run was achieved.

Runs 4 and 5 departed significantly from the feeding plans of the
first three runs. Early year cow and heifer pre—calving feed rates
were increased to reflect the common practice of boosting energy intake
prior to calving. Run 4 also added a schedule of feeding calves supple—
mentary concentrates during the later summer months. These increased
concentrate allocations are reflected in the higher concentrates consumed
values in Table 7.5. The overall financial result was still slightly
better than the base run, by 3.5%, but a drop from the previous runs.
Run 5 eliminated the summer concentrate supplements to calves of Run

4, but was otherwise identical to it. Its overall financial result was

 

 

 

 

284

a gain from the results of Run 4, but still worse than Run 3. A 9.8%
improvement over the base run was obtained.

Run 6 made another significant change by extending the grazing
season, where no supplementary feeding is made, from T = 0.70 through
T = 0.80. This latter time value is the beginning of the wintering
season as defined with the use of the variable TFALL. This increase
in grazing period is significant because of the large number of cattle
which are present in comparison to the rest of the year. Calves are
able to eat quite a lot with full weaning being only a short period

into the future (TWEAN = 0.85). Elimination of this period of feeding

 

saved expensive feed stocks by substituting forage which is relatively
low in cost. The overall financial effects were startlingly good——
a 58.6% improvement over the base run.

Runs 7 and 8 use Run 6 as a base and differ from it by increasing
or decreasing post—calving cow concentrate supplementation, respectively.
Observation of the overall concentrate consumptions listed in Table 7.5
shows roughly 10,000 kg increases in Run 7, and 10,000 kg decreases
in Run 8, from the base levels of Run 6. Overall financial effects
reflect these levels of change in concentrate consumption, with Run 7
dropping to only 26.2% better than the base run, and Run 8 increasing
to 83.5% better than the base run.

The above discussion of the effects of alternative feeding plans
has concentrated on the financial effects without mention of some more
subtle feeding effects. One of these effects is the condition of the
breeding cow herd as related to calving, lactation, and rebreeding.

Table 7.6 gives an idea of the feeding plan effects on cow condition

 

 

 

285

by presenting ranges of weights of cohort l cows (at T = 1.0) for each
of the eight runs. Three basic groupings may be made from the eight
runs: (1) Runs 1 and 8, (2) Runs 2, 3, 4, 5, and 6, and (3) Run 7.

Runs 1 and 8 presumably have comparable levels of breeding cow condition
as the weight ranges are very similar. Run 8 is vastly better than

Run 1 financially, so it would be preferred to Run 1. Runs 2 through

6 have very similar weight ranges implying a uniform cow condition

among them, while Run 6 has much better financial outcomes than the

others. Run 6 should then be preferred over the others. Finally,

 

Run 7 has a somewhat better condition than either of the other two groups.

Choice of the best overall run of these eight is difficult
because of the inverse relationship between the two measures of outcomes.
Figure 7.7 plots these conflicting results. Decisions about what is
preferable among these groups of runs—-numbers 6, 7, and 8—— must be
made on the basis of the weights assigned to the two measures of
performance. If the weight differences are relatively unimportant,
then Run 8 is best. If the weight differences are very important, then
Run 7 is best. Perhaps Run 6 is best under moderate importance of both
measures. The decision maker must decide for himself.

Profit maximization (or loss minimization) is an open ended pro—
position. This demonstration of the capability of the model has touched
on three areas which seem likely to be important to achievement of the
goal. Of course, many additional aspects have not been examined at all.
The results of these model runs do tentatively support the proposition

that profit maximization implies natural breeding not AI, sales of weaned

 

 

 

 

 

286

calves immediately not retention, and a tight level of feeding. ‘Run

6 is probably characteristic of such feeding levels. Other conclusions
could possibly be drawn here if the assumptions about price, weather,
and crop production change significantly. Additionally, a more sophis—
ticated model which includes an improved model of the energy intake/
reproductive potential interactions might obtain somewhat different

and more conclusive results with regard to the effects of the feeding

plan alternatives discussed here.

