• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 Table of Contents
 Introduction
 Method of measuring and paying...
 Problem and objectives
 A conceptual model of sugarcane...
 Identifying the crucial elements...
 The general yield prediction...
 Characteristics of the data
 Classification of the fields
 Percent of recoverable sucrose
 Net tons
 A conceptual model for the replacement...
 Asset interdependence
 The cane grower's maximand
 Administration grower
 Optimal replacement for sugarc...
 Policy program
 Harvest program
 Demonstrating the decision process...
 The policy program
 A restricted lp solution
 Calculating annualized value of...
 The harvest program
 Concluding remarks
 Conclusions
 Possible improvements of the...
 Risk and uncertainty
 Appendix 1: Definitions
 Appendix 2: Prices of raw sugar...
 Appendix 3: Mathematical formulation...
 The harvest program
 The replacement program
 Reference
 Back Cover














Group Title: Bulletin / University of Florida. Agricultural Experiment Station ;
Title: An Analysis of the stubble replacement decision for Florida sugarcane growers /
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00026748/00001
 Material Information
Title: An Analysis of the stubble replacement decision for Florida sugarcane growers /
Series Title: Bulletin / University of Florida. Agricultural Experiment Station ;
Physical Description: 74 p. : ill. ; 23 cm.
Language: English
Creator: Crane, Donald R., 1946-
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville, Fla
Publication Date: 1982
Copyright Date: 1982
 Subjects
Subject: Sugarcane -- Florida   ( lcsh )
Sugarcane -- Forecasting -- Florida   ( lcsh )
Stubble mulching -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references (p. 72-74).
Statement of Responsibility: Donald R. Crane ... et al..
General Note: January 1982.
 Record Information
Bibliographic ID: UF00026748
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: ltuf - ACF1031
oclc - 09269844
alephbibnum - 000404816

Table of Contents
    Front Cover
        Page i
    Title Page
        Page ii
    Table of Contents
        Page iii
    Table of Contents
        Page iv
    Introduction
        Page 1
    Method of measuring and paying sugarcane production
        Page 2
        Page 3
    Problem and objectives
        Page 4
        Page 5
    A conceptual model of sugarcane production in Florida
        Page 6
        Page 7
    Identifying the crucial elements for yield prediction
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    The general yield prediction model
        Page 14
        Page 15
    Characteristics of the data
        Page 16
        Page 17
        Page 18
        Page 19
    Classification of the fields
        Page 20
        Page 21
    Percent of recoverable sucrose
        Page 22
        Page 23
        Page 24
    Net tons
        Page 25
        Page 26
        Page 27
    A conceptual model for the replacement decision
        Page 28
        Page 29
    Asset interdependence
        Page 30
    The cane grower's maximand
        Page 31
    Administration grower
        Page 32
        Page 33
    Optimal replacement for sugarcane
        Page 34
        Page 35
    Policy program
        Page 36
        Page 37
    Harvest program
        Page 38
    Demonstrating the decision process for a hypothetical firm
        Page 39
        Page 40
        Page 41
    The policy program
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
    A restricted lp solution
        Page 47
        Page 48
    Calculating annualized value of challengers
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
    The harvest program
        Page 54
        Page 55
        Page 56
    Concluding remarks
        Page 57
        Page 58
    Conclusions
        Page 59
        Page 60
    Possible improvements of the model
        Page 61
    Risk and uncertainty
        Page 62
    Appendix 1: Definitions
        Page 63
        Page 64
    Appendix 2: Prices of raw sugar and returns to sugarcane growers
        Page 65
        Page 66
    Appendix 3: Mathematical formulation of the optimization models
        Page 67
        Page 68
    The harvest program
        Page 69
    The replacement program
        Page 70
        Page 71
    Reference
        Page 72
        Page 73
        Page 74
    Back Cover
        Page 75
Full Text
January 1982
32JZ
January 1982


An Analysis of the
Stubble Replacement Decision for
Florida Sugarcane Growers

Donald R. Crane, Thomas H. Spreen,
Jose Alvarez, and Gerald Kidder


VLOGRCULTURA


LIBRARY


'JAN 0 7 1983


Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
F A. Wood, Dean for Research


Bulletin 822










An Analysis of the
Stubble Replacement Decision
for Florida Sugarcane Growers

Donald R. Crane, Thomas H. Spreen,
Jose Alvarez, and Gerald Kidder

















AUTHORS
Donald R. Crane is a former graduate assistant in the Department of Food and
Resource Economics, University of Florida, now Project Development Officer,
Agricultural Cooperative Development International, Washington, D.C. Thomas
H. Spreen and Jose Alvarez are Assistant Professors in the Department of Food
and Resource Economics and Gerald Kidder is an Associate Professor in the
Department of Soil Science, University of Florida.








CONTENTS

Introduction .......... .............. ............ ......... 1
The Florida Sugarcane Industry .............................. ... 1
Sugarcane in the Florida Economy ........................... . 1
Organization of the Florida Sugar Industry .......................... 1
Method of Measuring and Paying Sugarcane Production ................. 2
Problem and Objectives ................ .......................... 4
Organization of the Study ................. ........................ 6

A Conceptual Model of Sugar Production in Florida ........................ 6
An Overview of Sugarcane Growth and Sucrose Accumulation .............. 6
Identifying the Crucial Elements for Yield Prediction ...................... 8
The General Yield Prediction Model ................................ 14

Estimating Prediction Equations ................. ..................... 14
Sample Survey Design ................ ........................... 14
Characteristics of the Data ................. ....................... 16
Classification of the Fields ................. ....................... 20
M odel Estimation ............... .................... ........... 20
Empirical Specification of Variables ................................. 20
Percent of Recoverable Sucrose ................ .................. 22
NetTons ............ .............................. 25

A Conceptual Model for the Replacement Decision ......................... 28
Asset Replacement ................. .............................. 28
Asset Interdependence ................ .......................... 30
The Cane Grower's Maximand ................... ........... ..... 31
Independent Grower ................ .......................... 31
Administration Grower ................ ........................ 32
Optimal Replacement for Sugarcane ................................ 34
Policy Program ........ ........................... ........... 36
Harvest Program ......... ... .................... ......... 38
Replacement Program ................ ......................... 38

Demonstrating the Decision Process for a Hypothetical Firm .................. 39
Description of the Firm ................ .......................... 39
The Policy Program ............................................. 42
A n LP Solution ..................................... ........... 42
A Restricted LP Solution ................ ................ ... 47
An Approximate Integer Solution ........................... .. 47
Calculating Annualized Value of Challengers ........................ 49
The Harvest Program ................ ........................... 54
The Replacement Program ................ ....................... 54








Concluding Remarks ................ ............................. 57
Summary .............. ......................... ....... 57
C conclusions ........................ ................ . ...... 59
Limitations ......................... ........ ...... .......... 59
Possible Improvements of the Model ................. ................ 61
Alternative Crops ........................................... 61
Producer/Processor System ................ ................... .. 61
Risk and Uncertainty .............. .......................... 62

Appendix 1: Definitions ................ ........................... 63

Appendix 2: Prices of Raw Sugar and Returns to Sugarcane Growers ........... 65

Appendix 3: Mathematical Formulation of the Optimization Models ............ 67
The Policy Program ............ .................................... 67
The J-arvest Program ................ ........................... 69
The Replacement Program ................. ....................... 70








INTRODUCTION
THE FLORIDA SUGARCANE INDUSTRY
SUGARCANE IN THE FLORIDA ECONOMY1
Sugarcane has been cultivated since at least 8000 B.C. (Barnes,
1974, p.2) and today is widely grown throughout the world's tropical and
semitropical regions. In Florida sugarcane has been produced commer-
cially since 1920 (Zepp, 1976). Prior to 1960, however, Florida sugar
production was not significant, with only three mills in operation. With
the ban on importation of Cuban sugar and lifting of domestic sugarcane
acreage restrictions in 1960, the industry grew rapidly.
In 1976 eight mills were producing raw sugar worth an estimated
$200 million to the Florida economy from sugarcane grown on approx-
imately 300,000 acres of muck soil located at the southern end of Lake
Okeechobee (Brooke, 1977). Only citrus and livestock products are more
important than sugarcane to the agricultural economy of Florida (Kidder
and Lyrene, 1976).
In recent years, Florida has been vying with Hawaii for the lead in
domestic sugarcane production. Cane is also grown in Louisiana and
Texas. Sugarcane grown in these four states accounts for approximately
42 percent of domestic raw sugar production; sugarbeets grown in cooler
climates, account for the remaining 58 percent. In 1975, Florida con-
tributed 16 percent of domestic sugar production and slightly over 1 per-
cent of world production (Kidder and Lyrene, 1976).

ORGANIZATION OF THE FLORIDA SUGAR INDUSTRY2
During the period covered by this study (1968 through 1977), eight
raw sugar mills processed the cane produced in Florida. Although some
of the raw sugar was refined in the state, most was shipped to Savannah,
Georgia, New Orleans, Louisiana, or elsewhere for refining (Zepp,
1976).
Over half the sugarcane produced was grown by corporations for
sugar extraction in their own mills. Nearly 40 percent of the cane was
produced for grower-owned cooperative mills, while less than 10 percent
was grown by independent producers for sale to a mill (Kidder and
Lyrene, 1976). Cane grown either by a corporation for use in its own mill
or by a cooperative member for use in the cooperative mill will be re-

1. For a more thorough treatment of the role of the sugar industry in
Florida's economy, consult Thomason (1979), IFAS (1975), or Zepp (1976).
2. For an interesting account of the organization of the industry in its early
years see Turk (1943).







ferred to as "administration cane," while cane grown by an independent
producer will be referred to as "independent cane."
The 1974 crop was grown by 135 farms ranging in size from less than
10 acres to over 60,000 acres; the average was 2,200 acres per farm
(Zepp, 1976). There were, however, only about 50 independent pro-
ducers (Gascho, 1975).

METHOD OF MEASURING AND
PAYING SUGARCANE PRODUCTION3
Although various modes of payment for cane have developed
around the world (Maxwell, 1927), payment for independent cane grown
in Florida prior to the end of 1974 was regulated by the terms of the
Sugar Act, and the system has continued essentially unchanged. The pro-
visions of the Sugar Act did not apply to administration cane.
When an independent grower delivers sugarcane to a mill, the cane
is weighed. A standard percentage deduction is taken from gross weight
as an allowance for "trash" delivered with the cane. The result is the
"net weight," which is measured in tons, hence giving rise to the unit of
measurement, "net tons." The sugarcane clear of trash is called "net
sugarcane." Juice from the cane is then sampled to determine the pro-
portion of sucrose in the juice. On one basis of this test, a "standard
quality factor" is assigned to the cane. The product of net tons and the
standard quality factor is called "standard tons," and this is the unit of
measurement to which the purchase price is applied.
Administration cane has never been subject to the provisions of the
Sugar Act. Consequently, growers of this cane frequently do not concern
themselves with standard tons, nor do they routinely record "sucrose in
normal juice" in their permanent records. Instead, they favor the
calculation of "yield" of commercially recoverable sugar as a percent of
gross tonnage of cane delivered, using the Winter-Carp Formula (Meade
and Chen, 1977, pp. 788-791). In Florida it is a common practice to con-
vert from "theoretical" yield to "actual" yield by adjusting for
discrepancies between estimated and actual total sugar recovery.
In general, the field records which cane growers use to make produc-
tion decisions in Florida show gross tons of cane produced for each field.
Sucrose content may be indicated either as sucrose in normal juice or as
yield. Direct comparison of mechanically- and hand-harvested cane from
growers records is not very meaningful because mechanically harvested
cane contains about 10 percent trash as compared to only about 5 percent
for hand-cut cane (Zepp and Clayton, 1975, pp. 37-38). Thus, gross ton-


3. Appendix 1 contains definitions of terms used by the sugarcane industry,
and should be consulted by those readers not familiar with the industry.







nage is inflated whenever cane is mechanically cut. This problem is ag-
gravated whenever sucrose content is measured as "yield," since this
quantity is based on gross weight.
To facilitate comparison of mechanically- and hand-harvested cane,
sugarcane production may be converted to a net-tons basis and sucrose
content may be calculated as commercially recoverable sugar expressed
as a percent of net weight ("percent recoverable sugar" or PRS). An ap-
proximate measure of net tonnage produced per field can be obtained by
deducting 5 percent of recorded gross weight for hand-cut cane or 10 per-
cent for mechanically-cut cane.
When sucrose in normal juice is known, PRS can be determined by
reference to Table 1, which is based on an average rate of sucrose
recovery for the industry.
An approximation of PRS can be obtained from recorded yield
figures by dividing by 0.95 for hand-harvested cane or by 0.90 for
mechanically-harvested cane, respectively, in order to convert from a
gross weight to a net weight basis. Table 2 may be used to determine the



TABLE 1. Conversion from percentage of sucrose in normal juice to PRS.
Percentage of sucrose PRS
in normal juice
5.0 2.785


3.600

4.415

5.230

6.180

7.105

7.975

8.845

9.725

10.605

11.480

12.350

13.200

14.020


SOURCE: U.S. Congress (1972, p. 12)







standard quality factor when either PRS or pounds of sugar per ton of
cane is known. In the present study it is convenient to measure sugarcane
production in terms of net tons and PRS.


PROBLEM AND OBJECTIVES
Sugarcane is propagated vegetatively by placing 20-inch sections of
stalk, known as seed cane, in rows 5 feet apart, which insures true clones.
It is a perennial plant which grows back each year after harvest from the
portions of the stalk left under the ground. The subsequent crops are
known as ratoon or stubble crops. A number of factors generally com-
bine to cause cane and stubble production to decline with subsequent ra-
toons. The stubble is normally replaced between three and ten years after
planting (Kidder and Lyrene, 1976).
A number of costs are incurred when the stubble is replaced. They
include the cost of plowing under the old stubble, the cost of field
preparation, and cost of seed cane. Generally there are additional oppor-
tunity costs associated with the loss of revenue from one crop while the
field is put to fallow; however, the cane may be grown in rotation with
corn or vegetables, and rotation with rice appears to be a promising alter-
native (Alvarez, 1978, and Alvarez et al., 1979).
Sugarcane may also be immediately replaced without allowance for
a fallow period. This practice, generally called "successive planting" in
Florida, usually results in lower productivity but avoids the loss of
revenue associated with fallowing. The fallow, if used, may be either a
flood fallow or a dry fallow, and certain maintenance costs are incurred
either way. The flood fallow requires constant pumping to maintain
standing water in the field. The dry fallow requires additional weed con-
trol measures. The main purpose of the flood fallow is to kill pests in the
soil, such as grubs and wireworms.
Florida sugarcane producers face the problem of whether replace-
ment of the stubble in a particular field is economically justifiable at a
given time. The replacement decision hinges on expected future revenues
and, therefore, it is necessary to predict, in some manner, future produc-
tivity for the existing stubble crops as well as for the potential replace-
ment.
Producers currently use a variety of rules of thumb for the stubble
replacement decision. Yield predictions are based on the grower's
knowledge and experience and as much information and advice as he can
accumulate in his mind at the time. No fully satisfactory, formal decision
model currently exists. The present decision procedures may be
characterized as more art than science; however, the large number of
variables which must be considered, the complexity of the relationships
among them, and the large number of fields which must be








TABLE 2. Standard quality factor for converting net tons of cane to standard
tons of cane.


