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NAVY BEAN PRODUCTION SYSTEMS IN MICHIGAN

BY
Ghassan Al-Soboh

A THESIS

Submitted to
Michigan State Univeristy
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1983

COPYRIGHT BY

GHASSAN AL-SOBOH

1983

ABSTRACT
NAVY BEAN PRODUCTION SYSTEM
IN MICHIGAN
BY
Ghassan Al Soboh

With the development of the new high-yielding upright
navy bean variety (Swan Valley), it was believed that its
productivity could be further improved by using different
production management systems. Two navy bean varieties,
Swan Valley (upright) and Fleetwood (standard), were tested
to determine the yields and header losses under two
different row spacings (70 cm and 35 cm) and two harvesting

methods (conventional and direct).

A mixed-integer linear programming (MILP) model was
developed to come up with the appropriate decisions as to
which navy bean variety to plant (Swan Valley or
Fleetwood), planting system to follow (wide rows or narrow
rows), harvesting method to apply (direct or conventional)
and machinery set to use in the production.

This study also considered the impact of having two
mixed crop systems (navy bean-corn and navy bean-sugar
beet) on the farmer's profit in Michigan. Mixed-integer
linear programming models were developed to find the most

profitable crop to produce under the fluctuation of the

Ghassan A1 Soboh

crops' market prices, the profit to be made under different
percentages of a mixed—crop system, and the machinery set
to contribute in each production system.

The model results indicated that the upright navy bean
variety, Swan Valley, planted in 70 cm rows spacing and
harvested directly was more profitable than corn. While

sugar beets were found to be the most profitable crop.

Approved .
Maj Pro essor

a.» .
Approved I .1441 @cg/

Department Chairman

ACKNOWLEDGMENTS

I thank my God who gave me the health and the power to
accomplish this work successfully.

I would like to thank Nuha, My loving wife, for her
encouragement, support and patience during my study.

I also would like to thank:

S Ajit Srivastava, my academic advisor who put me on the
right way to the right target, for providing
encouragement, professional guidance, and his
editorial help during writing this thesis.

5 Tom Burkhardt, who served on my guidance committee,
for his willingness to take time to help clarify and
edit this thesis.

5 James Kelly, who served on my guidance committee, for
his willingness to take time to clarify the nature of
the agricultural production in Michigan, and his
effort to improve this thesis.

5 Al Rotz, for his help in providing the information
about the machinery cost model.

5 Roy Black, for his comments on the linear programming

model.

LIST OF
LIST OF
LIST OF
CHAPTER

1

TABLE OF CONTENTS

TABLES O O O O O O O O O O O O O O O
FIGURES O O O O O O O O O O O O O O O
SYMBOLS O O O O O O O O O O O O O O 0

INTRODUCTION . . . . . . . . . . . .

1.1 Basis of the Problem . . . . . .

1.2 Literature Review . . . . . . .
1.2-1 Harvesting Practice--

Developments . . . . .

1. 2- 2 Machinery Selection Model

Approaches . . . . . . .

1.3 Objectives . . . . . . . . . . .

 

 

METHODOLWY O O O O O O O O O O O O

2.1 A Mixed- -Integer Linear Program-

 

mine A roach (MILP) . . . . .

2.2 Assumptions . . . . . .
2 2—1 Tillage System . . . . .
Weed Control . . . .

 

2- 2
2 3 Fertilizer Applications
2-4 Planting Systems . . .
2 5

2 6

System of Cropping . . .
Insect and Disease Contro
2- 7 Harvesting Methods . . .

all-0.0.0.00

2.

ATA COLLECTION . . . . . .
1 Navy Bean Production . .
2 Corn Production . . . .
3 Sugar Beet Prdduction .
4 .
5 .

 

 

 

Field Machi inery . . .
Machiner Cost Model .
3.5- 1 Mogel Description
3. 5-2 Model Results . .

3.6 Power Requirements . . .
3.7 Prediétin the Number of

 

 

L'.’

U’
m

 

chi-0.0000000
ol—IooooooOoO

O m. o O o O o 0 o 0

Days for F1eld Work . .

 

AVY BEAN PRODUCTION MODEL .

.1 Model Formulation . . .

.2 Model Adjustments . . .

.3 Model Results . . . . .

.4 Sensitiv1ty Analysis . . .

1.4-1 Shadow Prices and Slack
4.4-2 The Cost of Forcing

Nonoptimal Activities Into

the Optimal Solution . . .

4.4-3 Range of Optimality . . .

 

 

 

 

ii

viii
ix

9-5—5

101
103

CHAPTER

5

NAVY BEAN-CORN PRODUCTION MODEL

5.1
5.2
5.3
5. 4

5.5

6.5

TABLE OF CONTENTS (continued)

 

Model Adjustments . . . .
MOdel Results . . . . . .
Sensitivity Analysis . .
514- 1 Shadow Prices and Slack
5.4-2 The Cost of Forcing in
Nonoptimal Solution . . .
5.4-3 Range of Optimality . . .
Testing Different Percentages of

Model Formulation . . . . .

 

 

 

S

 

Bean and Corn in the Navy Bean-
Cdrn Production Model . . . . .
. - A
Corn Production System . .
5 2 Model Adjustment . . . . .
5-3 Model Results . . . . . .
5 4 A 50 Percent Bean-
50 Percent Corn Production
System . . . . . . . . . .
5.5-5 Model Results . .-. . . .

 

U‘U'IU‘
coo

5.5-6 A 25 Percent Bean- 75 Percent

Corn Production System . .
5.4-7 M0681 RESUltS o o o o o o

BEANS - SUGAR BEET PRODUCTION MODEL

Model Formulation . . . . . .
Model Adjustment . . . . . . .
Model Results . . . . . . . .

SensitivityAnalysis . . . . .
6.4-1 Shadow Pr ces and Slacks .

 

 

 

 

6.4-2 The Cost of Forcing Nonoptima

Activities into Optimal

Solution . . . . . . . .
6. 4-3 Range of Optimality . . .
Testing Different Percentages of

 

Navy Beans and Sugar Beet in the

 

Navy Bean-Sugar Beet Product1on
"Odel- . C O C O C O O C O
6. 5- 1 A 75 Percent Sugar Beet -

 

25 Percent Navy Bean Production

"Odel O O O O O
6.5- 2 Model Adjustment . .

6.5-4 A 50 Percent Sugar Beet -
50 Percent Navy Bean Production

Model . . . . . . .

iii

Percent Bean- -25 Percent

1

106
106
122
123
123
123

125
126

129

129
132
133

133
138

138
140

143
143
160
162
162
162

166
168

171

171
175
175

177

TABLE OF CONTENTS (continued)

CHAPTER

5-5 Model Results . . . . . . . . . . 181
5-6 A 25 Percent Sugar Beet -

75 Percent Navy Bean Production

Model . . . . . . . . . . . . . . 181
6.5-6 Model Results . . . . . . . . . . 183

6.
6.

 

7 SUMMARY AND CONCLUSIONS . . . . . . . . . . . 186
7 O 1 summar I O O O O O O O O O O O O O O O 18 6

7.2 Conclusions . . . . . . . . . . . . . . 191
7.2-178cope and Limitation . . . . . . 193

7.2-2 Future Research Needs . . . . . . 194

REFERENCES 0 O O O O O O O O O O O O O O O O O O O O 195

APPENDIX A
Mixed Integer Linear Programming Models
For Solving Navy Bean Production
Systems in Michigan . . . . . . . . . . A-1

APPENDIX B
The Computer Results of the Mixed Integer
Linear Programming Models . . . . . . . B-1

APPENDIX C
Linear Programming Package by Harsh
and BlaCk (1975) o o o o o o o o o o o 0 C-1

APPENDIX D

Machinery Cost Computer Program by
ROtZ (1981) o o o o o o o o o o o o o o 0-1

iv

 

 

Table

2-1

2-3

2-4
2-5

3-10

3-11
3-12

3-13
3-14

LI ST OF TABLES

Tillage Systems for Navy Beans Production
in Michigan . . . . . . . . . . . . . . .
Rates and Type of Herbicide Used for
Controlling Weed in Navy Bean Fields
Planted in Wide Rows . . . . . . . .
Rates and Type of Herbicide Used for
Controlling Weed in Navy Bean Fields
Planted in Narrow Rows . . . . . . . .
Rates and Type of Herbicide Used for
Controlling Weed in Corn Fields . . . . .
Rates and Type of Herbicide Used for
Controlling Weed in Sugar Beet

Fields . . . . . . . .
Rates and Kinds of Fertilizers Used for
Navy Bean, Corn, and Sugar Beet

' PrOdUCtion O O O O O O O O O O O O O O 0

Summary of Navy Bean Production Data . .
Summary of the Yields Conducted over

a Three-Year Period for Swan Valley

and Fleetwood . . . . . . . . . . . . . .
Summary of Corn Production Data . . . . .
Summary of Sugar Beet Production Data . .
Kinds and Sizes of Implements Used in

the Models . . . . . . . . . . . . . . .
Purchase Price of Selected Implements

(In Dollars Per Unit) . . . . . . . . . .
Purchase Price of the Implements

Involved in Navy Bean, Corn, Sugar

Beet Production . . . . . . . . . . . .
Summary of the Selected Implement

Costs (For Ten Year Period) . . . . . . .
Power Requirement for Implements in
Medium-Textured Soil . . . . . . . . . .
Power Requirements for Selected
Implements in Medium-Textured Soil and
the Relevant Tractor Sizes . . . . . . .
Machine Capacities (ha/hr) for

Selected Implements . . . . . . . . .
Predicted Portion of Days Suitable for
Field Work in Saginaw at a 0.8 Level of
Probability . . . . . . . . . . . .
Number of Hours Assigned to Field
Operations . . . . . . . . . . . .
Calendar Days and Number of Available
Hours for Field WOrk at 0.8 Probability
Level for Bean Production . . . . . . . .

Page

22

26

27

28

29

30
43
45
47
49
51

54

55
58
61

62
65

72
74

75

fl

Table

3-15

3-16

3-17
4-1

4-3
4-4

6-5

LIST OF TABLES (continued)

Calendar Days and Number of Available

Hours for Field Work at 0.8 Probability
Level for Corn Production . . . . .
Calendar Days and Number of Available

Hours for Field Work at 0.8 Probability
Level for Sugar Beet Production . . . .
The Estimated Life of Machines . . . .

The Land Area that Can Be Covered by an

Implement During Available Days and Time

Required to Cover 200 Ha . . . . . . .
Summary of the Adjusted Annual Cost of
Tractors 1, 2, 3 Over Ten Year Period .
Summary of the Final Solution of the
Navy Bean Production System . . . . .
Summary of the Shadow Prices and the
Slacks for the Navy Bean Production
Model . . . . . . . . . . . . . . . . .

The Land Area that can be Covered by an
Implement During the Available Workable
Days and Time Required to Cover 200 Ha
Summary of the Final Solution of the

Navy Bean-Corn Production Model . . . .
Summary of the Final Solution of the

75 Percent Navy Bean - 25 Percent Corn
Production Model . . . . . . . . . . .
Summary of the Final Solution of the

50 Percent Navy Bean - 50 Percent Corn
Production Model . . . . . . . . .
Summary of the Final Solution of the

25 Percent Navy Bean - 75 Percent Corn
Production Model . . . . . . . . . . .

The Land Area that can be Covered by an
Implement During the Available WOrkable
Days and Time Required to Cover 200 Ha
Summary of the Adjusted Annual Cost

of Tractors 1, 2, 3 Over Ten Year Period

Summary of the Final Solution of the
Navy Bean - Sugar Beet Production

Model . . . . . . . . . . . . . . . . .
Summary of the Shadow Prices and the
Slacks Obtained from the Navy Bean-
Sugar Beet Production Model . . . . . .
Summary of the Final Solution of the

25 Percent Navy Bean - 75 Percent

Sugar Beet Production Model . . . . . .

vi

Page

76

77
78

91
96

97

100

116

124

134

139

141

156

161

163

164

176

 

 

 

LIST OF TABLES (continued)

6-6 Summary of the Final Solution of the

50 Percent Navy Bean - 50 Percent

Sugar Beet Production Model . . . . . . . . . 182
6-7 Summary of the Final Solution of the

75 Percent Navy Bean - 25 Percent

Sugar Beet Production Model . . . . . . . . . 184

vii

Figure

LIST OF FIGURES

Pulling operation of navy bean (conventional)
harvesting method). . . . . . . . . . . . .
Windrowing operation of navy bean
(conventional harvesting method). . . . . .
Direct harvesting method of navy bean. . . .
Possible ways of matching tractor 1 (T1)

and selected implements. . . . . . . . . . .
Possible ways of matching tractor 2 (T2)

and selected implements. . . . . . . . . . .
Possible ways of matching tractor 3 (T3)

and selected implements. . . . . . . . . . .
Possible ways of matching tractor 4 (T4)

and selected implements. . . . . . . . . . .

. Summary of the profits under different

percentage of navy bean - corn. . . . . . .

Summary of the profits under different
percentage of sugar beet - navy bean. . . .

viii

Page

38
39
40
67
68
69
70

142

186

armzmm<wmuoze

 

LIST OF SYMBOLS

Crop Symbols

Fleetwood planted in 35 cm and harvested. D
Fleetwood planted in 70 cm and harvested. D
Fleetwood planted in 70 cm and harvested. C
Swan Valley planted in 35 cm and harvested. D
Swan Valley planted in 70 cm and harvested. D
Swan Valley planted in 70 cm and harvested. C

Corn

Navy beans

Sugar beets

Machine Symbols

Tractor
Moldboard plow
Chisel plow
Fertilizer spreader
Field cultivator
Row planter

Row cultivator
Sprayer

Bean puller

Bean windrower
Beet topper

Beet lifter
Harvester

ix

1 . INTRODUCTION

1.1 Basis of the Problem

 

For many years, dry edible beans have played a
significant role in people's diets, especially in
developing countries. Where the price of meat is
relatively high and people eat primarily food from cereal,
grain legumes, and root crops. Navy beans have occupied an
important part of Michigan's agriculture. During 1950-54
Michigan produced 22 percent of the 0.8. dry beans. This
rose to over 40 percent between 1960-64, but has been
declining, and was 28 percent in 1976. It is, therefore,
important to maximize the crop productivity and minimize
the production costs in order to satisfy the increased
demand at an acceptable price level.

There are currently two navy been production systems
in use in Michigan. One is the conventional method which
involves planting the navy beans in wide rows (70 cm) and
makes use of a blade puller, windrower, and a combine with
a pickup header to accomplish the harvesting operation.
The second system is the direct harvesting method which
allows for planting the navy beans in either wide rows (70
cm) or narrow rows (less than 50 cm), and makes use of only

a combine with a pickup reel and a flexible floating

 

cutterbar to carry out the harvesting operation.

The direct harvesting method offers several potential
benefits to bean producers. With direct cutting, the
number of field operations would be reduced by the
elimination of pulling and windrowing. In addition, risk
of weather damage would be decreased since all unharvested
beans would be left standing rather than on the ground as
they are after pulling or windrowing. Furthermore, the
harvested beans would probably be of better quality because
of the reduced amount of soil and stones in the beans. The
direct harvesting method has slowly increased in popularity
among farmers. This can be attributed mainly to the
excessive losses caused by applying the direct harvesting
methods to the old navy bean varieties. With the
development of the high yielding upright navy bean variety
(Swan Valley), it was believed that its productivity could
be further improved by using a different production
management system (Kelly et a1, 1981).

With these considerations in mind, navy bean producers
are thus concerned with which navy bean variety to produce,
Swan Valley (upright) and Fleetwood (standard) planting
system to follow (wide rows or narrow rows) and harvesting

method to use (conventional or direct). In addition,

 

because of the fluctuation of the crop's market prices,
navy bean producers are also concerned about alternate crop
that can be planted with navy beans to reduce the market
risk using the same machinery set available for navy bean

production, with respect to crop rotation systems.

 

1.2 Literature Review

1.2-1 Harvesting Practice_—Developments

During the period from 1947 to 1958 practically every

known method of bean harvesting operation had been tried in

Michigan. The various harvesting methods may be classified

as

1.

9.
10.

follows:

Pulling by a blade type cutter usually in the form of
a cultivator attachment

Cutting with rotary crop cutter

Windrowing with a bean windrower or with a side
delivery rake

Bunching by moving segments of windrows into bunches
or by using a buncher attachment on a puller
Stacking either by hand or machine

Hauling to a thresher or to barn storage for winter
threshing

Stationary threshing

Threshing machine converted to a combined
harvester-thresher by the addition of a chassis and
pneumatic tires, auxiliary motor and special pickup
feeder

Use of a special bean combine

Small grain combine fitted with "bean attachment"

equipment

 

McColly (1958) reported on research conducted in
Michigan which indicated that a blade-type bean harvesting
method tends to push dirt and stones into the windrow with
the beans. In direct combining tests, a combine with a
finger-type reel was more efficient than the standard
bat-type reel because the tines could be adjusted to
incline slightly upward as they lifted the bean plant
toward the cutterbar. This action saved many bean pods
from being severed by the sickle and decreases cutterbar
and shatter losses by 50 percent. The report also
indicated that in direct cutting of beans the rigid
cutterbar ran in the soil part of the time in order not to
cut an excessive number of low-hanging pods.

Gunkle and Anstee (1962) reported that the performance
of the direct-harvester, rubber-fingered belt attachment on
red kidney and white narrow beans was satisfactory.

Average losses with this rubber-fingered device on red
kidney beans ran 2.62 bushel per acre. Some difficulty was
encountered in using this unit on very low-growing beans.
Under these conditions there were considerable scatter
losses and plugging in the throat area. A special belt
puller attachment was also designed, constructed, and field
tested for the self-propelled combine. The initial results
indicated that losses were over double those resulting from

conventional harvesting. But after the attachment was

 

modified the losses reduced to an average 2.87 bushel per
acre. The double-belt puller was also tested and results
indicated that when operating in optimal conditions at a
speed of 1 to 2 miles per hour, the losses were slightly
less than 1 bushel per acre.

Pickett (1971) conducted an experiment for evaluating
the performance of a floating cutterbar and pickup reel for
direct harvesting of edible beans. The report indicated
that a floating cutterbar followed the ground surface well
if the header height was properly set. The pickup reel did
not effectively convey the bean plants across the cutterbar
because of the short plant height and neither the reel
fingers nor the reel bats were close enough to each other
to effectively handle bean plants. Also header losses may
be reduced by modifying the reel or developing another
means of conveying.

Pickett (1972) conducted another experiment for
evaluating the row direct-cut header. The individual row
unit header consisted of the basic grain header plus four
modified bean buckets each having a reel. The results
indicated that the row unit header cut the beans within 2
inches of the ground with little loss when the header was
centered on ridged bean rows and the beans were standing
well. Increasing the reel index caused the plant to be hit

while being cut resulting in increased shattering losses.

 

Visual observations of the headers during operation and
samples of losses collected indicated that a higher
percentage of the loss from the row unit header was due to
beans still in pods rather than for the floating bar
header. Many of the pods lost by the row unit header were
still attached to the plant but some were attached and
laying on the ground.

Frushour and Johnson (1974) developed a new pull-type
combine suitable for harvesting either peanuts or edible
dry beans or both. This new machine reportedly offered
these advantages:

1. A capacity equal to or greater than that of the
self-propelled combine, especially in weedy or green
conditions

2. A quality of beans from this new design consistently
better than that from modified small grain combine

3. Much lower cost than a self-propelled combine of
equivalent capacity.

Quick and Buchele (1974) conducted an experiment on
soy beans to study the effect of using a combine with a
flexible cutter bar on the header losses. The report
indicated that total header losses were reduced by 39.9
percent compared to a combine with a standard cutterbar.
Also they listed the advantages of using the floating

cutterbar attachment as follows:

1. A highly significant reduction in header losses

2. The ability to cut uniformly lower by accommodating to
ground irregularities

3. . Higher forward speed for the same header loss level

4. Some degree of rock protection for header

5. Smoother crop feeding under the platform auger.

According to Pickett (1975), in two years of tests
using the conventional harvesting method in Michigan,
gathering loss was approximately 10 percent when operating
at 2.5 to 3 miles per hour in standing beans. With the
direct harvest method using a combine with a floating
cutterbar under typical field conditions, the header loss
may be 15-25 percent.

Kelly et al (1982) reported that four upright black
and navy bean varieties (Swan Valley, Fleetwood, Domino,
and T-39) were tested in two counties in Michigan during
the 1981 harvest season. The results in Saginaw county
indicated that the header losses via the direct harvest
method ranged from 17.3 percent (in T-39) to 41.3 percent
(in Fleetwood), while gathering losses ranged from 7.7
percent (in Fleetwood) to 16 percent (in Domino) via the
conventioal harvesting method. In Gratiot county, the
header losses were reported in the range of 6.7 percent (in
Swan Valley) to 11.4 (in Fleetwood) using the direct

harvesting method, while the gathering losses in the

conventional method ranged from 1.9 percent (in Swan
Valley) to 8.3 percent in (Domino).

Considering the effect of pod and grain moisture
content on threshing loss and damage of navy beans, McDow
(1949) reported a splitting effect on navy beans that may
have been caused by poor machine adjustment and/or low
grain moisture content. According to King and Riddles
(1962), damage to beans (and to other crops) could be
reduced by avoiding high cylinder speed even at fairly
low-moisture content. Hoki and Pickett (1973) reported the
damage to the seed coats only increased from 5 percent at
an impact velocity of 10.5 m.sec"1 to over 60 percent
at a velocity of 17.78 m.sec‘1. Narayan (1969)
reported optimum moisture content for minimum ”checking" of
navy bean seed coats in the range of 13.4 to 15.6, and it
is usually stated that beans should be harvested when grain
mositure content is in the range of 15 to 20 percent.

Pickett (1973) reported that an increase in cylinder
speed resulted in decreased threshing loss and an increased
damage for each level of bean moisture content. Also the
report indicated that excellent conditions for harvest
include navy bean moisture between 17 and 20 percent and
pod moisture as low as possible, preferably below 12

percent.

10

Singh and Linvill (1977) developed a model for the
rate of change of navy bean pod moisture content as related
to temperature change. Their analysis indicated that the
coefficients of the difference between pod and grain
moisture terms were not statistically different, but pod
moisture and temperature change coefficients were
significantly different.

The results obtained regarding the direct harvesting
method of navy beans indicated that some difficulty was
encountered in using the rubber-fingered belt attachment on
very low-growing beans. However, the double-belt puller
gave better results (Gunkle et a1, 1962). The use of a
combine with a finger-type feed was found to be more
efficient than the standard type (McColly, 1958). However,
neither the reel fingers nor the reel bats were close
enough together to effectively handle bean plants (Pickett,
1971).

When considering cutterbar performance, the standard
cutterbar was found to run in the soil part of the time in
order not to cut an excessive number of low-hanging pods
(McColly, 1958). However, the flexible floating cutterbar
was found to follow the ground surface well if the header
height was properly set and to reduce header losses

compared to the standard cutterbar (Pickett, 1971, 1972).

 

11

The results about the reel index indicated that
increasing the reel index caused the plants to be hit while
being cut resulting in increased shattering losses
(Pickett, 1973). Increasing the cylinder speed resulted in
decreased threshing loss and increased damage for each
level of moisture content. Also excellent conditions for
harvest were reported as bean moisture of 17-20 percent
and pod moisture as low as possible (Pickett, 1973).

With the development of the new high yielding upright
navy bean variety (Swan Valley), that header losses were
less in Swan Valley compared to Fleetwood (standard navy).

These header losses were classified under four
categories:

1. Shatter losses: loose or free beans and beans in pod
detached from the plant.

2. Stalk losses: beans in pods attached to stalk pieces
which were cut but not collected.

3. Stubble losses: beans in pods attached to the free
standing stubble left by the machine.

4. Lodge losses: beans in pods attached to stalks or
branches abnormally longer than the stubble which

slipped under the cutter bar (Kelly et al, 1982).

12

1.2-2 Machinery Selection Model Approaches

Machinery selection is an important part of machinery
management. The complexity and the magnitude of the
machinery selection problem in the analysis of crop
production systems has led to numerous efforts to develop
analytical models as a decision aid. Link (1967) suggests
an ”activity net work" technique to estimate net returns
and machine optimum size. In this approach, some factors
were ignored. The most important of these were system
effects and weather risk. All the machines on a farm are
interrelated through a set of operating procedures and
practices. Machines used for different crops may influence
on each other as, for example, hay-harvesting and
corn-cultivation machinery.

Hughes (1974) developed a simulation model for
selection of field machinery system and estimation of
system cost. Some problems were encountered in terms of
energy requirements, time required for field work, and
estimating the life of field machines.

Danok et a1. (1978) developed an optimization model to
solve simultaneously for machinery selection, crop

production, and labor hiring for a state farm in Iraq. The

13

cropping possibilities considered in the model were wheat,
flax, clover, safflower, cotton, and corn. The production
of each crop involved plowing, disking, planting,
irrigation, and harvesting operations.

Singh and Holtman (1979) developed a heuristic
algorithm to evaluate and compare selected crop production
systems over a range of farm sizes with respect to costs
and requirements for machinery, labor, and fossil fuels for
field work. The crop production systems considered
involved corn, soybeans, field beans, wheat, and alfalfa
using no till, chisel plow, or moldboard plow tillage
practice.

Krutz et al (1980) used a linear programming model
(i.e., the Purdue model B-93 and the International
Harvester pro-Ag program) to evaluate alternative farming
situations in order to provide general guidelines of
machinery selection for corn/soybeans crop production. The
report indicated that linear programming models can be
extremely useful tools to individual farm managers for
evaluating machinery-sizing decisions for a particular
situation. They can also be useful for conducting
quasi-research studies to determine equipment size,
capacity, and profit relationships of a more general

nature.

14

Danok et al. (1980) used a mixed integer programming
technique for solving the problems of crop and machinery
choice. The model maximizes profit, which is cropping
profit less machinery cost, subject to the following:

1. Constraints on resources which link machinery and
cropping activities

2. Constraints that reflect mutual exclusivity of
machinery

3. Constraints which link machine set purchase and use

4. Constraints on other cropping resources

Whitson (1981) used a linear programming model to
maximize returns to the fixed resources of a farm given the
limitation of land, hours of available field time (weather
risk), machinery characteristics (size, kind, etc.).

Linear programming models have been applied as a
useful tool to maximize net profit or to minimize total
cost with respect to available resources. The linear
programming technique was used to select the best crop mix
with consideration of the machinery complement. An example
is the Purdue model by Krutz 1980. Mixed integer linear
programming models were applied where several alternate
machinery components were stored in data blocks, and the
model searched for the best set to match the best crop mix
(an example is Danok's model 1978). Heuristic models

assumed that field operations must be completed within

15

specific calendar periods so that profit can be maximized.
The objectives of these models were to compare and select
crop production systems over a range of farm sizes with
respect to labor, machinery requirements, and fuel (an
example is the Singh model 1979 and Wolak, 1981).

It is obvious from the previous research work that
MILP model has been used successfully to evaluate
machinery-sizing decisions for a particular situation.
Therefore, it was adopted to solve navy bean, navy
bean-corn and navy bean-sugar beet production system in
Michigan with respect to the following constraints:
1. Land size,
2. Available machinery,
3. Available time,
4. Power requirements,

so that profit can be maximized.

1.3 Objectives

 

The overall objective of this study was to evaluate
and compare two navy bean varieties in Michigan, Swan
Valley (upright) and Fleetwood (standard navy), applying
different management systems to maximize the net profit.
In order to meet the overall objective, the specific

objectives were as follows:

16

1. To develop an MILP model which utilizes parameters
collected in the field and from pertinent literature
to select
a. The navy bean variety to be recommended (Swan

Valley or Fleetwood)

b. The type of planting system to follow (wide rows

or narrow rows)

c. The kind of harvesting method to apply

(conventional or direct)

d.‘ The machinery set to use in the selected navy bean

production system

2. To determine the net profit obtained from the selected
navy bean production system and analyze the
sensitivity of the optimal solution.

This study also considered the impact of having two
mixed crop production systems (navy bean-corn, and navy
bean-sugar beet) on the farmer's profit in Michigan. The
specific objectives were as follows:

3. To develop an MILP model in order to
a. Select the most economical crop to be produced in

each production system

b. Estimate the net profit that could be made under

different percentages of a mixed crop system

c. Select the types and sizes of farm machinery to

contribute to each production system.

17

4. To analyze the sensitivity of the optimal solution in
the navy bean-corn and navy bean-sugar beet production

systems.