Table 7.6 Mature Breeding Cow Conditioning Effects
From Alternative Feeding Plans

 

 

 

 

 

 

 

Weights at T = 1.0

Run Average Minimum Maximum

(kg) (kg) (kg)
1 386 358 419
2 405 372 440
3 406 371 440
4 406 370 440
5 406 370 440
6 396 367 440
7 417 380 443
8 385 351 [ 423

 

 

 

 

 

 

 

 

287
Financial
Rank
best . Run 7
middle . Run 6
worst . Run 8
worst middle best Condition

Rank

Figure 7.7 Plot of the rankings of runs 6,7, and 8 according
to financial ranking and condition ranking

 

 

 

 

288

V11.3 Summary

Three demonstration examples have been presented to illustrate
the capability of the simulation model to assist decision makers in
ongoing operational decisions and in investment planning. The question
of early versus late weaning was decided in favor of late weaning. 0f
the three paths tested for achieving a steady—state breeding cow herd
of 200 animals, the best method was to begin with 200 bred heifers and
generate herd replacements internally. Profit maximization turned Out
to imply natural breeding as opposed to artificial insemination, sales
of all weaned calves immediately following weaning rather than retention
for later sales, and a tight level of herd feeding. All of the conclu-
sions determined through these demonstrations are tentative, because
the purpose of these investigations was merely to illustrate the capa—
bility of the model, not to come to a definitive conclusion about a
particular decision rule of management. Confirmation of these findings
could be achieved through more extensive testing with the simulation
model in conjunction with improved data.

The deterministic nature of this model and its output variables
could be modified to allow running in a Monte Carlo mode of operation.
This would provide confidence intervals on the Output variables as
related to randomness in the various variables of this system. For
example, the weather variables used in the runs at present are deter-
ministic not random as they are in nature. Forage growth should,
therefore, be a stochastic variable responsive to the random variable
values of solar radiation, average temperature, and rainfall. The
financial variables of the model would then be stochastic in response

to different levels of forage growth for any given management policy.

 

 

 

 

 

 

289

Confidence intervals could be determined around the financial outcomes
indicating the degree of fluctuation of them from weather variation.
Managers might prefer policies which while less attractive on the
average have less variation around the mean. The preferences of the
manager toward uncertainty could then enter into his decisions regard—
ing investment and management policy.

These three demonstration examples do confirm the usefulness of
the simulation model in assisting management decision makers. Both
ongoing operating decisions and project investments of a realistic
nature can be evaluated with the model in its current form. A tool
such as this model should allow decision makers to perform better since
a much wider range of alternatives is open to analysis and objective
comparison. Information is generated which the manager can use to
significantly reduce the risk and uncertainty which are associated
with particular management strategies. While the development of this
model is costly, the operating expenses of using it are extremely
small in comparison to the potential advantages that can be gained
from better responses to economic forces and the environment. Many
questions of significance could be answered in a day of programmer
time and $50 worth of computer time, as measured on the MSU CDC 6500.

The great flexibility of the model should make it of interest to many

different users.

 

 

 

 

 

 

 

CHAPTER VIII
SUMMARY AND CONCLUSIONS

This thesis will end with a summary of the preceding seven
chapters, the conclusions to be drawn from the development and use

of the model, further extensions and improvements to the model, and

implementation of the model.

VIII.1 Summary

The preceding chapters have discussed in great detail the
development and use of a system simulation model of a beef cattle
enterprise for the purpose of investigating alternative management
decision making strategies. Chapter IV developed the general de—
scription of the modeling approach that has been taken, while Chapter
V discussed the details of the mathematical model as implemented in
the FORTRAN subroutines listed in the User's Guide to the Beef Cattle
Enterprise Simulation Model, a separate volume from this thesis. The
details of the growth prediction and reproductive impact component
can be found in Schuette [48]. This simulation model represents a
strong attempt to fully model the time dynamics and reproductive
dynamics of a beef cattle herd; this is an area which has been ne—
glected up to this time. Furthermore, the intent of this thesis has
been development of a practical tool for decision makers which can

be helpful in providing evaluations of alternative decisions.