Pounds sugar per
ton of cane


8.25

8.50

8.75

9.00

9.25

9.50

9.75

10.00

10.25

10.50

10.75

11.00

11.25

11.50

11.75

12.00

12.25

12.50

12.75

13.00

13.25

13.50

13.75

14.00


Standard
quality factor

.9079

.9348

.9617

.9887

1.0156

1.0425

1.0695

1.0964

1.1233

1.1502

1.1772

1.2041

1.2310

1.2580

1.2849

1.3118

1.3387

1.3657

1.3926

1.4195

1.4465

1.4734

1.5003

1.5272


SOURCE: Halsey (1976).







simultaneously evaluated suggest that a more formal, explicit decision
model may be of value to bring greater quantity of information to the
decision.
This study is intended to provide a formal framework for the stub-
ble replacement decision. A more fundamental goal is to publicize the
problem of sugarcane stubble replacement and develop a model which is
a reasonable and convincing first approximation to the solution of the
problem.
The objectives of the study are:
1. To estimate yield prediction equations for sugarcane growth in
the Everglades Agricultural Area using explanatory factors
readily available from growers' records;
2. To integrate yield prediction equations into a decision model for
the stubble replacement problem.

ORGANIZATION OF THE STUDY

A conceptual model for sugar production in the Everglades
Agricultural Area was devised with the aid of textbooks, sugarcane
growers, and local agronomists. Deteriorating-asset replacement theory
was adapted for use in the stubble replacement problem. Yield prediction
equations were specified and estimated based on a sample of 125 cane
fields over the ten-year period 1968-1977. These equations were used in
an expository fashion to generate yield predictions for a hypothetical
farm. The predictions were then used as input for the decision model,
which produces an overall farm policy, a harvest schedule for the current
period, and a schedule of yields to be replaced after harvest. This bulletin
reports these stages, and discusses possible improvements and extensions
of the model.



A CONCEPTUAL MODEL OF SUGAR
PRODUCTION IN FLORIDA
AN OVERVIEW OF SUGARCANE GROWTH AND
SUCROSE ACCUMULATION
Sugar production may be viewed as the result of two component
processes: the vegetative growth of the sugarcane plant and the ac-
cumulation of sucrose. These processes are separately modeled in this
study: (i) given a set of environmental conditions, one can be determined
without reference to the other, (ii) they respond differently to changes in
environmental conditions, (iii) they change in different ways over time,
(iv) individually estimated functions may be useful for purposes other







than sugar yield prediction (e.g., a predictor of vegetative growth may be
useful in a study to consider transportation requirements), and (v) the
method of payment differs between independent and administration
cane (this point is discussed later).
Vegetative growth is generally measured in terms of cane stem
elongation, because "the correlation between increments in length and in
volume is sufficiently high in sugarcane to justify the substitution of sim-
ple length measurement for the laborious determination of volume" (van
Dillewijn, 1952, p. 97). Growth is not uniform; rather it "starts very
slowly in the germinating bud and it increases gradually till a maximum is
reached which is followed by gradual decrease" (van Dillewijn, 1952, p.
97). Thus, for a given stand of cane there is generally a period of rapid
growth as the "grand growth period" which is normally timed to coin-
cide with the period most favorable to growth in terms of radiation,
temperature, and moisture. The relationship illustrated in Figure 1 was
described by van Dillewijn for Java (1952, p. 101) and for Florida by
Allen (1974).
The accumulation of sucrose in cane is called ripening. In order for
ripening to occur the rate of growth of cane must be retarded (Humbert,
1968, p. 545). This is so because the assimilates of photosynthesis may be
used either for growth or for storage in the stem (van Dellewjin, 1952, p.
322). According to Humbert:
Low temperature is perhaps the most effective single factor in incurring
ripening. As the seasons change, a prolonged period of cool weather will
retard growth and improve the sucrose content even when the crop is amply
supplied with nitrogen and soil moisture. An excellent example would be
the cane growth in the organic soils of Florida with a high water table. The
fall months with their lower temperatures, bring about cane maturity. The
return of warm weather will, in the absence of other limiting factors, such
as drought or nitrogen deficiency, bring about a resumption of rapid
growth, a rise in reducing sugars and a decline in their percentage of
recoverable sucrose. (Humbert 1968, p. 545).
Thus, as temperatures change over time, cane growth and sucrose con-
tent tend to respond in opposite directions, as illustrated in Figure 2.
Since Florida cane is normally harvested during the cool season, that
portion of Figure 2 most applicable as an estimator of sucrose content at
harvest (the portion of the sucrose content curve above that portion of
the horizontal axis corresponding to the cool season) may be approx-
imated as a quadratic function of time concave to the origin. Barnes
(1974, pp. 359-360) reports this type of relationship for two studies
measuring sucrose content at harvest time.
Ripening may also be induced artificially by withdrawing water from
the plant or by treating it with a chemical to retard metabolism
(Humbert, 1968, p. 593). Chemical ripening is now widely used on early
harvested Florida cane.











-Accumulated
Growth



Monthly Growth
Increment





Spring Summer Fall

FIGURE 1. Grand growth period of sugarcane within a year.
SOURCE: van Dillewijn (1952, p. 101)


Cool Warm Cool
Season Season Season


FIGURE 2. Relationship of cane growth to sucrose content as the seasons pro-
gress.
SOURCE: van Dillewijn (1952, p. 323)


IDENTIFYING THE CRUCIAL ELEMENTS FOR YIELD PREDICTION

Model specification requires identification of the "crucial ele-
ments" of the process. Accordingly, a list of potential determinants of
sugar yield was drawn up based on textbook expositions. Sugarcane
growers and local agronomists were consulted to determine which
elements are likely to be important under Florida growing conditions.







Since the purpose of the exercise is to demonstrate an estimation pro-
cedure of practical importance to sugarcane growers, the list of variables
was further reduced to include only those whose measurements are
generally recorded by cane growers or which are readily available from
secondary sources. This list is given in Table 3, and each item is discussed
below.
Item 1: Cane variety. Varieties of cane may differ in at least three
ways in their ability to produce sugar. They may differ in (i) total leaf
surface or in efficiency of utilization of leaf surface, (ii) average percent
of sucrose, or (iii) time of ripening (van Dillewijn, 1952, p. 321). In
Florida, early, late, and midseason varieties are grown with differing
production characteristics.
Item 2: Soil type. The sugarcane producing soils of south Florida
may be arbitrarily classified as: (i) "custard apple" muck, (ii) "stand-
ard" muck, or (iii) sand (Snyder et al., 1978). Custard apple is a true
muck, high in mineral content, located in a narrow band adjacent to
Lake Okeechobee. This soil is reputedly conducive to vegetative growth.
Standard muck includes all of the organic soils except custard apple. The
standard muck soils are spongy peat soils much lower in mineral content
than custard apple. Soils with over 50% sand are classified as sand.
These soils are mostly in the western portion of the sugarcane region.
Sandy soils are reputedly conducive to sucrose accumulation, because
nitrogen may be withheld, in contrast to the organic soils which are con-
tinuously replenished with available nitrogen as a by-product of
microbial oxidation of the soil itself.
Item 3: Average soil depth. This factor may be important on
shallow soils as it related to water table management but data were not
readily available on an individual field basis.
Items 4-9: Fertilizers and chemicals. The level of available
nutrients in the soil is obviously important to growth. Ideally, fertilizer
applications would be made according to needs estimated by a soil sam-
ple or foliar analysis. Unfortunately these and other chemical application
data are not available on a field basis.
Item 10: Cultivation practice. Data are not readily available. The
situation is similar to that for items 4 through 9.
Item 11: Water table management. Although there is some
evidence that an exceptionally high water table may reduce yields in
Florida (Snyder et al., 1978, pp. 10-11), the relationship of water table
depth to yield is still the subject of research. Unfortunately, no useful
data exist in growers' records.
Item 12: Rainfall. Moisture is essential for growth; conse-
quently, rainfall is the most crucial determinant of yield in many of the
world's cane-producing regions. In Florida, however, the abundant
waters of Lake Okeechobee provide year-round irrigation at virtually no








TABLE 3. List of factors thought to contribute to sugarcane growth or sucrose
accumulation in Florida and disposition with respect to inclusion in
the general model.
Disposition
Sugarcane Sucrose
Item Factor growth accumulation
1 Cane Variety include include

2 Soil type include include

3 Average soil depth omit A omit A

4 Phosphorus omit A omit A

5 Potassium omit A omit A

6 Trace minerals omit A omit A

7 Lime omit A omit A

8 Pesticide omit A omit A

9 Herbicide omit A omit A

10 Cultivation practice omit A omit A

11 Water table management omit A omit A

12 Rainfall omit B omit B

13 Mode of harvesting include include

14 Skip planting omit A omit A

15 Distance from lake include include

16 Year of crop cycle include include

17 Yield from previous crop include include

18 Period of harvest include include

19 Age of cane include include

20 Pest infestation omit A omit A

21 Disease omit B omit B

22 Number of freezes per year include include

23 Accumulated hours of freezing
temperatures include include

24 Average temperature growing season include include

25 Solar radiation growing season include include
aOmission code: A = data not available; B = not felt to be significant.







cost to the grower. Although rainfall does not appear to be a crucial fac-
tor in Florida, some growers believe that rainfall might be important,
possibly because it is correlated with other environmental factors. Local
agronomists, on the other hand, feel that inclusion of radiation and
temperature data should account for any indirect effects of rainfall.
Item 13: Mode of harvesting. In Florida, cane is harvested either
by hand or by a number of mechanical harvesting processes (Zepp and
Clayton, 1975, p. 35-36). Mechanical harvesting may retard growth and
sucrose accumulation in the succeeding ratoon crop, and it may reduce
the recoverablility of sugar in the current crop. Mechanical harvesters are
more likely to uproot stools, damaging their viability. Harvesters may
also lead to soil compaction, which tends to reduce yields in ratoon crops
(Humbert, 1968, pp. 11-13). Soil compaction, however, may be less of a
problem in the spongy organic and sandy soils of Florida than elsewhere.
Item 14: Skip planting. Some growers follow the practice of
planting seed pieces in fields of ratoon cane in cases where the stand has
become thin. While the effect of such a practice on yield is obvious,
growers who use it do not record which fields have been skip-planted.
Item 15: Distance from Lake Okeechobee. Growers and
agronomists unanimously agree that the moderating influence of the lake
on temperatures is beneficial for cane grown near its shores. The effect
diminishes gradually, moving away from the lake. Furthermore, soil
depth tends to diminish as distance from the lake increases, and since no
variable is included for soil depth, distance from the lake may serve as its
proxy.
Item 16: Year of crop cycle. It is generally recognized that yield
diminishes with successive ratoons, but the mechanism is not well
understood. However, it is known that
The vigor and productivity of ratoons, and the number of successive
ratoons which can profitably be grown before it is desirable to plough out
the old stools and replant, depend on a number of factors, not least of
which is the ratooning power of the variety of cane.... [Other factors] in-
clude loss of tilth in the root zone of the soil, depleted vigor caused by in-
sect and disease damage to roots, ratoon-stunting disease encouraged by
failure to take what are not the standard precautions, inadequate water,
and many others. (Barnes, 1974, p. 277)
In addition, it is known that root systems of ratoon crops tend to be
less well developed (Humbert, 1968, p. 30). This phenomenon is related
to the top-dominance characteristics of cane. Top-dominance is a hor-
monally controlled mechanism which insures that the uppermost bud of
a portion of stalk will grow first in preference to lower buds (Barnes,
1974, p. 264). This causes the root systems of subsequent ratoons to be
more shallow than those of previous crops, as illustrated in Figure 3.
It has been estimated that ratoon-stunting disease, mentioned by
Barnes as a leading cause of yield decline, probably accounts for losses of





















FIGURE 3. The effect of top-dominance on the rooting position of subsequent
ratoons. C, cutting; P, stalk of plant crop; R1, first ratoon stalk;
R2, second ratoon stalk.
SOURCE: van Dillewijn (1952, p. 153)

at least 10 percent of the total crop yield in Florida (IFAS, 1975, p. 113).
This disease can be controlled by heat treatment of seed cane. However,
the disease is symptomless, and growers may not be aware of losses.
Barnes (1974, p. 279) expresses the opinion that most of the causes of
yield decline in ratoons can be controlled. Nevertheless, ratoon yield
decline is a fact in Florida. Kidder (1978) reports that published research
data for the 1968-75 period revealed that first ratoon sugar per acre was
about 86.0 percent of plant crop sugar while second ratoon sugar was
about 78.2 percent of plant crop sugar.
Item 17: Yield for previous crop. When a field man is asked to
estimate yield from a particular field, one of the first things he does is to
consult the previous history of the crop. Past yield may give a good in-
dication of the general health and vigor of the stools involved.
Item 18: Period of harvest. This is particularly important for
sucrose accumulation, because sucrose storage in the stem is regulated by
the seasons, and, sucrose content increases as the harvest season pro-
gresses. This variable, in conjunction with the age of cane at time of
harvest, may be important for growth as an indicator of how well the ac-
tual growing period was matched to the period most favorable to growth.
Item 19: Age of cane. As can be seen from Figure 1, growth ac-
cumulates over time; therefore, volume of cane harvested will be ex-
pected to increase with age.
With respect to sucrose accumulation, it is suggested that:
Age and condition of the cane play dominant roles in maturity. Young cane
given sunlight, nutrients and moisture will produce vigorous vegetative
growth, storing little sugar. As the cane passes its 'boom stage of growth',
the rate of growth subsides, its top becomes smaller, and more sugars are
stored in the stalk. As it approaches its normal harvesting age the moisture







and nitrogen levels drop and its reducing sugars are converted to sucrose.
(Humbert. 1968. p. 547)
Item 20: Pest infestation. Costs associated with insect pests or
their control have been estimated to account for more than 5 percent of
the total value of Florida's annual sugarcane crop (IFAS, 1975; p. 113),
while rats account for an annual loss between $2 and $4 million (Lefeb-
vre, et al., 1978). Infestation may vary widely from field to field and
from year to year, causing considerable yield variation. Unfortunately,
growers do not record the incidence of pest infestation.
Item 21: Disease. Growers and agronomists were unanimous in
the opinion that disease (apart from ratoon-stunting disease, which can-
not be detected) was not a significant factor in Florida sugarcane during
the period of this study.
Item 22: Item 23: Freezing temperatures. Sugarcane grown in
Florida is susceptible to frost damage. Injury is caused by the rupture of
cells that occurs when the cell fluids freeze (Humbert, 1968, p. 52). A
crop is normally in peril of frost damage twice in its cycle: during its first
winter when it is quite young, and during the second winter, when it is
approaching harvest. The worst result of a severe freeze is damage to the
apical bud of young cane, which will drastically reduce growth
(Humbert, 1968, p. 54). Frost damage is of no consequence from growth
in mature cane, since it is virtually full-grown, but sucrose may be af-
fected. Irvine (1969) reports that sucrose quality was adversely affected
by a freeze of 11 hours at 250 F, but was actually improved by a freeze of
6 hours at 25' F. He also reports that a freeze of 4 hours at 21 F was suf-
ficient to completely freeze mill cane, while 48 hours were required to
achieve the same result at 31 F. Thus, it is quite difficult to determine
what constitutes a freeze or what ultimate damage will result. Irvine
(1969) and Gascho and Miller (1977) show that varieties of cane differ in
their ability to withstand frost.
Item 24: Average temperature-growing season. Since growth is
the result of a chemical process, temperature is an important factor (van
Dillewijn, 1952). In sugarcane, very little growth will take place when the
temperature is below 600F (van Dillewijn, 1952, p. 116; Humbert, 1974,
pp. 47-50).
Item 25: Solar radiation. Photosynthesis is the process which
converts solar radiation to carbohydrates. These carbohydrates may be
used either for growth or sucrose accumulation (van Dillewijn, 1952).
There is an interrelationship between temperature and radiation. For
each temperature there is a minimum light intensity for survival, health,
and growth; the higher the temperature, the higher the minimum level of
radiation required (Lauritzen et al., 1946). The importance of solar
radiation and growing season temperatures for sugarcane growth in
Florida is shown by Allen (1974, 1976) and by Allen et al. (1978).