2. METHODOLOGY
2.1 A Mixed Intgger Linear Prggrammgng Approach

(MILP)

General linear programming* involved selection of a
set of decision variables and their quantities that
maximize a linear objective function subject to a series of
linear restrictions and the requirement that the decision
variable cannot be negative. In other words, linear
programming models deal with the problems of allocating
limited resources among competing activities in the best
possible (i.e., optimal) way. The standard LP matrix model

can be presented as follows:

 

 

 

 

Activity Resource usage Amount of
Resource 1 2 . . . . n resource available
1 311‘ a12 am b1
2 a21 a22 aZn b2
3
m am1 am2 amn bm
Z/Unit C1 C2 Cn
Level X1 X2 Xn

*Frederick S. Hillier and Gerald J. Lierman, Introduction
to operations research, Stanford University, 1980.

18

19

where Xj 8 Level of activity j for j = 1, 2, . . . n
z - Overall measure of effectiveness
Cj 8 The increase in 2 that would result from each
unit increase in Xj for j = 1, 2 . . . n)
bi 8 The amount of resource i available for
allocation (for i = 1, 2 . . . n)
aijs Amount of resource i consumed by jth unit
of activity
The mixed integer linear programming mode can be used
where some of the variables (say, 1 machine type in this
model) are restricted to integer values but the rest are
ordinary, continuous variables. In this case, this model

can be presented in algebraic terms as follows:
n

Max Z 3 2 Cij
i=1

subject to: n

i=1
and Xj integer for j = 1, 2 . . . I (I<n)
XjZO for j = 1' 2 o o o n

A linear programming package designed by Hansh and
Black (1975) was used to solve the MILP models. This
package can handle modest- sized of linear programming when.
the objective is maximized subject to series of

constraints.

20

2.2 Model Assumptions

 

2.2-1 Tillage system

Tillage practices continue to play an important role
in the seedbed preparation process. Traditionally, farmers
have practiced tillage operations in terms of standard
treatments for all fields regardless of the kind of soil,
amount of crop residues, or species and amounts of weeds.
Generally, there are two major tillages in use in Michigan:
primary tillage and secondary tillage.

Primary tillage involves complete treatment of the
surface soil to reduce soil strength, destroy weeds, cover'
plant material, and arrange aggregates. The moldboard plow
is the best suited to the more level fields, especially
those containing fine-textured soil. The chisel plow is
increasing in popularity in several parts of the state.
This implement is superior to the moldboard plow on sandy
soil and where there is a slope, because it leaves some
crop residue on the surface of the soil. Other advantages
of using the chisel plow are as follows:

1. Decreasing both wind and water erosion
2. Lower power requirements per unit width
3. Greater tillage width
Secondary tillage operations are intended to create

refined soil conditions following primary tillage. Disk

21

harrows and field cultivators are common secondary tillage
tools used in early spring for leveling the soil surface.

Many factors affect the choice of a tillage system and
the type of tillage implements. In general most farmers
practice primary tillage in fall using either a moldboard
or chisel plow. Other farmers practice the primary tillage
operation in spring because of inappropriate weather condi-
tions during fall. Secondary tillage in spring is done
with disk harrows or field cultivators. In this study
spring-primary tillage operation and fall-secondary tillage
were assumed to be involved in navy beans, navy bean-corn,
and navy bean-sugar beet production systems. Table 2-1
represents the major tillage systems applied for beans in
Michigan.

In the navy bean production model, moldboard and
chisel plows were assumed to be included in primary tillage
implements, and field cultivators as secondary tillage
implements.

In the navy bean-corn, and navy bean-sugar beet
models, moldboard or chisel plows were assumed to be
included as primary tillage implements depending upon the
type of tillage implement that would be chosen in the navy
bean production model. The reason for this assumption is
to make use of the same tillage tool for the navy bean,
navy bean-corn, and navy bean-sugar beet production

systems.

22

TABLE 2-1

TIllage Systems for Navy Beans
Production in Michigan

System Tillage ' Time
l‘b. Code

of Tillage

7

Spring

 

A O O O O O O O O O O O O
1 B O O O O O O O O O O O O

C O O C O O O O O O O O O

A SW11 0 O O O O O O O

. No-till
. Primary-plant
. Primary-secondary-plant

. No-till

. Primary-plant
. Primary-secondary-plant

. Secondary-plant

. Secondary-plant

. Secondary-plant

2 B sumoil O O O O O O O O

C SMil 0 O O O O O O O

A Prm O O O O O O O O 0 Plant
3 B Prmq O O O O O O O O

C Primary-secondary . . . . Plant

D Primary-secondary . . .

A Subsoil-primary . . . . . Plant
4 B Subsoil-primary . . . .

C Subsoil-primary-secondary Plant

D

A

Subsoil-pr imam-secondary Secondary-plant

SGJRCE: L.S. lbbertson and R.D. Fraser, eds. g1 Bean

Productiéon: Principles and Practices.

 

 

Extension Bulletin 1251 ,

Cooperative Extension Service and Agricultural Experiment Station,

Michigan State University,
East Lansing, August 1978.

23
2.2-2 Weed Control

The effect of weed competition on the growth of row
crops has been a serious problem in many areas. Yield is
usually reduced as a result of weeds sharing nutrients,
light, space, and water with row crops. In some crops, weed
growth may increase harvest losses and may also cause
problems when dry weedy material goes through the combine
into the grain. Therefore, weeds must be controlled to
increase yields, and maximize economic returns by selecting
an appropriate weed control program that can fit the area
and the crop conditions.

Two weed control practices have been used to overcome
the weed competition. First is mechanical cultivation
which involves controlling weeds between rows after seeds
are planted or after plants have emerged. Second is the
use of herbicide which can contribute successfully if it is
applied beside the cultivation. In this case, weeds
between rows can be controlled mechanically while weeds
beside plants can be controlled chemically.

Currently, there are three methods for applying
herbicides. The first is the 'preplant incorporated"
method (PPI). In this method the herbicide is incorporated
in the upper 5 to 7.5 cm of the top soil layer by using some

form of a harrow before planting.

24

The second is the "preemergence" method. In this
method the herbicide is applied to soil surface when the
crop is planted. The herbicide finds its way, with the
help of timely rains to the zone of weed seed germination
(5 to 7.5 cm below the soil surface).

The third method is the "postemergence" application.
In this case, herbicide is applied after the crop has
emerged from the soil.

In this navy bean production model, beans planted in
wide rows were assumed to be treated chemically and
mechanically to control weeds. Preplant herbicides were
assumed to be placed by harrows in the weed seed
germination zone to control weeds chemically, while
tractor-mounted cultivators were considered to be used for
controlling weeds mechanically.

In the narrow row system, beans were assumed to be
treated only chemically by the use of preplant and
preemergence herbicide applications.

It has been found that effective weed control in corn
production involves the use of herbicides beside mechanical
cultivation (Extension bulletin E-1429). Therefore, in the
navy bean-corn model, the existing weeds in the corn field,
were assumed to be treated by preemergence herbicide
applications and row cultivators, although some farmers
prefer to use only the chemical application to control the

weed in the corn fields.

25

Weed control in sugar beet fields is important because
weeds harbor insects and serve as alternative hosts for
many diseases and cyst nematodes. There are several
options open to the sugar beet grower for weed control. In
the navy bean-sugar beet model, weeds in sugar beet fields
were assumed to be treated by postemergence herbicide
applciation, and by the use of row cultivators.

Tables 2-2, 2-3, 2-4 and 2-5 represent the rates and
the type of herbicides used for controlling weeds in navy
beans planted in wide and narrow rows, corn, and sugar beet

fields, respectively.
2.2-3 Fertilizer Applications

The amount of fertilizer needed for a crop is closely
related to the nutrients already in the soil. The best way
to determine the amount of nutrients available in the soil
is with a soil test. The values obtained from the soil
tests are correlated with the response by plants to applied
nutrients (Extension bulletin E-550). I

Although, different farms need different kinds and
rates of fertilizer, application number 1 in Table 2-6 was
used as a standard practice in the navy bean production
model. In the wide row system (70 cm row spacing) the
fertilizer was assumed to be placed 5 cm to the side of

seed rows and 5 cm below the seeds during the planting

26

TABLE 2-2

Rates and Type of Herbicide used for
Controlling Weeds in Navy Bean
Fields Planted in Wide lbws

 

 

Weed Controlled Time Herbicide Name mtg/h;
Annual broad leaf EPTC (Eptan) 2.5
+
(Including night Preplant Cnloranben (Amiben) 2.24
shade
+
and
Trifluralin (Treflan) 0.56
Annual grass) OR
Profluralin ('Iblban) 0.84

~

WRCE: Michael Barrett and Willian Meggitt, Weed Control for

Field gm. Extension Bulletin E-434, Cooperative-fictensionriervfce,
Micfiigan State University, East Lansing, 1982.

 

 

*Eptam and Amibai can be mixed with either Treflan or 'lblban.

27

TABLE 2-3

Rates and Type of Herbicide Used for
Controlling Weeds in Navy Bean
Fields Planted in

 

 

 

Narrow lbws
wWeed Controlled Time' Herbicide Name Kg /ha
Annual broad leaf EPTC (Eptam) 2.5
4.
(Including night Preplant Trifluralin (Treflan) 0.56
shade)
. +
and
Profluralin ('Iblban) 0.84
Annual grass
Followed Chloramben (Amiben) 2.24
by OR
Dinoseb (Premerge) 5.0
Pre- OR
emergence
Chloranben (Amiben) 1.12
+
Dinoseb (Premerge) 3.36

 

SCIJRCE: Michael Barrett and Willian Meggitt, Weed Control for
Field (335g. Extension Bulletin E—434, Cooperative Extension Service,
Mic gan tate University, East Lansing, 1982.

28

TABLE 2-4

Rates and Type of Herbicide Used for
Controlling Weed in Corn Fields

‘ J —L_ _.l

Wéed Controlled Time Herbicide Name Kg/ha

 

Annual broad leaves, Pre- Atrazine 1.13
annual grasses (in- emergence

eluding panicun 4-

green foxtail,

giant foxtail Lasso 2.26
witchgrass and

crabgrass )

.4 _A

SGJRCE: Michael Barrett and William Meggitt, V3239 Control for
Field . Extension Bulletin E-434, Cooperative Extension Service,
M1c gan State University, East Lansing, 1982.

 

29

TABLE 2-5

Rates and Type of Herbicide Used for
Controlling Weed in Sugar Beet

Weed Control led Time

Fields

 

Herbicide Name Kg/ha
Annual broad leaves Desmdiphan (Betanex) 0.56
Post- +
emergence
(Including anart- Phemnediphan (Betanal) 0.56
weed) ,
+
Endothall (H 273) 0.56

 

SCIJRCE: Michael Barrett and William Meggitt, fled Controfilfi for
Field CroE. Extension Bulletin E-434, Cooperative Extension Seerce,
Micfiigan State University, East Lansing, 1982.

 

30

TABLE 2-6

Rates and Kinds of Fertilizers used for
Navy Beans, Corn, and Sugar Beet

 

 

Product ion
Appl . Fertilizer
No. Crop Name Rate (Kg/ha)
N 56
1* Navy
beans P205 84
K20 1 12
Zn 3 . 36
Mn 9
N 150
2** Corn P205 70
K20 90
N 80
3*** 5:22; P205 75
K20 1 50

*SCXJRCE: crop 81d Soil Science Department, Michigan State Uni-
versity, East Lansing, Michigan.

**S(11RCE: Farm Management, Department of Ag. Econanics,
Missouri.

***SCIJRCE: D.D. Warncke and D.R. Christensen, Fertilizer Recom-
mendations: Vegetable and_Field Crgps in Michigan. ExtensIm BuI-
Ietin E-SSO. Cooperative Extension Service, Michigan State Univer-
sity, East Lansing, Michigan, December 1981.

31

operation, while it was assumed to be broadcast prior to
planting time in the narrow row system (35 cm) using the
fertilizer spreader. These assumptions were made because
these practices were adopted during the experimental stages
in 1980, 1981, and 1982.

Fertilizer recommendations (N+P20 + K20) for corn
production fluctuated from place to place depending upon
the soil test and the yield goal. In Table 2-6 aplication
2 represents the amount of fertilizer considered in the
navy bean-corn model for corn production. This fertilizer
was considered to be banded by planters at planting time
(Extension bulletin E-1429)

In considering sugar beet production in Table 2-6,
application 3 was adopted to the navy bean-sugar beet model
for sugar beet production. This fertilizer was also as-
sumed to be applied by planters at planting time (Extension

bulletin E-1524).
2.2-4 Planting Systems

Optimum plant population is essential for high yields.
A very high population or seeding rate can result in
excessive plant competition for water and nutrients.
Below-optimum seeding rates can result in incomplete use of

water, nutrients, and light.

32

For many years, 70 cm (28 inch) row spacing has been
practiced for planting navy beans in Michigan because
farmers can take advantage of the same machinery set for
planting, spraying, and cultivating some other similar
crops such as corn, soybeans, and sugar beets. At this row
width and 5 cm spacing in the row, 45 kg of seeds are
required, giving density of about 250,000 plants per
hectare (100,000 plants per acre) if all seeds germinated.
Beans are normally planted between 5 to 7.5 cm deep in
moist soil depending upon the type of soil (Extension
bulletin E-1251).

Most farmers use the conventional harvesting method
(using a puller, windrower, and a combine with a pickup
header to harvest the 70 cm row spacing beans.

Recently, some new varieties have been developed which
can stand up better compared to the conventional varieties.
Therefore, there is a tendency toward planting beans in
narrow rows (50 cm or less) and applying the direct
harvesting method (using only a combine with a floating
cutterbar and a pickup reel) to harvest the crop. At 35 cm
(14 inches) row width about 67 kg of navy bean seeds are
required per hectare, giving densities of about 375,000

plants per hectare (150,000 plants per acre).

33

In this particular study, two navy bean varieties
(Swan-Valley and Fleetwood) were considered in the model to
be planted in two-row spacing systems (70 cm and 35 cm) in
order to compare and select the more appropriate row
Spacing system to practice.

Plant population has a significant effect on corn
yield. Although the optimum population will vary with
yield level, test results show 45,000 to 50,000 plants per
hectare at harvest to be an optimum population over a
rather wide yield range (Extension bulletin E-1429).

Row width is another production practice which affects
corn yield. Planting corn at 70 cm row spacing width with
a 14 kg seeding rate per hectare has given good results in
the experiments conducted in East Lansing experiment
station. It is recommended that corn seeds be planted 1.5
to 3 cm deep in cool soil, and between 3 to 6 cm deep
during late planting when the soil surface is more likely
to become dry (Extension bulletin E-1429).

Commercial sugar beet growers plant sugar beets at 15
to 20 cm spacing between seeds in the row. When growing
beets for the first time, it is recommended that a 5 to 7.5
cm spacing be used. Generally, row width is governed by
spacing used in other crops. In the sugar beet-navy bean
model, sugar beet seeds were assumed to be planted at a 70
cm spacing in 70 cm rows at a seeding rate of 1.13 kg per

hectare (Extension bulletin E-1524).

34

2.2-5 System of Cropping

Cropping systems refers to the detailed organization,
method of operation and practices used in producing a
series of crops. A good cropping system would reduce soil
erosion to a practical minium, reduce the risk of an
explosion in an insect disease and weed population and
improve a crop productivity.

In this particular study, the effect of cropping
system on navy bean, corn, and sugar beet was not taken
into consideration assuming that the farmer would follow a
cropping system as to maintain a good yield level. The
MILP models in this case reflect the cropping system in one
year as to compare among different crop production
possibilities and select the most appropriate production

system.
2.2-6 Insect and Disease Control
It has been noticed that the incidence and the

severity of a particular disease vary from year to year,

due to environmental and management practices. Several

35

species of pests may also appear in large number during
some years causing damage to field crops. Therefore,
farmers have practiced different methods of disease and
pest control programs in order to protect the yield and the
quality of crops before the damage is done. The use of a
combination of methods which cause as little environmental
damage as possible in the process is the basis of all pest
and disease control programs (Extension bulletin E-1251).

Chemical application by sprayers is a common field
operation in crop production. The PTO-driven trailed
sprayers were considered to be involved in the navy beans,
navy bean-corn, and navy bean-sugar beet production systems
for applying chemicals during the insect and disease

control programs.
2.2-7 Harvesting Methods

Two navy bean harvesting methods have been practiced
in Michigan. One is the conventional method which makes
use of pullers, windrowers, and combines. With the
conventional harvesting method, beans are pulled by pullers
when seed moisture content drops to approximately 20
percent. Then these plants are windrowed with either
center delivery or side delivery windrowers. Collecting
and threshing operations are carried out using combines

with pickup attachments.

36

The second method is that of direct harvesting which
makes use of combines with pickup reels and flexible
floating cutterbars to combine and thresh beans. Figures
2-1 and 2-2 represent the conventional harvest method
(pulling and windrowing operations), while Figure 2-3 shows
the direct harvesting method.

Both navy bean harvesting methods were tested during
1980, 1981 and 1982 harvesting seasons with two varieties
(Swan Valley and Fleetwood). The results of these
experiments were used in the navy bean model to study the
impact of different navy bean production systems on the
farmers' profits.

It has been found in the direct harvesting method that
the performance of a combine equipped with a flexible
floating cutterbar is better than a rigid cutterbar.
Therefore, two different sizes of self-propelled combines
equipped with different heads (pickup heads for harvesting
beans conventionally and pickup reels with flexible
floating cutterbar for harvesting beans directly) were
assumed to be involved in harvesting beans while the same
combines equipped with 4 or 6 rows were assumed to be used
in harvesting corn. The sizes of the combines were chosen
to suit the land size of 200 ha which was assumed in the

MILP model.

37

There are several alternatives for harvesting sugar
beets in Michigan, the most common method is to use beet
toppers and beet lifters. Therefore, both types of
implements were considered in the navy beans-sugar beet

model to contribute in harvesting beets.

38

 

Fig. 2-1. Pulling operation of navy bean (conventional
harvesting method).

39

'w... I "

jwll ‘“

O.

 

Fig. 2-2. Windrowing operation of navy bean (conven-
tional harvesting method).

40

 

Fig. 2-3. Direct harvesting method of navy bean.

3. DATA COLLECTION

3.1 Navnyean Producpion

 

There are currently two navy bean planting systems in
use in Michigan; wide rows and narrow rows. In wide rows,
beans are usually planted in 70 cm row spacing and
harvested conventionally using a puller, windrower, and a
combine with a pickup header attachment, or harvested
directly using a combine with a flexible floating cutterbar
and finger-type reel. Beans planted in narrow rows (35 cm)
are usually harvested directly.

The data collected during the investigation about the
two navy bean planting systems included the following:

1. Although the rates and the kinds of fertilizers
fluctuate according to the type of soil, the rates of
fertilizers were assumed to be the same for both
planting systems (wide rows and narrow rows).

2. Interviews with farmers and county extension agents
revealed that farmers were using almost the same kinds
and application rates of insecticides and fungicides
for both planting systems.

3. According to the information collected from the
Michigan State University Crop and Soil Science
Department, the seeding rate for both navy bean

varieties (Swan Valley and Fleetwood) are the same

41

42

under the same row spacing width.

Table 3-1 represents the navy bean production data
collected during the investigation.

. With the development of the high-yielding, upright
(Swan Valley) variety it was believed that its productivity
could be further improved by using a different
production-management system (Kelly et al, 1982). There-
fore, several experiments were conducted in Saginaw and
Gratiot Counties during the 1980-81 and 82 harvest seasons
to estimate the yields and header losses for Swan Valley
and Fleetwood applying different production systems.

In 1980 and 81 experiments, Swan Valley and Fleetwood
were planted in 70 cm rows and harvested conventionally and
in 35 cm rows were harvested directly (Kelly et al, 1980,
1982). The yields and losses collected for both navy bean
varieties were collected and averaged. In the 1982
experiments, Swan Valley was planted in 70 cm row spacing
and directly harvested. The yield and the header losses
were recorded.

Because of insufficient data about the header losses
for Fleetwood planted in 70 cm and directly harvested, some
samples were taken from Fleetwood planted in 50 cm and
directly harvested to estimate the yield and the header
losses. The percentage of header losses in 50 cm rows was
taken as a base for estimating the approximate header

losses in 70 cm row spacing.

43

TABLE 3-1

Sumnary of Navy Bean Production Data

_J_

 

 

 

Requirements Unit Swan Talley Fleetwood
70cmrows 35cmrows70cmrows 353nm

Seeding rate log/ha 45.0 67.0 45.0 67.0
Fertilizer lag/ha 270.0 270.0 270.0 270.0
rate

Herbicide . kg/ha 5.3 10.6 5.3 10.6
rate

Seed price $/kg 0.88 0.88 0.88 0.88
Fertilizer $/kg 0 .47 0 . 47 0 . 47 0 . 47
price

Herbicide S/kg 14.15 14.15 14.15 14.15
price

Pesticide $/kg 40.0 40.0 40.0 40.0
*Navy bean $/kg 0.44 0.44 0.44 0.44
price

SCIJRCE: Dr. Jim Kelly, (k‘op and Soil Science Department,
Michigan State University.

A

.-

Personal commnication with extension agents and some local

dealers.

Michigan Statistical Abstract 1981. 16 ed.

Business Research, Wayne State University, April 1982

Detroit:

Bureau of

44

Other sources of losses (threshing, straw walker, shoe
and leakage) were considered to be 4 percent from the total
yield for both varieties under both harvesting methods.

The summary of the results are presented in Table 3-2.
It is obvious from the results that Swan Valley variety
planted in 70 cm and directly harvested gave the best
yield. This result can be attributed to the crop-lodging
problem in the narrow-row system during harvesting time
which caused excessive losses. In the conventional method,
the estimation of beans lost during pulling and windrowing
were inaccurate because some beans were buried during
pulling and windrowing. In the direct harvest method, the
header losses were counted under four categories; shatter

losses, stalk losses, stubble slooses and lodge losses.

3.2 Corn Production

 

Corn acreage and yield per hectare have both increased
substantially in Michigan over the past 15 years. Corn may
be grown in a wide range of soils from sands to clays to
muck. However, without irrigation, highest yields are
obtained on the finer-textured soils.

Date of planting trials at Michigan State University
have consistently shown a yield advantage for corn planted
in late April or early May over that planted later in May

or early June (Extension bulletin E-1429).

45

TABLE 3-2

Sunnary of the Yields Conducted over a Three-Year
Period for Swan Valley and Fleetwood

Direct‘ Harvest Conv. Harvest

 

 

 

Variety Unit 70 cm rows 35 cm rows 70 cm rows
Swan Valley log/ha 2605 1808 1903
Fleetwood kg/ha 1660 1 130 1788

¥

SCXIRCES: Dr. Jim Kelly, Crop and Soil Science Department,
Michigan State University and personal data collection during the
1981 and 1982 harvest season.

46

Data collected during the investigation about corn

production indicated the following:

1.

Fertilizer recommendations (N + P205 + K20) for

_ corn are made by a soil test laboratory taking into

consideration not only the soil test level but also the
yield goal and the kind of soil tested. In this
particular study, applying 150 kg of nitrogen (N), 70
kg phosphate (P205), and 90 kg of potash (K20)

per hectare were assumed in the model. (See Table 2-6)
The average corn yield per hectare was estimated over a

ten year period (72-81) from the Michigan Statistical

Abstract (1981).

The average corn price in the market was also estimated

over ten years period from the Michigan Statistical

 

Abstract (1981).

A summary of the corn production data is shown in

3.3 Sugar Beet Production

Sugar beets are usually grown in Michigan for sugar

production under contract with a sugar company. Beets can

be grown on mineral soils ranging from loamy sands to clays

and on organic soils.

47

TABLE 3-3

Sumnary of Corn Production Data

A .4.‘ _ J__ L__

 

mguirements Unit Value
Seeding rate log/ha 14.0
Herbicide rate kg/ha 3.4
Fertilizer rate kg/ha 310.0
Seed price $/kg 0.18
Fertilizer price $/kg 0.33
Herbicide price $/kg 15.0
Insecticide + $/kg 40.0

Fungicide

Corn yield bu/ha 238.00
Corn price $/bu 2.37

__‘. L1

SOJRCES: Michigan Statistical Abstract 1981. 16 ed.
Detroit Bureau of Business Research, Wayne State University,
April 1982, and pesonal commnication with extension agents,
and some local dealers.

 

48

Sugar beets should be planced as early as possible.

In the southern half of lower Michigan, April 15 to 20 is a

good starting period. Further north this date will usually

have to be delayed somewhat (Extension bulletin E-1524).

Data collected during the investigation about sugar
beet production indicated the following:

1. Seeding rate per hectare may be varied from place to
place depending on seed size, row width and space in
rows.

2. The amount of fertilizer needed is best determined by a
soil test, but for this particular study, applying 90
kg of nitrogen (N), 85 kg of phosphate (P205), and
170 kg of potash (K20) per hectare were taken into
consideration (see Table 2-6).

3. The average beet yield per hectare was estimated over a
five-year period (77-81) from the Michigan Statistical
Abstract (1981).

The average pgice of sugar beets was also estimated over a

five-year period (77-81) from the MicMigan Statistical

Abstract (1981). —

The summary of sugar beet production data are show in

Table 3-4.

49

TABLE 3-4

Smmary of Sugar Beet Production Data

 

Requirements Unit Value
Seeding rate _ log/ha ' 1.13
Fertilizer rate lag/ha 345.0
Herbicide rate kg /ha 1. 7
Seed price $/kg 45.0
Fertilizer price $/klg 0.41
Herbicide price $/kg 20 .0
Insecticide + S/kg 40.0

Fungicide
Sugar beet price $/tonne 30.0
Sugar beet yield tonne/ha 50.0

A A

‘ SGJRCES: MicMigan Spasistical Abster 1981. 16 ed.
Detroit Bureau of Business Research, Wayne State Univer-
sity, April 1982, and pesonal conuunication with extension
agents, and some local dealers.

50

3.4 Field Machinesy

 

In order to study a crop production system, it is
necessary to focus on field machinery as a major component
of a farm system. The selection of field machinery,
available in the market with their relevant prices, has to
meet a set of interacting constraints including the
following:

1. Crop to be grown

2. Field operations

3. Available machinery

4. Soil type (it was assumed to be medium textured soil)
5. Weather conditions

Production land area (it was assumed to be 200 ha)

\I 0‘
0

Labor supply.

In this case, the mixed-integer linear programing
model can compare different machinery sets and select the
most economical one with respect to the existing
constraints.

The kinds and sizes of field machinery chosen to be
involved in navy beans, corn and sugar beet production are

shown in Table 3-5.

51

TABLE 3-5

Kinds and Sizes of Inplements
Used in the Models

 

Inplements Unit Marketed in Michigan
Tillage tractors kw 59.7 89.5 119.3
Utility tractor kw 37.3
Catbines m 4.0 5.0 5.6
Windravers m 2.8 4.2 5.6
Bean pullers m 2.8 4.2 5.6
Chisel plows m 2.4 3.1 3.4
Mold board plows m 2.0 2.4 2.8
Field cultivators m 3.8 4.7 5.6 6.6
Sprayers m 1.4 1.8 2.7
lbw planters m 3.0 4.5 6.0
lbw cultivators m 3.0 4.5 6.0
Beet toppers m 2.1 2.8
Beet lifters m 2.1 2.8
Fertilizer spreader m 3.0

 

SCIJRCES: Official Guide, Michigan Equipnent Dealers

Association, Lansing, Michigan, 1982. Hannibal A. Muhtar,

Dissertation for the degree of Ph.D. , Michigan State

University, 1982.

Camunication with dealers.

52

3.5 Machinepy Cost Model

 

3.5-1 Model Description

The machinery cost model by Rotz et a1. (1982) was
used to calculate the cost of using the selected implements
for navy beans, corn and sugar beet production. This
program computes the total costs of owning and operating
farm machines, tractors and trucks. The model includes the
fixed costs of capital, interest, insurance, shelter,
repairs and maintenance, and variable costs of fuel,
lubrication and labor. Inflation is modeled for all costs
with a separate rate used for machinery, fuel, and labor.
Income tax deductions are modeled to include depreciation,
interest, and operating cost along with an investment
credit of 10 percent of the initial machine cost. Tax
deductions are subtracted from the sum of all other costs
to give a total cost. All machines are considered to be
purchased with a loan and a 20 percent down payment. The
term of the loan is set at 5 years with an interest rate of
12 percent per year.

This model was adopted to calculate the machinery cost
because it deals with a cash flow method of analysis which
is better suited than the fixed/variable cost method to
model inflation's effect on costs since all costs are

modeled as they occur.

53

In order to use the model it should be provided with
appropriate input data which varies depending upon the type
of machine to be analyzed. There are three major forms for
the data to model the costs of either a tractor, or farm
machinery. These data forms are listed below:

A. Tractor or self-propelled machine (type 2 or 3)

1. Machine code, name

2. New cost, age, power, annual use (hr), fuel type

3.. (If used) purchase price, hours on machine
B. Implement (type 4 to 15)

1. Machine code, name

2. New cost, age, annual use (hr), width, speed

3. (If used) purchase price, hours on machine.

