• TABLE OF CONTENTS
HIDE
 Front Cover
 Table of Contents
 Introduction
 Objectives
 The spatiotemporal optimization...
 Spatiotemporal model
 Spatiotemporal model assumptio...
 Empirical specification of the...
 Supply
 Fattening in a feedlot
 Slaughtering fed cattle
 Transportation
 Empirical results
 Optimal routing scheme
 Acreage requirments for the optimal...
 Average costs
 Sensitivity analysis
 Changes in initial animal cost
 Variation in corn price
 Summary and conclusions
 Outlook for the future
 Implications for future resear...
 Reference
 Back Cover














Group Title: Bulletin / Agricultural Experiment Station, University of Florida
Title: An analysis of feeding and slaughtering cattle in Florida /
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00026745/00001
 Material Information
Title: An analysis of feeding and slaughtering cattle in Florida /
Series Title: Bulletin / Agricultural Experiment Station, University of Florida
Physical Description: vi, 64 p. : ill., maps ; 23 cm.
Language: English
Creator: Moseley, Anne E., 1952-
Spreen, Thomas H
Pheasant, Jim W
Publisher: Agricultural Experiment Stations, Institute of Food and Agricultural Sciences, University of Florida
Agricultural Experiment Station, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1987
Copyright Date: 1987
 Subjects
Subject: Beef cattle -- Economic aspects -- Mathematical models -- Florida   ( lcsh )
Beef cattle -- Feeding and feeds -- Mathematical models -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references (p. 62-64).
Statement of Responsibility: Anne E. Moseley, Thomas H. Spreen, Jim W. Pheasant.
General Note: Cover title.
General Note: "August 1987."
 Record Information
Bibliographic ID: UF00026745
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 - AES1077
oclc - 17699266
alephbibnum - 000958273
issn - 0096-607X ;

Table of Contents
    Front Cover
        Page i
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
    Introduction
        Page 1
    Objectives
        Page 2
    The spatiotemporal optimization model
        Page 3
    Spatiotemporal model
        Page 4
        Page 5
    Spatiotemporal model assumptions
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Empirical specification of the model
        Page 11
        Page 12
        Page 13
        Page 14
    Supply
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Fattening in a feedlot
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Slaughtering fed cattle
        Page 33
        Page 34
        Page 35
        Page 36
    Transportation
        Page 37
        Page 38
    Empirical results
        Page 39
        Page 40
        Page 41
        Page 42
    Optimal routing scheme
        Page 43
        Page 44
        Page 45
    Acreage requirments for the optimal solution
        Page 46
    Average costs
        Page 47
        Page 48
        Page 49
    Sensitivity analysis
        Page 50
        Page 51
    Changes in initial animal cost
        Page 52
        Page 53
        Page 54
    Variation in corn price
        Page 55
        Page 56
        Page 57
    Summary and conclusions
        Page 58
        Page 59
    Outlook for the future
        Page 60
    Implications for future research
        Page 61
    Reference
        Page 62
        Page 63
        Page 64
    Back Cover
        Page 65
Full Text
August 1987

021


Bulletin 873 (technical)
1,


An Analysis

of Feeding and Slaughtering

Cattle in Florida




Anne E. Moseley
Thomas H. Spreen
Jim W. Pheasant






Agricultural Experiment Station
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
J.M. Davidson, Dean for Research






























































Anne E. Moseley is Economic Analyst, Thomas H. Spreen is Associ-
ate Professor, and Jim W. Pheasant is former Assistant In, Food
and Resource Economics Department, IFAS, University of Florida,
Gainesville, FL 32611.