THE GENERAL YIELD PREDICTION MODEL
As noted previously, the production of sugar from a crop of sugar-
cane may be viewed as the result of two processes: (i) growth of cane
and (ii) accumulation of sucrose. The quantity of sugar commercially
recoverable from a crop of Florida cane at a given point in time is,
therefore, given by

(1) So,= x N,
where S = quantity of recoverable sugar;
S= a measure of accumulated recoverable sucrose;
No= a measure of accumulated vegetative growth.
The components of (1) are given by:
(2) oX =X(V, G, M, X, Y, X,, H, O. B, T, W, Z)
(3) No= v(V, G, M, X, Y, N,, H, O. B, T, W, Z)
where V= variety of sugarcane;
G = soil type;
M= mode of harvesting;
X= distance from Lake Okeechobee;
Y=year of crop cycle;
X, =a measure of past performance with respect to sucrose
production;
N, = a measure of past performance with respect to vegetative
growth;
H= period of harvest;
O = age of cane;
B = freezing temperatures;
T= growing season temperatures;
W= solar radiation;
Z= a composite of all other relevant variables not specifically
included in the model.


ESTIMATING PREDICTION EQUATIONS

SAMPLE SURVEY DESIGN
Since the ultimate purpose of this study is to demonstrate a decision
technique which may be used by individual firms, an appropriate
sampling procedure would be to select an actual firm and discuss the
elements of the decision process, including yield prediction, step by step.
Unfortunately, no firm was willing to participate in this way, because of
the concern that the firm could be easily identified, thereby revealing in-







formation to divulge to competitors. A number of firms, however, were
willing to participate anonymously, provided that the data collected were
mingled with data from several other firms so that participants could not
be identified. Thus, the decision technique could be demonstrated for a
hypothetical composite firm.
In selecting firms to be included in the composite, the guiding princi-
ple was to obtain a "sufficient" quantity of information at a "reason-
able" cost. The idea that the composite firm ought to be representative
of the entire industry was abandoned because many small firms do not
maintain adequate records from which to obtain data. Furthermore,
there are substantial "set-up" costs associated with the inclusion of each
producer which prejudice against the inclusion of small firms. Set-up
costs are primarily associated with the time required to: (i) move from
one sampling location to another, (ii) be introduced to the officers of the
firm, (iii) learn the recording system, and (iv) locate record books from
previous years. Since more observations may be obtained from large
firms than from small, the unit cost per observation inclusive of
allocated set-up costs is less for large firms than for small firms.
To insure variation in soil type, climatic factors, and distance to the
lake, a uniform geographic distribution of fields to be sampled was con-
sidered important.
Six firms agreed to participate in the study. They met the desired re-
quirements of being average or larger in size in terms of acreage farmed,
possessing suitable records, and having locations that provided
reasonably uniform geographic distribution of fields throughout the
sugarcane producing region.
Fields were then randomly selected from each farm or plantation of
the firm. A total of 125 fields were included in the sample. Observations
were taken for each season4 between 1967 and 1976, provided the firm
was in existence, the field still belonged to the firm, and the data were
properly recorded. The ten-year period was chosen to provide variation
in weather data.
The sampling procedure resulted in a total of 1025 observations.
Many of these were not useful for yield prediction because the field was
in fallow, lagged values were not known, or the observation was defec-
tive in some other way. The number of observations in the complete sam-
ple varies depending upon the equation which is to be estimated;
however, it is approximately 750.


4. The word "season," when used in this paper, always refer to the harvest
season which begins in the fall of one year and ends in the spring of the next year.
The harvest season is often referred to in the form 1976-1977; however, the con-
vention is adopted here of citing only the year in which the harvest begins. Thus,
the season just referred to would be called simply 1976.






A number of observations were eliminated from the complete sam-
ple to form a restricted sample for two reasons:
i) A total of 29 varieties were included in the complete sample, but
many of these had only a few observations. Therefore, varieties with
fewer than 20 observations were eliminated.
ii) Observations of cane beyond the fifth year of their crop cycle are
believed to reflect an upward bias with respect to tonnage of cane pro-
duced, similar to the bias detected by Ward and Faris (1968, pp. 809)
when estimating yields of plum orchards. The problem is that as the cane
ages, stools with a history of high productivity are allowed to ratoon,
while those not producing up to expectations are replaced. Thus, obser-
vations of cane greater than five years old are chosen from an excep-
tional subset of the population and, consequently, are eliminated from
consideration. Predictions beyond the fifth year proceed by extrapola-
tions, if necessary.



CHARACTERISTICS OF THE DATA
Because of the way the sample was collected, the data may not be
fully representative of the industry as a whole. For this reason the sample
will be briefly compared with the industry in terms of varietal composi-
tion and yield performance. Table 4 shows the percentage share of
acreage occupied by present leading sugarcane varieties for the industry
as a whole for seasons 1967 through 1976. Table 5 shows the percentage
of fields contained in the complete sample for these same varieties plus
two additional varieties which represent a significant portion of the sam-
ple.
Comparing Tables 4 and 5 reveals that variety Cl 41-223 is under-
represented in the sample for the early seasons but over-represented for
the late seasons. CP 57-603 is over-represented, while CP 63-588 is
under-represented. Cl 41-191 is over-represented because this variety is
generally grown on sand, and sand land was deliberately sampled out of
proportion, since the participants and agronomists were especially in-
terested in observing the behavior of cane on sand. Variety Cl 49-198 was
not included in Table 4 because it is no longer grown in Florida.
Table 6 compares net tons and PRS for the industry with the com-
plete and restricted samples for each season from 1967 through 1976.
Table 6 shows that the restricted sample does not differ from the com-
plete sample very much, but the sample appears to differ from the in-
dustry. In the early seasons, net tonnage for the sample tends to run
about five tons ahead of the industry. In late seasons this advantage falls
to about two tons. PRS tends to run about a percentage point higher for
the sample than for the industry throughout the harvest period.











TABLE 4. Share of acreage for present leading sugarcane varieties for the Florida sugarcane industry for seasons 1967 through 1976.
Season


1967 1968 1969 1970 1971
-----.................. .--------------------- -------nerci


1972 1973 1974 1975 1976
ent----------------------------- ------------


21.3 15.3


Cl 54-336

Cl 54-378

CP 57-603

CP 56-59


CP 63-558

CP 62-374

Cl 59-1052

Cl 61-5-
SOURCE: (Kidder, 1976, p.2)


2.0 2.0

1.4


2.3 3.5

S2.0

2.9


3.3 3.6 3.6 4.3 5.3 5.9

2.4 4.2 6.0 6.9 6.8 6.0

2.9 2.2 1.9 1.6 1.4 2.0

5.9 6.7 10.9 11.4 13.6 13.3

6.4 13.9 19.5 25.7 34.6 39.4

1.5 2.8 3.3 3.5 3.3 3.3


Variety


Cl 41-223












TABLE 5. Proportion of leading sugarcane varieties by number of fields in the complete sample for seasons 1967 through 1976.
Season
Variety 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
--------------- -------------------------- ----percent------ ----------------------------------

C1 41-223 65.6 59.6 56.5 56.9 60.0 56.0 42.1 32.0 30.3 27.4

C1 54-336 3.3 4.3 2.2 2.0 1.7 1.2 1.9 3.0 4.2

C1 54-378 4.9 6.5 4.3 5.8 6.7 6.0 6.3 6.8 7.1 5.3

CP 57-603 3.3 6.5 9.8 10.0 8.3 6.3 6.8 6.1 5.3

CP 56-59 3.9 3.3 7.1 15.8 17.5 21.2 16.8

CP 63-588 2.2 5.8 5.0 8.3 9.5 9.7 9.1 14.7

CP 62-374 2.4 3.2 1.9 1.0

C1 59-1052 1.0 3.0 7.4

CI 61-5 1.0 1.0 1.0

C1 41-191 1.6 2.0 2.2 2.0 1.2 3.2 8.8 9.1 11.6

Cl 49-198 4.9 10.6 8.7 7.9 3.3 2.4 1.0 -







TABLE 6. Mean values for net tons of sugarcane and PRS for the industry
compared with those for the complete and restricted samples for
seasons 1967 through 1976.
Years Ia CS RS

1967
Net tons 34.3 38.3 39.5
PRS 10.8 12.2 12.2


1968
Net tons
PRS

1969
Net tons
PRS

1970
Net tons
PRS

1971
Net tons
PRS

1972
Net tons
PRS

1973
Net tons
PRS

1974
Net tons
PRS

1975
Net tons
PRS

1976
Net tons
PRS


29.6
10.0


38.1
10.3



31.5
10.1



29.0
10.6



34.9
10.6



31.4
9.8


Source for industry means: Kidder (1976).
aCode: I = industry; CS = complete sample; RS = restricted sample.


31.3
11.0







CLASSIFICATION OF THE FIELDS

Cross tabulations of varieties versus soil type revealed that certain
varieties are grown on only one soil type. Other varieties are grown on
both custard apple and standard muck, but no variety is grown on both
muck and sand. The seven varieties which constitute the restricted
sample and the soil types on which they are grown are summarized in
Table 7.
Nine soil-variety combinations can be identified from the listing in
Table 7. Classification of the fields into these nine categories proved
useful in estimation of yield prediction equations, because variety and
soil type are two important factors in determining yield.

TABLE 7. Soil-variety combinations.
Variety Soil type

CP 63-588 Standard Muck

Cl 41-223 Custard Apple
Standard Muck

CP 56-59 Standard Muck

Cl 54-578 Standard Muck

CP 56-603 Custard Apple
Standard Muck

Cl 41-191 Sand

Cl 49-198 Standard Muck



MODEL ESTIMATION

The estimation of equations predicting net tons and percent of
recoverable sucrose proved to be a tedious task. For details on the
specifics of the estimation see Crane (1979). We include only a brief
outline here.

EMPIRICAL SPECIFICATION OF VARIABLES
In order to estimate the parameters of equations (2) and (3), the
following variables were defined:
D, = 1, variety = CP 63-588 and soil type = standard muck;
= 0, otherwise;







D2 = 1, if variety =
= 0, otherwise;
D3 = 1, if variety =
= 0, otherwise;
D4 = 1, if variety =
= 0, otherwise;
D5 = 1, if variety =
= 0, otherwise;
D, = 1, if variety =
= 0, otherwise;
D, = 1, if variety =
= 0, otherwise;
D, = 1, if variety =
= 0, otherwise;
D, = 1, if variety =
= 0, otherwise;


Cl 41-223 and soil type = custard apple;

CI 41-223 and soil type = standard muck;

CP 56-59 and soil type = standard muck;

Cl 54-378 and soil type = standard muck;

CP 56-603 and soil type = custard apple;

CP 56-603 and soil type = standard muck;

Cl 41-191 and soil type = sand;

Cl 49-198 and soil type = standard muck;


F, = 1, if the observation pertains to the ith firm;
= 0, otherwise;
Y = year of cycle;
M = 1, if the field was mechanically harvested (current year);
= 0, otherwise;
H = the period of harvest measured in two-week periods begin-
ning with October 1;
O = age of the cane expressed as the number of two week periods
prior to September 1;
X = distance from the field to Lake Okeechobee measured in
miles and rounded to nearest half mile;
X, = percent or recoverable sucrose lagged one year.
Several specifications of variables to measure the effect of a freeze
(B) were formulated. The accumulated number of hours below or be-
tween two freezing temperatures was calculated for the period beginning
two weeks after planting or harvesting and running through the date of
next harvest. These variables were hours below 320 F, hours between
320 F and 280 F, hours below 300 F, etc. To measure growing season
temperatures (T), the variable A was defined as follows:
A = accumulated degree days for the period April through August,
where degree days for a single day are determined following
Allen et al. (1978) as Ad = max {0,[(A max A min)/2] 60}
and A max and A min are highest and lowest temperatures
recorded for the day in degrees Fahrenheit.
Two measurements of solar radiation (W) were formulated. These
were:
W = solar radiation measured in average monthly Langley units for
the five month period April through August.







W, = solar radiation measured in adjusted average monthly Langley
units, where the adjustment is W, = 0.08 W, + 0.10 W2 + 0.12
W3 + 0.14 W4 + 0.16 Ws, and W, through W, are average
monthly Langley units for the months April through August,
respectively (see Allen et al., 1978).
Other relevant variables not specifically identified in (2) and (3) were
a measure of the effect of successive planting, and a set of binary
variables to capture the effect of time were defined as
T, = 1 if the field is harvested in year i;
= 0, otherwise.
The data and solar radiation (W) and degree days (A) are such that only
one value per year over all fields is recorded. Thus the specification of
variables T, results in a singular regressor matrix. Modified time binary
variables were defined as
T, = 1 if the field was harvested in 1968 or 1969;
= 0, otherwise;
T2 = 1 if the field was harvested in 1970 or 1971;
= 0, otherwise;
etc.


PERCENT OF RECOVERABLE SUCROSE
A full model was initially estimated with percent of recoverable
sucrose as the dependent variable. The firm effects were assumed to af-
fect the intercept only. The soil-variety binary variables (Dg) were in-
teracted with all continuous variables (Y, H, O, X, W, and the freeze
variable) in linear, quadratic, and cubic form. For example, distance
from the lake (X) was entered into the model as
9 9 9
a,X+a2X+aD3X +g E 1,DX+g E ygDgX+ Eg 6,DX
g= g1 g= 1

where a,,a2,a3,3g,"yg, and 6g are parameters to be estimated. Thus the
soil- variety binary variables were allowed to act as both slope and in-
tercept shifters.
The number of parameters in the full model approached 200. Given
little a priori information on the relative importance of each individual
term in the full model, there was no satisfactory manner to systematically
reduce the size of the model through the elimination of significant terms.
An ad hoc approach was adopted.5 The estimated parameters from the
full model were examined individually. The rule of thumb for statistical

5. Suggested by Dr. Ramon Littel, Department of Statistics, University of
Florida.







significance was that the ratio of the estimated coefficient to its estimated
standard error (t-ratio) be greater than 2. All interaction terms which
were not significant were dropped from the model and pooled. For those
interaction terms which were significant, both the interaction variable
and the continuous variable itself were retained, even if the continuous
variable not interacted was not significant.
After elimination of insignificant terms, the equation for percent of
recoverable sucrose was re-estimated, the result given by (4).
(4) X, = 5.68 0.02 D2 + 0.94 D3 + 0.12 D4 + 2.37 D,
(5.39)6 (-0.04) (2.09) (0.35) (2.82)

-0.82 6 0.47 D, + 5.09 D8 0.32 D9 + 1.46 F2
(-2.48) (-0.61) (4.02) (-1.08) (3.18)

+ 0.93 F, + 1.51 F4 + 1.51 F, + 0.75 F6 + 0.17767462 Y
(3.38) (7.32) (7.89) (3.10) (2.41)

+ 0.85 M + 0.03211000 Xz + 0.00580883 W 0.1436332 Bm
(3.88) (0.20) (3.21) (-2.64)

+ 0.01201211 B2 0.00035629 B3 + 0.19628524 H
(1.89) (-2.11) (9.69)

0.23961797 D3Y 0.23314462 D4Y 0.38954293 DY
(-2.67) (-1.87) (-2.53)

0.25215579 DY 0.5486552 DY 0.43917486 DaXz
(-1.10) (-2.97) (-2.61)

2.30190866 DX 0.94290504 D4Bm + 0.19268439 D4B2,
(-5.98) (-2.52) (2.45)

0.00895522 D4B3 0.25377194D5H 0.17303305 DH;
(-2.31) (-2.52) (1.96)

R2 = 0.5178; R2 = 0.4842; MSE = 0.9455; c.v. = 8.60%7

where


6. The figures in parentheses are the ratios of the estimated parameters to their
estimated standard errors.
7. R2 is the coefficient of determination; R2 is Theil's adjusted R2; MSE is
means square error; and c.v. is the coefficient of variation.