 

 

 

 

 

 

 

291

A general model of a beef cattle enterprise which leans toward
the land-extensive cow/calf form of operation has been viewed as con—

taining five major system components. These are

..-

cattle herd demographics—-a description of the herd at each
point in time by age, sex, function, and, weight;

forage growth component—-dynamic plant growth of forage as

influenced by climatic variables and mechanical and animal
harvesting of plant material;

feed stock component——accounting for the quantity and
quality of cattle feed stocks through time;

nutrient impact component-~determination of the response of
cattle to feed intake rates in terms of growth and of
reproduc tive po tent ial;

management decision-making component——the decisions and

actions needed to manage the herd on both long- and short-
term bases.

Additionally there are several secondary components which determine

the financial effect of actions, generate proper values of exogenous

variables through time, etc. Figure 4.12 is repeated here to summarize

the components of this system and the interconnecting variables.

A key feature of the management decision making component is the
distinction between decisions which the model itself can determine
endogenously and those which must await exogenous control by the model
user. Currently there are seven instances in which the model must stop
and be restarted with appropriate control variable values determined by
the user after study of the preceding simulation results and the current
states of the system.

These seven events are organized into five "deci—

sion points" which correspond, in part, to natural cattle phenomena.

These decision points occur when:

 

 

 

 

 

 

 

 

 

 

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293

(1) spring plant growth begins

(2) herd breeding begins

(3) calf weaning occurs

(4) mature cow culling occurs

(5) working capital falls below $2,000

(6) feed stock levels fall below the requirements for the
next two successive simulation time increments

(7) final harvest feed stock levels are more than a specified
per cent out of balance with winter feed requirements.

Further and extensive use of the model may reveal decision rules
which can be incorporated into the management decision making component
and reduce the number of events which require exogenous control by the
model user.

A primary reason for requiring exogenous user decisions is the
long time delays characterizing this system and the highly volatile
prices in cattle markets during recent years. Control variable values
optimized with reference to some suitable objective function are con-
ditional on the price and other variable expectations that were used;
these values may be far from optimal under different exogenous variable
conditions. In response to this situation the management decision
making component has been designed to require exogenbus user decisions
at points where long time delays make automatic decision rule actions
infeasible. Thus the above list of events has been determined to
require exogenous control.

The present simulation model, as it is described in Chapter V and
the User's Guide...., fulfills the problem statement requirements as

given in III.4. This is not to say that improvements and extensions

 

 

 

 

 

 

 

 

 

 

294

cannot be made——certainly they can, a later section of this chapter
will review such areas in some detail. The model is fully capable of
examining many questions of long-range management decision making, as

is evidenced by the illustrative sample runs of Chapter VII.

V111.2 Conclusions

This thesis has developed a batch interactive simulation model of
a beef cattle enterprise system. With the exception of land allocation
and crop production aspects, the entire system has been modeled as
FORTRAN programs and subroutines. The entire model requires 130000
octal words of core as run on the MSU CDC 6500. This is a very large
memory requirement, but it could be reduced through more sophisticated
programming. Running costs of the model are quite low, with the cost
of a single year of simulated time requiring approximately $7.50. A
budget of $50 for computer time, and a day's salary for a programmer
familiar with the model's operation, could obtain very significant
information for use by management decision makers.

The model is designed to be, and is capable of, investigating the
effects of management decisions on the physical and financial variables

commonly of interest to actual decision makers. The goal throughout

 

this thesis project has been to develop a practical tool to allow deci-
sion makers increased ability to evaluate the consequences of their
decisions on the enterprise. This goal has been accomplished. Improve—
ments and extensions remain, but the present form of the model is capable
of profitable use in operational decisions and investment planning.