TABLE OF CONTENTS


Page

Introduction ............................................ 1
Objectives........................................... 2

The Spatiotemporal Optimization Model................... 3
Static Plant Location Model......................... 3
Spatiotemporal Model................................ 4
Spatiotemporal Model Assumptions.................... 6
Identification of Specific Locations................ 11

Empirical Specification of the Model.................... 11
Supply............................................... 15
Backgrounding........................................ 15
Fattening in a Feedlot............................... 21
Slaughtering Fed Cattle........... .................. 33
Demand.............................................. 37
Transportation....................................... 37

Empirical Results...................................... 39
Optimal Solution................................... 39
Optimal Routing Scheme............................... 43
Interpretation of Dual Information.................. 43
Acreage Requirements for the Optimal Solution....... 46
Average Costs ....................................... 47

Sensitivity Analysis................................... 50
Regional Cost Differences ................ ........... 50
Changes in Initial Animal Cost....................... 52
Seasonal Calf Prices ................................ 52
Variation in Corn Price ............................. 55

Summary and Conclusions................................ 58
Conclusions.......................................... 58
Outlook for the Future................ .. ............ 60
Limitations............................. ............ 60
Implications for Future Research.................... 61

References............................................... 62







LIST OF TABLES


Table Page

1 Feeder Calf Availability.................... ... ... 15

2 Quarterly Feeder Calf Supply by Region............ 16

3 North Florida Forage Quality and Quantity......... 18

4 Central Florida Forage Quality and Quantity...... 19

5 South Florida Forage Quality and Quantity......... 20

6A Backgrounding and Feeding Costs for a Four-Quarter
Weight Gain Program, North Florida............... 24

6B Backgrounding and Feeding Costs for a Four-Quarter
Weight Gain Program, Central Florida.............. 25

6C Backgrounding and Feeding Costs for a Four-Quarter
Weight Gain Program, South Florida................ 26

7A Backgrounding and Feeding Costs for a Five-Quarter
Weight Gain Program, North Florida............... 27

7B Backgrounding and Feeding Costs for a Five-Quarter
Weight Gain Program, Central Florida............. 28

7C Backgrounding and Feeding Costs for a Five-Quarter
Weight Gain Program, South Florida............... 29

8A Backgrounding and Feeding Costs for a Six-Quarter
Weight Gain Program, North Florida................ 30

8B Backgrounding and Feeding Costs for a Six-Quarter
Weight Gain Program, Central Florida.............. 31

8C Backgrounding and Feeding Costs for a Six-Quarter
Weight Gain Program, South Florida............... 32

9 Amount of Corn and Sorghum Silage Fed Per Animal
in the Feedlot Program, North Florida............. 34

10 Amount of Corn and Sorghum Silage Fed Per Animal
in the Feedlot Program, Central Florida........... 35

11 Amount of Corn and Sorghum Silage Fed Per Animal
in the Feedlot Program, South Florida............. 36

12 Population by Demand Region and Quarterly
Regional Demand ..................................... 38







13 Cost per Animal per Trip between Supply and
Backgrounding Regions ........................... 40

14 Cost per Animal per Trip between Backgrounding
and Feedlot Regions................................ 41

15 Cost per Animal per Trip between Slaughterplant
and Demand Regions................................ 42

16 Optimal Paths for Backgrounding, Feeding, and
Slaughtering Florida Calves...................... 44

17 Imputed Marginal Value for Supply Regions by
Quarter.......................................... 45

18 Imputed Marginal Value for Demand Regions by
Quarter.......................................... 46

19 Total System Costs and Optimal Plant Configurations
for Eight Different Levels of Supply.............. 48

20 Estimated Average Costs for Eight Different Levels
of Supply....................................... 48

21 Summary of Optimal Solutions for Restricted
Location Model.................................... 51

22 Summary of Optimal Solutions for Base and
Seasonal Calf Price Models....................... 54

23 Summary of Optimal Solutions for Varying Corn
Price Models..................................... 56

24 Summary of Optimal Solutions for Seasonal Calf
Prices and Varying Corn Prices.................... 57







LIST OF FIGURES


Figure Page

1 Simplified Tableau Indicating the Temporal
Dimension......................................... 10

2 Delineation of Supply and Backgrounding
Regions........................................... 12

3 Delineation of Feedlot/Slaughterplant
Regions........................................... 13

4 Delineation of Demand Regions.................... 14

5 Average Cost Curve for the Florida Feeding and
Slaughtering Industry............................ 49

6 Estimated Relationship Between Weaned Calf Prices
and the Average Cost of Beef...................... 53

7 Estimated Relationship between Corn Prices and
the Average Cost of Beef for Fixed and Seasonal
Calf Price Models.................................. 59