See Appendix D for further information about the
model. The purchase prices of the selected implements are
shown in Table 3-6.

The final purchase price estimates of the implements
used in navy beans, corn, sugar beet production are shown

in Table 3-7.

54

TABLE 3-6

mrchase Price of Selected Inplanents

(In Dollars Per Unit)

 

 

Inplements Unit $/Unit
Tractor kw 224.0
Bean puller m 492.0
Chisel plow m 1,312.0
Moldboard plow m 2,707.0
Field cultivator m 656.0
Raw planter m 1,969.0
lbw cultivator m 984.0
Beet topper m 3,281.0
Beet lifter m 7,218.0
Sprayer m 2000.0 base price plus

66.0 per meter

 

RIJRCES: Hannibal A. Muhtar, Dissertation for the degree
of Ph.D., Michigan State University, 1982.

Purchase Price of fhe Implements involved
In Navy Bean, Corn, Sugar Beef

55
TABLE 3-7

 

 

 

 

 

Producflon
lmplemenfs Code Uni? Size Purchase P. 5

Uflilfy fracfor TI kw 37.3 8,355.00
Tillage iraclor 12 kw 59.7 13,375.00
Tillage fracfor T3 kw 89.5 20,000.00
Tillage fracfor T4 kw 119.3 26,723.00
S.P. Combine H1 kw 108 59,090.00
S.P. 001!)an H2 1" 16707 71,330.00
S.P. Combine wifh H3 kw 108 64,090.00
plckup.H

S.P. Combine wifh H4 kw 167.7 76,330.00
pickup H

S.P. Combine wlih H5 kw 108 68,641.00

corn H.

S.P. Combine wl+h H6 kw 167.7 85,521.00

corn H.
Puli-fype windrower W, m 2.8 4,500.00
Pull-fype windrower W2 m 4.2 5,000.00
Pull-fype windrower W3 m 5.6 5,500.00
Bean puiier 81 m 2.8 1,377.00
Bean puiier 82 m 4.2 2,065.00
Bean puiier B} m 5.6 2,755.00
Chisel plow C, m 2.4 3,149.00
Chisel plow 02 m 3.1 4,068.00
Chisel plow C3 m 3.4 4,461.00
Moldboard plow M1 m 2.0 5,414.00
Moldboard plow M2 m 2.4 6,497.00
Moldboard plow M3 m 2.8 7,580.00
Field cuifivafor F1 m 3.8 2,492.80
Field culfivaior F2 m 4.7 3,083.20
Field cuilivafor F3 m 5.6 3,673.60
Field cultivator F, m 6.6 4,329.00

56
TABLE 3-7 Confinued

 

 

impiemenfs Code Unlf Size Purchase P. S
Sprayer S, m 1.4 2,092.00
Sprayer 52 m 1.86 2,122.00
Sprayer 33 m 2.77 2,133.00
Row planfer R, m 3.0 5,907.00
Row pianfer R2 m 4.5 8,860.00
Row planfer R3 m 6.0 11,814.00
Row cuifivafor V, m 3.0 2,952.00
Row cuifiva+or V2 m 4.5 4,428.00
Row cultivaior V3 m 6.0 5,900.00
Fertilizer spreader 21 m 3.0 5,000.00
Bee+ fopper P1 m 2.1 6,890.00
Beam Tupper P2 m 2.8 9,187.00
Beam iiffor L, m 2.1 15,158.00
Beef lifter ' L2 m 2.8 20,210.00

 

SOURCE: Roberf G. Whife, Deierminingficepacifies of farm machines. E-1216.
Cooperaflve Ex+ension Service, Michigan Sfa+e Universiiy, Easf Lansing, April
1978.

 

57

3.5-2 Model Results

The data required to execute the program were entered
in the computer to calculate the following parameters for a
ten year period:
1. Ownership cost
. Repair and maintenance

Fuel

Total present value

U1 O“ W N
e

. Average annual cost

The calculation of labor cost was completed in the
mixed-integer linear programing models rather than in the
cost model. The reason for that is to allow the MILP
models to compute the labor cost only when machinery was
under field operation. In this case, more accurate results
can be obtained. In the MILP model the labor cost was
assumed to be 6.0 dollarc per hour. The summary of the

selected implement costs are presented in Table 3-8.
3.6 Powsr Requirements

Obtaining a satisfactory match between tractor
horsepower and implement size is an important phase of farm
machinery management. Implements too large for available
horsepower will cause tractor overloading, excessive tire

slippage, a higher incidence of tractor breakdowns, and

58
TABLE 3-8

Summary of the Selected implement Costs
(For Ten Year Period)

 

 

Ownership Repair 8 Total P. Average
implements Code Cost Maintenance Fuel Value Annual Cost

Utility Tractor T1 8,050.0 10,555.0 40,453.0 59,058.0 6,575.0
Tillage tractor 72 12,887.0 16,896.0 64,747.0 94,530.0 10,523.0
Tillage tractor 13 19,270.0 25,265.0 97,066.0 141,602.0 15,764.0
Tillage tractor T4 25,789.0 33,814.0 129,598.0 189,202.0 21,063.0
S.P. Combine H, 55,924.0 19,001.0 15,930.0 90,855.0 10,115.0
S.P. Combine H2 67,508.0 22,937.0 24,735.0 115,180.0 12,822.0
S.P. Combine with H} 60,656.0 20,609.0 15,930.0 97,195.0 10,820.0
SfPkaZmbine with H4 72,240.0 124,545.0 24,735.0 121,520.0 13,528.0
53;?k22mbine with H5 64,963.0 44,191.0 23,426.0 132,580.0 i4,760.0
ngfncgmbine with H6 80,939.0 55,058.0 36,375.0 172,373.0 19,190.0
corn H.
Pul i-type windrower w, 3,671.7 2,502.0 0.0 6,174.0 686.0
Pull-type windrower W2 4,130.7 2,817.3 0.0 6,948.0 772.0
Pull-type windrower W3 4,589.7 3,132.3 0.0 7,722.0 858.0
Bean puller Bl 1,264.0 1,276.0 0.0 2,540.0 283.0
Bean puiier 82 1,896.0 1,130.0 0.0 3,026.0 337.0
Bean puiier B3 2,530.0 1,037.0 0.0 3,566.0 397.0
Chisel plow C‘ 2,891.0 1,244.0 0.0 4,136.0 460.0
Chisel plow 62 3,735.0 1,041.0 0.0 4,749.0 529.0
Chisel plow C3 4,096.0 942.0 0.0 5,038.0 561.0
Moldboard plow M1 4,971.0 5,604.0 0.0 10,575.0 1,177.0
Moldboard plow M2 5,965.0 5,306.0 0.0 11,271.0 1,255.0
Moldboard plow M3 6,960.0 5,066.0 0.0 12,026.0 1,339.0
Field cultivator F, 2,288.0 431.0 0.0 2,719.0 303.0
Field cultivator F2 2,831.0 363.0 0.0 3,194.0 356.0
Field cultivator F3 3,372.0 316.0 0.0 3,688.0 411.0
Field cultivator F4 3,973.0 279.0 0.0 4,253.0 474.0

59

TABLE 3-8 Contl nued

 

 

Ownership Repair 6 Total P. Average
implements Code Cost Maintenance Fuel Value Annual Cost

Sprayer s1 1,920.0 1,920.0 0.0 3,398.0 378.0
Sprayer s2 1,948.0 1,566.0 0.0 3,515.0 391.0
Sprayer s3 2,004.5 1,609.6 0.0 3,614.1 402.0
Row planter R, 5,424.0 5,128.0 0.0 10,552.0 1,175.0
Row planter R2 8,135.0 4,020.0 0.0 12,155.0 1,353.0
Row planter R3 10,847.0 3,383.0 0.0 14,23o.o 1,584.0
Row cultivator v1 2,710.0 1,620.0 0.0 4,330.0 482.0
Row cultivator v2 4,066.0 1,171.0 0.0 5,237.0 583.0
Row cultivator v3 4,591.0 1,981.0 0.0 6,571.0 732.0
Fertilizer spreader Z1 4,591.0 1,363.0 0.0 5,953.0 663.0
866+ topper P1 7,571.0 4,327.0 0.0 11,899.0 1,322.0
868+ topper P2 10,095.0 5,773.0 0.0 15,868.5 1,763.0
Beet lifter L1 16,657.0 9,569.0 0.0 26,226.0 2,914.0
Beet litter L2 22,208.0 12,846.0 0.0 35,055.0 3,895.0

 

60

unsatisfactory performance in general. Implements that are
too small will result in inefficient operation, low
production, and increased costs.

Due to the wide range of implements used in navy
bean, corn, and sugar beet production, it is impossible to
match all implements perfectly to the tractor horsepower
available. Therefore, the objective is to match as
effectively as possible the tractor power available and the
power requirements of the majority of the "heavy draft"
machines.

The PTO power requirement for the selected implements
in medium-textured soil were calculated depending upon the
following parameters:

1. Type of soil
. Implement width

Implement speed

Depth of plowing (for tillage implements)

U1 15 u N
e

. Draft force per unit width kw/m

Table 3-9 represents the power requirement (kw/m) for
selected implements in medium textured soil. The final
results for the power requirements, for the implements
contributing in navy bean, corn, and sugar beet production
systems, in medium textured soil, are presented in Table

3-10. The machine capacities (ha/hr) for selected

61

TABLE 3-9

Power Requirement for Inplements
in Medium-Textured Soil

 

 

Inplements P10 power kw/m
Bean puller 7.31
Windrower 4.00
Chisel plow 24.40
Moldboard plow 27.90
Row planter 8.8
Sprayer 3.6
lbw cultivator 7.2
Beet topper 9.8
Beet lifter 39.1

 

Modified from Donnell Hunt, Farm Foyer and Machinngian-
ement , Iowa State University Press, Ames, Iowa. 1975. Hannibal
A. Mfifitar, Dissertation for Degree of Ph.D. , Michigan State
University, 1982.

62
TABLE 3-10

Power Requiremenfs for Seiec+ed impiemenfs
in Medium-Texlured Soil and the
Reievanf Tracfor Sizes

 

 

implements Code Size PTO power Tracfor Size Code
(m) (kw) (kw)

Bean puiier 81 2.8 20.46
Bean puller 82 4.2 30.70
Bean puller B3 5.6 40.93
Bean windrower w, 2.8 11.20
Bean windrower "2 4.2 16.80
Bean windrower w} 5.6 22.40
Fuller 8 windrower 81 + H‘ 2.8 31.66 37.3 T'
Puller 8 windrower 82 + Hz 4.2 47.5 59.7 T2
Puiier 8 windrower 83 + H3 5.6 63.3 89.5 T}
Chisel plow C, 2.4 58.56 59.7 T:
Chisel plow 02 3.1 75.64 89.5 or 119.3 T3, T4
Chisel plow C3 3.4 82.96 89.5 or 119.3 T3, T1
Moldboard plow M1 2.0 55.8 59.7 T2
Moldboard plow M2 2.4 66.96 89.5 or 119.3 T3, T‘
Moldboard plow M3 2.8 78.12 89.5 or 119.3 T3, T;
Field cuifivafor F, 3.8 32.49 37.3 T,
Field cuifivafor F2 4.7 40.185 59.7 T2
Field cuiflvafor F3 5.6 47.88 59.7 T:
Field culflvafor F4 6.6 56.43 59.7 T2
Sprayer S, 1.4 5.04 37.3 T1
Sprayer 52 1.86 6.7 37.3 T,
Sprayer 53 2.77 10.0 37.3 T,
Row planfer R, 3.0 26.40 37.3 T1
Row pianfer R2 4.5 39.60 59.70 T2

Row planfer Rs 6.0 52.7 59.70 T2

63

TABLE 3-10 Confinued

 

 

impiemenfs Code Size PTO power Tracfor Slze Code
(m) (kw) (kw)
Row cu1+1va+or v, 3.0 21.80 37.3 T,
Row cuiflvafor V, 4.5 32.40 37.3 T,
Row cuifivafor V3 6.0 43.20 59.67 T2
Ferfiiizer spreader 2, 3.0 11.1 37.3 T,
Beef topper P, 2.1 20.58 37.3 T,
Bee+ tapper P2 2.8 27.44 37.3 T,
Beefi lifter L, 2.1 82.11 119.3 T,

866+ ilffer‘ L2 2.8 109.48 119.3 7,

 

64

implements are shown in Table 3-11. Figures 3-1, 3-2 and
3-3 represent the possible ways of matching implements with
selected tractor sizes (37.34, 59.7, 89.5 and 119.3 kw).
For example, Tractor 1 (T,) can match in the MILP model
with implements in one of twelve ways depending upon the

size of implement required to cover 200 ha of land.

3.7 Predicting the Number of Suitable

Days for Field Work

Timing field operations is an important part of
successful crop production. The effects of untimely
operations could influence management decisions involving
the selection of machinery and labor systems.

The variation in weather from year to year and its
resultant impact on the number of good days available for
soil preparation, planting, spraying, cultivation and
harvest has been a major uncertainty in making good
selection and choices. Therefore, the manager's ability to
make proper system selections and to schedule men and
machines depends to a high degree on his ability to predict

available working time in the field during any part of the

crop season.

Machine Cepacifies (ha/hr) for Selecfed implemenis

651

 

 

impiemenfs Code Efficiency Mld+h Speed Capeclfy
(m) (km/hr) (ha/hr)
S.P. Combine H,,H5 65 4.0 4.8 1.25
S.P. Combine H2,H6 65 5.0 4.8 1.56
'S.P. Combine
wifh pickup H3 65 5.6 6.0 2.18
"S.P. Combine

wifh pickup H4 65 7.0 6.0 2.73
B. windrower W, 80 2.8 5.6 1.17
B. windrower H2 80 4.2 5.6 1.76
B. windrower w} 80 5.6 5.6 2.35
Bean puller B, 80 2.8 5.6 1.17
Bean puller 82 80 4.2 5.6 1.76
Been puiier 83 80 5.6 5.6 2.35
Chisel plow C, 85 2.4 7.2 1.468
Chisel plow 02 85 3.1 7.2 1.897
Chisel plow c3 85 3.4 7.2 2.08
Moldboard plow M, 80 2.0 7.2 1.15
Moldboard plow M2 80 2.4 7.2 1.38
Moldboard plow M3 80 2.8 7.2 1.61
Field culflvaior F, 90 3.8 7.2 2.46
Field cultivaior F2 90 4.7 7.2 3.00
Field cuifivaior F3 90 5.6 7.2 3.62
Field culflvafor F4 90 6.6 7.2 4.62
Sprayer S, 65 1.4 8.1 .73
Sprayer $2 65 1.86 8.1 .97
Sprayer S3 65 2.77 8.1 1.45
Row planfer R, 60 3.0 8.1 1.45
Row planfer 82 60 4.5 8.1 2.18
Row pianfer R3 60 6.0 8.1 2.91

66

TABLE 3-11 Conflnued

 

 

lmplemenfs Code Efficiency Hldfh Speed Capaclfy

(S) (m) (km/hr) (ha/hr)

Row cuifivafor V, 85 3.0 4.8 1.22
Row culfivafor V2 85 4.5 4.8 1.83
86. culflvafor v3 85 6.0 4.8 2.44
Fertilizer spreader Z, 80 3.0 7.2 1.72

Beef f0pper P, 70 2.1 4.8 .7
Beef 'i‘opper P2 70 2.8 4.8 .94

Beef liffer L, 70 2.1 4.8 .7
Beef iiffer 1.2 70 2.8 4.8 .94

 

SOURCE: Roberf G. HHlfe, Defermining Capacifies of Farm Machines.
E-1216. Cooperafive Exfension Service, Michigan Sfafe Unlversify, Easf
Lansing. April 1978.

* SP Combine (HS-4.0 m) was assumed +0 pickup a windrwo of navy bean
planfs windrowed from 8 rows (5.6 m).

"SP Combine (H4-5.0 m) was assumed +0 pick up a windrow of navy bean
pianfs windrowed from 10 rows (7.0 m).

81,W1
F1
51,2,3
Rl'
V1,2
21
91,2

Bean puller l, Windrower 1
Field cultivator

Sprayer 1,2,3

Row planter 1

Row cultivator 1,2
Fertilizer spreader

Beet topper 1,2

 

Fig. 1 Possible ways of matching tractor 1 (T1) and selected

implements.

 

 

Puller 2, Windrower 2
Chisel plow l
Moldboard plow 1
Field cultivator 2,3,4
Row planter 2,3

Row cultivator 3

Possible ways of matching tractor 2 (T2) and selected
implements.

 

33, W3 : Puller 3, Windrower 3
C2 : Chisel plow 2

M2,3 : Moldboard plow 2,3
F3,4 : Field cultivator 3,4

Pig. 3 The possible ways of matching tractor 3 (T3) and selected
implements.

BEE
”1.1..

Fig. 4

7O

Chisel plow 2,3
Mbldboard plow 2,3
Beet lifter 1,2

The possible ways of matching tractor 4 (T4) and selected
implements.

71

Rotz et al. (1982) developed an algorithm to provide
suitable days data for different locations in Michigan.
The-results of this model has been found to have less than
15 percent error.

In this particular study, the predication of suitable
days for field work in Michigan conducted by Rotz et al.
(1982) was used in the MILP models to compute the number of
the available hours for field work in Saginaw. Table 3-12
represents the predicted portion of days for field work in
Saginaw at .8 probability level. (A probability level of
0.8 indicates that 8 years or more out of 10 the portion of
the days indicated will be suitable.) The number of hours
available for field work at 0.8 probability level for navy
beans, corn and sugar beets were calculated as follows:

1. The calendar days within which field operations can be
performed were organized depending upon the weather
history of Michigan and some recommendaitons from
specialists.

2. The actual number of days available for field work were
calculated by multiplying the available days for
executing each field operation by the corresponding

portion of days suitable for field work.

72

TABLE 3-12

Predicted Portion of Days Suitable for
Field Wbrk in Saginaw at a
0.8 level of Probability

Period Portion of days

A A

1- anharvest operations

April 20 - 30 .34
May 1 - 10 .66
May 11 - 20 .62
May 21 - 31 .71
June 1 - 15 .66
June 16 - 30 .72
July 1 - 15 .80
July 16 - 31 .79
Aug. 1 - 15 .65
Aug. 16 - 31 .71
Sept. 1 - 15 .75
Sept. 16 - 30 .68
Oct. 1 - 15 .64
Oct. 16 - 31 .58
‘Nov. 1 - 15 .42
NOV. 16 - 30 .11

2- Harvest operations

Sept. 1 - 15 .53
Oct. 1 - 15 .49

 

SOURCE: C. Alan Rotz et a1. ”Prediction of suitable days
for field work." Michigan State University, 1982.

73

3. The actual number of hours available for field work
were then calculated by multiplying the number of
actual days available for field work by the
.corresponding number of hours per day within which each
field operation can be performed.

4. Each number of hours available for a field operation
was then compared with the recommended hours for a
machine to execute the field work. If the recommended
number of hours were less than the calculated hours,
the recommended hours would be used in the MILP models;
otherwise the calculated number of hours would be taken
into consideration.

Table 3-13 summarizes the number of hours per day
within which field operations can be performed. The final
results of the calculated number of hour available for
field work at probability .8 for navy beans, corn, and
sugar beets are presented in Tables 3-14, 3-15 and 3-16
respectively. The estimated life of selected farm

machinery are listed in Table 3-17.

74

TABLE 3-13

Nmber of Hours Assigned to Field Operation

 

 

Operation Nmber of Hours per Day
Fall plowing 12
Fertilizer application 12
Field cultivation 12
Planting 12
Raw cultivation 12
Spraying 12
Direct harvesting beans 8
Convent. harvesting beans 10
Corn harvesting 10
Sugar beet harvesting 12

,A- ‘ J A

SQJRCE: Francis J. Wolak "Development of a field
machinery selection nodel.” Dissertation for the degree of
Ph.D., Michigan State University 1981.

75

TABLE 3-14

Calendar Days and Nunber of Available Hours
for Field Work at 0.8 Probability Level
for Bean Product ion

k g
—v

 

Operation Execution Date Nmber of Hours

Fall plowing 10/9 to 11/27 135.0
Fertilizer application 5/1 to 5/15 121.0
Spring cultivation 5/9 to 5/29 160.0
*Planting 5/30 to 6/19 154.0 (80.0)
lbw cultivation 6/20 to 7/5 ‘ 135.0
Spraying 6/20 to 7/5 135.0
Direct harvesting beans 9/5 to 10/10 153.0
Convent. harvesting beans 9/10 to 10/20 192.0

- Pulling and windrow 96.0

- Ombining 96.0

 

SGJRCE: Francis J. Wolak "Development of a field machinery
selection nodel.” Dissertation for the degree of Ph.D. , Michigan
State University 1981.

*When average annual use exceeds the recoumended nun'ber of
hours, machine will wear out before it becomes obsolete.

76

TABLE 3-15
Calendar Days and timber of Available Hours

for Field Work at 0.8 Probability Level
for Corn Product ion

A... ’ A

 

(perat ion Execution Date Number of Hours
Fall plowing 10/9 to 11/27 135.0
Fertilizer application 10/9 to 11/27 135.0
Spring cultivation 4/20 to 5/10 120.0
*Planting 4/24 to 5/10 160.0 (80.0)
Spraying 4/15 to 5/15 165.0
lbw cultivation 6/1 to 6/18 144.0
Harvesting 10/10 to 11/12 153.0

 

SCIJRCE: Francis J. Wolak “Development of a field machinery
selection model." Dissertation for the degree of Ph.D., Michigan
State University 1981.

*When average annual use exceeds the recannended number of
hours, machine will wear out before it becomes obsolete.

77

TABLE 3-16

Calendar Days and Nunber of Available Hours
for Field Work at 0.8 Probability Level
for Sugar Beet Production

 

Querat ion Execution Date Nunber of Hours
Fall plowing 10/25 to 11/25 124.0
Spring cultivation 4/10 to 5/10 160.0
*Planting 4/15 to 5/15 *(80.0)
Spraying 5/22 to 6/12 163.0
lbw cultivation 5/22 to 6/12 163.0
Harvesting 10/1 to 11/13 230.0

*4 _L

a

SGJRCE: Francis J. Wolak ”Development of a field machinery
selection nodel.” Dissertation for the degree of Ph.D. , Michigan
State University 1981.

*Recaimended nunber of hours for using planter.

78

TABLE 3-17

The Estimated Life of Machines

 

Machine Years Until Wear Out Hours per Year for
Gasolete Life Wear Out Life to
Hours Equal Obsolescence
Life*
Tractors
Wheel-type 10 1000 1000
Track-type 15 15000 1000
Tillage inplements
Cult ivators 12 2500 208
Moldboard plow 15 2500 167
Seeders
Grind drill 15 1200 80
lbw crop planer 15 1200 80
Harvesting equipment
Carbine, S.P. 10 2000 200
Sugar beet harvester 10 2500 250
Windrower 10 2500 250
Fertilizer equipment 8 1200 150

A—

SCIJRCE: R.A. Keeper, R. Bainer and E.L. Eager, Principles of
farm machinery. AVI Publ. 00., Inc., 'Ihird Ed., 1978.

*When average annual use exceeds this nunber of hours, machine
will wear out before it becomes obsolete.

4 NAVY BEAN PRODUCTION MODEL

4.1 Model Formulation

 

The algorithm which follows was developed to evaluate
and compare navy bean production systems in Michigan
involving conventional and direct harvest methods. A mixed
integer linear programming model was formulated with 44
columns (activities) and 38 rows (constraints) to select
the navy bean variety to recommend (Swan Valley or Fleet-
wood), the planting system to follow (wide rows or narrow
rows), the harvesting method to apply (direct or conven-
tional), and finally the number and type of farm machinery
to use so that the profit can be maximized.

The following

equations overview the navy ean MILP model structure:

The objective function:

 

Maximize Z = - X1WD1 ' XZWDZ - X3WC3 ' X4SD1 ‘ XSSDZ

‘ x63C3 ' x70, ' x831 ‘ x9H1 ' x10T1

- x11T2 ' x12T3 ‘ x13141

' x14112 ‘ x15M3

- x16C1 X17% X18% x1921 x20F1
‘ x2192 x2213 x2394 x24R1 x25R2
' x26R3 x27V1 x28V2 x29V3 x3031
- x3152 x3233 x3331 x3432 x3533
- x36W1 x37W2 x38W3 x3931 x4032
- x4,n3 X42H4 X43La X4488

79

where z
where Xn

WD1

WD2

wc3

SD,

SD2

5C3

Table

80

The total net profit for the selected navy bean
production system.

Level of activity n for n = 1 . . . 44 (column
number)

Insecticide and fungicide cost $/ha for
Fleetwood planted in 35 cm row spacing and
directly harvested

Insecticide and fungicide cost S/ha for
Fleetwood variety planted in 70 cm row spacing
and directly harvested

Insecticied and fungicide cost $/ha for
Fleetwood variety planted in 70 cm row spacing
and conventionally harvested

Insecticide and fungicide cost $/ha for Swan
Valley variety planted in 35 cm row spacing and
directly harvested

Insecticide and fungicide cost S/ha for Swan
Valley variety planted in 70 cm row spacing and
directly harvested

Insecticide and fungicide cost S/ha for Swan
valley variety planted in 70 cm row spacing and
conventionally harvested

The navy bean seed price S/kg

The fertilizer cost $/kg

The herbicides cost S/kg

3-1 represents the summary of navy bean produc-

tion data used in the navy bean MILP model.

Tm : The annual cost of
m = 1,2,3

Mm : The annual cost of
m - 1,2,3

Cm : The annual cost of
m = 1,2,3

2, : The annual cost of
$/yr

Fm : The annual cost of
where m = 1,2,3,4

Rm : The annual cost of
m = 1,2,3

Vm : The annual cost of
m = 1,2,3

Sm : The annual cost of
m = 1,2,3,

Bm : THe annual cost of
m = 1,2,3

Wm : The annual cost of
m = 1,2,3

Hm : The annual cost of
m 8 1,2,3,4

81

using

using

using

using

using

using

using

using

using

using

using

tractor m $/yr where
moldboard plow m $/yr where
chisel plow m $/yr where
the fertilizer spreader
field cultivator m $/yr

row planter m $/yr where
row cultivator m $/yr where
sprayer m S/yr where

bean puller m $/yr where
windrower m S/yr where

harvester m S/yr where

Table 3-8 summarizes the total annual costs for each

implement used in the navy bean MILP model

La :

SB :

The labor cost per hour $/hr

The market sale price of navy beans S/kg.

82

The objective function (net profit) was maximized
subject to a series of constraints illustrated by
relationships 4-1 through 4-38 where the equation numbers
represent the constraing number, and the subscripted X's
value show the columns (activity) number.

Landpconstraint:

 

X,a, + x2a2 + X3a3 + x4a4 + X5a5 + x636 $.b1 (4-1)
where:
Xn : Represents the level of activity n (land area)
which the computer is going to assign for the
selected navy bean variety where n = 1, . . .6

(column's number)

an : Is a vector (value) of ones (under three systems
of Fleetwood variety and three systems of Swan
Valley variety see Appendix A-i row 4)
where n a 1, . . . 6 (activity number)

b, : Is the land area limitation (it was set to be 200

ha)

Yield constraint:

 

f X1Y, - xzrz - X3Y3 - X4Y4 - sts — X5Y6
+ x44Y44,£ 0 (4-2)
where:

Xn : Is the level of activity n (size of Land in ha)
where n I 1, . . .6

x44 : Is the level of selling activity (the yield
going to be sold)

Yn : Is the yield kg/ha (for the Fleetwood under three
systems and Swan Valley under three systems)
where n = 1, . . . 6

Y44 : Is a vector of 1 under selling activity

83

Seeding rate constraint:

 

X,Se, + X4Se4 - X7Se7 5_0 (4-3)
where:
xn : Level of activity n (size of land in ha)
where n = 1, 4, 7
Sem: The amount of seed required (kg/ha) for navy
beans planted in 35 cm row spacing where m = 1,4
Se7: Is a vector of -1 ( avalue of -1 under column
7, the seed price $/k9)
Seeding rare cogstraint:
' x23e2 + X3Se3 + X58e5 + X6Se5 - X7Se7 g 0 (4-4)
where:
Xn : Level of activity n (size of land in ha)
where n = 2, 3, 5, 6, 7
Sem: The amount of seed required (kg/ha) for beans
planted in 70 cm row spacing where m = 2, 3, 5, 6
Se7: Is a vector of -1 (a value of -1 under column 7,
the seed price $/kg)
Fertilizer rate constraint:
X,Fe, + szez + X3Fe3 + X4Fe4 + XSFeS + X6Fe6
- X8Fe3 $_O (4-5)
where:
Xn : Level of activity n (size of land)
where n = 1, 2, 3, 4, 5, 6, 8
Fem: The amount of fertilizer required (kg/ha)
where m = 1, . . . 6
Fe3: Is a vector of -1
Herbicidg rate gonstraint:
X1He, + xznez + X3He3 + X4He4 + xsnes + x5He5
- xgHeg 5.0 (4-6)

84

where:
Xn- : Level of activity n (size of land in ha)
where n = 1, . . . 6

and 9 (column number)

Hem : The amount of herbicides requied (kg/ha) where
m = 1, . . . 6
He9 : Is a vector of -1 (a value of -1 under column 9

the herbicide price $/kg)
Plowing_9peratiog:
x,P0, + xzpoz + x3903 + x4po4 + xspos + x6906

 

' x13P013 "X14PO14 ' x15P°15 ' x16P016 ' x171’017

' X18P°18..S 0 (4‘7)
where:
xn : Level of activity n (number of tillage implements)

where n = 1, . . . 6 and

13, . . . 18 (column number)

Is a vector of ones where m = 1, . . . 6

Pom
POk

Is a matris of the number of hectares that each
tillage implement can cover during the tillage
time where K 8 13, . . . 18 (the number of
hectares that tillage implement k can cover
during tillage time was calculated by
multiplying the implement capacity ha/hr by the
number of hours available for field work.)
Applyinqrfertilizer:

x11"1 + X4F4 ' x19F‘19_<. 0 (4-8)
where:

xn : Level of activity n (number of fertilizer
spreaders) where n - 1, 4, 19

(column number)

85

fm : Is a vector of ones where m = l, 4 (for beans
planted in narrow rows)
£19: The number of hectares that the fertilizer
spreader can cover during the application time.