An accomplishment of this thesis has been construction of a

realistic model of the dynamics of herd growth and reproductive dynamics

 

   

 

 

 

 

 

295

across the entire range of cattle types and uses. A second
accomplishment has been the development of an interactive management
decision making component which makes decisions endogenously, if pos—
sible, and asks the user for exogenous decisions where needed. A
third accomplishment has been the development of a forage growth com—
ponent which uses exogenous weather variables and forage removal (by
machines and by animals) to obtain forage dynamics. This model is
data oriented and can be used independently of the main simulation
model. A fourth accomplishment has been development of a discrete
time delay subroutine which is capable of having a dynamic delay time
and proportional losses from the intermediate storage values.

Since this thesis has not been used in a practical setting to
date, its major accomplishment has been to contribute to the integra—
tion of separate stocks of knowledge and understanding of the beef
cattle enterprise operation. This has involved areas of agricultural
economics, animal husbandry, cattle physiology, crop sciences, and
management decision making. The system science methodology for mod—
eling and simulation of general systems has been the integrating
factor which has been responsible for development of this model.

The three demonstration examples of Chapter VII have been
tentative investigations that are intended to illustrate the capa-
bility of the model to evaluate a wide range of questions of interest
to management. The conclusions reached in that chapter should be
considered preliminary and are, of ccurse, conditional on the prices
and other exogenous variables used. Briefly summaried, the following

conclusions were made:

 

 

 

 

 

 

296

(1) Late weaning of calves is preferred to early weaning.

(2) Investments designed to obtain a steady-state cow herd
of a specified size within a stated three—year period should
begin with bred heifers.

(3) Profit maximization implies no retention of weaned calves
for later sales. Natural breeding should be employed
instead of artificial insemination. And a tight feeding
schedule should be adopted.

These conclusions could be confirmed by further evaluation using the

simulation model to test other conditions and exogenOus variable

values, if no better strategies were to be discovered.

V111.3 Improvements and Extensions to the Model

Few modeling efforts reach an end point from which improvement
and extension are not possible. This model is no exception; there
are a number of areas of improvement and extension that will be
discussed in this section.

A fundamental factor in this simulation model has been
representation of the cattle population dynamics using a mix of dis—
crete and distributed time delay models. There is some error in this
approximation due to the nature of the FORTRAN subroutines which are
used to represent these time delays. The distributed delays work
quite well with large population numbers; but as the population drops,
the error becomes larger and larger in significance. For example,
in the bull cohort, populations in the delay model are usually in the
neighborhood of ten animals with a cow herd of 200 animals. With this
few animals, the delay model functions rather poorly; after a three—
year simulation run, the number of bulls is down to five or six

indicating that the distributive effect moving the animals through

 

 

 

 

 

 

 

 

297

the delay is operating too rapidly. An improvement to the simulation
model would be development of a delay routine which could handle
small populations without excessive error.

Several small changes could be made in the financial component.
First, rather than loans being segregated into short and long term,
as is presently done, there could be a multiple loan structure, with
each loan having its own unique repayment pattern, interest rate, etc.
Second, depreciation is currently based on the average total purchase
value and an average depreciation lifetime rather than depreciation
based on individual items. A breakdown of such physical assets into
groups sharing common depreciation lifetimes and times since purchase
would be fairly easy to accomplish and would give much more accurate
results. Finally, Subroutine PRCOST determines the costs of animal and
crop production disaggregated to the level listed in Table 5.1. Improve—
ment in the determination of these costs could be achieved through pa-
ramater estimation studies for those parameters listed in Table 5.3 or
through development of an entirely new structure to determine production
costs on the basis of physical reSOurces used during a simulation
increment.