Xz = natural logarithm of the distance from the field to Lake
Okeechobee measured in miles and rounded to the nearest half
mile;
B, =the product of the number of accumulated hours between the
temperatures of 28 F and 300 F and the natural logarithm of the
distance from the field to Lake Okeechobee measured in miles and
rounded to the nearest half mile plus one;
and all other variables are defined as before.
Period of harvest (H) seems to be a significant factor in determining
PRS. The response is modeled linearly here because higher order terms
were not found to be significant when protesting. The results do not con-
firm a priori expectations which envisioned a quadratic relationship.
Probably this is due to the fact that the sample data are an aggregate of
fields observed only once at the time the grower chose to harvest
them. This is complicated by the fact that growers have a definite idea of
the acceptable range of PRS for harvesting. They test standing cane for
PRS frequently throughout the season and harvest a field when it comes
up to standard. This process tends to reduce variability in the observa-
tions.
The positive response of PRS to mechanical harvesting is also con-
trary to prior expectation. Mechanical harvesting was expected to bruise
cane to a greater extent than hand harvesting. This would result in the
milling of a greater proportion of cane tops, which contain a high level of
invert sugar, and these conditions were expected to impede the recovery
of sugar. Such was not the case, however. A possible explanation for the
positive response is that average time for harvesting to milling is less for
mechanical systems, and this may reduce deterioration. Such an explana-
tion cannot be given much credence on the basis of sample alone. A com-
plicating factor is that a large proportion of the observations of
mechanically harvested cane are for sandy soil which generally promotes
high PRS. Nevertheless, research concerning the effects of mechanical
harvesting on PRS appears to be in order. With respect to year of cycle,
(Y) many varieties seem to exhibit a slight decrease in PRS, while a slight
increase was observed for variety CP 63-588. It should be noted that CP
63-588 was chosen as the variety to which all others are compared
because a preview of the data seemed to indicate that it is an average
variety with respect to both net tons and PRS. It was hoped that other
varieties would respond to environmental conditions in a similar way,
thereby reducing the number of variables required by the model. This
strategy seems to have worked well except for the variable Y in PRS
equations.
The time variables (T) were not significant individually, and did not
improve model fit; thus they were dropped from the model.







NET TONS

Initial analysis indicated that net tonnage declined as the stubble
aged. When the mean values for net tons of cane were plotted against
year of crop cycle (stubble age), the result resembled Figure 4. This sug-
gests that the decline of net tonnage may be represented by an exponen-
tial decay function. When the data were stratified according to
soil/variety groups, rates of yield decline were observed, suggesting that
a decay factor should be estimated for each soil/variety group. Thus the
following model was specified:

9
N, = a + El 3gD, exp (-geY) + ZP
g=1

where Q, is the decay rate for the g'h soil/variety group, Z is a composite
of all other variables in the model, and F is a vector of parameters
associated with other variables,
The preceding model is non-linear in the parameters. Specification
searches, on the other variables in the model, such as the freeze variables,




40-


36-


32-


28-
I-
z 24-


20-


16-






1 2 3 4 5 6

FIGURE 4. Typical relationship of net tons of cane to year of crop cycle.







were still required. The expense of an involved specification search via
non-linear estimation would have been substantial. An alternative ad hoc
approach was taken. First an estimate of L for each variety group was
obtained by specifying Ng (net tons for soil/variety group g) as solely a
function of Y:
(5) N, = wexp (- gY) E
where e is the disturbance. Taking the natural logarithm of both sides
of (5) gives
(6) In (N,) = In(w) Q Y + In (e)

Ordinary least squares was applied to (6), yielding a preliminary estimate
of Qg. The estimated values of Qg were substituted into the exponential
decay function. The exponential function was treated as a constant and
specification search was conducted on the other variables in the model.
For details, consult Crane (1979, pp. 75-80). Once a specification of the
complete model was chosen then the model was re-estimated using a non-
linear estimation procedure in order to gain more precise estimates of Qg.
The resulting model was

(7) No=0.00183680A +3.92F2+4.28 F3+ 2.32 F4+ 5.54 F,+ 10.11 F6
(0.49)8 (1.04) (1.93) (1.21) (3.18) (4.55)

6.50 U+ 39.89719081 E, + 42.36686120 E2+ 20.72549548 E3
(-2.25) (4.94) (5.01) (3.03)

+ 38.80605163 E4+ 28.89592754 E, + 48.27300512 E6
(5.04) (3.25) (5.09)

+ 48.29756186 E7+24.803191116 E8+ 34.40631495 E9
(4.73) (2.59) (2.06)

-5.17 M-0.60799543 X+0.2836737 W, +0.70592518 0
(-2.37) (-5.53) (1.13) (4.15)

+ 0.31254383 H-0.29841355 B,-2.6946803 D3X+ 0.50716890 D30;
(2.08) (-3.32) (-3.33) (2.31)

R2=.6747, R =.6495; MSE = 51.44; c.v. = 19.82%
where E,= Dg exp( gY):


8. The figures in parentheses are ratios of the parameters to their asymptotic
standard errors. See Gallant (1975, p. 80).







e, = 0.352;
Q2 = 0.244;
Q3 = 0.255;
Q4 = 0.246;
65 = 0.097;
Q6 = 0.128;
Q7 = 0.140;
08 = 0.073;
Q9 = 0.320;
U = 1, if the observation is for plant cane successively planted;
= 0, otherwise;
B, = accumulated number of hours below 320 F in the period
beginning two weeks after planting or harvesting and running
through the end of the season in which the cane was planted
or harvested;
and all other variables are defined as in (4).
The variable U pertains only to plant cane of a successive crop. It was
anticipated that ratoons of a successive crop would consistently produce
less than ratoons of a fallowed crop, but this relationship cannot be
established. The coefficient of U, -6.50, indicates that plant cane of a
successive crop yields 6.50 tons less, on the average, than plant cane of a
fallowed crop.
M is the indicator variable associated with mechanical harvesting. Its
coefficient, -5.17, indicates that on the average, mechanically harvested
cane produces 5.17 less net tonnage of cane. The sign of the coefficient was
not unexpected, as the data were adjusted by a 5 percent deduction for
trash for handcut cane and a 10 percent deduction for mechanically
harvested cane. The magnitude of the coefficient, however, was surpris-
ing, as the differential in trash deduction cannot account for a 5-ton dif-
ference. The explanation may, in part, lie in the fact that almost all cane
on sand is mechanically harvested and yields lower tonnage.
The weather variables A and B, possess coefficients which conform to
a priori expectation. The coefficient of X, distance from Lake
Okeechobee, demonstrates the beneficial influence of the lake on cane pro-
duction. The estimated coefficient of X, -.608, indicates that for each
mile farther from the lake, tonnage decreases, on the average, by 0.608
tons. Thus a field ten miles from the lake with similar soil type, planted
with the same variety, and managed by the same firm, would be expected
to yield over 6 tons less cane per acre than a field next to the lake.
The time variable (T) was not shown to be significant. This is similar
to the result found for the PRS equation. This result indicates that effects
due to time are captured by the weather variables. This is consistent with
the consensus that producers respond little to changes in input or output
prices.








A CONCEPTUAL MODEL FOR THE
REPLACEMENT DECISION

The sugarcane grower is faced with a tradeoff between declining
sugar yield and the cost of replacing aging stubble, which includes the
cost of seed cane, the cost of plowing under the old stubble, cultivation,
leveling and replanting, and possibly the loss of revenue during a year of
fallow plus any costs of fallow maintenance. This problem has been ad-
dressed by Halsey (1976). His approach, however, does not incorporate
the concept of time-value of money.
In this section we develop a conceptual model of the stubble replace-
ment decision. The discussion is brief, and the interested reader is re-
ferred to Crane (1979, pp 24-53) for a more detailed exposition.

ASSET REPLACEMENT

The aging stubble may be viewed as an asset with declining produc-
tivity. According to Terborgh, the replacement decision consists of two
separate operations. The first is the selection of a "challenger," that is,
the best possible replacement for the existing stubble. The second is to
determine whether the challenger is valid, i.e., whether the "defender"
(the existing stubble) is replaceable. Other authors, including Perrin
(1972, 1974), have adapted a deterministic model for use in agriculture
and have applied it to the problem of deciding when to replace apple or-
chards. The first operation, selection of the challenger, relies heavily
upon Preinreich's model (Preinreich, 1940), commonly referred to as the
constant chain model. The challenger is specified as an infinite chain of
identical replacements and hence is associated with "replacement
policy." This concept is a modification of Hotelling's model (Hotelling,
1925), in which a single asset is considered without replacement and
which, therefore, is associated with "retirement policy."
The concept of a constant chain model requires some further
development. Suppose a field is planted and allowed to ratoon s 1 years
and thus s crops are harvested before replacement. If R, is the net revenue
associated with year t (t = 1, . s) and r is the discount rate, then the
discounted return (D,) over the lifetime of that stubble is
s
(8) D, = E (1+r)-'R,- K
t=

where K is the initial cost of planting. If in year s the field is replanted
and kept another s years, then the return over the lifetime of that stubble,
discounted to the present, is








(9) D2 = (l+r) [ E (1+r)-'R,- K
t=1
= (l+r) -sD,.

The discounted return (D) associated with an infinite chain of identical
replacements is

(10) D = D, + (1+r)sD, + (1 +r)-"D, + ..

This expression is an infinite geometric series, as (10) can be re-written as

(11) D = D,(1 + (l+r)-s + (l+r)- + . .)

=D,
= 1 -(1+r) -
or

(12) D- E E (1+r) -'R, K
1-(1 +r)-1 t=1

Equation (12) expresses the discounted return from an infinite chain
of identical replacements, where each replacement is to keep the stubble s
years. The expression inside the brackets of (12) is the discounted return
from one stubble, and the factor outside the brackets converts this to an
infinite chain.
Selection of an appropriate challenger requires that equation (12) be
maximized with respect to s. Denote the maximized discounted net return
by D*.
The analysis may now proceed to the determination of whether the
challenge is valid. In a going concern, the life of the defender may be ex-
tended one, two, or more years, but eventually it will be replaced by the
best available challenger. Assuming no technological advance, then the
replacement alternatives are: (i) replace the defender immediately or (ii)
extend the life of the defender by T years and then replace. An ap-
propriate selection criterion is to compare the net present values of the
infinite revenue streams generated by each alternative. This criterion may
be expressed as:
T
(13) replace if D* > E (1+r)-'E, + (l+r)-7D*
t=1

where Et is expected net revenue in year t if the defender's life is ex-
tended. In this form replacement is justified when the challenger's con-







stant chain exceeds the defender's own constant chain, in which the first
link is the present value of net revenues obtained by extending the life of
the defender T years.
In the case where there is no salvage value, and expected net revenue
from the asset is declining such that E, > E,., for t, then we may con-
sider, without loss of generality, only the case where the defender's life is
extended one year (T= 1) (Crane, pp 28-29). Then (13) becomes

(14) replace if D* > (1 + r)-' E, + (1 + r)-1 D*

Manipulating the inequality (14) yields

(15) D* 1 D* > 1 E ,
1+r l+r

(16) D* r > 1 E,,
l+r l+r

(17) rD* > E,.

Equation (17) says replace if r D* > E,. E, is the return if the existing
stubble is allowed to ratoon one more year; rD* is given by (18),


(18) rD*= r E [ (l+r)-'R, K
1-(10 +r)- t=1


and is seen to be the discounted net return from an infinite chain of iden-
tical replacements multiplied by the interest r. rD* may be interpreted as
the annualized value of D* where D* is the principal of an annuity in
perpetuity. In other words, rD* may be viewed as the average return
from the infinite chain associated with the challenger.
Decision rule (17) is convenient and provides the basis for the stub-
ble replacement decision.

ASSET INTERDEPENDENCE

There is a complicating factor relating to sugarcane production in
Florida which prevents direct application of equation (17). Cane growth
takes place during the warm season from April to September, when
sucrose content is low. When cool weather arrives, growth is retarded
and sucrose accumulation in the stalk begins. Sucrose accumulates
throughout the cool season for most varieties of cane. Thus, sugar yield
is generally approaching its maximum in March. A portion of sugarcane
fields in Florida must be harvested before they reach maximum yield to







allow time for processing the whole crop through the sugar mills (Kidder
and Lyrene, 1976). This is because the high capitalized value of sugar
mills requires an extended harvest and grinding season in order that fixed
costs be averaged over a large production volume (le Grande, 1972, p.
193).
Arrangements are made between growers and processors in which
growers agree to deliver cane throughout the harvest period of November
to March. Thus, the grower is constrained through mill quotas in the
choice of when to harvest, and sugar yield depends directly upon date of
harvest. Therefore, the annualized value of challengers for a particular
field cannot be computed without considering date of harvest for that
field. For example, suppose a particular challenger is to have this
schedule: fallow, harvest plant cane, and let the field ratoon two times.
The return from the challenger will differ if plant cane is harvested in
March, first ratoon harvested in January, and second ratoon harvested
in December, compared to the same number of ratoons, but always
harvested in March. The replacement decision cannot be made on a field
by field basis; rather, all fields must be considered simultaneously in
order to maximize total revenues to the firm subject to the mill delivery
quotas.


THE CANE GROWER'S MAXIMAND
In developing a replacement model, we must take into account the
differences between independent growers, who sell their cane to a mill,
and administration growers, who may be either corporations growing
cane for processing in their own mills or growers who are members of a
milling cooperative. This distinction is useful because administration
growers have a direct stake in the profitability of raw sugar processing,
whereas independent growers do not.

INDEPENDENT GROWER
Assuming the cane grower's sole objective is to maximize the net
present value of his infinite income stream, the independent cane
grower's maximand may then be stated on a per acre basis, for conven-
ience, as:

(19) Max R, = R C
where R, = net revenue per acre;
R = gross revenue per acre; and
C = operating cost per acre.
Gross revenue per acre may be stated as:
(20) R = pQ







where Q = number of standard tons per acre,
p = price received per standard ton on dollars.9
Standard tons may be calculated by applying a standard quality factor to
net tons as:

(21) Q = fN
where f = standard quality factor, and
N = net tons per acre.
A formula to determine f as a function of percent of recoverable sugar
may be given as:

(22) f = 0.19375 + 0.1077 X
where X is percent of recoverable sugar (PRS).10 Substituting from (20),
(21), and (22), equation (19) becomes:
(23) Max R, = pN(0.19375 = 0.1077X) C."
Equation (23) is constrained by the inherent capabilities of available
sugarcane varieties with respect to attainable magnitudes of N and X.