Field cultivatiqp:

 

tha1 + tha2 + X3ha3 + X4ha4 + Xshas + X6ha6
' xzohazo ' x21h321 ' x22h622 ' X23’1323 i 0 (4‘9)
where:

Xn : Level of activity n (number of field cultivators)
where n = l, . . . 6 and 20, . . . 23

ham: Is a vector of ones where m = l, . . . 6

hak: The number of hectares that field cultivator k
can cover during the field cultivation time,
where K = 20, 23

Plantingrgperationr

 

X1PL1 + xsz2 + X3PL3 + X4PL4 + XSPLS + XGPL6
' x24PL24 ' x25PL25 ' x26PL26 5.0 (4‘10)
where:

Xn : Level of activity n (number of row planters)
where n I 1, . . . 6 and 24, . . . 26

PLm: Is a vector of ones where M = l, . . . 6

PLk: The number of hectares that row planter k can
cover during planting time, where

k 8 24, . . . 26

86

Row cultivation:
X2Cu2 + X3CU3 + X5Cu5 + X5Cu6 - X27Cu27
- X28Cu28 - X29Cu29 5 0 (4-11)
where:
Xn : Level of activity n (number of row cultivators)
where n = 2, 3, 5, 6, 27, 28, 29
Cum: Vector of ones for beans planted in wide row
system where m = 2, 3, 5, 6
Cuk: The number of hectares that row cultivator k can
cover during the cultivating time where k = 27,
. . . . 29
Spraying operation:
x15P1 + XZSPZ + X3SP3 + X4SP4 + x5895 + X6SP6
‘ 14305930 " x3131’31 ' x3251’32 i 0 (4'12)
where:
Xn : Level of activity n (number of sprayers)
where n = 1, . . . 6 and 30, . . . 32
SPm: A vector of ones for m where m = 1, . . . 6
SPk: The number of hectares that sprayer k can cover
during spraying time where k = 31, . . . 33
Beanrpullingfoperatiog:
X3Pu3 + X6Pu5 - x33Pu33 - X34Pu34
- x35Pu35‘50 (4-13)
where:

Xn : Level of activity n (number of bean pullers)

where n a 3,6,33,34,35

87

Pum: A vector of ones for m where m = 3, 6 (only for
beans planted in 70 cm and conventionally har—
vested)

Puk: The number of hectares that bean puller k can
cover during pulling time where k = 33, 34, 35

Windrowingggperation:

X3Wn3 + x5Wn6 - X36Wn36 - x37Wn37 - X38Wn33,£ 0 (4-14)

where:

Xn : Level of activity n (number of windrowers)
where n = 3, 6, 36, 37, 38

an: A vector of ones for m = 3, 6 (only for beans

' planted in 70 cm and conventionally harvested)

Wnk: The number of hectares that windrower k can cover

during windrowing times where k = 36, 37, 38

Combining operation:

 

X3Co3 + x6C06 - X4,Co41 - x42Co44 5 0 (4-15)
where:
Xn : Level of activity n (number of harvesters)
where n = 3, 6, 41, 42
Com: A vector of ones for m = 3, 6 (only for beans
planted in 70 cm and conventionally harvested)
Cok: The number of hectares that harvester k with
pick-up header can cover during combining time,
where k = 41, 42
Harvesting gperation:
thrl + xzhrz + x4hr4 + Xshrs - X39hr39
- X4ohr40.$ 0 (4-16)

where:

Xn :

hrm:

hrk:

88

Level of activity n (number of harvesters)
where n = l,2,4,5,29,40

A vector of ones for m = 1,2,4,5, (only for
beans harvested directly)

The number of hectares that harvester k can

cover during harvesting time where k = 39, 40

Usage of tractor l:

’ x1013310 + x19T319 + x20T320 + x24T324 + x27T327

+ x28T328 + x30Ta30 + x31Ta31 + x32Ta32

+ 833T333 5.0 (4'17)
where:

Xn : Level of activity n (number of implements)

T310 : The recommended annual number of hours for
tractor l to be used for executing field
operation: (it was assumed to be 1,000 hrs.)

Tam: The number of hours under which each field

operation can be performed by tractor 1 using
implement m where m = 19, 20, 24, 27, 28, 30, 31,
32, 33. (The number of horus under which a field
operation can be performed were calculated by
dividing the land area (200 he was assumed in

this model) by the implement capacity ha/hr).

Usage_of tractor 2:

' x11T311 + 313Ta13 + x16Ta16 + x21T321 * x22T322

+ X23Taz3

xstazs + x26T326 + X29T329

+
+ X34Ta34 5,0 (4-18)

where:

Tall:

89

Level of activity n (number of implements)

The recommended annual number of hours for
tractor 2 to be used for executing field
operation: (the number of hours were assumed to
be 1,000).

The number of hours under which each field
operation can be performed by tractor 2 using
implement m, where m = 13, 16, 21, 22, 23, 29

and 34.

Usagg of tractgr 3:

‘ x12T312 + X14T314 + x15Ta15 + x17Ta17 + xl8Tal8

+ X35Ta35 5.0' (4-19)
where:
xn : Level of activity n (number of implements)

T312:

Tam :

The recommended annual number of hours for
tractor 3 to be used for executing field
operations (the number of hours were assumed to
be 1,000).

The number of hours under which a field
operation can be performed by tractor 3 using

implement m, where m = 14, 15, 17, 18 and 35.

90

Labor Consrraint:

 

x13La13 + x14La14 + x15La15 + x16La16 + x17La17

+ x18L318 + x19La19 + x20La20 + x21La21 + xzzLazz

+

+

x231923 + x241'324 + x25L325 + x26L326 + x271'327
x28L328 + x2914329 + x30La30 + x31La31 + x32La32

+ x331'333 + x34La34 + x351'335 + x39La39 + x40La40

+ x41La41 + x42La42 ' x44La44.£ 0 (4'20)
where:
Xn : Level of activity n (number of implements)

Lam:

where n = 13, . . . 35 and 39, . . . 44
Represents the number of hours required to
accomplish a field operation for a land size of
200 ha, where m = 13, . . . 42 (the summary of
the number of hours required for each implement
to fulfill a field operation are presented in

Table 4-1.

La44: Is a vector of -1 which implies the summation of

all of hours required for navy bean production for

calculating the labor cost.

The initial results from the previous model indicated

that planting Swan Valley variety in 70 cm row spacing and

applying the direct harvesting method is the most

profitable system at this stage that can be followed, but

the numbers of field machinery selected by the model was

fractional instead of integers which does not represent

91

TABLE 4-1

The Land Area that Can Be Covered by an Inplement
mring Available Days and Time Required
to Cover 200 Ha

A A L A
V

 

Inplement Code Nmber of Hectares* Number of Hours"
Moldboard plow M, 155 174
Moldboard plow M2 187 145
Moldboard plow M3 217 124
Chisel plow C, 200 135
Chisel plow C2 255 105
Chisel plow C3 270 100
Fertlizer spreader z, 209 116
Field cultivator F, 332 81
Field cultivator F2 393 66.6
Field cultivator F3 480 55.2
Field cultivator F4 579 43.2
Row planter R, 117 138
lbw planter R2 174 91.7
Row planter , R3 232 68 .7
Row cultivator V, 165 164
Row cultivator V2 248 109
In» cultivator V3 330 82
Sprayer S, 100 120.5
Sprayer $2 135 200
Sprayer S3 200 135
Bean puller +

windrower B,+W, 1 13 170
Bean puller +

windrower 828112 169 113
Bean puller +

windrower B3+W3 225 85
Harvester H, 191 160
Harvester H2 239 128
Harvester

(conventional) H3 209 92
Harvester

(conventional) 11,, 262 73

 

TNu‘rber ofhectares . [field capacity ofin anlement (Haihfif x
nunber of hours available for field work (hr)]

*mmber of hours - [land size (ha)] :- [field capacity of an
inplenent (ha/hr)]

92

the terms of the real world. Therefore, a specific
technique was followed to force the noninteger number of
selected kinds of implements to be integers by adding the
following constraints 4-1 through 4-38 where the equation
number represents the row (constraint) number, and the
subscripted x's value show the column (activity) number.

Forcing the tillagg implements to be integers:

 

X,5Fr,5 + x,6Fr,6 + x,7Fr,7 + X,8Fr,3 = 1 (4-21)
where:

xn : Level of activity n (number of tillage
implements) where n = 15, . . . 18

Frm: A vector of ones for m s 15, . . . 18. These
vectors of ones were set only under the tillage
implements that can cover 200 ha or more during
tillage time to guarantee the number of tillage

implements to be integers.

x,5Fr,5 5,1 (4-22)
X,6Fr,6,5 1 (4-23)
X,7Fr,7 r 1 (4-24)
X,8Fr,3 g 1 (4-25)

Equations 21 to 25 were set to force the model to
select just one integer kind of a tillage implement that

can cover the 200 ha within the time limit.

93

Forcingrrhe number of rield cultivators togbe integers:
x20Fr20 + X2,Fr2, 1 x22Fr22 + x23"1’23 = 1 (4‘25)
where:
Xn : Level of activity n (number of field cultivators)
where n = 20, . . . 23
Frm: A vector of ones for m = 21, . . . 23. These
vectors were set only under field cultivators
which can cover 200 ha or more during cultivating

time to guarantee the number of cultivators to be

integers.
X20Fr20 5.1 p (4-27)
x2,Fr2, r 1 (4-28)
X22Fr22 5_1 (4-29)
X23Fr23 5,1 (4-30)

Equations 27 to 30 were set to force the model to
select only one size of field cultivator.

Forcing the row planters togbe integgrs:

 

X26Fr26 3 1 (4-31)

Forcingrthe row cultivators to or integers:

 

X28Fr28 + X29Fr29 ' 1 (4'32)
XZBFrZB 5,1 (4'33)
X29Fr29 g 1 (4'34)

Forcing the sprayers to be integers:

X32Er32 8 1 . (4-35)

94

Forcing the combine to be integers:
x40Fr4o = 1 (4-36)
Forcing_tractor 1 and tractor 2 to be integers:
x,oFr,o 8 1 (4‘37)
(4-38)

4.2 Model Adjustments

The tractor usage in the farming process represents
one of the most important factos affecting the total annual
cost of crop production. In the MILP model the tractor
usage was assumed to be 1000 hrs per year to estimate the
annual cost of using Tractor 1, 2, and 3. However, the
results obtained from the navy bean production model
indicated that the actual number of hours for the tractor
usage were as follows:

1. Utility tractor 1 (T, - 37.2 kw): 435 hours per
year, 300 hrs of which were assumed to be used for
handling transportation, making turns, etc., other
than farming activities.

2. Tillage tractor 1 (T2 - 59.7 kw): 442 hours per
year, 100 hrs of which were assumed to be for
non-farming activities (handling, transportation,

turns, etc.)

95

3. Tillage tractor 3 (T3 - 89.5 kw): 400 hours per
year, 100 hrs of which were assumed to be for
nonfarming activities.

These actual number of hours for tractor usage were
fed in the machinery cost model by Rotz et al. (1981) to
calculate the total cost for using Tractor 1, 2, and 3.
The results obtained from the machinery cost model are

summarized in Table 4.2.

4.3 Model Results

 

The navy bean production model results indicated that
planting the Swan Valley variety in 70 cm row spacing and
applying the direct harvesting method is the most
profitable system that can be followed at this stage. A
navy bean producer can make in this system up to
$144,604.00 profit from 200 ha land which approximately
equals $723.00 per ha. the summary of the navy bean
production model results is presented in table 4-3. These
results show the kinds and the sizes of implements selected
by the model and represents the amount of seed, fertilizers
and herbicides applied for Swan Valley planted in 200 ha

land with 70 cm row spacing.

96

TABLE 4-2

Sunnary of the Adjusted Annual Cost
of Tractors 1, 2, 3 (her
Ten Year Period

 

Implement Code Ownership Repair 8 Fuel Total Average
Cost Maintenance Present Annual
Value Cost

Utility tractor Ti 8050 2786 17597 28434 3165
Tillage tractor '12 12887 4576 28618 46081 5130
Tillage tractor T3 14270 5832 38872 63929 7117

 

97

TABLE 4-3

Summary of the Final Solution of the
Navy Bean Production System

 

 

Itens Size Final Solution

Land Size 200 ha Swan Valley
planted in 70 cm
wectafiggéging
method

Seeds 9000 kg

Fertlizer 54000 kg

Herbicide 1060 kg

Utility tractor 37.3 kw 1

Tillage tractor 59.7 kw 1

Chisel plow 2.4 m 1

Field cultivator 6.6 m 1

lbw planter 6.0 m 1

lbw cultivator 6.0 m 1

Sprayer 2.7 m 1

S.P. conbine 5.0 m 1

Total yield 521 tonne

Hour requirement 604 hr

Total profit $144,604.00

Total Profit per Hectare 723.00 $/ha

 

98

4.4 Sensitiyity Analysis

 

Sensitivity analysis is the study of how the optimal
solution and the value of the optimal solution to a linear
programming change, given changes in the various coeffi-
cient of the variables in the model. There are several
reasons why sensitivity analysis is considered so important
from the managerial point of view. First of all, a farming
system operates in a dynamic environment; cost of machines,
labor, chemicals and crops change over time. Sensitivity
analysis can also be used to determine how critical
estimates of coefficients are in the solution to a linear
programming. As another phase of sensitivity analysis, it
is possible to calculate the cost of adding resources to
relax the bending (limiting) constraints. Thus, the
sensitivity analysis provides a good tool for additional

valuable information for the decision maker.
4.4-l Shadow Prices and Slacks

Shadow price is an economics term used to indicate the
impact of increasing the right hand side for a linear
programming constraint by one unit. In other words, it is

the value of one additional unit of the resource associated

99

with linear programming, while the slack variable

represents the amount of unused resource. In the navy bean

production model, those two variables were analyzed by the

computer. The results of these analyses are summarized in

Table 4-4.

These results indicate the following:

If the farmer is going to rent one more hectare of
land he is willing to pay up to $847.00 per year
otherwise it is not profitable to pay more than this
value. This shadow price represents the value of the
crop minus the operating cost for.producing one he of
beans.

If the farmer is going to sell this crop, he is
willing to accept .44 $/kg and up.

If the farmer is going to purchase one more kg of navy
bean seeds, fertilizer and herbicides, he is willing
to pay up to .88, .47 and 14.15 $/kg respectively.

If the farmer is going to plow one more hectare of
land, he is willing to pay up to 10.68 $/ha to rent a
plow.

By using the field cultivator F4 (6.6 m), row

planter R3 (6.0 m), and the row cultivator V3 (6.0
m). The farmer will have excess 379, 32, and 130 ha
of land respectively. (Land can be covered in addi-

tion to 200 ha of land assumed t in the MILP model.)

Sumery of the Shadow Prices and the
Slacks for the Navy Bean

100

TABLE 4-4

Product ion Model

A‘

 

Itens Unit Shadow Price Value Slack Value
Land $/ha 847.87
Yield S/klg .44
Seed $/kg .88
Fertilizer $/kg .47
Herbicides $/kg 14 . 1 5
Plowing $/ha 10.68
Field cultivation ha 376
Bean planting ha 32
Row cultivation ha 130
Saraying S/ha 10.68
Bean harvesting

(directly) be 39
Using tractor 1 hr 865
Using tractor 2 hr 658
Using tractor 3 sm 7.11
Labor S/hr 6.00

 

10.

101

If the farmer is going to spray one more hectare of
land, he is willing to pay up to 10.68 $/ha to rent a
sprayer.

By using harvester H2 (5.0 m), the farmer will have
excess 39 ha of land can be covered by this size of
harvester.

By using tractor T, (37.3 kw) and tractor T2 (59.7
kw), the farmer will have excess 865, and 658 hours
per year respectively to cover 1000 hours per year for
each tractor.

If the farmer is going to rent a tractor T3 (89.5
kw), he is willing to pay up to 15.76 $/hr to use the
tractor. I

If the farmer is going to use additional employees to
fulfill the field work, he is willing to pay 6.0

dollars per hour for each employee.

4.4-2 The Cost of Forcing Nonoptimal Activities

Into the Optimal Solution

It is a measure of the economic impacts of forcing in

nonoptimal activities into the final solution. The results

102

obtained from the computer analysis are shown as follows:

1.

Planting Fleetwood in 35 cm row spacing using the

direct harvest method instead of planting Swan Valley

.in 70 cm rows using the direct harvest method would

cost the farmer $690.89 for each hectare of land.
Planting Fleetwood in 70 cm row spacing and applying
the direct harvest method would cost a farmer $415.80
more for each hectare of land compared to planting Swan
Valley in 70 cm rows and applying the direct harvest
method.

Planting Fleetwood in 70 cm rows and applying the
conventional harvest method, would cost the farmer
$365.48 more for each hectare of land compared to
planting Swan Valley in the optimal solution.
Planting Swan Valley in the narrow row system (35 cm)
and applying the direct harvest method would cost a
navy bean producer $392.57 more for each hectare of
land compared to planting Swan Valley in 70 cm rows.
Planting Swan Valley in 70 cm rows and harvesting
conventionally would cost the farmer $314.88 more for
each hectare of land compared to the direct harvest
method.

Forcing moldboard plow 1 (M,--2.0m) or moldboard plow
2 (M2--2.4m) or moldboard plow 3 (M3--2.8m) into
plowing operation would cost $1145.93, $1859.94 and

$1322.78 per year, respectively.

103

7. Forcing field cultivator (F1--3.8m) would cost $31.00
per year.

8. Using row planter l (R1--3.0m) or row planter 2
(R2--4.5m), would add $2,003.00 and $1,903.00 per
year, respectively to the total costs.

9. Using harvester l (H1--4 rows) instead of harvester 2
(H2--5 rows) would add $11,075.00 per year to the
total cost.

It should be noted from these results that forcing an
implement into the final solution would also force the
corresponding tractor (T1, T2, or T3) to be in the
final solution. This would result in some additional cost
attributed to the cost of using a tractor in the total

annual cost of an operation.

4.4-3 Range of Optimality

The range of optimality is defined as the range of
values over which the objective function coefficient for a
variable may change without changing the optimal solution.
The results obtained from the computer analysis indicated
the following:

1. Planting Swan Valley variety in 70 cm rows and

applying the direct harvest method would still

hold in the optimal solution as long as the

104

insecticides and fungicides cost per hectare does
not exceed $385.00

The optimal solution can hold as long as the Swan
Valley seed price is less than $9.25 per kilo-
gram.

The fertilizer price can go up to $3.26 per kg
without affecting the optimal solution for the
model.

The optimal solution can be held as long as the
herbicide market price is below $156.54 per kg.
Using tractor l (T1--37.3 kw), tractor 2
(T2--59.7 kw), or tractor 3 (T3--89.5 kw) in

the farming process depends on the corresponding
equipment that can be matched with a tractor.
Using the chisel plow l (C1--2.4m) would still
be in the optimal solution as long as the total
annual cost is $1,446.00 or lower and as long as
tractor 2 (T2--59.7 kw) is the most profitable.
This situation may change if tractor 2 is no
longer in the Optimal solution.

Using the field cultivator 4 (F4--6.6m) would no
longer be in the optimal solution if the cost of
use exceeds $826.00. In this case field
cultivator 2 (F2--4.7m) would be the candidate

for replacing field cultivator 4.

10.

11.

12.

105

Using row planter 3 (R3--6.0m) would be in the
optimal solution as long as the annual cost for
the planter does not exceed $2,464.00 per year.
Otherwise planter 2 (R2--4.5m) would be the
competitive machine that might replace it.

Using the row cultivator 3 (V3--6.0m) would be

in the optimal solution as long as the annual cost
for that implement does not exceed $804.00.
Otherwise row cultivator 2 (V2--4.5m) would be
the candidate to replace row cultivator 3.

Using sprayer 3 (S3--2.77m) would no longer be

in the optimal solution if the annual cost of use
exceeds $1,177.00. In this case sprayer 2
(Sz--l.86m) would be the competitor to replace
sprayer 3.

The use of harvester 2 (H2--5.0m) would be in
the optimal solution as long as the total annual
cost of using this harvester is below $13,669.00.
Otherwise harvester 1 (H,--4.0m) would be the
alternative choice.

This optimal solution can be held as long as the

navy bean market price is $.15 per kg and up.

5 NAVY BEAN-CORN PRODUCTION MODEL

5.1 Model,Fgrmu1ation

 

Crop selection, machinery selection, and field work
scheduling are interrelated and require an integrated
planning process that can evaluate simultaneously the
effects of machinery purchase and crop production
alternatives within the resource constraints imposed on a
farm.

A mixed integer linear programming model was
formulated with 45 columns (activities) and 39 rows
(constraints) to accomplish the following:

Evaluate and compare navy been (specifically, Swan

Valley variety planted in 70 cm and harvested

directly which give the best results in the navy bean

production model), and corn production in Michigan.

This algorithm was developed to find:

1. Which crop was more beneficial to the farmers.

2. What profit could be made under different land

percentages of navy bean and corn

3. What machinery set to contribute to a selected

crop production system.

The following equations described the MILP model

structure:

106

107

The objecriveifunction:

 

Maximize z 8 -X,Be - XZCO - x388 - X4FB - XSHB - XGSC
-x7rc - x880 - ng, - x,oT2 - X,,T3
“X12C1 ' x13C2 ’ x14‘33 ' x15F32 ' x16FB3
-X,7FB4 - x,ercz - X,9FC3 - x2080,
-X2,RB, - xzzaaz - X23RB3 - X24RC,
-X25RC2 - x26R03 - x27va, - X23V82
‘X29VB3 ' x30VC-1 ' x31VC2 ' x32VC3
-x33ss, - X34882 - X35883 - x3550,
-x37scz - X388C3 - X39HB, - X40882

-X41HC1 - X42HC2 ' X4333 - X44SC - X45LA

where:

z : The total net profit $/yr

Xn : Level of activity n, where n = 1 . . . . 45
and it indicates the column number.

CO : Insecticide and fungicide cost ($/ha) for
corn production.

SB, SC : Seed prices (S/kg) for navy beans and corn,
respectively.

FB, FC : Fertilizer costs (S/kg) for beans and corn,
respectively.

HB, HC : Herbicide costs ($/kg) for beans and corn,

respectively.
Table 3-9 represents the summary of corn production data

used in the navy bean-corn model:

CM

FBm,

Ram ,

VBm I

SBm'

HBm'

SB
SC

LA

ch

RCm

vcm

50,,

EC,“

108

Annual costs of using tractor m ($/year)
where m = 1,2,3,.

Annual cost of using chisel plow m ($/year)
where m 8 1,2,3.

Annual costs of using field cultivator m
($/year) for bean and corn production,
respectively, where m = 2,3,4.

Annual costs of using row planter m (S/year)
for planting beans and corn, respectively,
where m = 1,2,3.

Annual costs of using row cultivator m
(S/year) for cultivating beans and corn,
respectively, where m = 1,2,3.

Annual costs of using field sprayer m
($/year) for spraying beans and corn,
respectively, where m = 1,2,3.

Annual costs of using harvester m ($/Year)
for harvesting beans and corn,
respectively, where m = 1,2.

Market sale price of navy beans ($/kg).
Market sale price of corn ($/bu).

Labor cost per hour ($/hr, assumed to be

$6/hr).

Table 3-8 summarizes the total annual costs for each

implement used in the navy bean-corn production model.

109

The objective function was maximized subject to a

series of constraints illustrated by equations (5-1)

through (5-39), where the equation number represents the

row number (constraint number), and the subscripted X's

indicate the column number (activity number).

Land constraints:

 

X131 ‘1' X232 3 L), (5'1)
where:
Xn : Level of activity n (land area in ha)

an

ID1

where n = 1,2.

Is a vector (value) matrix of ones for bean
and corn production where n 8 1,2.

Is a land area limitation (it was set to be

200 ha).

Yield constraints:

 

-X,Y, + 1:431:43 r 0 (5-2)

—x2Y2 + x44Y44 5,0 (5-3)

where:

Xn : Is the level of activity n (size of land in ha)
where n 8 1,43 in the first equation and 2,44 in
the second.

Y, : Represents the navy bean yield level (kg/ha).

Y43 : A vector of 1 under selling bean activity.

Y2 : The corn yield level (bu/ha).

A vector of 1 under selling corn activity.

Seeding rate

110

constraints:

 

X,Se, - x3Se3 g 0 (5-4)
XZSeZ - X58e5 5.0 (5-5)
where:
xn : Level of activity n (size of land),
where n = 1,3 and 2,6.
Se, : Amount of required navy bean seed (kg/ha).
Se3 : A vector of -1 under navy bean seed price
(S/k9)
Sez : Amount of corn seed required (kg/ha).
Se5 : A vector of -1 under corn seed price ($/kg).
Ferrilizer rate constraints:
X,Fe, - x4re4' r 0 (5-6)
xzrez - x7re7 r 0 (5-7)
where:
Xn : Level of activity n (size of land),
where n = 1,4 and 2,7.
Fe, : Amount of fertilizer required for bean
production (kg/ha).
Fe4 : A vector of -1 under fertilizer market price
(s/kgi.
Fez : Amount of fertilizer required for corn
production (kg/ha).
Fe7 : A vector of -1 under fertilizer market price

($/k9).

Herbicides
X1H81
82392

where:
xn
He,
Hes

H62

H88

rate constraints:

XSHeS i 0 (5'8)
XBHeB S 0 (5'9)

Level of activity n (size of land),

where n = 1,5 and 2,8.

Amount of herbicide required for bean
production (kg/ha).

A vector of -1 under the herbicide market
price (S/kg).

Amount of herbicide required for corn
production (kg/ha).

A vector of -1 under the herbicide market

pricel($/k9).

Plowing operation:

 

X1PO, + X2P02 ' X12P012 - X13PO13
-X,4PO,4 S’O (5'10)

where:

xn

Pom

POk

O.

Level of activity n (number of tillage
implements) , where n = 1,2,12,13,14.
Is a vector of ones under bean and corn
production where m = 1,2.

Is a vector of the number of hectares chisel

plow k can cover during plowing time where k

12,13,14.

Fieldrcultiyation:

x1351 ‘ x153315 ’ x16Ha16 ' x1733175. 0 (5'11)

where:

Xn :
Ha, :
Ham :
Xzflaz
where:

X” :
H32 :
Ham :

112

Level of activity n (number of field
cultivators), where n = 1,15,16,17

A vector of 1 under bean proudction

Is a matrix of number of hectares

that field cultivator m can cover during the

cultivating time where m = 15, . . .17

' x18Ha18 ' x193319 ‘ x209320 3.0 (5’12)

Level of activity n (number of field
cultivators), where n = 1,18,19,20

A vector of 1 under corn production

Is a matrix of number of hectares that field
cultivator m can cover during cultivating time

Where 1“ - 18’ e e e 20

Egantingyoperation:

 

x1PL1 ' x21PL21 ' x22PL22 ' x239L235. ° (5’13)
where:
xn : Level of activity n (number of row planters),
where n = 1,21,22,23.
pL, : A vector of 1 under bean production.
me : Represents the number of hectares that row

planter m can cover during planting time

where m = 21, . . . 23.

113

X21’1'2 ‘ X24131424 ' Xzsl’Lzs ’ x26PL26 S. 0 (5‘14)

where:
xn : Level of activity n, where n = 1,24,25,26.
pL2 : A vector of 1 under corn production.
me : Represents the number of hectares that row

planter m can cover during corn planting time
where m = 24, . . . 26.