Several small changes associated wtih the population demography
component could be instituted with relatively small effort. First,
the variable ADDRTi(t) is used currently to add or subtract animals
from herd cohorts as a whole. An improvement would be a variable
which could add or subtract animals to specific cohort subpopulations.
This would be more in line with typical practice of purchasing spe—

cific types and ages of animals rather than the mixture of ages that

 

 

 

 

 

 

 

298

ADDRTi(t) in its presentform assumes. Second, grade changes as a
result of aging and of changing body proportions could be modeled
better than is currently done in subroutine WEIGHT. A limitation
here, however, is the fact that price grades for cattle are still
assigned on the basis of appearance, which cannot be programmed.
Finally, death rates for herd cohorts could be made functions of
weather values and season quite readily.
Improvements could be made in the method of assigning feed
intake levels to the animals within the slaughter cohorts. Pres—
ently, these cohorts use the same feeding plan structure as the re—
maining herd cohorts; that is, the level of TDN from concentrates and
from roughages and the distribution of these among the potential feed
stocks is specified by the user. Computation of feeding rate and selling
date could be optimized using a number of methods readily available.
These optimized values would, however, be conditional on the expected
prices for cattle and feed stocks which the user has dictated to the
model at the previous decision point. Numerous feed lot optimization
models have been constructed in recent years which could either be
adapted or incorporated into this model in their entirety to provide the
optimization of feeding rate and sales date for the two slaughter cohorts.
A major distinction between the two slaughter cohorts and the remaining
herd cohorts which allows the slaughter cohorts to have feeding rates
optimized is that the reproductive implications of feeding rates do
not enter the optimization problem because the slaughter cohorts by

their very nature have already been excluded from reproduction.

 

 

 

 

 

 

299

The harvest of forage by mechanical means is currently performed
on all land parcels regardless of whether animals are grazing there or
whether particular conditions merit special consideration. An improve-
ment to the forage growth component which would remove this difficulty
is having specified harvest fractions for each land parcel rather
than a common value imposed on all land parcels. This addition would
make control over forage growth and harvest much more realistic at a
very small development cost. A further improvement in this regard
would be increasing the number of land parcels allowable from the cur—
rent five to perhaps 20. This increase would provide for investigation
of more sophisticated grazing management policies.

An improvement of a more substantial nature involves the
characterization of feed stocks in terms of moisture content. The per
cent of moisture of any feed stock at each point in time would be used
to convert to a dry matter basis as needed in the nutrient impact com—
ponent. Reporting forage growth and feed stock production and stor-
age on a wet basis w0uld conform more closely to actual field prac—
tices. An additional complication, however, w0uld be the fact that
crop prices are usually dependent upon the moisture content. Some
price/moisture relationships would have to be devised for each feed
stock.

An improvement which would substantially increase the realism of
the nutrient impact component would be inclusion of protein content of
feeds on an explicit basis. The current presumption is that protein
needs are satisfied when energy needs (TDN) are satisfied. In actual
practice protein deficiencies are rather common among high—energy-content

feed stocks; this has lead to the widespread use of protein Supplements.

 

 

 

 

300

An improvement to the model which would increase its ease of
operation for runs with long time horizons would be development of
a set of decision rules which would operate as defaults to action
normally taken by the user himself at a decision point. The time
needed to run the model in its current form, which has no default
decision rule capability, is too long for many multi—year investment
questions. The decision rules which would be required to accomplish
this improvement would be called into action by the user by a control
variable flag set during the model initialization phase. Considerable
testing would be required to develop these rules, but the increase

flexibility of operation of the model would be quite welcome.

Extensions
The preceding paragraphs of this section have discussed numerOus
areas where the structure of the current model could be improved. The
remainder of this section will review several areas of extension of
the model; i.e., areas that are at present excluded from the system
model. The topics to be discussed are land allocation, crop produc-
tion, more subtle nutrient impacts on growth and reproduction, and
stochastic variables.
Land allocation is one of the fundamental resource allocation
questions which are excluded from the model in its current form.
Given a particular land area with specified physical characteristics
and price expectations, there are basic questions about the use to which
that land, or subsections of it, will be directed. Even restricting
the choice to agricultural uses still leaves open what parts are to be

used for crop production, what parts are to be assigned to grazing,

 

 

 

 

 

 

 

301

and what parts are to be unused for the present. The current version

of the model takes specified land parcels as restricted for grazing
purposes and reads in as data specified time series of crop production;
this is obviously assuming a great deal about prior management decisions
concerning land allocation. These presumptions are not serious diff—
iculties in many of the short term uses of the model; howaver, in
longer time horizon investigations (particularily in project planning)
lack of a land allocation mechanism could limit the use of this model.