ADMINISTRATION GROWER
For the grower of administration cane, the appropriate maximand
has not yet been identified, because payment by standard tons does not
fully allocate processing costs. To achieve efficient allocation of process-
ing costs to cane purchases, the price should, as a minimum, be adjusted
for sucrose content. A case could also be made for adjusting price to ac-
count for trash and fiber content as well. A number of studies have
shown that the presence of trash will inhibit sucrose recovery and retard


9. The price paid to the grower per standard ton of cane delivered may be
calculated byp = 0.75 + 1.15 PNy,
where P,, = New York spot price for raw sugar in cents per pound
(Derived from Table 25, Appendix 2). Using the 1976 average spot price
for domestic raw sugar of 13.31C gives a price per standard ton of
$14.56. Inclusion of 73C per standard ton as a molasses payment brings
this to $15.29. (For an explanation of the molasses payment see Appen-
dix 2).
10. Derived from Table 2.

11. Equation (23) may be restated as: Max R = p (0.019375 N + 10.77 S) -
C, since S = N(X/100) where S is number of tons of sugar per acre. Evaluated at p
= $15.29, this becomes Max R = 0.0296 N + 164.67 S C. Considering the
small coefficient for N and the normal range of values of N (20 to 60 tons), it ap-
pears that a strategy to maximize revenue based on standard tons of cane is little
different from a strategy to maximize revenue based on the quantity of sugar pro-
duced per acre.







the milling rate;12 therefore, a simple substraction of trash weight is not
sufficient to account for all the losses due to trash. An increase in fiber
content will also reduce the milling capacity (le Grand and Martin, 1970,
p. 7).
Calculation of the latter two effects is less straightforward than is
the effect of sucrose content. The information necessary to calculate
them is not routinely recorded; presumably the magnitudes are less than
for the sucrose effect. Therefore, only adjustment for sucrose content
will be treated here. This does not mean that adjustments for trash and
fiber content may not prove important, but merely that a full treatment
is beyond the scope of this study.
Sucrose adjustment. The variable operating expenses of harvesting,
hauling, and processing are primarily a function of the gross tonnage of
cane handled. The capacities of harvesters (human as well as mechanical)
and transport vehicles and the grinding capacity of the mill are all limited
on the basis of tonnage of cane. If trash content is taken as a given con-
stant, processor operating costs may as well be expressed on a per net ton
basis. Thus, the operating expenses of harvesting, hauling, and process-
ing to be imputed per ton of sugar produced are inversely related to the
percentage of recoverable sugar in the cane handled. This relationship
may be expressed as:

(24) C, = (C, /X) x 100

where C, = processor operating cost per ton of sugar,
C, = processor operating cost per net ton of cane,
X = percent of recoverable sugar per net ton of cane
(PRS).

The rate of change of operating cost per ton of sugar for small changes in
X is given by:

(25) ac, 0ooc
ax X2

For participating processors during the 1975 season, Brooke (1977)
found the average operating cost per net ton of cane for harvesting and
hauling to be $6.50, and for processing, $7.22, giving a total operating
cost to the processor of $13.62 per net ton. The average percent of
recoverable sugar in Brooke's study was 10.52 percent. Evaluating (25) at
these levels gives


12. See: Bianchi and Keller, 1952; Etheredge and Henry, 1943; Keller and
Schaffer, 1951; Louisiana State University and AMC, 1946.







(26) C, = -100(13.62) = 12.31.
ax (10.52)2
Therefore, a decrease of 1.00 in value of X (e.g., X falls from 10.52 to
9.52) will increase processor operating costs per ton of sugar by about
$12.00. This response is significant, and will be considered by the grower
of administration cane.
The sucrose adjustment may be conceived as an offset to a change in
the cost of producing raw sugar as a consequence of a change in the cost
of processing the net sugarcane from which it is derived. The sucrose ad-
justment may be stated on a per acre basis as
(27) 6 = ZS
where 6 = sucrose adjustment per acre;
S = tons of recoverable sugar per acre;
Z = a processing factor to prorate the differential
processing cost for each ton of sugar produced.
The processing factor is given by
(28) Z = C C

where C, = average processor operating cost per ton of
sugar;
C = professor operating cost per ton of sugar for the
cane actually being milled.
Substituting from (24) into (28) gives

(29) Z = [(c, / X) (CN/X)] 100

where c, = processor operating cost per net ton of cane;
X = average PRS;
X = actual PRS.


OPTIMAL REPLACEMENT FOR SUGARCANE
The replacement decision may be reached with the aid of a series of
three optimization models. The three programs are called: (i) policy pro-
gram, (ii) harvest program, and (iii) replacement program. These pro-
grams are related as illustrated in Figure 5. This decision process takes
place during September of Season 1.
The policy program is comparable to Terborgh's operation of select-
ing the best challenger. This program requires, as input, information
describing the available resource set. This information includes types of
land and varieties of cane as well as forecasts of product and factor
prices and of weather conditions. The policy program does not consider













































FIGURE 5. Diagram of the three-step replacement procedure.


the state of cane actually growing during Season 1; rather, it addresses
the questions of how one would organize resources, which varieties
would be grown on each type of land, how many years each would be
grown, and during which period each would be harvested, if one were to
begin the operation free of the encumbrance of existing stools of cane
and if all forecast variables actually were to attain expected values. The
output of the policy program can be used to identify logical rational pat-
terns from which a number of "reasonable" challengers can be defined.


35







An annualized value can be computed for each of these challengers; and
this information is required as input to the replacement program. The
policy program serves as a screening device to reduce the multitude of
potential challengers to a manageable number.
The harvest program not only requires the same types of-informa-
tion input as the policy program, but it also requires information con-
cerning the state of existing crops as of September, Season 1, which will
permit prediction of yield for each field of cane for each potential
harvest period. The harvest program then produces a revenue-
maximizing harvest schedule. While the harvest program is of con-
siderable value to the cane grower in its own right, its principal purpose
in the current study is to date the harvest of a particular field of cane dur-
ing Season 1, so that the age of cane as of September, Season 2, can be
calculated. This information is valuable for the prediction of yield for
each field during Season 2.
The replacement program compares the forecast revenues from each
defending field and possible period of harvest with the annualized values
for the appropriate challengers. The solution of the replacement pro-
gram indicates which fields are to be left to ratoon in Season 2 and which
are to be replaced in order to maximize revenue. In the case of fields to
be replaced, the replacement program identifies the replacing challenger.
For those fields not replaced or those successively planted, the program
generates an optimum harvest schedule in Season 2. The grower,
however, will update this schedule as new weather information is re-
ceived during the growing season.

POLICY PROGRAM
The choice of which varieties to grow and how long to grow them is
similar to the choice of a crop rotation plan as discussed by Hildreth and
Reiter (1951, p. 144). However, whereas Hildreth and Reiter concentrate
upon the determination of a rotation for a particular parcel of land,
from which an overall farm plan may be inferred, the approach taken
here will be to determine the overall farm plan for a typical year and infer
the crop rotation from this. 1 For instance, if the farm plan in the typical
year calls for a quarter of the land each to be placed in fallow, plant
cane, first ratoon cane, and second ratoon cane, then it may be inferred
that the crop cycle on any particular field begins with a fallow and that
cane is grown for three harvests before the stubble is plowed under and
the field put to fallow once more. The farm policy will be assumed to
repeat itself from year to year indefinitely until a change in the cost struc-
ture of technological advance favors a new policy.


13. Walker (1972, p. 6) has used such an approach.







Of course, the probability that any actual farm ever replicates the
rotation implied by the solution to this policy program is effectively zero,
since the policy is based only on expected values while actual crop per-
formances vary considerably. The purpose of the harvest and replace-
ment programs is to bridge the gap between policy and practice. The pur-
pose of the policy program is merely to assign reasonable values to ap-
propriate challengers which may be used as minimum standards of per-
formance required of defending crops.
It is convenient to classify the land on the basis of soil type and
distance from Lake Okeechobee. The normal harvest season from Oc-
tober 31 through March 31 may be divided into eleven 14-day periods.14
Traditionally, a fallow period has been introduced between each
crop cycle. This fallow may be either a dry fallow or a flood fallow; the
distinction will not be made here. In recent years, however, it has become
more popular to plant a short term crop in the interim or to replant cane
immediately. The latter practice is known as "successive planting."
When cane is successively planted, yields for the plant crop and all ra-
toon crops are expected to be lower than for cane which has been fal-
lowed. Furthermore, replacement is expected to occur at an earlier date
for successively planted cane than for fallowed cane. However, the cost
of maintaining a fallow and the loss of year's revenue are avoided.
The policy program does not consider alternative crops, but the suc-
cessive cropping alternative is included. It is specified that a given field of
a successively planted crop must be succeeded by a fallow, but a fallowed
crop may be succeeded by any of the three types of crop rotations as
described below.
i) After a fallow, a variety of cane, i, is grown for a number of years,
I, and is then succeeded by a fallow and another crop cycle of I years and
so forth.
ii) After a fallow, a variety of cane, i, is grown for a number of
years, I, and is followed by a successive crop of variety i*, which may or
may not be the same as i. Variety i* is allowed to grow for Jyears. After
this, the rotation repeats.
iii) Following a previous crop as a successive crop, variety i* is
allowed to grow for J years. After a fallow, variety i is grown for Iyears
and the rotation is repeated.
It is possible to calculate the annualized value of challenger c as
follows:



14. Cane is normally not harvested prior to October 31 except for planting
material (seed cane). This operation will be treated as completely separate from
sugar production and will not be included in the farm plan. Harvesting of cane
may run into April, but most firms attempt to finish by the end of March.







(30) A, = g p
where pi = net present value of the first link in the
constant chain of challenger c,
g = r is the capital recovery factor,

r = discount rate
s = the number of years in each link of the
constant chain.
The policy program can be formulated as an integer programming
problem. A mathematical formulation of the problem is given in Appen-
dix 3.


HARVEST PROGRAM
The next step toward optimal replacement is a model to determine
the optimal schedule for harvesting the current crop. This program is
most useful in September as an aid to scheduling before the harvest
season begins; however, it may be recalculated at any time during the
season should circumstances such as a severe freeze materially alter ex-
pected revenue per acre for any of the remaining fields. Since this pro-
gram is only concerned with harvest scheduling, fields in fallow are
disregarded.
The harvest program can be formulated as an integer programming
problem. A mathematical formulation of the problem is given in Appen-
dix 3. The problem can be viewed as an assignment problem that is, a
problem of assigning fields to harvest periods. Thus the mathematical
formulation is a special case of the classic transportation problem; it can
be solved via linear programming and will have an optimal integer solu-
tion.15
The solution to the harvest program provides information on ex-
pected yield of the crop in the current year and expected age of the crop
just prior to the start of the following season. This information is useful
in forecast of yields and revenues for the following season.


REPLACEMENT PROGRAM
It is now possible to determine an optimal replacement pattern by
forecasting expected revenues for all fields for the following year, and
comparing these projected revenues with the annualized value of each of


15. There exists a variety of algorithms designed to exploit the special struc-
ture of the transportation problem to allow for faster solution; see Hillier and
Leiberman (1974, pp. 119-135).







the available challengers. The forecast includes those fields currently in
fallow, since the replacement decision has already been made for these.
The replacement program is a model which determines an optimal
harvest schedule next season by simultaneoulsy considering existing
fields and potential challengers. Mathematically, it is equivalent to the
harvest program, and as such is a special case of the classic transporta-
tion problem. Thus, it may be solved via linear programming and yield
optimal integer solutions. A mathematical formulation is given in Ap-
pendix 3.
The solution to the replacement program completes the optimality
routine and provides the information needed to decide whether a given
field should be allowed to ratoon, should be replaced with a successively
planted crop, or should be placed in fallow after being harvested in the
current season. This decision process requires prediction of revenues
more than a year in advance.


DEMONSTRATING THE DECISION PROCESS
FOR A HYPOTHETICAL FIRM

DESCRIPTION OF THE FIRM

A hypothetical firm is used to illustrate the decision process; no ac-
tual firm of its size is likely to exhibit the degree of complexity described
here. The types of decision to be made, however, are the same types
which must be made by all sugarcane growers in Florida. The reader is
urged to pay less attention to the problem specification 6 to the solution
technique, since it is quite easy to make use of additional information by
incorporating appropriate restrictions into the model. The solution ob-
tained for this hypothetical firm should in no way be considered a recom-
mendation to be followed by any individual firm.
The hypothetical firm, hereafter called Firm F, produces sugarcane
in such a way that productivity is dependent primarily upon the varieties
selected, when they are harvested, how many years they are allowed to
ratoon, and weather variables. In this case, operating costs (other than
differential costs of the successive planting option) are not a factor in the
decision process. Therefore, the maximand for Firm F, which is assumed
to be an administration grower, reduces to
(31) max R = p(0.019375 + 0.1077 X] N + Z N (X/100)
where R = gross revenue per acre;
X = PRS;
N = net tons;

16. The number of fields, specific varieties considered, etc.







p = price per standard ton of cane;
Z = the sucrose adjustment, 129.468 (1362/X).
Firm F operates a number of plantations comprising a total of 55
fields ranging from 0.5 to 19.5 miles from Lake Okeechobee. These
fields are grouped into six land classes according to soil type and distance
from the lake as shown in Table 8. The varieties considered for illustra-
tion purposes are shown in Table 9.
Production on the firm's 55 fields is considered for three seasons, 0
through 2. The decision process is being conducted during September of


TABLE 8. Land classification for Firm F.
Distance of Average distance Number
Land Soil land class boundaries of fields of
class type from Lake Okeechobee from Lake Okeechobee fields
---------------------------- miles -----------------------

1 custard apple 2 0.857 8

2 standard muck 2 1.417 6

3 standard muck 2--5 4.000 8

4 standard muck 5--10 7.375 12

5 standard muck 10 15.643 14

6 sand 2 1.786 7


TABLE 9. Variety/soil-type groups to be considered in Firm F.
Maturity Soil
Variable Variety characteristic type

D, CP 63-588 mid-season standard muck

D2 Cl 41-223 late custard apple

D, Cl 41-223 late standard muck

D, CP 56-59 mid-season standard muck

D, Cl 54-378 early standard muck

D, CP 57-603 late custard apple

D7 CP 57-603 late standard muck

D, Cl 41-191 late sand

D, Cl 49-198 early/mid standard muck








Season 1. The firm must decide when each of the fields should be
harvested during the current season. If the fields are allowed to ratoon,
the firm must also decide which of the harvested fields to replace, using
projections of performance in Season 2. Information about the state of
the fields in Season 0 is presented in Table 10.