Row cultivator:

X,Cu, - X27Cu27 - X23Cu23 - X29Cu29 5,0 (5-15)
X2Cu2 - X30Cu3o - X3,Cu3, - x32Cu32 3,0 (5-16)
where:

xn : Level of activity n (number of row
cultivators), where n = 1,27 . . . 29
and 2,30 . . . 32.

Cu,Cu2 : A vector of 1 under bean and corn
production, respectively.

Cum : A vector of the number of hectares that row

cultivator m can accomplish during
cultivating time in a bean field, where m =
27 . . . 29 (F2,F3,F4).
Cuk : A vector of the number of hectares that row
cultivator k can perform during cultivating
time in a corn field, where k = 30 . . . 32

(Fsz3rF4).

114

Sprayigg operation:

x13P1 ' x335P33 " X343934 " x353935 S. 0 (5‘17)

x23P2 ‘ x365936 ' x3731337 ' x385P38 _<. 0 (5'19)
where:

Xn : Level of activity n (number of sprayers),

SP1! SP2

Spm

Spk

where n = 1,33 . . . 35 and 2,36 . . . 38.

A vector of 1 under bean and corn

.production, respectively.

Number of hectares that field sprayer m can
cover during spraying time in a bean field,
where m = 33, . . . . 35 (S,,SZ,S3).
Number of hectares that field sprayer k can
perform during spraying time in a corn

fiéld' Where k g 36’ e e e 38 (S‘pSZ'S3).

Harvestipg_operation:

1 x,hr, - X39hr39 - x40hr40 £_0 (5-19)
xzhrz - X4,hr4, - X42hr42 r 0 (5-20)
where:

Xn : Level of activity n (number of harvesters),
where n = 1,39,40 and 2,41,42.

hr,, hr2 : A vector of 1 under bean and corn
production, respectively.

hrm : Number of hectares that harvester m can

accomplish during bean harvesting time,

where m = 39,40 (H,,H2).

115

hrk : Number of hectares that corn harvester k
can cover during corn harvesting time,
where k = 41,42 (H5,H6).

The results obtained about the number of hectares an
implement can cover within the time limit are shown in
Table 5-1. It should be noted that the same implements
used for executing field operations for navy bean
production were used for corn production but under
different sequence numbers. This technique was used to
distinguish between bean field operations and corn field
operations because some field operations for bean and corn
production may have different time limits to accomplish the
field work, which could result in different sizes of
implements to be selected by the model.

Usaggrof tractor 1:

 

- x9T39 + x15Ta15 + x18Ta18 + x21T321 + x241‘324
+ x271‘327 + x28Ta28 + x30Ta30 1 x31Ta31 + x33Ta33

+ x34T334 + x351’335 + x36T336 + x37Ta37 + x38Ta38

5,0 (5-21)
where:
xn : Level of activity n (number of implements)

u Tag : Recommended number of hours for tractor 1
to be used for executing field operation

(it was assumed to be 1,000 hrs).

116

TABLE 5-1
The Land Area that can be Covered by an Implement During

the Available Workable Days and the Time Required
to Cover 200 Ha

__‘_ __ L_- k

Implement Code Nunber of Hectares* Nunber of Hours“

 

Chisel plow C, 200 135
Chisel plow C2 255 105
Chisel plow C3 270 100
Field cultivator F2 295 66.6
, Field cultivator F3 360 55.5
Field cultivator F4 432 43.2
Row planter R, 117 139
lbw planter R2 174 91.7
lbw planter ~ R3 232 68.7
Raw cultivator V, 176 164
Row cultivator V2 263 109
Row cultivator V3 351 82
Sprayer S, 120 274
Sprayer $2 160 200
Sprayer S3 236 135
Corn harvester H5 191 160
Corn harvester H6 239 128

*Nmber of hectares - [field capacity of an inplement (ha/hr)] x
nulber of hours available for field work (hr)]

1MNutber of hours 3 [land size (ha)] 9 [field capacity of an
inplement (ha/hr)]

Tam

117

Number of hours under which each field
operation can be performed by tractor 1
using implement m where m = 15,18,21,24,
27,28,30,31,33,34,35,36,37,38 [the number
of hours under which a field operation can
be performed were calculated by dividing
the land area (200 ha was assumed in this

model) by the implement capacity (ha/hr)].

Usage of rractor 2:

 

-;X10Ta1o + x,2Ta,2 + x,6Ta,5 + x17Ta17 + x19Ta19

+ x20T320 + x22T322 + x23T323 + Xstazs + x26Taz6

+ x29Ta29 + x32Ta32 g 0 (5-22)
where:

Xn : Level of activity n (number of implements)

Ta,o : Recommended number of hours for tractor 2
to be used for executing field operation
(the number of hours was assumed to be
1,000 hrs).

Tam : Number of hours under which a field

operation can be fulfilled by tractor 2
using implement m, where m =

12,16,17,19,20,22,23,25,26,29 and 32.

118

Usage of Tractor 3:

- X,,Ta,, + X,3Ta,3 + X,4Ta,4 r_0 (5-23)
where:

Xn : Level of activity n (number of implements)

Ta,, : Recommended number of hours for tractor 3
to be used for executing field operation
(the recommended number of hours were set
to be 1,000 hrs).

Tam : Number of hours under which a field

operation can be accomlished by tractor 3

using implement m, where m = 13,14.

Labor constraints:

x12La12 +
+ x17La17

+ X22L322
+ x27L327

+ X32La32
+ X37La37

+ X42La42

where:

Lam

x13La13 + x14La14 + x15La15 + x16La16

+

+

+

+

x18La18 + X19La19 + xzoLazo + x21La21
x231-323 + x24L324 + XzsLazs + x26L326
x28L328 + x29Laz9 + x3014830 + x31La31
x33La33 + x34La34 + x35La35 + x36L336
x38La38 + x39La39 + x40La40 + x41La41
0 (5-24)

[A

x45La45

Level of activity n (number of implements),
where n = 12, . . . 42

and 4S.

Represents the number of hours required to
accomplish a field operation for a land

size of 200 ha, where m = 12, . . . 42 (the

119

summary of the numbers of hours required
for each implement to fulfill a field
operation were shown in Table 4-1.

La45 : Is a vector of -1 which implies the
summation of all number of hours required
for navy bean and corn production for
calculating the labor cost.

The number of hours required for each implement to

accomplish field work was presented in Table 5-1.

The initial result obtained from this model indicated
that planting navy beans is more profitable to farmers than
planting corn. However, the number of implements selected
by the model were fractional numbers rather than integers
which is not feasible. Therefore, some constraints were
added to the model to force the previously selected
implements to be integers. These constraints are listed as
follows:

Forcingrthe number of chisel plow§_to be an integer:

X12Fr,2 + X13Fr13 + X14Fr14 g 1 (5'25)
X,2Fr,2 i 1 (5-26)
X,3Fr,3 i 1 (5-27)

X,4Fr,4 £,1 (5'28)

120

where:
xn : Level of activity n (number of chisel
plows).
Frm : A vector of ones for m = 12,13,14. These

vectors of ones were set only under the
size of chisel plow that can cover 200 ha
or more within the time limit to guarantee
that the number of tillage implements be
integers.

Forcing the number of field cultivators to be an integer:

X15Fr,5 + x,6Fr,5 + x,7Fr,7 8 1 (5-29)
x,5Fr,5 5.1 (5-30)
X,6Fr,6 £_1 (5-31)
X,7Fr,7 3.1 (5-32)
where:
Xn : Level of activity n (number of field

cultivators).
Frm : A vector of ones for m = 15,16,17
(F2,F3,F4).
Forcing the number of row_planrerspto be an integer:
, x23Fr23 = 1 (5-33)
where:
x23 : Level of activity (number of row

planters).

121

Fr23 : A vector of 1 under only row planter 3 that
can cover 200 ha within the time limit.

Forcing the number of row cultivators to be an integer:

X28Fr23 + x29Fr29 = 1 (5-34)
x28Fr28 £_1 (5-35)
X29Fr29 i 1 (5-36)
where:
Xn : Level of activity n (number of row

cultivators).

Fr‘m : A vector of ones under row cultivators
number 2 and 3 because they are capable of
cultivating 200 ha or more within the time
limit.

Forcing the number of harvesters to be an integer:

x4291342 = 1 . (5-37)
where:
x42 : Level of activity n (number of

harvesters).

Frm : A vector of 1 under harvester number 2
which is capable of harvesting 200 ha
within the time limit.

Forcing the number_of tractors to be an integer:
X9Fr9 = 1 (5-38)
x,oFr,0 = 1 (5-39)

122

where:
xn : Level of activity n (number of tractors).
Frm : A vector of 1 under utility tractor 1 and

tillage tractor 2.
5.2 Model Adjustments

In the MILP model the tractor usage was assumed to be
1000 hours per year which in fact does not represent the
real world system. However, the results obtained from the
navy bean-corn production model indicated that the actual
number of hours for utility tractor 1 (T, - 37.3 kw)
usages was 435 hours per year, 300 hours of which were
assumed to be used for nonfarming activities (handling,
transportation, turns, etc.). While the number of hours for
using tillage tractor 2 (T2 - 59.7 kw) and tillage tractor
3 (T3 - 89.5 kw) were found to be 442 and 400 hours,
respectively. Therefore, the total annual cost of using
tractor 1, 2, and 3 were recalculated using machinery cost
model by Rotz et a1. (1981). The results of these
calculations are presented in Table 4r2. The new annual
costs of using tractor 1, 2, and 3 were then fed into the
MILP model to calculate the net profit for the navy
bean-corn production model which intended to select the most
profitable crop can be produced with respect to the

agronomic and machinery requirements.

123

5.3 Model Results

 

The results obtained from navy bean-corn production
model indicated that under present corn yield level (6037.00
kg/ha) and market price (0.93 $/kg), navy bean production
is more profitable than corn. A navy bean producer can
realize up to $135,801.00 in profit from a 200-ha farm which
equals approximately $680.00 per ha. A summary of the navy
bean—corn production model results is presented in Table
5-2. These results illustrate the amount of seed,
fertilizer, and herbicides required for the Swan Valley
variety planted in 200 ha and represent the type and size

of implements selected by the model.

5.4 ‘Sensitiviry Analysie

5.4-1 Shadow Prices and Slacks

Shadow price is an economics term used to indicate the
impact of increasing the right-hand side for a linear
programming constraint by one unit. The slack variable
represents the amount of unused resource. The results of
shadow prices and slack variables were presented in Table

4-30

124

TABLE 5-2

Sunmary of the Final Solution of the
Navy Bean-Corn Production Model

 

Itens Size Final Solution
Land Size 200 ha Navy Bean
Agronanic Requirements

Seeds 9000 kg

Fertilizer 54000 kg

Herbicide 1060 kg

Machinery Requirements

Utility tractor 37.3 kw 1
Tillage tractor 59.7 kw 1
Chisel plow 2.4 m 1
Field cultivator 6.6 m 1
lbw planter 6.0 m 1
lbw cultivator 6.0 m 1
Sprayer 2.7 m 1
S.P. combine 5.0 m 1
Labor Requirements 604 hr
Total yield 521 tonne
'10tal profit $144604.00

Net profit per ha 723.00 $/ha

125

5.4-2 The Cost of Forcing in Nonoptimal Solution

The cost of forcing in nonoptimal solution is an

economics term used to indicate the impact of forcing

nonoptimal activities into final solution. The results

obtained from the computer analysis indicated the

following:

1.

Planting corn instead of navy beans, would cost
the farmer $582.00 more for each hectare of land.
Forcing field cultivators (F,--3.8m) into the
optimal solution would add $31.00 to the total
annual cost.

Using row planter 1 (R,--3.0m) or row planter 2
(R2--4.5m) instead of row planter 3 (R3--6.0m)
would increase the total annual cost by $2,003.00
and $1,903.00, respectively.

Using row cultivator 1 (V,--3.0m) instead of row
cultivator (V3--6.0m) would add $1466.00 to the
total annual cost.

Forcing sprayer 1 (S,--1.4m) or sprayer 2
(Sz--1.86m) instead of sprayer 3 (S3--2.7m)

into the optimal solution would add $1,416.00 and

$772.00 per year, respectively.

126

6. Using harvester 1 (H,--4m) instead of harvester
2 (H2--5m), would add $11,075.00 per year to the
total annual cost.

It should be noted from these results that forcing an
implement into the final solution would also force the
corresponding tractor (T,, T2, or T3) to be in the
final solution. This would result in some additional cost
attributed to the cost of using a tractor in the total

annual cost of an operation.
5.4-3 Range of Optimality

The range of optimality indicates the range of values
over which the objective function coefficient for a vari-
able may change without changing the optimal solution. The
results obtained from the computer analysis indicatd the
following.

1. Planting Swan Valley variety in 70 cm rows and
applying the direct havesting method would still
hold in the optimal solution as long as the
insecticide and fungicide costs per hectare do not
exceed $560.00

2. The optimal solution can be held as long as the
Swan Valley seed price is less than $12.45 per

kilogram.

127

The fertilizer price can go up to $2.39 per kg
without affecting the optimal solution for the
model.

The optimal solution will hold as long as the
herbicide market price is below $112.40 per kg.
Using tractor 1 (T,--37.7 kw), or tractor 2
(T2--59.7 kw), or tractor 3 (T3--89.5 kw) in

the farming process depends upon the corresponding
equipment that can be matched with a tractor.
Using chisel plow 1 (C,--2.4m) would no longer
be in the optimal solution if the cost of use
exceeds $1,446.00 per year and as long as tractor
2 (T2--59.7 kw) is in the optimal solution.

The use of field cultivator 4 (F4--6.6m) would
still be in the Optimal solution as long as the
total annual cost was $906.13 and lower. Other-
wise, field cultivator 3 (F3--5.6m) would be the
candidate for replacing field cultivator 4.

The use of row planter (R3--6.0m) would be in
the optimal solution as long as the annual cost
for the planter does not exceed $2,689.00.
Otherwise, row planter 2 (R2--4.5m) would be the

competitve machine to replace it.

10.

11.

12.

128

The use of row cultivator 3 (V3--6.0m) would be
in the optimal solution as long as the annual
cost for the cultivator does not exceed
$1,244.40. Otherwise, row cultivator 2
(V2--4.5m) would be the candidate for replacing
row cultivator 3.

The use of sprayer 3 (S3--2.77m) would no
longer be in the optimal solution if the annual
cost of use exceeds $2,607.00. Otherwise,
sprayer 2 (82--1.86m) would be the competitive
for replacing sprayer 3.

The use of harvester 2 (H2--5m) would still be
in the optimal solution as long as the total
annual cost of using the harvester is below
$13,090.24. Otherwise, harvester 1 (H,--4m)
would be the alternative machine.

This optimal solution can be held as long as the
navy bean market price is higher than $.24 per
kilogram and the corn market price is less than

$4.92 per bushel.

129

5.5 Teetingypifferent Percentages of Bean and Corn
in the Navy Bean-Coranroduction Model

5.5-1 A 75 Percent Bean-25 Percent Corn
Production System

In order to study the economic impacts of having a
system of 75 percent beans and 25 percent corn (150 ha beans
and 50 ha corn) on the farmer's profit, some changes took
place in the previous navy bean-corn model. It is obvious
that although the same field operations had to be
accomplished with the same implements for both navy beans
and corn, the execution time and the time limit are
different for some of these field operations. Therefore,
constraints number 25 to 37 were substituted from the
previous model with the following constraints to satisfy the
new condition and to have integer number of implements.

Forcing_the navy bean land size te be 150 ha:

X,Fr, 8 150 (5-25)
where:
x, : Is a level of activity 1 (size of land for

planting bean).
Fr, : A vector of 1 under navy bean activity in

order to force the navy bean land size to be

150 ha.

130

Forcing the number of chisel plows to be anvinteger:

X12Fr1z + x13*‘1'13 + x14““: = 1 (5‘25)
X,2Fr,2 3,1 (5-27)
X13Fr13.
X,4Fr,4 r 1 (5-29)
where:
xn : Level of activity n (number of chisel plow).
Frm : A vector of 1 under chisel plow 1, 2 and 3.

It should be noted that these vectors of ones
were set under the size of chisel plow that
can cover 200 ha, since the plowing time for
both crops can be accomplished at the same
time of the year.

Forcing the number of field cultivators to be_an integer:

X,5Fr,5 + X18Fr18 g 1 (5‘30)
where:
Xn : Level of activity n (number of field

cultivators).

Frm : A vector of 1 under field cultivator 2
(F2--4.7m). It should be noted that the
same field cultivator (F2--4.7m) was used
to cultivate the bean land and the corn
land, because the execution time is differ-
ent and F2 is capable of covering the land

size for each crop within the time limit.

131

Forcing the number of row_p1anters to be an integer:

X22Fr22 + XZSFrZS = 1 (5‘31)
where:
xn : Level of activity n (number of row

planters).

Frm : A vector of 1 under row planter 2
(R2--4.5m). It should be noted that
although the row planter existed under
columns 22 and 25, these columns refer to
the same row planter (R2--4.5m) because the
planting operation is performed at
different times for beans and corn.

Forcing the number ofrrow culrivators to be integers:

X27Fr27 + X30Fr30 = 1 (5-32)
where:
Xn : Level of activity n (number of row

cultivators).

Fr : A vector of 1 under row cultivator 1
(V,--3m). This row cultivator existed
under two columns because of the same
previous reasons.

Forcing the number of epreyers to be an integer:

X35Fr35 + X38Fr38 3 1 (5-33)

132

where:
xn : Level of activity n (number of sprayers).
Frm : A vector of 1 under sprayer 3 (S3--2.7m).

Forcing the number of harvesters to be an integer:

x395'1'39 + x41Fr41 ? 1 (5-34)
where:

xn : Level of activity n (number of harvesters).

Frm : A vector of 1 under harvester (H,--4m). It

should be noted that the same harvester was
used to harvest beans and corn but from
different headers.

Forcing tractor 1 and 2 to be an integer:

X9Fr9 = 1 (5-35)
x,oFr,o = 1 (5-36)
where: A
xn : Level of activity n (number of tractors).

Frm : A vector of 1 under tractor (T,--37.3 kw)

and tractor 2 (T2--59.7 kw).

5.5-2 Model Adjustment

 

It was found from the previous model adjustment results
that the total net profit tended to jump up 6.5 percent by
involving the actual number of hours rather than 1000 hours
for tractor usage. Therefore, in the following navy
bean-corn production systems, a correction term of 6.5
percent were added to the total net profit for each system

to obtain a more realistic figure for the profit.

133
5.5-3 Model Results

The results from this model indicated that a farmer
can make up to $119,622.00 per year if 150 ha of land is
planted with beans and 50 ha is planted with corn, which
equals approximately $598.00 per hectare. The final
results of this model are presented in Table 5-3 and shown

in Figure 5-1.

. 5.5-4 A 50 Percent Bean-50 Percent Corn
Production System

In order to study the economic impact of having a farm
with 50 percent beans and 50 percent corn (a land of 100 ha
beans and 100 ha corn was assumed in this model) on the
farmer's profit, some changes were made in the main navy
bean-corn model. These changes were included, deleting
constraints number 25 to 39 and adding instead the
following constraints to satisfy the new production
conditions.

Forcing the size of land to be 100 ha beans and 100 ha

corn 8

 

X,Fr, = 100 (5-25)

134

TABLE 5-3

Sunmary of the Final Solution of the
75 Percent Navy Bean — 25 Percent
Corn Production Model

 

Itans Size Final Solution
Land 150 ha Navy Bean
Land 50 ha Corn
Bean Agronomic Requirements

Seeds 6750 kg

Fertilizer 40500 kg

Herbicide 795 kg
Corn Agronomic Requirements

Seeds 700 kg

Fertilizer 15500 kg

Herbicide , 170 kg

Machinery Requirements
Utility tractor
Tillage tractor
Chisel plow
Field cultivator
lbw planter
lbw cultivator

Sprayer
S .P. cotlbine

U109

1510001515qu
0

55955???

dddddd-‘d

O
oqomqe-qw

Labor Requirements 766.7 hr
Total bean yield 390.75 tonne
Total corn yield 301.88 tonne
Total profit $119662.00

Net profit per ha 598.00 $/ha

135

where:
x, : Level of activity 1 (planting navy beans).
Fr, : A vector of 1 under navy bean production.

Eprcing the number of chisel plows to be an integer:

X12Fr12 1 111391513.+ x14Fr14 = 1 (5‘25)
x12 3,1 (5-27)
x,3Fr,3 £_1 (5-28)
x,4Fr,4 3,1 (5-29)
where:
X“ : Level of activity n (number of chisel
plows).
Frm : A vector of ones under chisel plow 1, 2, and 3.

It should be noted that these vectors of ones
were set under the size of chisel plow that
can cover 200 be since the plowing operation
time for both crops can be accomplished at the
same time of the year.

Forcing the number of field cultivators to be_§n integer:

X,5Fr,5 + x,8Fr,3 3 1 ‘ - (5'30)
where:
Xn : Level of activity n (number of field

cultivators).

Frm A vector of ones under field cultivator 2

(Fr2--4.7m).

136

It should be noted that the same field
cultivator was used to cultivate the bean
land and the corn land, because the
cultivation is executed at different times
and cultivator F2 is capable of covering
the land size for each crop within the time

limit.

Forcing the number of row planters to be an integer:

X2,Fr2, + X24Fr24 = 1 (5-31)
where:'
xn : Level of activity n (number of row
planters).
Frm : A vector of 1 under row planter 1 (R,--3.0m).

It should be noted that row planter 1 was
used to plant beans and corn within the time

limit for each.

Forcing the number of row cultivators go be an integer:

X27Fr27 + X30Fr3o ‘ 1 (5'32)
where:
Xn : Level of activity n (number of row

Frm

cultivators).

A vector of 1 under row cultivator 1

(V,--3m). This row cultivator existed under
two columns just to indicate that the same row
cultivator is used at different times of the

year for beans and corn.

137

Forcingrtne number of sprayers to be an integer:

X33Fr33 + x36Fr36 = 1 (5‘33)
where:

xn : Level of activity n (number of sprayers).

Frm : A vector of 1 under sprayer (S,--1.4m), which

was set to be used for Spraying the bean
field and corn field at a different time.

Forcing the number of harvesters to be‘en integer:

x39Fr39 + X4,Fr4, 8 1 (5-34)
where:l

xn : Level of activity n (number of harvesters).

Frm : A vector of ones under harvester 1

(H,--4.0m). It should be noted that the
same harvester was used to harvest beans and
corn but with different headers.

Forcing rractor 1 and 2 to be an integer:

X9Fr9 8 1 (5-35)
x,oFr,0 = 1 (5-36)
where:
xn : Level of activity n (number of tractors).
Frm : A vector of 1 under tractor 1 (T,--37.3 kw)

and tractor 2 (T2--59.7 kw).

138

5.5-S Model Results

The model results indicated that a farmer can make up
to $91,404.00 per year if 100 ha of land is planted with
beans and 100 ha is planted with corn, which equals
approximately $457.00 per hectare. The final model results

are shown in Table 5-4 and were given in Figure 5-1.

5.5-6 A 25 Percent Bean-75 Percent Corn
Production System

This system was studied in order to find the economic
impact of having 25 percent bean and 75 percent corn (land
of 50 ha beans and 150 ha corn) on the farmer's profit.

The same technique followed in the 75 percent bean-25
percent corn production model was also involved in this new
system but with some changes. These changes are presented
according to the following constraints while the rest of
the constraints remained fixed.

Forcing the land size to be 50 ha beans and 150 ha corn:

X,Fr, 8 50 (5-25)
where:
x, : Level of activity 1 (size of land for

planting navy beans).

Fr, A vector of 1 under navy bean production.

139

TABLE 5-4

Sumnary of the Final Solution of the
50 Percent Navy Bean - 50 Percent
Corn Production Model

 

 

Items Size Final Solution
Land 100 ha Navy Bean
Land 100 ha Corn
Bean Agronanic Requirements
Seeds . 4500 kg
Fertilizer 27000 kg
Herbicide 530 kg
Corn Agronomic Requirements
Seeds ' 1400 kg
Fertilizer 31000 kg
Herbicide 340 kg
Machinery Requirements
Utility tractor 39.3 kw 1
Tillage tractor 59.7 kw 1
Chisel plow 2.4 m 1
Field cultivator 4.7 m 1
lbw planter 3.0 m 1
R741 cultivator 3.0 m 1
Sprayer 1.4 m 1
S.P. oonbine 4.0 m 1
Labor Requirements 952 hr
Total bean yield 260.6 tonne
Total corn yield 603.76 tonne
Total profit $91404.00

Net profit per ha 457.00 $/ha

 

140

Forcing the number of eprayers to be an integer:

X34Fr34 + X37Fr37 3 1 (5'25)
where:
Xn : Level of activity n (number of sprayers).

Frm : A vector of 1 under sprayer 2 (82--1.8m)

for spraying bean's field and corn's field

at different time of the year.

5.5-7 Model Results

The model results indicated that a farmer can make up
to $64,685.00 per year if 50 ha of land is planted beans
and 150 ha is planted corn, which approximately equals to
$323.00 per hectare. The final model results are presented

in Table 5-5 and were shown in Figure 5-1.

141

TABLE 5-5

Sumnary of the Final Solution of the
25 Percent Navy Bean - 75 Percent
Corn Production Model

 

Itets Size Final Solution
Land 50 ha Navy“ Bean
Land 150 ha Corn
Bean Agronanic Requirenents

Seeds 2250 kg

Fertilizer 13500 kg

Herbicide 265 kg
Corn Agronomic Requirements

Seeds . 2100 kg

Fertilizer 46500 kg

Herbicide . 510 kg

Machinery Requirements

Utility tractor 37.3 kw 1

Tillage tractor 59.7 kw 1

Chisel plow 2.4 m 1

Field cultivator 4.7 m 1

Row planter 4.5 m 1

lbw cultivator 3.0 m 1

Sprayer 2.7 m 1

S.P. oonbine 4.0 m 1
Labor Requirenents 831.7 hr
Total bean yield 130.25 tonne
Total corn yield 951.30 tonne
Total profit $64685.00

Net profit per ha 323.00 $/ha

142

3/ Yr 7150..

   
 
 
 
 
 
  

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III/III/l/l.

700-

800-

 

550.

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SCHI—

 

 

 

 

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1 2 3 4 Navy bean-corn

Optimal solution (100% bean)
75% been and 25% com
50% been and 50% corn
: 25% bean and 75% com

bWNH

Fig. 5—1. Smmary of the profits under different percentage of
navy bean — corn.

6. NAVY BEANS -— SUGAR BEET PRODUCTION MODEL

6.1 Model Formulation

 

The MILP algorithm was developed to evaluate and
compare navy bean (Swan Valley variety planted in 70 cm and
harvested directly) production and sugar beet production in
Michigan. The objective of the model is to select the more
economical crop which can be produced so that the profit can
be maximized.

This model had variables which select a machinery
complement from an available set of tractors (37.3, 59.7,
119.3 kw), chisel plows (2.4, 3.1, 3.4 m), field cultivators
(4.7, 5.6, 6.6 m), row planters (3.0, 4.5, 6.0 m), row
cultivators (3.0, 4.5, 6.0 m), sprayers (1.4, 1.8, 2.7 m),
bean harvesters (4.0, 5.0 m), beet toppers (2.1, 2.8 m), and
beet lifters (2.1, 2.8 m). The purchase of fractional
machines was not allowed and machinery rental was not
considered.

The model was formulated as a mixed integer linear
programming with 47 columns (activities) and 44 rows
(constraints). The following equations overview the

structure.

143

144

The objective function:

 

Maximize z 8 X,B - X25 — x388 - X4FB - XSHB - XGSS

where:

SB,

FB,

HB,

SS

FS

HS

-X7FS - x888 - XgT, - x10T2 - x,,T4
"X1201 ' x13C2 “ X14133 ' x151132 ' x16FB3
-x,788, - x,8r52 - x,9rs3 - xzors4
~X2,RB, - x22R82 — X23RB3 - X24RS,
-X25R82 - X26RS3 - x27vs, - xzevaz
-x29vs3 - s3ovs, - s3,vs2 - x32vs3
-x33ss, - x34ssz - X35883 - X3585,
‘X37552 ' x38553 ' x39111 ‘ x40112 ' x41P1
“X4292 ' x431:1 ' x441'2 1 x45133 1 X46335

-X47LA

The total net profit $/Yr.

Level of activity n, where n 8 1 . . .47
(where n represents the column or activity
number).

Insecticide and fungicide cost ($/ha) for
navy bean.

Insecticide and fungicide cost ($/ha) for
sugar beets.

Navy bean and sugar beet seed price (S/kg),
respectively.

Fertilizer cost ($/kg) for navy beans and
sugar beet production, respectively.