Crop production is a second area where the present model could
be extended to increase the scope of the system under study. This
extension would naturally be more profitable (and likely mandatory)
if the model were also extended to include land allocation. In any
event it could be justified on its own as well. Some of the variables
which could be used would be crop fertilization, chemical pest and
weed control, irrigation, and the time of harvest. A necessary step
to development of crop production as a component of this model is
characterization of crop yield as a function of the above variables
and basic descriptors of land, such as soil nutrient level, soil
moisture, soil type, slope of the land, etc. It is possible that
existing crop growth models could be modified and then included
within this system model.

A number of areas within the realm of effects of nutrient intake
on growth and reproduction are not yet included in the work of
Schuette[48]. Since these aspects of the model have not been developed
by this author alone, they are discussed here as extensions rather than

as improvements. The following list summarizes these areas:

 

 

 

 

 

302

life cycle effects on reproductive potential from nutrient
deprivation during heifer growth,

compensatory growth after feeding rates have risen above
deprivation levels,

death rates as a function of the time—weighted nutrient
deficit,

effects of climate of the maintenance energy requirements
of cattle of various sizes,

calf birth weights a function of cow and heifer feed
intakes during gestation,

calf growth rates as influenced by nutrient intake levels,

age of first calving as an influence over total life cycle
reproductive potential.

Some of these items would be relatively simple to model, while others

might be quite difficult, given the current understanding of cattle

physiology.

The final area of extension to be discussed here concerns the

use of stochastic variables. the current model, as has been dis—

cussed in previous chapters, is completely deterministic, with the

exception of a single use of a stochastic variable in the nutrient

impact model.

exist in the real system processes that are now modeled deterministi~

cally.

Weather and price variables, which are exogenous, are treated

as deterministic; whereas they are actually random variables fluctu-

ating around a time-varying mean.

ables to the extent that disease—-which strikes unpredictably——causes

animal deaths. The effect of including stochastic variables would

be most apparent in studies of actions in a Monte Carlo format in which

it is the confidence interval of output variables which is of primary

interest to the user.

 

 

There are likely many points where stochastic variables

Death rates are also random vari-

 

 

 

 

303
VIII.4 Implementation

The final thoughts of this thesis must be directed to the use and
usefulness of the product of this dissertation effort—-a working simu—
lation model of a land extensive cow/calf beef cattle enterprise. The
goal of this model development has been construction of a decision
making tool to allow the manager of an enterprise to make decisions on
the basis of better information concerning his alternative choices.

This model is not designed to replace the decision maker, but rather to
assist him. This model allows the manager to explore non—traditional
modes of action which in the past had to be avoided simply because of

the uncertainty of the outcome. By exploring such actions via the model,
the manager learns useful information which will contribute to decreas-
ing the uncertainty involved. The cost of this information is the cost
of executing the model runs desired—-computer time, programmer time,

and decision maker time to guide the use of the model and to make any
interactive decisions required. The very large development costs of
this model need not be absorbed by future users. While the predictions
of the model are not withOut error, the author feels that use of the
model by decision makers to assist and augment their traditional methods
of analysis and information gathering will be worthwhile. Any final
doubts about the validation of the model should be dispelled by its
use in practical situations where its predictions are verified by the

events which transpire.

 

 

 

 

 

APPENDIX

 

 

a
l

APPENDIX

SYSTEMS SCIENCE REFERENCES

Churchman, T. W., The Systems Approach(De11, 1968).