TABLE 10. Description of fields operated by Firm F as of September 1, Season 1.
Distance Prior
Field from lake Soil Year of mode of Age of
Number in miles typea Variety crop cycle harvestb canec
301 1.0 0 Cl 41-223 3 0 15
302 0.5 0 Cl 41-223 8 0 17
303 0.5 0 Cl 41-223 8 1 17
304 1.5 0 C1 41-223 5 0 16
305 0.5 0 Cl 41-223 8 0 17
306 1.0 0 Cl 41-223 7 0 17
307 1.0 0 Cl 41-223 1 0 14
308 1.5 0 --- Od
309 0.5 1 CP 57-603 8 0 17
310 1.0 1 CP 57-603 8 0 17
311 1.5 1 CP 57-603 4 0 15
312 1.5 1 CP 57-603 1 0 14
313 2.0 1 Cl 41-223 1 0 15
314 2.0 1 --- 0 -
315 2.5 1 Cl 41-223 8 0 18
316 3.5 1 Cl 41-223 2 0 16
317 5.0 1 CP 63-588 2 0 16
318 5.0 1 Cl 41-223 1 0 15
319 5.0 1 Cl 41-223 2 0 18
320 4.5 1 Cl 41-223 3 0 18
321 4.0 1 Cl 54-378 2 1 22
322 4.0 1 --- 0 -
323 5.5 1 C1 54 378 2 0 22
324 8.5 1 Cl 41-223 1 0 15
325 6.5 1 Cl 54-378 4 0 22
326 6.0 1 CP 56-59 4 0 21
327 8.5 1 Cl 56-59 2 0 14
328 9.0 1 Cl 41-223 2 0 19
329 8.5 1 Cl 41-223 3 0 19
330 8.0 1 CP 56-59 2 0 20
331 6.0 1 CP 63-588 1 0 16
332 6.0 1 CP 63-588 2 0 16
333 6.0 1 --- 0 -

Continued







TABLE 10. Continued.


Prior
Soil Year of mode of Age of


crop cycle harvest cane'


Field
Number
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355


aO = custard apple; 1 = standard muck; 2 = sand.
b0 = hand harvested; 1 = mechanically harvested.
CIn two-week periods.
dA value of zero for year of crop cycle indicates that the field is held in fallow.


THE POLICY PROGRAM
AN LP SOLUTION
The first step in the decision process is to find the solution to a
policy program, as discussed previously. A matrix generator was written
for the policy program and each of the other decision programs so that
basic information necessary to specify the problem can be easily used to
generate the complete data set necessary to solve the problem in a format
suitable for use as input to a linear or integer program."7


17. All linear and integer programs are solved using the IBM MPSXVIM7.
The matrix generators are written in SAS 76.6D and will produce output in ap-
propriate format for either the LP or MIP options of MPSXVIM7.


Distance
from lake
in miles
7.5
12.0
12.5
15.5
10.5
16.5
14.5
16.5
18.0
17.5
18.5
19.5
19.0
10.5
15.0
1.5
2.0
2.0
1.5
2.0
2.0
2.0


typea
1
1
1
1




1
1
1
1




1
1
1
1
1
1
1
2
2
2
2
2
2
2


Variety

Cl 41-223
Cl 41-223
Cl 41-223
Cl 41-223
CP 56-59
CP 63-588
CP 56-59
CP 56-59
CP 56-59
CP 56-59
CP 56-59
CP 56-59


Cl 41-191
Cl 41-191
Cl 41-191
Cl 41-191
Cl 41-191
Cl 41-191







The information needed to set up the policy program is shown in
Table 11. Since the policy program attempts to identify a typical year in
an ideal farm plan, item 17 in Table 11, age of cane, must be postulated.
This is done as shown in Table 12.
Table 10 assumes that cane will be harvested during the season ac-
cording to its maturity characteristic but that heavier cane associated
with the earlier years of the crop cycle will be harvested later than the
lighter cane.
Harvest periods are two weeks long. Harvesting starts October 1;
however, during the first two periods cane is normally harvested only for
seed. Table 13 relates the variable for period of harvest (H) to calendar


TABLE 11. Information necessary to set up a policy program for Firm F.

Item Value specified


Number of land classes
Number of varieties considered
Successive planting option
Number of years of crop cycle allowed
Number of periods of harvest allowed
Restrictions on combinations of the above
Predicted gross revenue
Price per standard ton (p)
Cost of successive planting
Cost of fallow planting
Number of fields in each land class
Maximum number of fallow fields for each
land class


13. Maximum number of fields harvested per
period
14. Minimum number of fields harvested per
period
15. Average distance from lake for each land
class
16. Mode of harvest



17. Age of cane as of September 1
18. Accumulated hours below 32 F previous
season
19. Accumulated hours between 28 F and
30 F current season
20. Integer program option


6
7
yes
5
9
as discussed in text
generated by equations
$15
$140
$160
from Table 7

2 each for classes 4 and
5; 1 each for all others

6

4

from Table 7
land class 8 harvested
mechanically, other by
hand
from Table 11

from Table 13

from Table 13
no / yes







TABLE 12. Age of cane in two-week periods as of September 1 as postulated
for the policy program for Firm F.
Maturity Varieties Year of Age of cane in
characteristic included crop cycle 2-week periods
early Cl 54-378 53 21
>3 22

mid-season CP 63-588 -2 17
CP 56-59 3 18
Cl 49-198 4 19
5 20
late Cl 41-223 <2 14
CP 57-603 3 or 4 15
Cl 41-191 5 16



dates. Cane is normally harvested for sugar during periods 3 through 13,
although most firms attempt to finish the harvest as early in March as
possible. Firm F is assumed to harvest only during periods 4 through 12.
The yield predictions necessary to construct the policy program
assume that weather in the future will perform as the average of the ten-
season period 1967-1976. Therefore, weather variables are as follows:
degree days for the minigrowth period, April through August, A =
2072; solar radiation in Langley units for minigrowth period, W = 496;
solar radiation in adjusted Langley units for minigrowth period, W, =
295. Cool season temperatures necessary to construct variables Byand B,
are found in Tables 14 and 15.


TABLE 13. Harvest periods related to calendar dates.
Harvest period Calendar dates
1 Oct. 1 Oct. 14
2 Oct. 15 Oct. 28
3 Oct. 24 Nov. 11
4 Nov. 12 Nov. 25
5 Nov. 26 Dec. 9
6 Dec. 10 Dec. 23
7 Dec. 24 Jan. 6
8 Jan. 7 Jan. 20
9 Jan. 21 Feb. 3
10 Feb. 4 Feb. 17
11 Feb. 18 Mar. 3
12 Mar. 4 Mar. 17
13 Mar. 18 till end of harvest







TABLE 14. Average accumulated hours below 32 F and between 28 F and
30 OF by temperature station and period of harvest for the ten sea-
sons 1967-1976.
Temperature Period of Hours below Hours between
station harvest 32 OF 28 OF 30 F
South Shore 5 6 0.0 0.0
7 1.0 0.5
8 1.6 0.5
9 6.0 1.6
10 9.4 2.6
11 10.5 2.7
> 11 11.7 3.0

Okeelanta < 5 0.0 0.0
6 0.6 0.0
7 3.1 0.7
8 3.1 0.7
9 7.5 1.6
10 8.3 1.6
11 9.3 1.9
> 11 10.9 2.7
SOURCE: Federal-State Agricultural Weather Service (1969 through 1978).



TABLE 15. Average accumulated hours below 32 F for cane in its first cool
season (By) by temperature station and age of cane (0).
Age of cane Hours below 32 F (By)
(0) South Shore Okeelanta
< 16 0.0 0.0
16 1.2 1.6
17 2.3 2.6
18 5.7 3.4
19 10.1 7.8
20 10.7 7.8
>21 10.7 10.3
SOURCE: Federal-State Agricultural Weather Service (1969 through 1978).


It is assumed that the fields belonging to Firm F are deployed such
that, for land classes 4 and 5, Okeelanta Station is nearest; otherwise,
South Shore Station is nearest. Thus it is necessary to consider only
those.
To calculate the variables Bm take the value from the right-hand
column of Table 13 and multiply it by the natural logarithm of the







distance from Lake Okeechobee plus one (i.e., hours between 28 OF and
30 F x ln(x + 1)).
To calculate the variable By it is necessary to determine the period of
harvest or period of planting for the prior season. Adding one period to
this allows time for the cane to emerge from the ground; freezing
temperatures may occur from that time onward. Thus, accumulated
hours below 320F for the appropriate period are subtracted from the
season's total to determine the applicable number of hours. This is
related to age of cane as of September 1 in Table 15.
Returning to Table 11, we can see that, if every combination of land
class, variety, planting option (whether to fallow or successively plant),
year of cycle, and harvest period is permitted, the number of activities
which must be considered is 3780 (6 x 7x2x5x9). By referring to
Tables 8 and 9, however, variety/soil combinations which Firm F does
not wish to consider may be eliminated. Of the seven varieties con-
sidered, Cl 49-198 is grown only on sand, which appears only in land
class 6. Only two varieties may be grown on custard apple, Cl 41-223 and
CP 57-603. Six varieties may be grown on standard muck. Therefore,
since standard muck is the soil of land class 2 through 5, there are 24
(4 x 6) such combinations. Adding the three combinations of variety and
land classes will hereafter be called options. The restrictions referred to
in item 6 of Table 10 are those necessary to reduce the 42 potential
variety/land class combinations to the 27 options previously described.
This reduces the number of activities from 3780 to 2430 (27 x 2 x 5 x 9).
In the formulation of the policy program, each of these activities is
restricted to be an integer variable. This is an immense problem with
respect to the integer programming algorithm because processing time
and, consequently, the cost of obtaining a solution increase geometrical-
ly rather than arithmetically with the number of activities considered.
For this reason, some simplifying techniques are introduced which make
it impossible to verify optimality. Therefore, the output of the policy
routine is considered only a "very good" feasible solution. Still it can
help to define reasonable challengers which set minimum standards to
which defenders may be compared.
In an acutal case, of course, it is the responsibility of the grower to
decide how much money to spend searching for appropriate challengers
or, conversely, how informative the policy program must be for his pur-
poses. The expense of programming may be reduced by considering
fewer options, e.g. by eliminating or grouping varieties or by defining
fewer land classes to describe the total. The same objective can be ac-
complished by lengthening the harvest periods in order to consider fewer
of them by eliminating either of the planting options, or by reducing the
number of years of crop cycle permitted. Each of these tactics will prob-
ably reduce the quantity of information in the final solution.







The technique employed in the case of Firm F involves, as a first
step, the solution of the problem with the set of 2442 activities" using a
linear programming algorithm.
The solution value obtained is $1,589,040, which may be regarded as
the absolute maximum value for gross revenue which Firm F can obtain
from the specified resource set in a typical year.
Of the 27 available options (1 27) only the six described in Table 16
are in solution.

A RESTRICTED LP SOLUTION
Table 16 shows that wherever variety CP 57-603 is permitted to be
grown (i.e., on every land class except land class 6) it is the most prof-
itable variety to grow, according to the prediction equations previously
estimated. This result seems a bit suspicious, especially in view of data on
Table 2, which indicates that at no time since its introduction has variety
CP 57-603 accounted for more than 3.5 percent of total industry acreage.
In fact, its share is declining. The question was taken to a sugarcane
agronomist, who reported that variety CP 57-603 is susceptible to a
number of diseases and is thought to be intolerant to freezes. Thus, CP
57-603 may involve greater than average risk of failure, and growers are
hesitant to rely on this variety alone. In consideration of this situation,
the problem was reformulated to restrict CP 57-603 to be grown only
within five miles of Lake Okeechobee.
The LP solution of the restricted problem results in a functional
value of $1,473,160. It is unfortunate that the LP solution calls for such
things as the planting of 0.63636 fields with a particular variety, because
Firm F regards a single 40-acre field as the smallest parcel of land with
which it is practical to deal. This was the original reason for formulating
the problem as an integer program.

AN APPROXIMATE INTEGER SOLUTION
Feasible integer solutions may be obtained from the LP solution us-
ing "eyeball" techniques to rearrange activity levels. One such feasible
integer solution was found with a functional value of $1,433,520. This is
only $39,640 or 2.7 percent less than the optimal continuous solution for
the problem as specified by Firm F with variety CP 57-603 restricted to
fields within five miles of the lake. The options appearing in this feasible
integer solution are listed in Table 17.
Notice that options 18, 23, and 24 in Table 16 replace options 19 and
25 in Table 15. Thus, a late maturing variety is replaced by an early and a
mid-season variety.

18. Of the 2442 activities, 2430 are associated with gross revenue and six each
are associated with the cost of fallowing and successive planting.







TABLE 16. Description of options in the first linear programming solution of
Firm F's policy program.
Option Land Class Variety
2 1 CP 57-603
7 2 CP 57-603
13 3 CP 57-603
19 4 CP 57-603
25 5 CP 57-603
27 6 Cl 41-191



TABLE 17. Description of options in the linear programming solution of Firm
F's policy program with variety CP 57-603 restricted to be grown
only within 5 miles of Lake Okeechobee.
Option Land class Variety
2 1 CP 57-603
7 2 CP 57-603
13 3 CP 57-603
18 4 CL 54-378
23 5 CP 56-59
24 5 Cl-54-378
27 6 Cl 49-198



Activities in programming solutions are referenced by a code in the
format
opt h 'J'y 'K'H

where 'J' and 'K' are character constants pertaining to year of crop cycle
and period of harvest, respectively, which divide the code into segments
for easier interpretation; and
opt = a number identifying the option;
h = 1, if the option involves a fallowed crop;
= 0, if the option involves a successive crop;
y = a one-digit number for year of crop cycle;
H = a one or two-digit number for period of harvest
which in the case of Firm F can range from 4 to 12.
Thus the code 130J1K10 represents option 13 in its first year of crop cy-
cle (i.e., plant cane) which has been successively planted and is harvested
in harvest period 10.
Using the activity code just established, the approximate integer
solution is more fully described in Table 18 and revenue per acre
associated with each activity is presented in Table 19.







Consider the configuration of Table 18. All varieties, except the ear-
ly variety Cl 54-378 (18 and 24), exhibit the property that the heaviest
cane, associated with the early years of crop cycle, is harvested later than
lighter cane in order to take advantage of further growth and, particular-
ly, further accumulation of sucrose which results in more sugar per acre
in heavy rather than light cane. Where conditions are favorable for
growth, e.g. custard apple soil or standard muck close to the lake, cane
will be held for later harvest in preference to cane grown under less
favorable conditions. Consider, as an example of the foregoing, the rela-
tionship between options 7 and 13, both of which involve variety CP
57-603 grown on standard muck, and where 7 represents cane grown
within two miles of the lake and 13 represents cane grown from two to
five miles from the lake.
The response of PRS for the early variety Cl 54-378 to period of
harvest as determined by the regression equation is negative and linear.
Thus the LP algorithm selects heavier cane of this variety to harvested
first in order to take advantage of the higher sucrose levels."
Notice, however, that the mid-season variety CP 56-59 (23) is to be
harvested entirely in the last available harvest period; whereas, the later
maturing variety Cl 41-191 is to be harvested in mid-season. This is
because the prediction equation given by (4) does not predict much im-
provement in the sucrose level of Cl 41-191 throughout the harvest
season and, furthermore, Cl 41-191 tends to be lighter cane than CP
56-59. Cl 41-191 is guaranteed a place in the final solution because it is
the only variety which Firm F has considered for planting on its sand
land.
One interesting result is that as the problem is currently specified, it
will always pay to follow a fallowed crop with successively planted crops.
This may indicate that the cost of successive planting has been
underestimated. It may also be that current specification fails to account
for losses of productivity which may occur in ratoons of successive
crops, although such a relationship was not discovered in the sample.
Furthermore, the risk of pest build-up may be greater with successive
planting. It would seem worthwhile to conduct research in this area.

CALCULATING ANNUALIZED VALUE OF CHALLENGERS
For each option in the solution of the policy program there are two
challengers. This is so because the rotation for each class of land requires
two crop cycles. For example, the policy program seems to imply, for
land class 2, the rotation: fallow, 071J1K9, 071J2K8, 071J3K6,

19. A more accurate description of the maturity behavior of this variety may
involve a quadratic function. In such a case the lineup may not be straightfor-
ward.