Herbicide cost ($/kg) for navy beans and

sugar beet production, respectively.

145

The navy bean production data

in Table 3-1, while the sugar beet

are summarized in Table 3—4.

Tm
Cm
F8",

F8,“

Ram

Rsm

vsm

vsm

Annual cost of using
m 8 1,2,4.
Annual cost of using

m = 1,2,3.

: Annual cost of using

for cultivating bean
Annual cost of using

for cultivating beet

required were presented

production data required

a tractor ($/yr) where

a chisel plow m where

field cultivator m ($/yr)

fields where m = 2,3,4.

field cultivator m ($/Yr)

fields where m = 2,3,4.

(It should be noted that the field cultivators

used for tilling beet fields are the same

ones used for cultivating bean fields).

: Annual cost of using

row planter m (S/Yr) for

planting navy bean seeds where m = 1,2,3.

Annual cost of using

row planter m ($.yr) for

planting sugar beet seeds where m 8 1,2,3.

(It should be noted that the row planters used

for planting sugar beets are the same

ones used for planting navy beans).

Annual cost of using
for cultivating bean
Annual cost of using

for cultivating beet

row cultivator m ($/Yr)
fields where m 8 1,2,3.
row cultivator m ($/Yr)

fields where m 8 1,2,3.

58m

$8,,

146

(It should be noted that the row cultivators
involved for cultivating beet fields are the
same ones used for cultivating bean fields.)
Annual cost of using sprayer m ($/yr) for
spraying navy bean fields where m 8 1,2,3.
Annual cost of using sprayer m ($/yr) for
spraying sugar beet fields where m 8 1,2,3.
(Sprayers used for spraying sugar beet fields
were also used for spraying navy bean
fields).

Annual cost of using harvester m ($/yr) for
harvesting navy beans directly where m 8 1,2.
Annual cost of using beet topper m ($/yr)

for topping sugar beets where m 8 1,2.

Annual cost of using beet lifter m ($/yr)

for lifting sugar beets from the field where

m 8 1,2.

Table 3-8 summarizes the total annual cost for each

implement used in the navy bean-sugar beet production model.

BS
888

LA

Market sale price of navy beans ($/kg).
Market sale price of sugar beets ($/ton).

Labor cost per hour (S/hr assumed to be

$6/hr).

The objective function was maximized subject to a

series of constraints illustrated by equations (6-1) through

147

(6-44), where the equation number represents the row number

(constraint number), and the subscripted x's indicates the

column number (activity number).

Land constraint:

x,a, + x2a2 8 b, (6-1)
where:

Xn Represents the land area (hectares) where
n 8 1,2. I

an Is a vector of ones (value of ones)
under navy beans and sugar beet production
where n 8 1,2.

b, : Is a land size limitation (it was to be 200

ha).

Yield constraints:

 

-X,Y, + x45Y45 : 0 (6-2)
-x2Y2 + x46Y46 5.0 (6-3)
where:

Xn : Is the level of activity n (size of land in
ha) where n 8 1,45 in the first equation and
n 8 2,46 in the second.

Y, : Represents the navy bean yield level (kg/ha).

Y45 : A vector of 1 (value of one) under selling
beans activity.

Y2 : The sugar beet yield level ton/ha.

Y46 : A vector of 1 under selling sugar beet

activity.

Seeding rate:

 

148

X,Se, - X3Se3 _<_ 0 (6-4)

XZSez - x68e5 _<_ o (6-5)
where:

Xn : Level of activity n (size of land)

Se,

Se3

59.2

Se6

where n 8 1,3 and 2,6.

Amount of navy bean seed required (kg/ha).
A vector of -1 under navy bean seed price
($/k9).

Amount of sugar beet required (kg/ha).

A vector of -1 under sugar beet seed price

(S/kg).

Fertilizer rate constraints:

X,Fe, - X4Fe4 i 0 (6-6)

X2Fe2 - x7Fe7 3,0 (5-7)
where:

Xn : Level of activity n (size of land)

Fe,

Fe,,

Fez

Fe7

where n 8 1,4 and 2,7.

Amount of fertilizer required for bean
production (kg/ha).

A vector of -1 under fertilizer market price
($/kg) for navy bean production.

Amount of fertilizer required for sugar beet
production (kg/ha).

A vector of -1 under fertilizer market price

(S/kg) for sugar beet production.

149

Herbicidee rate consrraints:

 

x,He, - X5He5 §_0 (6-8)

X2He2 - X3He3 £_0 (6-9)
where:

xn : Level of activity n (size of land)

where n 8 1,5 and 2,8.

He, : Amount of herbicide required for bean
production (kg/ha).
Hes : A vector of -1 one under the herbicide
market price ($/kg) for bean production.
Hez : Amount of herbicide required for sugar beet
' production (kg/ha).
Heg : A vector of -1 under the herbicide market

price ($/k9) for sugar beet production.
Plowing operation:'

X1PO, + X2P02 - X12P012 - X13P013

- x,4P0,4 £_0 (6-10)
where:
xn : Level of activity n (number of tillage
implements) where n 8 1,2,12,13,14
POm : Is a vector of ones under bean and sugar beet
production where m 8 1,2.
Pok : Is a matrix (value) of the number of hectares

that chisel plow k can cover during plowing time
Field cultivation:

 

X11131 ' X1533”; " X,6Ha,5 " X,7Ha,7 i 0 (6-11)

150

where:
Xn : Level of activity n (number of field
cultivators) where n 8 1,15,16,17.
Ha, : A vector of 1 under bean production.
Ham : Is a matrix (value) of the number of
hectares that field cultivator m can
cover during cultivating time where
m 8 15 . . . 17 (F2, F3, F4).
Xzflaz ‘ x1811318 ' x1911319 ' x2011320 5. (6'12)
where:
xn : Level of activity n (number of field
cultivators) where n 8 1,18,19,20.
Ha2 : A vector (value) of 1 under sugar beet
production.
Ham : Is a matrix (value) of the number of

hectares that field cultivator m can
cover during cultivating time where
m g 18 e e e 20 (F2, F3, F4).

Planting operation:

 

x1PL'1 ’ x21PL21 ‘ x22PL22 ‘ x23PL23 5.0 (5'13)
where:
Xn : Level of activity n (number of row

planters) where n 8 1,21,22,23.

pL, : A vector of 1 under bean production.

me : Represents the number of hectares that row
planter m can cover during planting time
where m 8 21 . . . 23 (R,. R2. R3).

szLz ‘ x2491124 ' x25PL25 ‘ x269L26 5.0 (5'14)

where:

151

xn : Level of activity n (number of row planters)
where n 8 1,24,25,26.

pL2 : A vector of 1 under sugar beet production.

me : Represents the number of hectares that row
planter m can cover during planting time
where m 8 24 . . . 26 (R,,R2,R3).

Rog cultivation:

 

X,Cu, - x27Cu27 - X28Cu28 - X29Cu29,§ 0 (6-15)

X2Cu2 - X30Cu30 - X3,Cu3, - X32Cu32 g 0 (6-16)
where:

Xn : Level of activity n (number of row

cultivators) where n 8 1,27 . . . 29 and 2,
30 O O O 32.
Cu,,Cu2: A vector of 1 under bean and sugar beet,

production, respectively.

Cum : A vector of the number of hectares that row
cultivator m can accomplish during culti
vating time in a bean field, where
m 8 27 . . . 29 (V1, V2, V3).

Cuk : A vector of the number of hectares that row

cultivator k can perform during cultivating
time in a sugar beet field, where k 8
30 . . . 32 (V,, V2, V3).
Spreying operation:
x15P1 " x335933 " 11345934 ' x355935 .S. 0 (6'17)
x251P2 " x36SPB6 " x375937 " 1‘3851138 5. 0 (6'13)

where:

Sp,,Sp2:

Spm

Spk

152

Level of activity n (number of sprayers),
where n 8 1,33 . . . 35 and 2, 36 . . . 38.

A vector of 1 under bean and sugar beet
production, respectively.

Number of hectares that a field sprayer m can
fulfill during spraying time in a bean field,
where m 8 33 . . . 35 (S,, 82, 83).

Number of hectares that field sprayer k can
perform during spraying time in a sugar beet

Harvesting navy bean operation:

X11113," X39Hr39 ‘ X403440 _<_ 0 (6'19)
where:
Xn : Level of activity n (number of navy bean

Hr,

Hr,“

harvesters), where n 8 1,39,40.

A vector of 1 under navy bean production.
Number of hectares that a bean harvester can
cover during the harvesting time limit, where

Harvesting sugar beet:

--Topping operation:

X21302 ' X41TO4, " X42TO42 _<_ 0 (6.20)
where:
xn : Level of activity n (number of beet top—

T02

Tom

pers), where n 8 2,41,42.
A vector of 1 under sugar beet production.

The number of hectares that a topper m can

153

cover during the harvesting time limit where

m . 41, 42 (9,. 92).

--Lifting operation:

x2L2 ' x431143 ‘ X44L44 5.0 (5'21)
where:
Xn : Level of activity n (number of beet
lifters), where n82, 43, 44.
L2 : A vector of 1 under sugar beet production.
Lm : Number of hectares that lifter m can

perform during the harvesting time limit

where m843, 44 (L1,L2)

Usage of tractor l:

-X9Ta9 +

x15Ta15 1 x18Ta18 1x21T321 1 x24T324

1x27T327 1 x28T328 1 x30Ta30 1 x31Ta31 1 x33Ta33

1X34Ta34 1 x35T335

+X41Ta41

where:
xn

Tag

Tam

1 x36T336 1 x37Ta37 1 x38T338
1 x42Ta42£ 0 (6-22)

Level of activity n (number of implements).
Recommended number of hours for tractor l

to be used for executing field operation

(it was assumed to be 1,000 hrs.).

Number of hours under which each field
operation can be performed by tractor 1

using implement m where m815, 18, 21, 24, 27,
28, 30, 31, 33, 34, 35, 36, 37, 38, 41, 42.
[The number of hours under which a field

operation can be performed was calculated by

154

dividing land area (200 ha was assumed in

this model) by the implement capacity

(ha/hr).]

Usege of tractor 2:

’xlOTalO 1 x12T312 1 xl6Tal6 1 x171‘317 1 x191'319

+x20Ta20

1x291‘329
where:

Xn :

T310 :

Tam :

1 x22T522 1 x23T323 1 x251‘325 1 x26Ta26
1 x32Ta32..<. 0 (6-23)

Level of activity n (number of implements).
Recommended number of hours for tractor 2

to be used for executing field operations
(the number of hours was assumed to be 1,000
hrs.).

The number of hours under which a field
operation can be fulfilled by tractor 2 using
implement m, where m 8 12,16,17,l9,20,2
23,25,26,29 and 32.

Usage of tractor 4:

'X11Ta11

+X44Ta44
where:

Xn :

Tall :

1 x13T313 1 x1411314 1 x43Ta43

5_0 (6-24)

Level of activity n (number of implements).
Recommended number of hours for tractor 4
to be used for executing field operations

(the recommended number of hours was set to

Tam

155

be 1,000 hrs.)
Number of hours under which a field operation
can be accomplished by tractor 4 using imple-

ment m, where m 8 13,14,43,44.

Labor contraints:

 

x12L312

1x17La17
+X22La22

1x271-327
1X32L332
+X37La37
+X42L342
where:

xn

Lam

L347

+

+ + + + + +

x131813 1 x1418114 1 xlsLais 1 x16L316
X18Lal8 1 x1911319 1 x201-320 1 XZlLaZl
x2311323 1 x241-324 1 XzsLazs 1 x26L326
x28L328 1 X291'329 1 x301'330 1 x31La31
x3311333 1 x3411334 1 x3511335 1 x36La36
x38L338 1 x3914339 1 x4011340 1 x411841
X43La43 + X44La44 + X47La47 < 0 (6-25)

Level of activity n (number of implements)
where n812...44 and 47.

Represents the number of hours required to
accomplish a field operaiton for a land size
of 200 ha, where m812...44 (the summary of
the number of hours available for each field
operation are shown in Tables 3-14 and 3-16.
Is a vector of -l which implies the summation
of all the number of hours required for navy
bean and corn production for calculating the

labor cost.

The number of hours required for each implement to

accomplish a field work are presented in Table 6-1.

156

TABLE 6-1
The Land Area that can be Covered by an Inplement During

the Available Workable Days and the Time Required
to Cover 200 Ha

L

 

Inplement Code Nunber of Hectares* Nunber of Hours"
Chisel plow C, 200 135
Chisel plow C2 255 105
Chisel plow C3 270 100
Field cultivator F2 393 66.6
Field cultivator F3 480 55.5
Field cultivator F4 579 43.2
Row planter R, 117 178
Row planter R2 174 91.7
Row planter R3 232 68.7
lbw cultivator V, 200 164
Row cultivator V2 299 109
lbw cultivator . V3 397 82
Sprayer S, 120 274
Sprayer 82 160 200
Sprayer S3 236 135
Beet topper T, 161 285
Beet topper T, 216 213
Beet lifter L, 161 285
Beet lifter IQ 216 213

 

*Nmber of hectares 8 [field capacity of an implement (ha/hr” x
nunber of hours available for field work (hr)]

**Nutber of hours 8 [land size (ha)] 8 [field capacity of an
inplement (ha/hr)]

157

The initial result obtained from this model indicated
that planting sugar beets was more profitable to the farmers
than planting navy beans. However, the number of implements
selected by the model were fractional numbers rather than
intergers which is not feasible. Therefore, some
constraints were added to the model to force the previous
kinds of implements to be in intergers. These constraints
were listed as follows:

Forcing the number_of chiselrplows to be an interger:

 

X12Fr12 + X13Fr13 + x14Fr14 8 1 (6-26)
xlerlz S 1 , (6-27)
X13Fr13 $_l (6-28)
X14Fr14,gl (6-29)
where:
xn : Level of activity n (number of chisel plows).
Frm : A vector of ones for m812, 13, 14. These

vectors of ones were set only under the size
of chisel plow that can cover 200 ha or more
within the time limit to guarantee that the

number of tillage implements was an interger.

Forcing the number of field cultivators to be an integer:

XlaFrls + Xlgprlg + X20Fr20 3 1 (6‘30)
XIBFrIB S 1 (6-31)
X19Fr19 _<_ 1 (6'32)

XzoFrzo _<_ 1 (6-33)

158

where:
xn : Level of activity n (number of field culti-
vators).
Frm : A vector of ones for m8l8, 19, 20.

Forcing the number of rowrplanpers to be an integer:

x26Fr26 ' 1 (6-34)
where:
x25 : Level of activity (number of row planters).

Fr26 : A vector of 1 under only row planter 3 that
can cover 200 ha within the time limit.

Forcing the number of row cnltivatorsyto be integer:

X30Fr30 + X31Fr31 + X32Fr32 (6-35)
X30Fr3o 5,1 (6-36)’
X31Fr31 r 1 (6-37)
x32Fr32 £_l (6-38)
where:
xn : Level of activity n (number of row cultiva-
tors).
Frm : A vector of ones under row cultivators number

1, 2 and 3 because they are capable of
cultivating 200 ha or more within the time
limit.
Forcing the numper of spreyers to be an integer:
x38Fr38 ‘ 1 (6-39)

where:

159

xn : Level of activity n (number of sprayers).
Frm : A vector of 1 under sprayer number 3 which

is capable of harvesting 200 ha within the
time limit.

Forcingthe number ofgtoppers and lifters to be an integer:

x42Fr42 8 1 (6-40)

X44Fr44 8 1 (6-41)
where:
Xn . Level of activity n where n842, 44.
Fr42 : A vector of 1 under topper 2 which can cover
I 200 ha or more within the harvesting time

limit.

Fr44 : A vector of 1 under lifter 2 which can cover

200 ha or more within the harvesting time

limit.

Forcing the number of tractors to be integer:

X9Fr9 8 1 (6-42)
XloFr1o 8 1 (6-43)
xllFrll 8 1 (6—44)
where:
xn : Level of activity n (number of tractors).
Frm : A vector of ones under tractor 1 (T1.. 37.3

kw). and tractor 2 (T2 . . . 59.7 kw) and

tractor 4 (T4 . . . 119.3 kw).

160

6.2 Model Adjustment

 

In the MILP model the tractor usage was assumed to be
1000 hours per year to estimate the annual cost of using
tractor 1, 2, and 4. However, the results obtained from the
navy bean production model indicated that the actual number
of hours for the tractor usage were found as follows:

1. Utility tractor 1 (T, - 37.3 kw) : 648 hours per

year, 300 hours of which were assumed to be used for

nonfarming activities (handling, transportation, turns,

etc.).
2. Tillage tractor 2 (T2 - 59.7 kw) : 307 hours per

year, 100 hours of which were assumed to be for

nonfarming activities (handling, transportation, turns,

etc.).
3. Tillage tractor 4 (T4 - 119.3 kw) : 413 hours per

year, 100 hours of which were assumed to be used for

nonfarming activities.

These actual number of hours for tractor usage were fed
in the machinery cost model by Rotz et al. (1981) to
calculate the total annual cost for using tractor 1, 2, and
4. The results obtained from the machinery cost model are

summarized in Table 6.2.

161

TABLE 6-2

Summary of the Adjusted Annual Cost
of Tractors 1, 2, 3 Over
Ten Year Period

_L.

‘r

 

Inplement Code Ownership Repair 8 Fuel Total Average
Cost Maintenance Present Annual
Value Cost
Utility tractor Ti 8050 5272 26214 39536 4401
Tillage tractor T2 12887 2554 19877 35318 3932

Tillage tractor T3 25748 8202 53436 87386 9728

162

6.3 Model Results

 

The results obtained from the navy bean - sugar beet
production model indicated that under present sugar beet
yield level (50 ton/ha) and market price of (30 $/ton),
producing sugar beets was more beneficial to the farmers. A
farmer could make up to $214,066.00 profit from 200 ha of
land which equals approximately $1,070.00 per ha. The
summary of the navy bean - sugar beet model results are
presented in Table 6-3. These results illustrate the amount
of seed, fertilizer, and herbicides required for sugar beet
planted in 200 ha and represent the kinds and sizes of

implements selected by the model.

6.4 Sensitivity Analysis

 

6.4—l Shadow Prices and Slacks

Shadow price indicates the impact of increasing the
right hand side for a linear programming constraint by one
unit. While the slack variable represents the amount of
unused resource. In the navy bean - sugar beet production
model, the shadow price and slack variables for the avail-
able resources were analyzed by the computer. The results

obtained from these analyses are summarized in Table 6-4.

163

TABLE 6-3

Sumary of the Final Solution of the Navy Bean -
Sugar Beet Production Model

 

Itens Size Final Solution
Land Size 200 ha Sugar Beet
Beet Agronanic Requirements

Seeds 266 kg

Fertilizer 69000 kg

Herbicide 340 kg

Machinery Requirements
Utility tractor
Tillage tractor
Tillage tractor
Chisel plow
Field cultivator
lbw planter
lbw cultivator
Sprayer
Beet topper
Beet topper

Labor Requirements 872 hr

8010:

—I
NNNO‘O‘GUDOQ
O

a a e
mmqochwqw

asaasaa???

dd—i—Dddd—D-J-I

Total beet yield 10000 tonne
'lbtal profit $214066.00
'lbtal net profit per ha 1070.00 S/ha

_ A L __l

164

TABLE 6-4
Sunnary of the Shadow Prices and the Slacks

Obtained from the Navy Bean-Sugar Beet
Production Model

Items Unit Shadow Price Value Slack Value

 

Land $/ha 1233.70
Yield $/tonne 30 . 00
Seed $/kg 45.00
Fertilizer $/iog .41
Herbic ides $/kg 20 . 00
Plowing $/ha 55
Field cultivation ha 379
Sugar beet planting ha 32
lbw cultivation ha 197
Spraying ha 36
Beet topping ha 16
Beet lifting ha 16
Using tractor 1 hr 652
Using tractor 2 hr 793
Using tractor 4 hr 687

Labor $/hr 6.00

165

These results indicate the following:

If the farmer is going to rent one more hectare of
land, he is willing to pay up to $1233.7 per year,
otherwise it is not profitable to pay more than this
value.

If the farmer is going to sell his crop, he is willing
to accept $30 per ton and up.

If the farmer is going to purchase one more kg of sugar
beet seeds, fertilizer, and herbicide, he is willing to
pay up to 45, 0.41, and 20 $/kg, respectively.

By using chisel plow 3 (C3 - 3.4 m), and field
cultivator 4 (F4 - 6.6 m), the farmer will have

excess 55, and 379 hectare of land, respectively.
(Land can be covered in addition to 200 ha of land
assumed by the MILP model.)

By using row planter 3 (R3 - 6.0 m), row cultivator 3
(V3 - 6.0 m), and sprayer 3 (S3 - 2.7 m), the

farmer will have excess 32,197, and 36 hectares of
land, respectively.

By using beet topper 2 (P2 - 2.8 m) and beet lifter 2
(L2 - 2.8 m) for harvesting beets, the farmer will
have excess 16 hectare of land to cover for each

implement.

166

7. By using tractor 1 (T, - 37.3 kw), tractor 2 (T2 -
59.7 kw) and tractor 4 (T4 - 119.3 kw) the farmer
will have excess 652, 793, and 687 hours per year,
respectively to cover 1000 hours of tractor usage per
year.

8. If the farmer is going to use additional employees to
fulfill the field work, he is willing to pay $6.0 per

hour for each employee.

6.4-2 The Cost of Forcing Nonoptimal Activities
into Optimal Solution

The cost of forcing nonoptimal activities into optimal
solution is an economics term used to indicate the impact of
forcing nonoptimal activities into final solution. The
results obtained from the computer analysis indicated the
following:

1. Using chisel plow l (C,--2.4-m) instead of chisel
plow 3 (C3--3.4m) to plow the sugar beet field,
would cost the farmer $1,270.00 per year.

2. Using field cultivator 2 (F2--4.7-m) instead of
field cultivator 4 (F4--6.6m) for tilling the
sugar beet field would increase the total annual

cost by $842.00.

167

3. Using row planter l (R1--3.0m) or row planter 2
(R2--4.5 m) instead of row planter 3 (R3--6.0m)
would increase the total annual cost by $2,003.00
and $1,903.00 respectively.

4. Cultivating the sugar beet field by row cultivator
l (V1--3.0 m) instead of row cultivator 3
(V3--6.0 m) would increase the total annual cost
by $229.00.

5. Applying chemicals by sprayer l (S1--l.4 m) or
sprayer 2 (Sz--l.86 m) instead of sprayer 3
(S3--2.7m) would cost $2,022.00 and
$1,591.00 per year, respectively.

6. Using beet topper l (P1--2.l m) in the sugar beet
harvesting process instead of beet topper 2
(P2--2.8m) would increase the total annual cost
by $3,032.00.

7. Lifting the sugar beet by beet lifter l (L1--2.1
m) instead of beet lifter 2 (L2--2.8m) would cost
the farmer $4,624.00 per year.

It should be noted from these results that forcing an
implement into the final solution would also force the
corresponding tractor (T1, T2, or T4) to be in the
final solution. This would result in some additional cost
attributed to the cost of using a tractor in the total

annual cost of an operation.

168

6.4—3 Range of Optimality

Range of optimality is an economics term used to

indicate the range of values over which the objective

function coefficient for a variable may change without

changing the optimal solution. The results obtained from

the computer analysis indicated the following:

1.

Producing sugar beets instead of navy beans would
still be in the optimal solution as long as the
insecticide and fungicide cost per hectare does not
exceed $400.30.

The optimal solution of the navy bean - sugar beet
production model can be held as long as the price
of sugar beet seeds, fertilizer, and herbicides per
kilogram is less than $363.86, $1.45 and $231.95
respectively.

Using chisel plow 3 (C3--3.4 m) would no longer

be in the optimal solution, if the annual cost of
using this implement exceeds $862.58 per year. In
this case, chisel plow 2 (C2--3.l m) would be the

candidate to replace it.

169

Field cultivator 4 (F4--6.6 m) would still be in
the optimal solution as long as the total annual
cost is less than $906.13. Otherwise, field
cultivator 3 (F3--5.6 m) would be the competitive
implement to replace it.

Using row planter 3 (R3--6.0 m) would still be in
the optimal solution as long as the annual cost for
the planter does not exceed $2,689.00. Otherwise,
row planter 2 (R2--4.5 m) would be the

alternative implement to replace it.

The use of row cultivator 3 (V3--6.0 m) would be
in the optimal solution as long as the annual cost
for the cultivator does not exceed $1,239.12.
Otherwise, row cultivator 2 (V2--4.5 m) would be
the candidate for replacing it.

Using sprayer 3 (S3--2.77 m) would no longer be

in the optimal solution if the annual cost of using
that implement exceeds $2,607.00. In this case,
sprayer 2 (82--l.86 m) would be the competitive
for replacing it.

The use of beet topper 2 (P2--2.8 m) would still
be in the optimal solution as long as the annual
cost does not exceed $3,862.69: if so, beet topper
l (P1--2.1 m) would be the candidate to replace

it.

10.

110'

12.

170

Lifting the sugar beets by lifter 2 (L2--2.8 m)
would still be in the optimal solution as long as
the annual cost does not exceed $8,492.86.
Otherwise, beet lifter l (L1--2.l m) would be the
candidate to replace it.

Using tractor l (T1--37.7-kw), or tractor 2 (59.7
kw), or tractor 4 (T4--ll9.3-kw) in the farming
process depends upon the corresponding equipment
that can be matched with a tractor.

This optimal solution can be held as long as the
sugar beet market price is more than $22.79/tonne.
Otherwise producing navy beans would be more
profitable.

In the consideration of labor, the optimal solution
can be held as long as the wage of labor is

$8.00/hr or less.

171

6.5 Testing Difrerent Percentages of Nayy
geens and Sugar Beet in the Nayy Bean-
SugarfiBeet Eroduction Model

6.5-l A 75 Percent Sugar Beet - 25 Percent Navy Bean
‘ Production Model

In order to study the impact of having a system of 75
percent beets and 25 percent beans (150 ha beets and 50 ha
beans) on the farmer's profit, some changes took place in
the previous navy bean - sugar beet production model. It
was obvious that although the same field operations had to
be accomplished with the same implements for both navy bean
and sugar beet fields, the execution time and the time limit
were different for some of these field operations.
Therefore, constraints number 26-40 were substituted from
the previous model by the following constraints to satisfy
the new condition and to have integer number of implements.

Foroing the sugar beet land size to be 150 ha:

XZFIZ ' 150
where:
x2 : Is a level of activity 1 (planting sugar

beet).

172

 

Fr2 : A vector of 1 under sugar beet production.
Forcing the number of chisel plows to be integer:
x12Fr12 1 x13Fr13 1 x14Fr14 = 1 (6'27)
X12Fr12 3 1 (6-28)
x13Fr13 5,1 (6-29)
x14Fr14 5,1 (6-30)
where:
xn : Level of activity n (number of chisel plows).

Frm

A vector of ones under chisel plow 1,2,3. It
should be noted that these vectors of ones
were set under the size of chisel plow that
could cover 200 ha or more because the
plowing time for both crops was set to be at

the same time of the year.

Forcing the number of field cultivators to be an integer:

 

X15Fr15 + X18Fr18 = 1 (6-31)
where:
xm : Level of activity n (number of field cul-

Frm

tivators).

A vector of ones under field cultivator 2
(F2--4.7 m ). It should be noted that the
same field cultivator (F2--4.7 m) was used

to cultivate the navy bean land and the sugar
beet land because the cultivating time was
different for both crops and F2 was capable
of covering the land size for each crop

within the time limit.

173

Forcinggthe number of row planters to be an integer:

X22Fr22 + X25Fr25 = 1 (6-32)
where:
xn : Level of activity n (number of row planters,
R2).
Frm : A vector of ones under row planter 2 (R2

--4.5 m), which was capable of planting 150
ha of sugar beet and 50 ha of navy bean in
different time with respect to the time limit
for each crop.

Forcing the number of row cultivators‘to be an integer:

X27Fr27 + X30Fr3o 8 1 (6-33)
where:
Xn : Level of activity n (number of row cultiva-
tors, V1).
Frm : A vector of ones under row cultivator l

(V1--3.0 m). This row cultivator existed
under the two columns because of the same
reasons stated above.

Forcing the number of sprayers to be an integer:

x34Fr34 + x37Fr37 8 1 (6-34)
where:

xn : Level of activity n (number of sprayers).