Forrester, J. W., Industrial Dynamics(M.I.T. Press and John Wiley
and Sons, New York, 1961).

Manetsch, T. J. and G. L. Park, "Systems Analysis and Simulation
With Applications to Economic and Social Systems," Department
of Electrical Engineering and Systems Science, Michigan State
University, 1976.

Shannon, R. E., System Simulation: The Art and Science, Chapter 1
(Prentice Hall, Englewood Cliffs, 1975)

304

 

a

 

 

 

BIBLIOGRAPHY

 

 

4;.

 

 

BIBLIOGRAPHY

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Reserves for Beef Cattle Production Under Drought Conditions."
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2. Anway, J. C. "Consumer Simulation Model: A Canonical Mammal."

Proceedings of the 1973 Summer Computer Simulation Conference.
Montreal, Can.: pp. 835—840.

3. Baker, R. D.; Hodgson, J.; Treacher, T. T.; and Rodriguez, J. M.
"A Research Strategy Towards the Improvement of Grazing
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on Animal Production, Preconference Vol. 2, 1973.

4. Barnard, C. S. "Economic Analysis and Livestock Feeding."
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5. Brody, Samuel. Bioenergetics and Growth. Reinhold Publishing
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6. Brown, J. E.; Fitzhugh, H. A., Jr.; Cartwright, T. C.; Carpenter,
S. E.; and Crouch, E. K. Algebraic Models for Describing
Growth of Cows. Texas Ag. Expt. Sta. Progress Report 2979,
Texas A & M university, 1971.

 

7. Buchner, M. R. "An Interactive Optimization Component for Solving
Parameter Estimation and Policy Decision Problems in Large
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8. Burt, O. R. "A Dynamic Economic Mbdel of Pasture and Range
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9. Carpenter, J. A.; Fitzhugh, H. A., Jr.; Brown, J. E.; and Crouch,
E. K. Relationships Amonngrowth Curve Parameters and
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10. Cbndliffe, S. and Tucker, R. A User's Guide to BLIVOOO Herd
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305

 

 

 

 

306

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13. Dixon, J. J. G.
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Digest of 2nd Conference

 

 

14. Donnelly, J. R. "Summer Grazing."
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15. Dworak, R. A., and Hinds, F. C. A Model Evaluating Forages for
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16. Forrester, J. W. Industrial Dypamics. Cambridge: MIT Press,

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17. Friedman, Milton. Essays in Positive Economics.
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l9. Gittenger, J. P.
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20. Gaudriaan, J.
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IEEE

22. Hahn, G. J. "Sample Sizes for Monte Carlo Simulation."
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and Dean, G. W.
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2 .

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and Feeding Policies for Beef Cattle." Journal of Agricul—
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30. Knutson, P. H. "The Effect and Treatment of Price Level Changes
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31. Lehker, J., and Manetsch, T. J. Systems Analysis of Development
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Engineering Research. East Lansing: Michigan State
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32. Llewellyn, R. H. FORDYN: An Industrial Dynamics Simulator.
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33. Long, C. R., and Fitzhugh, H. A., Jr. Efficiency of Alternative
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34. Long, C. R.; Fitzhugh, H. A., Jr.; and Cartwright, T. C. Factors
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35. Long, C. R. ”Application of Mathematical Programming to Evaluation
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36. Long, C. R., C. R.; Cartwright, T. C.; and Fitzhugh, H. A., Jr.
'Systems Analysis of Sources of Genetic and Environmental
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Marion, P. T.; Riggs, J. K.; and Arnold, J. L. Calving Performj

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College Station:

 

37
Texas Ag. Expt. Sta. Progress Report 2963.
Texas A & M University, 1971.

38. Manetsch, T. J. and Park, G. L. "System Analysis and Simulation
with Applications to Economics and Social Systems."
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East Lansing:
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39. Oliver, J. E.
to Applied Climatology. New York:

pp. 261-264.
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