Table 18. Approximate integer solution for Firm F's policy program.


Harvest Period Number of
Fields in
Land Class a Fallow
4 5 6 7 8 9 10 11 12
1 020J3b 020J1 021J1
021J4 020J2
020J3
[8] [2]c [3] [2] [1]

2 070J2 070J1 070J1
071J1 071J2
071J1 071J2
[6] [2] [2] [1] [1]
3 130J1 131J1
130J2
130J3
130J2
130J3
130J4
[6] [6] [1] [1]

4 181J1 180J2 180J1
(2) (2) (2)
181J2 181J3
(2) (2)
[12] [4] [4] [2] [2]






Table 18. Continued.


Harvest Period Number of
Fields in
Land class Fallow
4 5 6 7 8 9 10 11 12


2401J
(2)
240J3
(2)
[4]


241J3 241J1
241J2
240J2
(2)
[1] [4]


270J2
270J3
271J1
271J2
271J3
[5]


231J1
231J2
231J3
[3]


2701J


a. Numbers in brackets are total number of fields in each land class.
b. Harvest period identifiers are omitted from activity codes since this information is contained in the column heading.
c. Numbers in brackets under harvest period are total numbers of fields for a period for each land class.








070J1K8, 070J2K6. In other words, following a fallow, one crop cycle of
three years is followed by a successively planted crop cycle of two years.
This rotation is repeated every six years. However, the rotation may as
well be thought of as beginning with the successive crop: 070J1K8,
070J2K6, fallow, 071J1K9, 071J2K8, 071J3K6. These may be thought of
as separate challengers where, in general, the more rapid flow of money
arising from the challengers beginning with a successive crop makes its
annualized value higher. As the problem has been specified, however, the
latter challenger can only replace fallowed crops while the former can
replace any crop.


TABLE 19. Expected revenues per acre for activities in the policy solution.
Land Expected gross Total gross revenue
class Activity code revenue per acre for each land class


020J1K8
020J2K8
020J3K6
021J1K9
021J2K9
021J3K8
021J4K6
TOTAL LAND CLASS 1

070J1K8
070J2K6
071J1K9
071J2K8
071J3K6
TOTAL LAND CLASS 2

130J1K7
130J2K7
130J3K7
131J1K8
131J2K7
131J3K7
131J4K7
TOTAL LAND CLASS 3


---------------------Dollars---------------------
1026
1070
974
1173
1094
1015
916
7268 x 40 290,720


1015
986
1162
1027
906
5096 x 40

963
975
893
1105
975
893
812
6616 x 40


203,840


264,640


Continued








TABLE 19. Continued.
Land Expected gross Total gross revenue
class Activity code revenue per acre for each land class
--------------------- Dollars ---------------------


180J1K3
180J2K2
181JlK1
181J2K1
181J3K2
TOTAL LAND CLASS 4


231J1K9
231J2K9
231J3K9
240J1K4
240J2K3
240J3K4
241J1K3
241J2K3
241J3K2
TOTAL LAND CLASS 5


270J1K6
270J2K5
270J3K5
271J1K5
271J2K5
27153K5


TOTAL LAND CLASS 6


(693)
(755)
(816)
(753)
(698)
7430 x 40


864
725
612
2 x (580)
2 x (654)
2 x (590)
715
654
596
7815 x 40


4013 x 40


SUBTOTAL $1,529,520
LESS COST OF FALLOW: (8 x 40 x 160) (51,200)
LESS COST OF SUCCESSIVE PLANT: (8 x 40 x 140) (44,800)
GRAND TOTAL $1,433,520
aExpected gross revenue per acre x 40 acres per field. Excludes fallow and successive
planting costs.


297,200


312,600


160,520







A program was written to compute annualized values for the
challengers. Designating the challengers discussed in the previous
paragraph as CH3 and CH4, their annualized values are calculated in
Tables 20 and 21.
The annualized values of all challengers are calculated in like man-
ner and the results are presented in Table 22.


TABLE 20. Annualized per acre value of CH3 with r = 0.15.
Year of Year of Net Accumulated
crop crop Discount present net present
rotation cycle factor Revenue value value
---------------------dollars-----------
0 0 1.0000 -160 -160 -160
1 0 0.8696 -0- -0- -160
2 1 0.7561 1162 879 719
3 2 0.6575 1027 675 1394
4 3 0.5718 906 518 1912
4 0 0.5718 -140 -80 1832
5 1 0.4972 1016 505 2337
6 2 0.4323 987 427 2764
........................................................................................................
Total net present value:
Capital recovery factor (g) = 0.15 : $ 2764
1-(1.15)-6 x 0.2642

Annualized value of CH3: $ 730



THE HARVEST PROGRAM

Of the 55 fields described in Table 10, the 47 which are not in fallow
are to be harvested during the current season (Season 1).
According to the LP solution, revenue to Firm F from this season's
harvest amounts to $1,302,160. This is $131,160 below the expected an-
nual revenue associated with the policy solution.
The harvest schedule is presented in Table 23.


THE REPLACEMENT PROGRAM

To decide whether to replace a particular field during the current
season, it is necessary to project the revenue expected from each of the 55
fields for each of the nine available harvest periods if the cane is allowed
to ratoon in the following season. These values are then compared with
the annualized values of the 14 challengers to find the combination of








TABLE 21. Annualized per acre value of CH4 with r = 0.15.
Year of Year of Net Accumulated
crop crop Discount present net present
rotation cycle factor Revenue value value
----------------------dollars------------
0 0 1.000 -140 -140 -140
1 1 0.8696 1016 884 774
2 2 0.7561 987 746 1490
2 0 0.7561 -160 -121 1369
3 0 0.6575 -0- -0- 1369
4 1 0.5718 1162 664 2033
5 2 0.4972 1027 511 2544
6 3 0.4323 906 392 2936

Total net present value:
Capital recovery factor (g) = 0.15 :$ 2936
1-(1.15)-6 x 0.2642

Annualized value of CH4: $ 776




TABLE 22. Annualized per acre values for 14 challengers with r = 0.15.
Land First year
Callenger Variety class fallow Annualized value
------- dollars -------
CH1 CP 57-603 1 yes 798
CH2 CP 57-603 1 no 855
CH3 CP 57-603 2 yes 730
CH4 CP 57-603 2 no 776
CH5 CP 57-603 3 yes 713
CH6 CP 57-603 3 no 768
CH7 C1 54-378 4 yes 514
CH8 C1 54-378 4 no 544
CH9 CP 56-59 5 yes 481
CHIO CP 56-59 5 no 506
CHII Cl 54-378 5 yes 454
CHI2 Cl 54-378 5 no 488
CHI3 Cl 41-191 6 yes 477
CHI4 Cl 41-191 6 no 512













TABLE 23. Harvest schedule of 47 fields for Firm F in Season 1.
Harvest period
4 5 6 7 8 9 10 11 12
F321 F326 F330 F328 F315 F302 F301 F311 F307
(762)a (554) (719) (593) (513) (590) (865) (839) (1109)
F323 F350 F343 F329 F319 F303 F304 F313 F312
(797) (775) (619) (524) (780) (528) (655) (922) (1114)
F325 F351 F344 F340 F320 F305 F316 F318 F327
(663) (652) (511) (515) (732) (600) (779) (876) (763)
F352 F353 F345 F349 F335 F306 F317 F324 F339
(572) (608) (372) (671) (601) (610) (742) (820) (736)
F354 F336 F309 F331 F332 F341
(667) (538) (595) (877) (726) (735)
F337 F310 F338 F342 F346
(529) (606) (685) (861) (590)
aFigures in parentheses are expected revenues per acre in dollars.







defenders and challengers which will maximize expected revenue in the
following season. Once again this problem is solved with an LP
algorithm, taking advantage of the special structure of the problem as a
transportation problem.
A list of fields to be replaced and the challengers which are to
replace them is given in Table 24.
Notice that of the 22 fields to be replaced, 19 are replaced with suc-
cessive crops (even-numbered challengers). If the replacement program is
followed, expected annualized revenue in Season 2 is $1,585,560. This is
$282,400 better than the current season's expected revenue and$152,040
better than a typical year of the policy program. This latter bonus is a
windfall for Firm F, since few of its fields have previously been suc-
cessively planted and, therefore, many of them are eligible for this form
of replacement. The acutal expected revenue from a challenger exceeds
its annualized value. The implied harvest schedule for Season 2 is
presented in Table 25.

TABLE 24. List of fields to be replaced and replacing challengers.
Field Challenger Field Challenger
F302 CHI F318 CH6
F303 CH1 F319 CH6
F301 CH2 F320 CH6
F304 CH2 F326 CH8
F305 CH2 F327 CH8
F306 CH2 F336 CHIO
F310 CH3 F337 CH10
F309 CH4 F340 CH10
F315 CH6 F344 CH10
F316 CH6 F345 CH10
F317 CH6 F346 CHIO



CONCLUDING REMARKS

SUMMARY
Net revenue from the production of sugarcane tends to decline at a
declining rate with year of crop cycle. Although replanting is costly,
eventually it will pay to replace the stubble. This problem can be explicit-
ly analyzed with the aid of asset replacement theory by combining
knowledge of the production process with information concerning
resource availabilities, predicted prices, and prediction of future yields
through regression equations, grower judgement, or a combination of
the two. The grower formulates a general policy which comprises a














TABLE 25. Implied harvest schedule for Firm F in Season 2.
Harvest period
4 5 6 7 8 9 10 11 12
F323 F321 F330 CH10 F324 F311 CH6 F342 F307
(739)a (721) (620) (506) (613) (751) (768) (679) (964)
F333 F325 F343 CH10 F328 F312 CH6 CH2 F308
(870) (617) (524) (506) (602) (986) (768) (855) (1226)
^ F334 F351 F348 CHIO F329 F313 CH6 CH2 F314
(865) (642) (805) (506) (566) (774) (768) (855) (1248)
F347 F352 F350 CH10 F335 F331 CH6 CH2 F322
(830) (584) (767) (506) (515) (707) (768) (855) (1217)
F353 CH8 CHIO F349 F332 CH6 CH2 F339
(592) (544) (506) (660) (603) (768) (855) (592)
F354 CH8 CHIO F355 F338 CH6 CH4 F341
(617) (544) (506) (828) (575) (768) (776) (592)
aFigures in parentheses are per acre expected revenues in dollars for fields and annualized revenues for challengers.







number of typical crop rotations. From these may be identified
challengers with associated annualized values. After obtaining a pro-
posed harvest schedule for the current season, expected revenues for all
fields can be projected to the following season. These revenues are com-
pared with the annualized values for challengers using mathematical pro-
gramming. This provides the firm with a list of fields to be replaced and
identifies the challengers to replace them.


CONCLUSIONS
Conclusion 1. There appears to be considerable scope for im-
proving the efficiency of resource utilization at the firm level in the sugar
industry through use of the decision models developed in this study. Cur-
rently, a variety of rules of thumb are used in the decision process. These
rules effectively eliminate a vast array of alternative solutions. There is a
high probability that the more exhaustive search for production alter-
natives made possible with the aid of mathematical programming will
result in more efficient use of available resources.
Conclusion 2. Since the mathematical programming solutions
depend upon prediction of revenues for further periods, the ability to
make such predictions accurately is valuable to the sugarcane growers.
The first step to improve the accuracy of predictions is to keep better
records of the production process. At present, most growers do not
record quantities of fertilizers and chemicals applied to particular fields,
cultivation practices, or quantities of cane lost to pests and diseases.
Predictions made in the absence of such information are less accurate.


LIMITATIONS
The most severe limitation of the replacement model is that it
depends upon prediction of sugar yields and prices.20 The mathematical
programming solutions are no better than the information upon which
they are based. The predictions of sugar yield used in this study are based
on regression equations which are unable to account directly for pest
damage, fertilizer and chemical usage levels, cultivation intensity, and
water management practices. Furthermore, temperatures are measured
at only seven locations throughout the producing region, and radiation is
measured only for Belle Glade after 1972 and only for Miami and Tampa
prior to that time.
To the extent that these equations can be improved, the decision
model is improved as well. The grower should use what he believes to be

20. Prediction of prices is a consideration which is not treated in this report,
but it is necessary for the grower to make such predictions in some manner.







the best possible predictions of yield, whether based on regression equa-
tions, direct prediction by field personnel, or some combination of these.
A second limitation is the way in which defenders and challengers
are permitted to interact. The policy program is designed to identify a
relatively small number of viable challengers from a very large set in
order to bring the problem within manageable proportions. It must be
acknowledged, however, that such limitation may result in a suboptimal
solution. In extenuation of the approach taken here, there appears to be
ample opportunity for improvement, if not maximization, of firm net
revenues.
Another limitation of the model is that no means of incorporating
information about the general health and productivity of existing stools
was found. Yet, cane growers claim that this is a major consideration in
their own decision process.
A fourth limitation concerns the environment in which cane is
grown. The organic soils which make up the bulk of land planted to
sugarcane are subsiding at the rate of about an inch per year due to
microbial oxidation. Since data were not available on the effect of soil
depth on yield, the prediction equations were not able to take this into
account. Yield behavior may differ from predictions to an unknown ex-
tent as fields become increasingly shallow. A time will come when much
of the land will be too shallow for cane production with conventional
technology. It is expected that eventually firms will be forced to leave the
industry. This calls to question the appropriateness of an infinite chain
replacement model. However, the longest complete rotation in the policy
solution (Table 18) is eight years. So long as the remaining life of the firm
is sufficient to allow two or more rotations, the infinite chain result is
probably a very close approximation to a solution defined over the ap-
propriate finite horizon, because the effect of events so far in the future
is greatly discounted. When soil depth becomes a significant factor,
however, it would be well to switch to a firiite planning horizon.
Exclusion of alternative crops from the rotation is a further limita-
tion. However, the model may be easily extended to include this
possibility, as discussed in the following section.
The final limitation is the assumption of risk neutrality. This
assumption allows formulation of the objective function in terms of ex-
pected revenue. Often, however, the decision maker is concerned with
the variance of revenue as well. In the production of sugarcane there are
numerous factors influencing revenue which are beyond the control of
the grower. Among these are temperatures, radiation, pests and diseases,
and product and factor prices. To the extent that the set of potential
revenue values may be represented by a probability distribution function
given a decision concerning the level of controllable variables, the prob-
lem may be reformulated to incorporate the decision maker's attitude
toward revenue variance.







POSSIBLE IMPROVEMENTS OF THE MODEL
Three potential improvements of the model are: (i) incorporation of
alternative crops in the rotation, (ii) solution from the perspective of the
combined producer/processor system, and (iii) accounting for attitudes
toward risk.

ALTERNATIVE CROPS
It is possible to incorporate alternative crops in the rotation by pro-
viding additional activities in the various decision programs. These ac-
tivities must be appropriately constrained. For instance, if rice is to be
grown during the period otherwise devoted to fallow, the constraints
must be altered to allow rice to satisfy the fallow requirements. If the
alternative crop alters expected revenue from other activities, this infor-
mation must be included. For instance, if high levels of phosphorus ap-
plied to corn inhibit sucrose production in sugarcane crops which follow,
then separate activities must be established to distinguish cane grown
after corn from that grown after a fallow.