Frm : A vector of ones under sprayer 2 ($2 - 1.86

m).
Forcing the number of harvesters to be an integer:

.x39Fr39 ‘ 1 (6-35)

174

where:
Xn : Level of activity n (number of bean
harvesters, H1).
Frm : A vector of 1 under harvester 1 (81--4.0 m)

Forcing the number of beet topper to be an integer:

 

x415'1’41 ‘ 1 (6-36)
where:
xn : Level of activity n (number of beet

toppers, P1).
Frm : A vector of 1 under beet topper 1 (Pl--
2.1 m). It should be noted that this imple-
ment was capable of executing 150 ha within
the time limit.
Forcing the number of beet lifters to be an integer:

 

X43Fr43 - 1 (6-37)
where:
X“ : Level of activity n (number of beet
lifters).
Frm : A vector of 1 under beet lifter 1 (LI--

2.1 m). It should be noted that this imple-
ment was capable of covering 150 ha within
the time limit.

Forcing tractor 1 and 4 to be an integer:

 

X9Fr9 - 1 (6-38)
xllprll = 1 (6'39)
where:
xn : Level of activity n (number of tractors).

Frm A vector of ones under tractor l (Tl"

37.3 kw) and tractor 4 (T4--119.3 kw).

175
6.5—2 Model Adjustment

It was found from the previous navy bean-sugar beet
model results that the total net profit jumped up 10 percent
after the model had adjusted by involving the actual number
of hours for tractor usage. Therefore, in the following
navy bean-sugar beet production systems, a correction term
of 10 percent will be added to the total net profit for each

system to get more realistic figure about the profit.
6.5-3 Model Results

The results obtained from this model indicated that a
farmer could make up to $183,406.00 per year on 200 ha of
land of which 150 ha was planted with sugar beets and 50 ha
planted with navy beans, which equals approximately $917 per
hectare. The final results of this model were further
improved by eliminating tractor 2 (T2--59.7 kw) and
operating row planter 2 (R2--4.5 m) with tractor 4
(T4--ll9.3 kw) instead. This procedure caused the total
profit to jump up to $194,661.00, which equals approximately
$973 per hectare, Table 6-5 and Figure 6-1 represent the

final results of this model.

176

TABLEG-S

Sumnary of the Final Solution of the
25 Percent Navy Bean - 75 Percent
Sugar Beet Production Model

 

 

Items Size Final Solution
Land 50 ha Navy Bean
Land 150 ha Sugar Beet
Bean Agronanic Requirenents

Seeds 2250 kg

Fertilizer 1350 kg

Herbicide 265 kg
Beet Agronomic Requirements

Seeds 169 kg

Fertilizer 51750 kg

Herbicide 255 kg
Machinery Requirements

Utility tractor 37.3 kw 1

Tillage tractor 119.3 kw 1

Chisel plow 3.1 m 1

Field cultivator 3.8 m 1

lbw planter 4.5 m 1

lbw cultivator 3.0 m 1

Sprayer 1.8 m 1

S.P. conbine 4.0 m 1

Beet topper 2.1 m 1

Beet lifter 2.1 m 1
Labor Requirements 1371- hr
'Ibtal bean yield 130.25 tonne
Total beet yield 7500 tonne
'Ibtal profit $194661.00

Total net profit per ha 973.00 $/ha

177

6.5-4 A 50 percent Sugar Beet - 50 percent Navy Bean

Production Model

In order to study the economic impact of having a farm
with 50 percent beans and 50 percent sugar beet (a land of
100 ha sugar beet and 100 ha navy beans), on the farmer's
profit, some changes took place in the main sugar beet -
navy bean production model. These changes included the
following:

1. Deleting constraints number 26 to 45.

2. Adding instead the following constraints to

. satisfy the new production condition.
Forcing the size of land to be 50_percenteeugar beet and

50_percent navy beans:

xlFrl = 100 ' (6-26)
where:
x1 : Level of activity 1 (land size for navy

bean production).
Frl : A vector of 1 under navy bean production.

Forcing the number of.chisel~plow toebe an integer:

xizFrlz + x135‘1‘13 + x14Fr14 ’ 1 (5'27)
xlerlz ‘5 1 (6-28)
x13Fr13 £_1 (6-29)
x14Fr14l$ 1 (6-30)

where:
xn : Level of activity n (number of chisel plows).
Frm : A vector of ones under chisel plow 1,2 and 3,

which are capable of plowing 200 ha of land
within the plowing time limit.

178

Forcing the number of field cultivators to be an integer:

X15Fr15 4’ X18Fr18 '3 1 (6‘31)
where:
xn : Level of activity n (number of field cul-

Frm

tivators,'F2).

A vector of ones under field cultivator 2
(F2--4.7 m). It should be noted that since
field cultivator 2 (F2--4.7 m) was used to
cultivate both bean land and the sugar beet
land, and the execution time was different,
F2 was capable of covering the land size

for each crOp within the time limit.

Forcing the number of row_planters to be an integer:

321Fr21 + x24Fr24 8 1 (6-32)
where:
xn - Level of activity n (number of row planters,
R1).
Frm : A vector of ones under row planter 1 (R1

--3.0 m). It should be noted that although
the row planter existed under columns 21 and
24, these columns referred to the same row
planter (R1--3.0 m) because the planting
operation was performed at different times

for beans and sugar beets.

179

Forcing the_number gf row egltivators to be an integer:

X27Fr27 + X30Fr3o = 1 (6-33)
where:
xn : Level of activity n (number of row cultiva-
tors, V1).
Frm : A vector of ones under row cultivator l

(V1--3 m). This row cultivator existed
under two columns because of the same rea-
sons stated above.

Forcing the numberegf sprayers t9 be an integer:

X33Fr33 + X36Fr36 = 1 (6-34)
where:

Xn : Level of activity n (number of sprayers, S1).

Frm : A vector of 1 under sprayer l (Sl--l.4 m).

Forcing the number of harvesters t9 be an integer:

x39Fr39 ‘ 1 (6-35)
where:
Xn : Level of activity n (number of harvesters,

HT) 0

Frm : A vector of 1 under harvester l (Bl--4 m).

180

Forcing the number of beet toppersfito befan integer:

x41Fr41 ' 1 (5-36,
where:
Xn : Level of activity n (number of beet toppers,
P1).
Frm : A vector of one under beet topper 1 (Pl--
2.1 m)

Forcing the number of beet lifters to be an integer:

X43Fr43 = 1 - (6'37)
where:
Xn : Level of activity n (number of beet lifters,

L1).
Frm : A vector of 1 under beet lifter l (Ll"
2.1 m).

Forcing the number of tractor l and 4 to be an integer:

X9Fr9 =1 (6'38)
x11Fr11 = 1
where:
xn 3 Level Of activity n (number of tractors,
T1 and T4).
Frm = A vector of 1 under tractor l (Tl--

37.3 kw) and tractor 4 (T4--ll9.3 kw).

181

6.5-5 Model Results

; The results obtained from the 50 percent sugar beet -
50 percent navy bean model indicated that a farmer could
make up to $174,966.00 per year if a land of 100 ha planted
sugar beets and 100 ha planted navy bean, which equals
$875.00 per hectare. The final results of this model are

presented in Table 6-6 and were shown in Figure 6-1.

6.5-6 A 25 Percent Sugar Beet - 75 Percent Navy Bean

Production Model

This system was studied in order to find the economic
impact of having 25 percent sugar beets (50 ha) and 75
percent navy beans (150 ha) on the farmer's profit. The
same technique followed previously in the 75 percent sugar
beet-25 percent navy bean model was also involved in this
new system, but with new considerations required as to the
land size and sprayer size. The following constraints
represent the only changes taken place in the previous

model.

182

TABLE 6-6

Sumnary of the Final Solution of the
50 Percent Navy Bean - 50 Percent
Sugar Beet Production Model

 

Items Size Unit Final Solution
Land 100 ha Navy Bean
Land 100 ha Sugar Beet
Bean Agronanic Requirements

Seeds 4500 kg

Fertilizer 27000 kg

Herbicide 530 kg
Beet Agronomic Requirements

Seeds 113 kg

Fertilizer 34500 kg

Herbicide 170 kg

Machinery Requirements

Utility tractor 37.3 kw 1

Tillage tractor 119.3 kw 1

Chisel plow 3.1 m 1

Field cultivator 3.8 m 1

Row planter 3.0 m 1

lbw cultivator 3.0 m 1

Sprayer 1.4 m 1

S.P. carbine 4.0 m 1

Beet topper 2.1 m 1

Beet lifter 2.1 m 1
Labor Requirements 1492.0 hr
Total bean yield 260.5 tonne
Total beet yield 5000 tonne
'Ibtal profit $174966.00

Total net profit per ha 875.00 S/ha

A

183

Forcing the land size to be 50 haesugar beet and 150 ha

navy beans:

 

X1Fr1 8 150 (6-26)
where:

x, : Level of activity 1 (navy bean production).

Frm : A vector of 1 under navy bean production.

Forcing the number of spreyers to be an integer:

X35Pr35 + X38Fr38 = 1 (6-34)
where:

x“. : Level of activity n (number of sprayers).

Frm : A vector of 1 under sprayer 3 (S3--2.7m) for

spraying sugar beet fields and navy bean

fields.
6.5-7 Model Results

The results obtained from the 25 percent sugar beet -
75 percent navy bean production model indicated that a
farmer could make up to $155,856.00 per year, with land of
50 ha planted sugar beet and 150 ha planted navy bean, which
equals $779.00 per hectare. The final results of this model

are presented in Table 6-7 and were shown in Figure 6-1.

184

TABLE 6-7

Sunnary of the Final Solution of the
75 Percent Navy Bean - 25 Percent
Sugar Beet Production Model

 

Items Size Final Solution
Land 150 ha Navy Bean
Land 50 ha Sugar Beet
Bean Agroncmic Requirements

Seeds log 6750 kg

Fertilizer kg 40500 kg

Herbicide kg 795 kg
Beet Agronomic Requirements

Seeds log 56.5 kg

Fertilizer kg 17250.0 kg

Herbicide leg 85.0 kg
Machinery Requirements

Utility tractor 37.3 kw 1

Tillage tractor 119.3 kw 1

Chisel plow 3.1 m 1

Field cultivator 3.8 m 1

Raw planter 4.5 m 1

Raw cultivator 3.0 m 1

Sprayer 2.7 m 1

S.P. conbine 4.0 m 1

Beet topper 2.1 m 1

Beet lifter 2.1 m 1
Labor Requirements 1306.7 hr
'Ibtal bean yield 390.75 tonne
Total beet yield 2500 tonne
Total profit $155856.00

Total net profit per ha 779.00 $/ha

 

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Samary of the profits under different percentage of

 

Optimal solution (100% beet)

75% sugar beet and 25% navy bean
50% sugarbeetand50% navybean
25% sugarbeetand75% navybean

sugarbeet—navybean.

7 SUMMARY AND CONCLUSIONS

7.1 Summary

With the development of the new high-yielding navy
bean variety (Swan Valley), it was believed that its
productivity could be further improved by using a different
production management system (Kelly et al., 1981).

Two navy bean varieties, Swan Valley (upright), and
Fleetwood (standard), were tested to study the economic
aspects of the conventional navy bean production system
versus the direct harvesting production system. Swan
Valley and Fleetwood varieties were planted in 70 cm and 35
cm rows. Beans planted in wide rows (70 cm) were harvested
directly and conventionally, while beans planted in narrow
rows (35 cm) were havested directly only.

The results obtained during the field experiemental
stage indicated that Swan Valley planted in 70 cm rows and
harvested directly tended to give the best results compared
to other alternative navy bean production systems. These
results might be attributed to the high yield level of Swan
Valley compared to Fleetwood and to the crop lodging
problem in the narrow row systems.

A mixed-integer linear programming technique was used
to find the appropriate decisions as to which variety to

plant (Swan Valley or Fleetwood), what planting system to

186

187

follow (wide rows or narrow rows), which havesting method

to apply (direct or conventional) and which machinery set

to use in the production with consideration of the

following aspects:

1.

The number of suitable hours available for field
work with a .8 probability level was calculated by
using the model of Rotz et al. (1981) about
predicting the number of suitable days available
for field work in Michigan.

The total annual costs of using different types of
implements available in today's market were
calculated depending upon the fixed/variable cost
model by Rotz et a1. (1981).

The power required to match each implement with an
appropriate tractor size was calculated depending
upon the fixed/variable cost model by Rotz et a1.
(1981).

The agronomical requirements for both navy bean
production systems were collected according to the
recommendations given by the same extension
bulletin and the actual application in the navy

bean experiment station in Saginaw.

188

The navy bean production model was developed as a
mixed-integer linear programming formulation with 44
columns and 38 rows. The results obtained from this model
indicated that planting Swan Valley variety in 70 cm row
spacing and applying the direct harvesting method was the
most profitable system that could be followed. A navy bean
producer could make up to $144,604.00 per year profit from
200 ha land which equals $723.00 per hectare.

The amount of navy bean seed, fertilizers, and herbicides
required for a land size of 200 ha was found to be 9000,
54000, and 1060 kilograms, respectively. The results also
indicated the types and sizes of implements involved in the '
previous navy bean production system.

Because of the fluctuation of a crop's market prices,
it was desireable to study the impact of having two mixed
crop systems (navy bean-corn, and navy bean-sugar beet) on
the farmer's profit in Michigan. A mixed-integer linear
programming technique was also involved to find the best
economical crop which could be produced, and the profit
value could be made under different percentages of the
mixed crop system considering the machinery requirements in
each production system.

The navy bean-corn production model was formulated as

a mixed-integer linear programming formulation with 45

189

columns and 39 rows. The navy bean-corn model results
indicated that under the present corn yield level (6037.00
kg/ha) and market price (0.93 $/kg), navy bean production
was more profitable than corn. This optimal solution could
be held as long as the navy bean market price was higher
than $0.2 per kg, and the corn market price was lower than
$0.19 per kg.

The results obtained from planting different
percentages of beans and corn applying different MILP
models indicated the following:

1. By planting 150 ha of beans 50 ha corn (75 percent
beans and 25 percent corn), a navy bean producer
could make $119,662.00 profit which equals
$598.00 per hectare.

2. By planting 100 ha beans and 100 ha corn (50
percent beans and 50 percent corn), navy bean
producers could make up to $91,404.00 per year
which equals $457 per hectare.

3. By planting 50 ha of land of beans and 150 ha of
corn (25 percent beans and 75 percent corn) the
farmer would make only $64,685.00. This profit is
equivalent to $323.00 per hectare.

In considering the navy bean - sugar beet production

system, a mixed-integer linear programming model was

formulated with 47 columns and 45 rows to select the most

190

economical crop to produce, the agronomical requirements to
apply, and the machinery set to use to maximize the total
profit.

The results obtained from the navy bean - sugar beet
production model indicated that under the present sugar
beet yield level (50 ton/ha) and market price of (30
$/tonne), producing sugar beets was more profitable to the
farmers. A farmer could make up to $214,066.00 profit from
200 ha of land which equals $1070.00 per hectare.

The results obtained from planting different
percentages of navy beans and sugar beets applying
different MILP models indicated the following:

1. By planting 150 ha sugar beets and 50 ha navy been

(75 percent sugar beets and 25 percent navy bean),
a profit of $183,406.00 per year could be made
which equals approximately $917.00 per hectare.
The final results of this model were further
improved by eliminating tractor 2 (T2--59.7 kw)
and operating row planter 2 (R2--4.5 m) with
tractor 4 (T4--4.5m) instead. This production
caused the total profit to jump up to $194,661.00
per year which equals $973.00 per hectare.

2. By planting 100 ha of sugar beets and 100 ha of

navy bean (50 percent sugar beet and 50 percent
navy bean), a farmer could make up to $174,966.00

per year which equals $875.00 per hectare.

191

3. By planting 50 ha of sugar beet and 150 ha of navy
beans (25 percent sugar beet and 75 percent navy
beans), a farmer could make up to $155,856.00 per
year, which equals $779.00 per hectare.

Finally, it should be noted that each production

system results included the following outputs:

1. The kind of crop(s) to be planted

2. The amount of seeds required

3. The amount of herbicide required

4. The amount of fertilizer required

5. The types and sizes of farm machinery contributing
in the selected crop production system

6. The total net profit from the system.

7.2 Conclusions

 

According to the results obtained from applying mixed
integer linear programming techniques on the navy bean,
corn, and sugar beet production systems in Michigan, the
following conclusions were drawn:

1. The MILP technique was a useful and successful tool in
farm decision problems because of the following:

a. The MILP model predicted the number and size of

the machinery required for a given farm

condition.

192

The selection of the number and size of machinery
required was carried out according to the time
limit for each field operation, the annual cost of
using each type of implement and the labor cost in
the best possible way to maximize the farmer's
profit.

The MILP model provided a good estimate of seeds,
fertilizers, herbicides, machinery, and labor
costs, and the total annual profit of a crop

production system.

The sensitivity analysis resulting from applying the

MILP models were extremely useful because of the

following:

a.

The sensitivity analysis indicated information
about the amount of unused resources (slacks) and
the price the farmer is willing to pay for each
additional unit of resource (shadow prices).

The sensitivity analysis provided information
about the economic impact of forcing nonoptimal
activities into the solution.

The sensitivity analysis also indicated the range
of values over which the objective function
coefficient for a variable may change without

changing the optimal solution.

193

7.2-1 Scope and Limitations

Some limitations were encountered during the study

which can be presented as follow:

1.

Data collected about yield of navy bean varieties
(Swan Valley and Fleetwood) applying different
production systems were not sufficient to build up
an accurate decision about these varieties. Some
figures were collected over a three-year period or
two-year period, while others were collected over
only a one-year period.

Because of poor weather conditions, resulting from
excess rainfall during the 1981 harvest season,
data collected did not reflect the expectations of
these varieties.

The impact of having different crop rotation
systems were not taken into consideration because
of insufficient data.

One type of soil (medium textured) was taken into
condition in the MILP models because of
insufficient data and the limited capacity of the
Harch and Black linear programming package

(1975).

The Rotz et al. model (1981) about calculating the
annual cost of using different farm machinery did
not include all types of machinery so that some
hand calculations were made to estimate the annual

costs of using this machinery.

194

7.2-2 Future Research Needs

The author believes that further attention and field

research is needed in the following areas:

1.

Since very little is known about navy bean varieties
(Swan Valley and Fleetwood) applying different
management systems, more agronomic study is needed on
these two varieties covering different row spacing
width applying direct and conventional harvest

method.

Other alternative tillage systems should be tested
with these varieties to see their economic impact on
the farmer's profit.

Different crop rotation systems which include the new
varieties with different production systems need to be
considered in future studies.

The MILP models need to be modified to be operable in
a microcomputer to make the use of this model easier.
The Harsh and Black package (1975) for the linear
programming needs to be modified to handle more
capacities of matrixes.

More machinery management data is required in the area
of fuel consumption, draft, speeds, slippage, under

various soil types and tillage systems.

REFERENCES

REFERENCES

Anderson, D.: Sweeney, D.: and Williams, T. (1982). An
introduction to management science. Third edition.
University of Cincinnati.

 

Bolen, J.S. and McColly, H.F. (1969). A Rotary Cutting
Mechanism for the Direct Harvest of Dry Beans. Trans.
of the ASAE, 12(6): 862-865.

 

Danok, Abdulla: McCarl, Bruce; and White, T. Kelley.
(1978). Machinery Selection and Crop Planning on a
State Farm in Iraq. Amer.ej. Agr. Econ., 544-549.

 

Endmann, M.H. et al. (1965). Field Bean Production in
Michigan. Extension Bulletin 513, Farm Science
Series, Cooperative Extension Service, Michigan State
University, East Lansing.

Graeme, R.: Quick, Wesley F., and Buchele. (1974).
Reducing Combine Gathering Losses in Soybeans.
Transactions of the ASAE, 1123-1126.

 

Gunkel, Wesley W. (1964). Direct Combine Harvesting of
Dry Beans. Proceeding of the 7th Research Conference
on Dry Beans, December 2-4, Ithaca and Geneva, New
York.

Gunkel, W.W. and Anstee, L.L. (1962). Direct Harvesting
of Dry Beans, Agricultural Engineering, 43: 6949697,
716. '

 

Gunkel, W.W. and Anstee, L.L. (1965). Bean Harvesting
Attachment, U.S. Patent 3, 168, 145.

Hillier and Lieberman. (1980). Intreduction to Operation
Research. Third edition. Stanford University.

 

Kelly, J.; Burkardt, T.: Verner, 6.: Adams: and Srivestava,
A. (1982). Comparison of Dry Bean Harvesting Method.
Annual Report on Bean Research, Michigan State
University, East Lansing.

Krutz, G.W.: Combs, R.F.: Parson, S.D. (1980). Equipment
Analysis with Farm Management Models. Transactions of
the ASAE, 25-28. 7

Link, David A. (1967). Activity Network Techniques
Applied to a Farm Machinery Selection Problem.
Transactions of the ASAE Paper No. 1993.

 

McColly, H.F. (1958). Harvesting Edible Beans in Michigan.
Trans. of the ASAE, 1(1): 68-71, 75.

 

195

196

McColly, H.F. and White, R.G. (1964). Harvesting Edible
Beans in Michigan. Agricultural Engineering
Department Information Series, AEIS #130, Michigan
State University, East Lansing.

Muhtar, H. (1982). Machinery Selection Model.
Dissertation for the degree of Ph.D., Michigan State
University, East Lansing.

Nave, W.R. and Cooper, R.L. (1974). Effect of Plant
Population and Row Width on Soybean Yield and
Harvesting Loss. Transactions of theeASAE, 801-803.

 

Pickett, L.K. (1971). Direct Harvesting of Edible Beans.
Saginaw Valley Bean and Beet Research Farm 1971
Research Report, p. 61-69. Michigan State University,
East Lansing.

Pickett, Leroy K. (1972). Direct Harvesting of Edible
Beans. Saginaw Valley Bean and Beet Research Farm
1972 Research Report, p. 58-61. Michigan State
University, East Lansing.

Pickett, Leroy K. (1983). Mechanical Damage and
Processing Loss During Navy Bean Harvesting.
Transaction of the ASAE, 1047-1050. 1.

Rosenberg, S.E.: Rotz, C.A.: Balck, J.K.; and Muhtar, H.
(1981). Prediction of Suitable Days for Field Work.
ASAE Paper No. 82-1032.

Rotz, C.A.: Black, J..: Savoi, P. (1981). Machinery Cost
Model Which Deals with Inflation. ASAE Paper No.
81-15180

Singh, B. and Linville, D.E. (1974). Determining the
Effect of Pod and Grain Moisture Content on Threshing
Loss and Damage of Navy Beans. Traneactions of the
ASAE, 226-227.

 

Singh, B. and Linvill, D.E. (1977). Field Drying of Navy
Beans in the Harvesting Period. Transactions of the
ASAE, 228-2310 I

 

Singh, Devindar: Burkhardt, T.H.: Holtman, J.B.: Connor,
L.J.: Robertson, L.S. (1979). Field Machinery
~ Requirements as Influenced by Crop Rotation and
Tillage Practices. Transaction of the ASAE, 702-709.

 

197

Singh, Devindar and Holtman, J.B. (1979). An Heuristic
Agricultural Field Machinery Selection Algorithm for
Multicrop Farms. Transactions of the ASAE, 763-770.

 

Wolak, F. (1981). Development of a field machinery
selection model. Dissertation for the degree of
Ph.D., Michigan State University, East Lansing.

APPENDIX A

Mixed Integer Linear Programming Models

For Solving Navy Bean Production Systems in Michigan

Mixed Integer Linear Programming Models

This appendix includes 18 mathematical models. Each one of

these models contains the following information:

1. Objective function - which occupies the first line in
an MILP matrix form. This function was set to be
maximized. It should be noted that each value in the
objective function represents the annual cost of using
one unit of an activity.

2. Resources - which are presented on the left side of a
matrix form to indicate the limited resources need to
be allocted among the competing activities.

3. Amount of resource variable - are presented on the
right side of a matrix form.

4. The amount of resource consumed by each unit of the
corresponding activity represented by values occupy

the main body of an MILP matrix form.

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APPENDIX B

The Computer Results of the Mixed Integer Linear

Programming Models

The Computer Results of the MILP Models

This appendix includes the computer results of the

mixed integer linear programming models. Each computer

output contains the following information:

1.

The objective function - which represent the total
profit S/year can be made from 200 ha of land.
Activities in solution — which represent the kind of
crOp to be planted, size of land, agronomic
requirements (seeds, fertilizer, herbicides), the size
and the number of machines to be used in the
production system and the number of hours required to
accomplish the field activities.

Shadow prices - which represent the value of one
additional unit of the resource associated with linear
programming.

Slacks - which represent'the amount of unused
resources.

The cost of forcing nonoptimal ativities into optimal
solution.

Range of optimality - which represent the range of
values over which the objective function coefficient
for a variable may change without changing the optimal

solution.

B-2
The Optimal Solution of the Navy Bean Production Model

(

OPTIMAL SDLL‘TION

OBJECTIVE FUNCTICI-i

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SCLUTION HOLDS

PRICE RANGE OVER UHICH OPTIFAL

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The Optimal Solution of Navy Bean - Corn Production Model

OBJECTIVE FUNCTICN

n.
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2

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The Optimal Solution of 75 Percent Navy Bean - 25 Percent Corn

Produotion Model

SSLVE

Po
OPTIMAL SOLUT

START Lo

3:)

(

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OBJECTIVE FUNCTION

4.
C.

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APPENDIX C

Linear Programming Package by Harsh and Black (1975)

Linear Program Package

A linear programming package designed by Harsh and
Black (1975) was used to solve the MILP models. In order
to use this package one needs to provide the following
requirements:

1. Matrix size (number of rows and columns)
2. Coefficient information

3. Row information

4. Objective values

This package was adopted because it can handle modest
size of linear programming where the objective is to
maximize subject to series of constraints.

In the MILP models, some constraints were added to
force number of activities to be integer rather than

functional number so that the LP package can handle it.

 

‘ Staff Paper.No. 75-10

AGRICULTURAL ECONOMICS LINEAR PROGRAM PACKAGE
VERSION 2 -- APRIL 1975

BY

- Stephen B. Harsh And J. Roy Black
Iichigan State University

INTRODUCTION

.A linear programming package designed to handle modest-sized linear
programming problems. ’The package will execute on a CDC-6500 computer.
It is a particularly useful package for teaching and some research prob-
lems because it is relatively simple to utilize from a user's viewpoint.

The.objective of the package is to handle linear programming prob-
lems of the following nature.

. Maximize: n .
‘ (1) ‘z--.-' cx
. - . 3.1- .13
Subject To: n
(2) 1: a g... or 1
. .J-l 1’ :03 ,

Where: -
.- i - l,2,...,m and
J - 1,2,...,n

To minimize Z, multiply cJ's by -1.

The package requires that cj's a1 '3, and b1' 8 be inputted. Slack
and artificial variables are automatica ly added.

 

PACKAGE DESCRIPTION

222229.15: , _

Tb use the linear programming package, the user will have to supply
the standard computer control cards (e.g., PNC, job card, password card,
etc.) which will be followed by the data deck for the package. The
-deck is as follows: , .

CARD 1: Name and Job Description.

A

A - Alpha-numeric description of the linear programming problem
(60 characters maximum)

‘

. CARD 2:. Options Used.

.llegrlcrlfi;lgflpd

Ihen A is equal to: '
O - No print; 1 - Print activities in solution.
[hen B is equal to: ‘ ' A
O 8 No print; 1 - Print shadow prices and slack values.
'hen C is equal to: - -
' O I No print; 1 - Print cost of forcing in nonoptimal activitie
ihen D is equal to: '
O - No.print; 1 - Print initial LP matrix for verification
purposes. '
Ihen E is equal to:
0 9 No print; 1 - Print price ranges.
Ihen P (save and restore matrix option) is equal to:
O - Neither save nor restore matrix; 1 - Save matrix from

this analysis for adjustments in next analysis; 2 - Restore
matrix from previous analysis for adjustments in this analysis;
3 I Both save matrix from this analysis for adjustments in
next analysis and restore matrix from previous analysis for
adjustments in this analysis.

CARD 3: Matrix Size Card.

l-g-l-g-l

fl - Number of rows
N - Number of columns

 

cum 4 To CARD F-l: Coefficient Information.
IT'I"""J""‘"

I I Row number (integer value)

J I Column number (integer value)

A13 I Coefficient for row I and column J. (Decimal value.
Decimal must be punched.) '

NOTE: Only need to enter nonzero A13 information.

‘ CARD F: End of Coefficient Information.
(Blank Card)

CARD F+l To G-l: Row Information.

.l" I 'T ' El-"’""" "' E"; - -\"' " -|

I I Row number (integer value)
R I Restriction type (integer value)

 

Restriction
Code Type
1 . (LE) i
2 - (EQ):-
3 (GB) 1

Bi.I Bight-hand side value for row I. (Decimal value..
Decimal must be punched.)

NOTE: A card is used for each row.

CARD 6: End of Row Information.
(Blank Card)

CARD G+1 To H-l: Objective Values.

l-“J'fl ----- era ------ I

J I Column number (integer value)
Cj I Objective value for column J. (Decimal value.
Decimal must be punched.)

NOTE: Only need to enter nonzero C3 information.

CARD B: End of Objective Values Information.

(Blank Card)

CARD 8+1: Next Analysis Name and Job Description.

F-_-,-I-----;....'

A I Alpha-numeric description of linear programming problem.

If STOP is coded in columns 1-4 of card, this will terminate
operation of package. If not; code rest of deck for next
analysis as for previous analysis starting with Card 2.

ERROR INFORMATION

The package checks for several input errors. 'hen one is found,
it generally indicates the card at which the error occurs and nature
of the error. The analysis is terminated when one is found.

. Errors particularly common are indicating row or column values
greater than matrix size or a wrong restriction type.

OUTPUT OF ANALYSIS

The output of the package includes the following:

(1)

C2)

(3)

List of data inputted.

a) ‘ij

'b) b1 and restriction type

c) c;

Type of solution.

a) Solution exists
b) System is inconsistent
c) System is unbounded

If a optimal solution exists, the following information is
printed:

a) Value of objective function
h) ’Activities in the optimal solution

c)
d)

8)

Values of the restrictions

Cost of forcing the nonbasis activities into the
optimal solution .

Price range over which the optimal solution held

000000

303
65

66

R6

100

PROGRAM LPCOMR (INPUTeOUTPUTI
LINEAR PROGRAM WRITTEN BY STEVE HARSH AND ROY BLACKODEPTe
OF AGR. ECON. MICHIGAN STATE UNIVERSITYoEAST LANSINGoMIo
VIAoTHE BIG M-METHOD-SUBROUTINE RONSET SETS UP THE SLACK.
SURPLUS AND ARTIFICIAL VARIABLES INCLUDING ATTACHING THE
APPROPRIATE PRICESoSUBROUTINE LPSOL IS THE SIMPLES ALGORITHM
ORIGINAL SIMPLEX METHOD USEDoARTIFICIAL VARIABLES HANDLED
COMMON/ IDPM(600180)9RHS(60)oINACT¢6OIOISACOLtaoIOIRWTY(6019

1 OSJIIBC)02C¢1SO) ‘
DIMENSION-ACTIIBOIQPERSONlbI—

DIMENSION JRPLIIBOIOJRPUIIBO)oOBJLIIBOIOOBJUIIBO)

FORMATI/I

READ-GSQJPERSONLIlctsl96.13.4—

FORMATI6A495X0III

IFIJeGTeOIGO To IRS

PRINT 669IPERSONII301819603)

FORMATIIHIOIXo///o| LINEAR PROGRAMMING ANALYSIS FOR '06A40/l/l’

DO 80 IsIOGO '

RPSIIIIOr

IRWTY¢1380

INACTCIIcO

ISACOLCIIIO

DO 82 JIIOISO

DPWIIOJ)IOO

CONTINUE

DO 84 JIIOISO

JRPUIJIsO

OBJLIJIIOO

JRPLCJIIO

OEJUIJIa9000OOOo

ACTIJ)sOe

OEJ‘JIIOe

ZCIJ)IOQ

READ»AOIORTIotOPTzoIOPTSOIOPTAOIOPTS

FORMATIGIII

READ SONOROWONOCOL

FORMATC2I3I

SUMIO

ICARDIO

READ 6OIJJOX.

FORMATI2I30F1704)

ICARDIICARD+I

IFIXeEOeOeOOANOOIOEOOOOANOOJOEOOOIGO To IIO

IFIIoLTeIeOReIoGToNOROUI CALL ERRIIaICARDoSUM)

IFIJoLTeIoOReJoGToNOCOL) CALL ERRIIOICARDOSUMI

110
1:2

:90

191

130

AR

1:5

141

IRI

15%

160

4o

60

DPWIIOJ38X

GO TO IOO

JCOLINOCOL

PEAD-ToIoIRHSTYORHSV

FORMATIIJOIIOFISOSI

ICARDIICARD+I

IIII+IRHSTY+RHSV

IFIIIoEOaOIGO TO I20
IFIIoLTeIeORoIoGToNOROWI CALL ERRI20ICARD0VUM)
CALL ROUSETIIOJCDLOIRHSTYORHSVOICARDQSUM)
GO TO IIZ

READ 9OJOX

.FORMATIISOFIGeBLw

IFIX eEOeOeOOANDOJeEOOOIGO TO I30
ICAROIICAPD+I

IPIJOLTeIeOReJeGTeNOCOLI CALL ERRISOICARDOSUMI
OBJIJIIX

GO TO I20

IFISUMOEOeOoOIGO-TO I25

PRINT 48

FORMATIJIH PROGRAM.TERMINATEDvFAULTY DATA)
GO TO 1R5"

IFIIOPTAoEOoOIGO TO I‘I

PRINT I

CALL LPDUMPINOROWONOCOLI

CALL LPSCLCNOROWOJCOLOIOPTSOISOLTYONOITERvOBJVI
IFIISOLTYOGTQOIGO TO I95

DO I60 IsIONOPOW

DO 165 JIIOJCOL

IFIINACTIIIeNEeJIGO TO I65

ACTIJIIRHSIII

GO TO 160

CONTINUE

CONTINUE

truoenmowmo TO 1'73

PRINT 49

FORMATIITH OPTIMAL SOLUTION)

PRINT I .

FORMATIZOH OBJECTIVE FUNCTIONIOZXOFISOAI
PRINT 60oOBJV

PRINT I

DO ITO JIIONOCOL

IFIACTIJIOEOaOIGO TD ITO

FORMAT(9H ACTIVITYOZXOISOZXOSH ISQFI504)
PRINT SOOJOACTIJI

I7U‘Cunrnwv:

I75 IPIIOPTZeEOeOI GO TO I85
PRINT I
PRINT I
PRINT 52

R2 FORMATIBSH SHADOW PRICESOSURPLUSESQAND SLACKSI
OO'IBO-IIIONOROW»

JIISACOLIII

IFIIRUTYIII eEOe 3IJIJ+I

PRINT SAOIOZCIISACOLIIIIOACTIJI
R4 FORMATIAH RONQZXOIAOZXOGH PRICEOZXoFISvoZXQTH EXCESSOZXQFlSoAI
IRO CONTINUE

IRS IFIICPTSOEOeOIGO—TO-I97
PRINT I
PRINT I
PRINT 56-

RG FORMATIAIH COST OF FORCING.IN NONOPTIMAL ACTIVITIES)
DO I90 JDIONOCOL
IFIZCIJIOEOeOQOIGO TO-I90»
PRINT SBOJOZCIJI

n8 FORMATI9H ACTIVITYOZXOI303H ISQFISoAI

100 CONTINUE
PRINT I'

PRINT I

I07 IFIIOPTSeEOoOIGO‘TO I95
00 70 IIIONOROU
213.90000000
KIIO'

22' 90000000

K230

DO TZ'JIIOJCOL

IFIDPMIIOJI CEO. OeOIGO TO 72
XcZCIJI/DPMIIOJ)
IFIXI’AOTZOTG

7a IF¢XoLEoZlIGO TO 72
KIIJ
ZIQX
GO TO 72-

76 IFIXOGEOZZIGO TO 72
KZIJ
221!"

72 CONTINUE
JRPLIINACT‘IIIIKZ'
OBJLIINACTIIIIIOBJIINACTIIII-ZZ
JRPUIINACTIIIIIKI

'70

«9'

soc
cos
as
R7
:6

106

In:

C-lO

OBJUIINACTIIIIIOBJIINACTIIII-ZI'

CONTINUE

PRINT 59 ‘

FORMATIGGH-PRICE RANGE OVER WHICH OPTIMAL SOLUTION HOLDS)
PRINT I

FORMATIZOXOIZH LOWER BOUNDOIOXOIZH UPPER BOUNDI

PRINT 600

FORMATI I9XQ9H ACTIVITYOEXOGH PRICEOSXO9H ACTIVITYOSXOGH PRICE)
PRINT 605

FORMATI9H ACTIVITYOZXOI4OZX0I402X0FI50492X9I40F150GI

DO 86 JBIONOCOL

IEIZCIJII 86087.86

PRINT BSVJOJRPLIJI*OBJLIJIFJRPUIJIOOBJUIJI“

CONTINUE

CONTINUE

GO TO 300‘

STOP

END

10
r2
14
:5

SUBRO
UTI
SUM,SUM+NE ERRII
Go To‘ ‘ TYPEOICAR
ppzNT :320304I0ITYPE U.SUM,
RETURN OICARD“
PRINT
I
:5 N 20ICARD
INT
1e
:5 N oICARD
INT I50 ICARD

:ETURN
RMATI
40H I
NPUT
ERROR
0C
OEFEICIENT MAT
RIXO
AT CA
RDOZX
OISI

FORMA NPU
T(3
FORMA ‘H‘t
TI3 T
p 3H NPU ERR
ORMATI3ZH ILLET ERR32:3HS VECTOR
GAL RES BJ FUNCT OAT CARD
TRICTION T$°~.AT CA;2xr‘5r
FE AT DOZX
. OISI
ROW ZXOIS
I

END“

 

C-IZ

SUBRCUTINE LPSOLINOROWQNOCOLOIOPTSOISOLTYoNOITERcoaJV)
COMMON/ IDPMIGOOIBOIORHSISOIoINACTISOIoISACOLIéoIOIRWTYISOIo
1 OBJ(180IOZCI180)
DIMENSION-COLKEYIGOI
ISOLTY81
PRINT 2I16 -
BI 16 FORMATI 1X0 'START Lo Po SOLVE H
Norfshs-x
200 NOITERINOITER-I-I
JZCMXaO
ZCMXSO.
DO IOI JIIONOCOLvI
2800
DO 102 IIIONOROUOI
KaINACTII}
I02 ZaZ+IDPMIIOJIIOBJIKII
2090 FORMATIIERROR CHECK*I
ZCIJIIZIOBJIJI
IFIZCIJIIIOBOIOIOIOI
103 IFIZCIJIIZCMX)10401019101
1A4 ZCMXsZCIJI
' JZCNXsJ
IO! CONTINUE
IFIJZCNX eGTe OIGO TO IIO
IFINOITEROGTaOIGO TO IIZ
PRINT :0 ‘
IO‘FORNATCSH CHECKI
RETURN
I12 Xa-I9*IIO’*SII
DO IIS IIICNOROUOI
JIINACTIII , .
IFIRHSIIIOEOeOoOI GO TO IIA
IFIOBJIJI eEOa XIGO TO 600
I14 IFIIRUTYIIIeEOeIIGO TO IIS
JsISACOLIII
ZCIJIIZCIJI+X
115 CONTINUE
OBJVaOe
DO IZO'IIIQNOROUOI
KSINACTIII
190 OBJVaoeJVIIRHSIII*OBJIKII
ISOLTYSO-
RETURN
600 PRINT 60

I13‘

I“!

I“

1C6

16¢

30»

1:“

IO
16°
I71

170

I76
I75

c-13.

FORMATIBZH'THERE ARE NO FEASIBLE SOLUTIONS)
RETURN

IFINOITEReLToMXITERIGO TO I13

PRINT ZO’

FORMATIZBH NO ITERATIONS EQUAL MAXIMUM)
RETURN

RMIN89OOOOOOOOO

NKRIO

DO ISO IsIoNOROUoI
IFIDPMIIoJZCMXIIISOOISOeISI
ReQHSCIIIDPMCIoJZCMX)
IPIR-RMINIISSOIS6OISO

RMINIR

NKRII

GO TO I50

DO”I60‘JIIONOCOLOI
RIIDPMINKROJIIDPMINKROJZCMXI
stDPMCIoJIIDPMIIOJZCMXI
IFIR2-RIII550I6°OISO‘

CONTINUE

PRINT SOONKRQI

FORMATIZAH-CYCLING HAS OCCURED ATQZXOIAQZXQIBI'
RETURN

CONTINUE

IFINKROGEoIIGO TO I69

PRINT SOOJZCMX

FORMATIZBH UNBOUNDED SOLUTION.ACTIVITY.2X¢I5)
RETURN

INACTINKRIIJZCMX

DO 171 IIIoNOPOWOI
COLKEYIIIIDPMIIOJZCMXI

DO ITO JIIONOCOLOI
DPMINKROJIsDPMCNKRoJI/COLKEYINKRI
RHSINKRIIRHSINKRI/COLKEYINKRI

DO I75 IIIONOROVOI

IFII 0E0. NKRIGO TO 175
RHSCIIIRHSIIIIIRHSINKRI*COLKEYIIII
IFICOLKEYIII aEOe OIGO TO I75

00 I76 JIIONOCOLOI

IFIDPMINKRVUI eEOe OIGO-TO I76
DPMItoJ320PMIIoJl-(DPMINKROJI*COLKEYIIII
CONTINUE

CONTINUE

GO TO 200

END

C-14’

SUSROUTINE ROVSET¢IoJCOLoIRHSTYoRHSVoICARDcSUM)
COMMON/ /OPM(60¢!80).RH$(60).INACTCSO)oISACOLCGO)oIRWTY¢60)c
I OSJCISOIOZCIISO)

JCOLIJCCL+I

INACT(I)aJCOL

ISACOLCI)IJCOL

IQVTYCI)§IRHSTY

RHStt)aRHSv
IFIIRWTYIIIOLTeIeOReIRUTYIIIeGTIBICALL ERRCZolCAROoSUM)
IF!RHS¢I)-LT.0.0I CALL ERRCZvICARDoSUM)
OPVCIOJCOLIII

IFIIRUTYCI) OCT. 1360 TO 202

OB’JIJCOL I'o‘e

GO TO 140

202 OBJIJCOLII-¢9*¢10**SII

IFIIRWTYttloEOoZIGO-TO'IIO“

JCOLIJCCL+I

OPMCIOJCOLII-I

, OBJIJCOLI'Oe
IaO RETURN
END

IDA CARDS LISTED ON 14 PAGES

APPENDIX D

Machinery Cost Computer Program by Rotz (1981)

Machinery Cost Computer Program

This model was used to estimate the total annual cost
of using the required implements in a crop production
system. The input data required to execute the program
varies depending upon the type of machine to be analyzed.
These data include machine purchase price, age (row
indicated new machine), power (in kw for tractor and
combine usage), width (in m for implements), fuel type (1 =
diesel, 2 I gasoline, 3 = petroleum gas, for tractor and
combine usage), and speed (km/hr for implements).

The computer output of Rotz model provides the
following information:

1. Ownership cost
. Repair and maintenance

Fuel

Total present value

U‘ b w N
e

. Average annual cost

MACHINERY COST COMPUTER PROGRAM

C. Alan Rotz

October, 1981

'The machinery cost program computes the total costs of own-
ing and operating farm machines, tractors and trucks. It
includes the cost of capital, interest, insurance, shelter,
repairs, maintenance, fuel, lubrication and labor. Infla-
tion is modeled for all costs with a separate rate used on
Inachinery, fuel and labor. Income tax deductions are modeled
.to include depreciation, interest, and operating costs along
‘with an investment credit of in percent of the initial
machine cost. Tax deductions are subtracted from the sum of
all other costs to give a total cost. This cost is given as
a total present value cost and as an equivalent annual cost.

Data Required bngrogram

When provided the appropriate input data, the machinery cost
program can be used to analyze the costs of farm machines,
tractors or automobiles. It can also be used to analyze the
costs of 'several machines or a full crop production sub-
system when supplied with data for all required machines.
Input data required by the program includes:

Machine Numeric code shown in table below. Entry

Type- of 15 branches of the program to read
your own repair and depreciation factors.
Entry less than 15 allows use of stored

factors.
Machine Age of machine in years. Zero indicates a
Age- new machine.

Wage Rate- Hourly charge for operator labor.

New Price— Dollar cost of the machine purchased new.

Power Rated power of tractor (PTO kilowatt)
Rating-

Annual Tractors - Average Annual use in hours.
Use- -. Machines - Average Annual use in hectares.

Fuel type- I. I Diesel 2. I Gasoline 3. I Liquid
Petroleum Gas.

Fuel Price per liter (decimal entered).
Price-

Machine Operating width of machine (meter).
Width- '

Machine Operating speed of machine in the field
Speed- (kilometer per hour).

Hours per Requested for automotive only. Average operation
year- of vehicle in hours per year.

Kilometer Requested for automotive only. Average fuel
per liter-_ consumption.

Information Assumed by Program

Some parameters for the cost analysis are set internally by
the program. , These parameters include income tax informa-
tion, inflation rates and loan information. The program
assumes an income tax rate of 25 percent. All machines are

depreciated for tax purposes over 5 years using the 1981,
Accelerated Cost Recovery System.

Three inflation rates are used to model a separate inflation
on machinery, fuel and labor. Machinery costs are inflated
.at the rate of 11 percent per year. Fuel inflation is set
at as percent per year while labor is set at 9 percent per
year.

The program converts all future costs to present value based
upon a discount rate. This discount rate is set at 12 per-
cent per year.

All machines are considered to be purchased with a loan with
a 20 percent down payment. The term of the loan is set at 5 ‘
years with an interest rate of 12 percent per year.

Additional information is assumed for the field efficiency,
repair factors and remaining value factors. These values
were set to appropriate values based upon informationn found
in popular text books on farm machinery management.

Impl ement Type B RC1 RC2 Rv1
Automotive 1 --- .055 1.8 .80
'Tractor 2 --- .025 1.6 .75
Combine, Sp. Eq 3 .70 .140 1.8 '.75
Moldboard Plow 4 .85 .610 1.3 .7!
Disk Harrow 5 .80 .230 1.8 .70
Chisel Implements 6 .80 .230 1.8 .70
Row Planter 7 .65 .670 1.6 .70
Drill 8. .60 .210 1.6 .70
Sprayer 9 .60 .710 1.4 .70
Howet- 1.. 085 0410 103 070
Conditioner '” '
‘Rotary mower- ll .85 .260 1.6 .70
Conditioner
Forage Equipment 12 .70 .330 1.3 .70
Wagon 13 --- .300 1.6 .70
Blower 14 --- .240 1.3 .70

Use of Program .

The machinery cost program is stored in a permanent file in
the Cyber 750. It is in compiled form for economical access
and use in a permanent file name ROTZMACHCOST. It can be
used by attaching a work file to the permanent file and exe-
cuting the work file. An example job is shown below.

for Interactive Use For Batch Use

(Log in) (PW card)
CONNECT, INPUT, OUTPUT. (Job card)
PROMPTION. (PW card)
ATTACH,W,ROTZMACHCOST. ATTACH,W,ROTZMACHCOST.
w. W.

. 7/8/9

(data cards) (deta cards)

99.. ' srep
(309 OUPI 6/7/8/9

Data'cards for the program can be given in any format, how-
ever, the numbers on the cards must be in proper order. The
proper order is dependent on the type of machine analyzed as
given below. Two data cards are required for each machine
analyzed unless the machine is purchased used. For a used
machine a third data card is needed to give the purchase
price and use on the machine.

RVZ

.84
.87
.88
.90
.90
.90
.90
.90
.90
.90

.90
.90

.90
.90

Form for Input Data

The input data required to execute the program varies
depending upon the type of machine to be analyzed. There
are three major forms for the data to model the costs of
either a tractor, farm machine, or truck. These data forms
are listed below.

raucx on AUTOMOBILE (Type 1)

(1) Machine code, Name
(2) New'cost, Age, km/yr, km/liter, Insurance cost
(3, If used) Purchase price, kilometers on vehicle

TRACTOR OR SELF-PROPELLED MACHINE (Typc.2 or 3)
(1) Machine code, Name

(2) New cost, Age, Power, Annual use, Fuel type
(3, If used) Purchase price, Hours on machine

INPLEMENTS ('1'ch 4 tOIS)

(1) Machine code, Name
(2) New cost, Age, Annual use, Width, Speed
(3, If used) Purchase price, Hours on machine

CHANGE OF PARAMETERS

Data can also be used to change parameters which have been
set internal in the program. Parameters can be changed by
using code 90. or 95. as shown.

90. DATA Fuel price, wage rate, Work time ratio, Insurance
& shelter rate, Income tax rate, Print level.

95. DATA Down payment, Interest rate, Discount rate,
Machine Inflation, Labor Inflation

END OF DATA
Date is required to specify the end of a system of machines

by assigning a code of 0. and a code of 99. should be
specified at the end of all systems. '

eeeeeeeeeeeeeeeeaeaeeeeeeeqeaeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaeeeeeeeeeee
e
HACHINERY COST PROGRAM
C. ALAN ROTZ
OIISIOI

R
D.R.!RI...IRIRRRIROARRIRRIRIIRRIRRIRRRRIIiiIRRRRRRRRRRIRIRRIRIRIRIIRRIIR

PROGRAM SYSECON¢INPUT,OUTPUT,TAPESIINPUT.TAPEA-OUTPUT)

CDHflON INECI NN.DPAY.IR.A,G.E,C,PP.UAGE.UTINE,TISR,TRI,PRNT
REAL TOWN<200),TREP(ZOO).TPUEL(200).TLAE(ZOO)oAC(ZOO),PVC(ZOO)
0.2(200).IR '

l

5 TPVC-0.0
IIO
IO READ (5,IOOIT.ZI.22

ircr.ro.o> co TO so

xr(r.so.90) asap *.FP,VAGB,WTIMB,TISR.TRI.PRNT

xrcr.ro.95) asap *.DPAY.1R.A.C.B.C

xr<r.ro.vo.on.r.so.vs> co TO 10

1r(T.ro.99> are?

I-IeI

2(1).z:

cant Hscou (7.21.22.?OVN(I).TRSF(I).TFU£L(I).TLAB(I),AC(I).FVC(I))
so To 10

so wnxrs<6.:xo)

waxrs(¢.120)

URITB(6,130)

watrr<6.1zo>

DO 60 K-I,I

wnxrr<a.ieo) 2(x),rowN<x).rarr<x).rrustcx).rtas¢x).2vc:x).ac<x)
60 rave-TPVC+PVC(x)

WRIT!¢6.120)

WRITB(6.150)TPVC

60 TD 5 ‘

c ronnar swarrnsnr

too roxnar¢r3.o.A10.A10)

110 ronnar(//.zsx."rnoatcrrn sversn costs")

:20 tonnartix.iz<eH------>)

130 FORMAT(3!,"COST“,4!,"DVNSR8HIP",2!,"RBPA!R".6X,”FUBL",
e38,“LABDR",SX,"TOTAL",4X,”AVBRAC£“,I,5!,"TYPB",6X.“CDSTS",
e4!,"&flAIN.",26!,"PV",6!."ANNUAL") ~

ieo FORHAT<13.A10,6E10.0)

:so , ronnarcax."rnzssur varur or svsrrn cosTs: s".rio.0)

are!

run .

ausnourxus nscou (7.21.22.TOWN.TREP.TFUBL.TLAB.AC.PVC)
common Intel NN,DPAY,IR.A.G.B.C.FF.VACE,VTIMS.TISR,TRI,PRNT
REAL ucosr.nxtrv.nrc.xxs.xur.tason.acar<s>,xn

Diurnsxou s:15>.nt1<is>.ncz<:5).av:<:s>.nvz<15).rrt¢3>.rra<3>

C

09

C INITIAL INPUT DATA

C

DATA r:1..1...7..as..e..a..as..a..6..es..es..7,1.,1..:.l

DATA act/.055..ozs,.14,.61..23..23..s7,.67..7:..41..ze..33.
4.3,.24,.OI

DATA nczli.e.1.6.i.h.:.3.1.a.1.e.1.6.1.s.1.3.1.3.:.6.x.3.i.6.:.3.
+1.!

DATA av:1.e..7s..7s..7..7..7..7..7..7..7..7,.7..7..1..7I

DATA av2/.ee,.a7..ee..9..9..9..9..9..9..9..9..9..9,.9..9I

DATA ACRE/.15..22..21..21,.211

DATA PPLI.169..25..26I,PPHI.203,.41,.49!,NNIiO/,TRII.ZSI,VTIHBI.0I
DATA TIBRI.Oil,Cl.iil.Al.121.3!.2!,CI.09I.DPAYI.2I.NMI5I,IRI.12I
DATA rel.32!.wacs/q.zs/.Pnurlz.ol

EEC-1.0 .
TARO-DLDUSB-FVC-DPC-TDVN-TRBPeTFUBLeTTD-TLAB-0.0

1r (7.80.13) aran *.s<r>.nc1<r).ac2<r).nvx<r).nvz<r:

IF (7-2) 20.25.30 .

C INITIAL SET UP POR AUTOMOBILE

20

C

asan *.NCOST.ACB.HILFY.HPC.INS
tUEL-HILFYIHPCIPP
USS-HILPYIGO. '

co TD 40

C INITIAL SET UP FOR TRACTOR

25

C

READ *,NCOST.AGE.HP.USS.PT
PUEL-PP'RP'USE*(PPL(PT)*(I.-VTIMEI+PPH(PT}*WTIHE)
GO TO 10

C INITIAL SET UP FOR HACHINERY

3O

35
40

43

IPIT.EQ.3) GO To 35

I? (T.EQ.I0.0R.T.EG.IQI READ ‘oNCOST.AGE.USE
IF (7.33.13.0R.T.EQ.IQI GO To 35

READ *,NCOBT.AGE.ACRE.V.D
EPC:W'S*E(T)II0-0

USE I ACREIEFC

FUEL I 0.0

EVO - "COST

IE (AGE.EQ.0) GO To ‘5

READ ‘,PCOST,OLDUSE

3V0 I PCOST

TARO - NCOST‘RCI(T)*(OLDUEEII000.I*’RC2(TI
J I AGE

END I AGE + NN

RV I NCOST'RVIIT)‘RV2(TI*‘END
I?(PRNT.EQ.IIVRITE(A,IOOIZIoz:
IPIPRN7.EQ.I)VRITE(6,II°I
IFIPRNT.EG.I)WRITE(‘.IZO)
IFIPRNT.EQ.IIVRITEI‘.IIOI

LOAN COST
DEATH - DPAY'RVO
PAY I (RVO-DPAYN)'IIR*(I.eIR)*'NH)/((I.+IR)*'NH-I.I
HURT I PAY’NN
DO 30 I I IoNN
J a J + I

D43

c
c CAPITAL COST
CAP - PAY
tr<x.aT.Nn>CAp . o. .
xrcx.:o.1)CAp - CAP + DPAYH
xr(x.So.NN) CAP . CAP — RV*(1.+C)**NN
c

C OWNERSHIP COSTS
TIS I TISR‘NCOST*(RV1(T)*RV2(T)"J+.5)*(1.+C)**I
IP(T.BO.1)TIS I TIS + INS*(1.+C)**I
TOWN I TOWN + (CAP+TIS)I(I.+A)**I

c OPERATING COSTS '
TAR - NSDSTtnc1(T>*<<0LDUSS+USSt<J-Aca>)Ixooo.)aracz<T>
an? . (TAR-TARO)*(1. c)*-1
TAno . TAR
TBS? . Tax? + nap/<1.+A>ttx
runnn g 1.:5trvznrt1.+a)a*x
TPUSL . Truzn 4 FUELLI(1.+A)**I
LABOR . 1.1awAcztUS2u<1.+c)utx
xr(T.cT.a)LASon . o.
TLAS - TLAB + LABOR/(1.+A)**I

C INCOME TAX DEDUCTIONS
D I 0.0
IP(I.LT.6) D I ACRP(I)'RVO
NORT I ANA£1(0..NORT-PAY)
IT I IR'HORT
TD I TRI*(D+IT+TIS+RSP+PUELL+LADOR)

IP(I.CO.I.AND.TRI.NE.O)TD I TD + .13RVO
TTD I TTD + TDI(1.¢A)**I

C TOTAL COST
TOTAL I CAP+TIS+REP+PUELL+LAIOR-TD
PVC I PVC + TOTALI(I.+A)'*I
OPC I OPC +'(TOTAL-CAP+IT)I(1;+A)**I

IP(PRNT.DO.I)WRITE(6.130)I.CAP.TIS.RCP.PUBLL.LABOR.TD.TOTAL
50. 'CONTINUE '

C PRESENT VALUE COSTS
AC I PVC*(A*(I.+A)'*NN)I((I.+A)**NN-I.)
.AOPC I OPC*(A*(1.+A)**NN)I((I.+A)“NN-I.)
IP(PRNT.IO.I)WRITE(6.IIO)

C PORNAT STATDNENTS

100 PORNAT(II.IC."PROJECTBD COSTS OP ".AIO.AIO.I)

IIO PORNATCIX.IZ(6H------))

130 PORNAT<1X."Y3AR".ZX.“CAPITAL”.ZX."INSURANCE",ZX"REPAIRS".
+4!.”PUEL".SX."LABOR".33.“!NCONB TAX".ZX."TOTAL",I.163.
of‘ SHELTER“.2X."& NAIN.“.3X.“& LUB.".12X.“DEDUCTIONS“)

130 PORNAT<I3.7P10.0)

1’0 PORNAT<P3.0.AIO.AIO)

RETURN
IND