PRODUCER/PROCESSOR SYSTEM
So far, the decision analysis has been conducted from the perspec-
tive of individual cane growers. In formulating the maximand for ad-
ministration growers, it was acknowledged that these growers have a
direct stake in profitability of mills. An alternative question which one
may wish to investigate is how to maximize revenue to the combined pro-
ducer/processor system.
The industry could benefit from taking a systems approach to
resource usage which combines the objectives of producing and process-
ing. Currently, the objectives of producer and processor frequently con-
flict. For example, consider a cooperative which pays members for cane
based on standard tons and which distributes profits on the same basis.
This system of payment fails to account for all the costs of processing as
indicated in the discussion of sucrose, trash, and fiber adjustments. For
one thing, no individual member has any incentive to reduce standard
tonnage in favor of processing efficiency. For another, equity in income
distribution requires that all members be allowed to send cane to the mill
throughout the season in spite of the fact that another delivery alloca-
tion could produce greater overall revenue. Thus, it would be possible to
increase the income to all members by reallocating the delivery alloca-
tions to achieve maximum efficiency of production and then to distribute
the realized profits to producers in an equitable manner.
This problem may be solved using the programs where the number
of fields to be considered includes all of the fields supplying the given
mill and where the right hand side reflects resource constraints to the







system as a whole. The maximand is that of the administrative grower
with the possible inclusion of trash and fiber adjustments as previously
discussed. Alternatively, the problem may be reformulated to incor-
porate the processing costs associated with various production alter-
natives as activities.

RISK AND UNCERTAINTY
The estimated yield prediction equations show the importance of
weather and the significant role it plays in sugarcane production. The
current formulation of the replacement problem does not incorporate
risk considerations into the proposed decision role.
To include risk into the model, the perspective of the sugarcane
grower's objective must be broadened. In current formulation, a certain
environment is assumed, and the grower attempts to maximize the pres-
ent value of the infinite revenue stream from sugarcane production.
Hillier (1969) has introduced a model for the evaluation of risky inter-
related investments which appears to be suited to the sugarcane stubble
replacement problem. Hillier suggests that the appropriate combination
of investments is that combination which maximizes expected utility of
net present value of the variable revenue stream.2' In other words, one
must be able to specify the variance of revenue associated with each in-
vestment in order to calculate the variance of the net present value of a
set of alternative investment. This is necessary to determine the expected
value of utility associated with each combination of investments. The
combination of investments which maximizes expected utility is selected.
In order to implement this model it is necessary to specify the decision
maker's utility function.22














21. This approach implies that only the first two moments of the distribution
function of revenue are important.
22. See Anderson et al. (1977, Ch. 4) for a discussion of utility function
specification.











APPENDIX 1
DEFINITIONS
The following terms are as defined by the Sugar Act (U.S. Congress,
1972a, pp. 2-5)23 for the purpose of establishing a "fair and reasonable" price
for sugarcane.
(a) "Price of raw sugar" means the daily spot quotation of raw sugar of
the New York Coffee and Sugar Exchange No. 10 domestic contract, ex-
cept that if the Director of the Sugar Division, Agricultural Stabilization
and Conservations Service, U. S. Department of Agriculture, Washington,
D.C. 20250, determines that such price does not reflect the true market
value of raw sugar, because of inadequate volume or other factors, he may
designate the price to be effective under this part which he determines will
reflect the true market value of raw sugar.
(b) "Season's average price of raw sugar" means (1) the weighted average
price of raw sugar for the months in which 1972-crop sugar is delivered to
the purchaser, determined by weighting the sample average of the daily
prices of raw sugar for each month in which sugar is delivered to the pur-
chaser by the quantity of 1972-crop raw sugar or raw sugar equivalent
delivered during each corresponding month, or (2) the average price of raw
sugar received by a processor who disposes of all of his sugar under a single
contract with a refiner or a cooperative sales organization composed of
processors.
(c) "Raw sugar" means raw sugar, 960 basis.
(d) "Net sugarcane" means the gross weight of sugarcane delivered by a
producer to a processor minus a deduction equal to the average percentage
weight of trash delivered with all sugarcane ground at each mill operated by
a processor. If the mill receives both hand-cut and machine-cut cane, the
average percentage weight of trash delivered with cane harvested by hand
shall be computed separately from that harvested by machine and the ap-
plicable trash deduction applied to the gross weight of cane harvested by
each method.
(e) "Trash" means green or dried leaves, sugarcane tops, dirt and all
other extraneous material delivered with sugarcane.
(f) "Standard sugarcane" means sugarcane containing less than 12.5 per-
cent sucrose in the normal juice.
(g) "Salvage sugarcane" means sugarcane containing less than 9.5 per-
cent sucrose in the normal juice.
(h) "Average percent sucrose in normal juice" means (1) the average per-
cent crusher juice sucrose of the producer's sugarcane multiplied by a fac-
tor representing the ratio of factory normal juice sucrose to factory crusher

23. Irrelevant definitions are deleted. Paragraph letters are taken from the
reference. For more information consult Meade and Chen (1977) or Barnes
(1974).







juice sucrose at the processor's mill; or (2) the average percent sample mill
juice sucrose of the producer's sugarcane multiplied by a factor represent-
ing the ratio of factory normal juice sucrose to the average sample mill
juice sucrose analysis of producer's sugarcane.
(i) "Average percent crusher juice sucrose" means the percentage of
sucrose in undiluted crusher juice as determined by direct analysis in
accordance with standard procedures.
0) "Factory normal juice sucrose" means the percentage of sucrose in
undiluted juice extracted by a mill tandem as determined by multiplying
factory dilute juice purity by factory normal juice Brix.
(k) "Factory crusher juice sucrose" means the percentage of sucrose in
undiluted crusher juice as determined by direct analysis.
(1) "Average percent sample mill juice sucrose" means the percentage of
sucrose solids in juice extracted from samples of each producer's sugarcane
by the sample mill.
(m) "Factory normal juice Brix" means the percentage of soluble solids
in undiluted juice extracted from sugarcane by a mill tandem as determined
by multiplying factory crusher juice Brix by a dry milling factory represent-
ing the ratio of factory normal juice Brix to factory crusher juice Brix.
(n) "Factory crusher juice Brix" means the percentage of soluble solids in
undiluted crusher juice as determined by direct analysis.
(o) "Factory dilute juice purity" means the ratio of factory dilute juice
sucrose to factory dilute juice Brix which are determined by direct analysis.











APPENDIX 2
PRICES OF RAW SUGAR
AND RETURNS TO SUGARCANE GROWERS

Prior to 1975 the domestic sugar price was protected by legislation
which was permitted to expire at the end of the 1974 crop (Zepp, 1976, p.
47). Writing in October 1976, Kidder explained the determinants of sugar
price as follows:
Although government tariff and trade policies play some role, the
world supply and demand for sugar is currently the paramount factor.
Unless prices become quite high (as they did in 1974), world demand for
sugar is rather constant, and changes in supply are the primary determinant
of the price. Favorable weather in the major sugarbeet producing areas of
Russia and Northern Europe and important cane producing countries such
as Brazil, Cuba, and India result in lower sugar prices. Poor weather in one
or more of these areas tends to raise prices. Because Florida's share of
world production is so small, changes in the Florida crop have little effect
on sugar prices (Kidder, 1976).
World and domestic sugar prices for the years 1966 to 1977 are
found in Table 26.
The percentage of total return from raw sugar going to producers is
in the range of 62 to 64 percent (Agricultural Stabilization and Conserva-


TABLE 26. World and U.S. raw sugar prices, 1966-77.

World price U.S. sugar
New York price (New
Year basis York spot)
----------------cents per pound---------
1966 2.82 6.99
1967 2.95 7.28
1968 2.96 7.52
1969 4.37 7.75
1970 4.88 8.07
1971 5.65 8.52
1972 8.54 9.09
1973 10.99 10.29
1974 31.62 29.50
1975 21.92 22.47
1976 13.36 13.31
1977a 10.96 10.99

Source: U.S. Department of Agriculture (1977, p. 34).
aThrough October only.







tion Service, n.d., and Halsey, 1976). Returns to producers and pro-
cessors are related to the New York spot price for raw sugar, as shown in
Table 27.
The Sugar Act also provided for a molasses payment to growers
equal to the product of 5.8 gallons times one-half of the excess of 4.75
cents per gallon of the weighted average net sales price per gallon of
blackstrap molasses based on the price f.o.b. tank truck or railroad car
at mill door (U.S. Congress, 1972a, p.6)


TABLE 27. Sugar revenue per standard ton of sugarcane by spot market sugar
price and by source of revenue.

New York spot
sugar price per lb. Return to Return to Total
(season average) grower processor return
----------cents--------- ------------------dollars per standard ton-----------------
6 6.15 3.58 9.73
8 8.45 4.92 13.37
10 10.75 6.26 17.01
12 13.05 7.60 20.65
14 15.35 8.94 24.29
16 17.65 10.28 27.93
18 19.95 11.62 31.57
20 22.25 12.96 35.21
22 24.55 14.30 38.85
24 26.85 15.64 42.49
26 29.15 16.98 46.13
28 31.45 18.32 49.77
30 33.75 19.66 53.41
32 36.05 21.00 57.05
34 38.35 22.34 60.69
36 40.65 23.68 64.33
38 42.95 25.02 67.97
40 45.25 26.36 71.61
42 47.55 27.70 75.25
44 49.85 29.04 78.89

Source: Halsey (1976).










APPENDIX 3
MATHEMATICAL FORMULATION
OF THE OPTIMIZATION MODELS

THE POLICY PROGRAM

L 1 11 I J
(3.1) Max R= E E E E (R ,kV h) -K U-K F
f=l h=O k=l i=l j=l
1 11 I J
s.t. (3.2) E E (Vik) + F,=Ne(e= ,2,...,L)
h=O k=l i=l j=l
11 1
(3.3) F,= E E VVilk (=l ,2,...,L)
k=1 i=l
11 1
(3.4) U,= E E VOilk l (f= 1,2,...,L)
k=1 i=l
11 1 11 1
(3.5) E E Vo,1lk i E E V ,, = 1,2,...,L)
k=l i=l k=l i=l


11 11
(3.6) L Vh+ < Vhk(i=1,2....J;
k=1 k= = 2,. . I;
h = 0,1;
= 1,2,...,L)

L I J
(3.7) E E E V hhuk < UBk(k= 1,2,...,11)
f=lh=Oi=lj=i

L 1 IJ
(3.8) E E Vhke > LBk (k= 1,2,...,11)
f=1 h=Oi=lj=l


(3.9) Vjk, UF, F, F 0, integer-valued







where R = expected total net revenue from the farm
policy;
R k = net revenues from the (h,i)thvariety of cane ex-
cluding costs of fallowing and planting in the
jh year of its crop cycle when harvested in the
kth period on the f th class of land where i in-
dicates the variety of cane planted and h = 0 if
the cane is successively planted'and h= 1,
otherwise;
Vhjke = number of fields harvested in the kth period
with cane of the (h, )th variety in the jh year
of its crop cycle grown on the f th class of land;
I = number of varieties
L = number of land classes,
J = maximum number of years a field may ratoon;
U = number of successively planted fields on the
fth class of land;

L
U = E U = total number of successively planted
e=
fields

K = cost of successive planting per field;
0
F, = number of fields in fallow of the fthclass of land;
L
F = E Fe =total number of fields in fallow;
-=1
K, = cost of fallow maintenance plus cost of field
preparation and replanting per field;
N, = number of fields of the f th class of land;
UBk = maximum number of fields which may be har-
vested in period k;
LBk = minimum number of fields which may be har-
vested in period k.
J = maximum number of years a field may ratoon;

The objectives of the various constraints are as follows: (3.2) requires the
total number of fields harvested plus the total number of fields in fallow
for each land class to be equal to the number of fields available for that
land class; (3.3) requires that the number of fallow fields for the f "'class
of land be exactly equal to the number of fields of plant cane not suc-
cessively planted in order to account for the fact that plant cane not suc-
cessively planted must be preceded by a fallow; (3.4) requires that the
total number of successively planted fields of plant cane for the f th class







of land be exactly equal to the sum of all fields of plant cane successively
planted for each of the I varieties and harvested throughout the season
on the f th class of land; (3.5) limits the number of successively planted
fields of plant cane for land class to no more than the number of fields
of plant cane not successively planted to enforce the assumption that a
successively planted crop may not follow a previously successively
planted crop; (3.6) ensures that the order of crop rotation is maintained
(i.e., excludes the possibility that a second ratoon may be grown on a
field not previously occupied by a first ratoon); (3.7) sets a maximum for
the number of fields which may be harvested in the k'hperiod; (3.8) sets a
minimum for the number of fields which may be harvested in the kth
period; (3.9) requires the variables to be non-negative and integer-
valued.


THE HARVEST PROGRAM

N 11
(3.10) Max R = L L R/kHF
f=l k=m

11
s.t.(3.11) E H = 1 (f=1,2,...,N)
k=m

N
(3.12) Y Hf < UBk (k=m,m+l,...,11)
fkk
f=1

N
(3.13) E Hf > LB, (k=m, m+l,...,11)
f=1

(3.14) Hfk = Oor 1.
where Ru = net revenue from all fields harvested;
Rfk = net revenue when field f is harvested in period k;
Hfk = 1, if field f is harvested in period k;
= 0, otherwise;
N = number of fields available for harvest;
m = 1, if the program is run prior to the harvest
season;
= the earliest harvest period to be considered
otherwise;
UBk = the maximum number of fields to be harvested
in the kth period;
LBk = minimum number of fields to be harvested in
the kth period.







The objectives of the constraints are: (3.11) to ensure that each field will
be harvested exactly once during the harvest season; (3.12) to set a max-
imum for the number of fields which may be harvested during the kth
period, (3.13) to set a minimum for the number of fields which may be
harvested during the kth period.


THE REPLACEMENT PROGRAM

N 11 No X
(3.15) MaxRr= E E R' H + E AVc
f=1 k=1 f=l c=I

11 X
s.t. (3.16) E H, + E Vc= 1 (f=1,2,...,No)
k=1 c=l

N No X
(3.17) E Ho + E r k* Vfc < UBk(k=l,2,...,11)
f=1 f=l c=l

N No X
(3.18) Hk + E E k* Vf >cLBk (k=1,2,...,11)
f=1 f=1 c=l

X k
(3.19) E k* V:I E H* (f= 1,...,n)
c= k=

(3.20) Hk = 0 or 1

(3.21) fc = 0 or 1



where
R = net revenue including an imputed annualized value for
replacement crops;
R' = net revenue for harvesting the defending crops on field
f in period k;
Ho = 1, if field fis harvested in period k;
= 0, otherwise;
A = annualized net revenue for the cth challenger (from
S(13));
VfC = 1, if field f is replaced by challenger c;
= 0, otherwise;
N = total number of fields in the farm;







X = total number of challengers;
k* = 1, if challengers c's rotation begins with a successive
plant, k is a permissible period in which to harvest, and
k is planting period of that crop.
= 0, otherwise;
UBk = maximum number of fields which may be harvested in
the kth period;
LBk = minimum number of fields which may be harvested in
the kth period;
H*
fk = optimal solution vector to the harvest program.


The objective of the constraints are as follows: (3.16) ensures that each
field is harvested exactly once or is replaced by precisely one challenger;
(3.17) sets a minimum for the number of fields to be harvested in period
k; (3.18) sets a minimum for the number of fields to be harvested in
period k; (3.19) ensures that if a particular field is replaced and suc-
cessively planted, then it was harvested early enough in the current
harvest season to allow successive planting.









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This public document was promulgated at an annual cost of $7550
or a cost per copy of $3.02 to provide information on the complex
decision of when to replace sugarcane stubble.



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Experiment Stations are open to all persons regardless of race, color, national origin,
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