Introduction


The development of crossbreeds during the early part of the
20th Century changed the Florida beef industry from scrub cattle
production to cow-calf production units with limited stocker and
feedlot production capacity (Shonkwiler). In 1984 Florida led
all southeastern states in the number of beef cows, and ranked
ninth relative to all other states (Florida Department of
Agriculture). Using average inventories of beef cattle for the
periods 1955 to 1959 and 1976 to 1980 for both Florida and the
United States, a 62 percent increase in Florida beef cattle
numbers was observed, while the inventory levels for the United
States as a whole increased by only 25 percent during the same
period (Shonkwiler and Spreen). At the same time Florida beef
production was expanding, U.S. per capital beef consumption
increased by almost 100 percent between 1959 and 1973 (Reimund,
et al.). In 1980, per capital beef consumption in the United
States was 76.5 pounds retail weight basis (USDA, 1982).
The Florida cattle industry produces an excess supply of
lightweight feeder cattle, which are marketed to buyers in
Texas, Arizona, and Oklahoma. In Florida, stocker calf out-
shipments or exports as a percentage of calves marketed
increased from 4.1 percent in 1955 to 82.3 percent in 1980
(Florida Crop and Livestock Reporting Service, 1981).
At the same time that feeder calves are being exported from
Florida, large quantities of carcass and boxed beef are imported
into the state because the Florida cattle industry does not
produce enough slaughter beef for Florida consumers. Thus,
Florida is considered a deficit beef production area (Jordan).
Concern has been expressed by those within the cattle industry
that because of increased transportation costs (due to
substantial increases in petroleum prices since 1972), producers
in Florida receive considerably lower prices for feeder calves
than do those producing and marketing calves closer to the major
demand points. If transport rates continue to grow, Florida
producers will continue to accept lower prices for feeder calves
than those received by producers closer to the major feeding
areas (Shonkwiler and Spreen). It also follows that consumers
must pay higher prices for beef imported from other states,
because of transportation costs which must be included in the
retail price.
It is reasonable for Florida cattle producers to consider
finishing feeder calves within the state, rather than exporting
calves to out-of-state feedlots. Since Florida would be a net
importer of beef, even if all feeder calves produced in the
state were finished, slaughtered, and consumed in Florida, it is
reasonable to assume that Florida-finished beef would be
consumed in Florida (Spreen).
Rapid U.S. population growth and increasing consumer in-
comes during the 1940's and 1950's caused a substantial increase
in the demand for high quality beef (Shonkwiler). Prior to the
1960's, the Midwest (the western Corn Belt states of Iowa,
Illinois, and Nebraska) had been the undisputed center for fed
cattle production, slaughter, and processing in the United
States. Fed cattle have been defined by the U.S. Department of







Agriculture as cattle fattened for at least 1 month on grain or
concentrate. Development of extensive feed grain production in
the southwest Plains states (Kansas, Oklahoma, and Texas)
encouraged the growth in fed cattle production in the southwest
region. As a result of this development, the centralization of
fed cattle slaughtering and processing changed from the upper
Midwest and other regions to the southwest Plains region
(Faminow and Sarhan, 1983b).
During the 1970's small-scale feedlots declined in impor-
tance in Florida. With the rapid decline in the number of
Florida cattle feeding operations and the rise of the southwest
commercial feedlot industry, a shift in the production marketing
system for beef cattle occurred in the state. Beginning in the
mid-1960's there was a substantial increase in the number of
cattle being shipped out of Florida. These large shipments
coincided with the expansion of the feeding industry in the
southwest (Shonkwiler).
Although the fed cattle slaughtering and processing indus-
try is concentrated in the southwest Plains, uncertainty exists
about the future of this region as a dominant producer of fed
cattle. Within that region, areas producing feed grain are
increasingly facing the prospects of declining groundwater and
increased irrigation costs (Faminow and Sarhan, 1983a).
With the uncertainty about the dominance of the southwest
Plains region in production of fed cattle, the Florida beef
industry can consider localization of fed cattle production.
Continued increases in transportation rates may prohibit long-
distance shipments of live animals. Florida beef cattle pro-
ducers may have financial incentives to retain animals for fed
cattle production.

Objectives
The overall objective of this bulletin is to determine
feasible locations for backgrounding Florida-weaned calves and
determine the size, number, and location of feedlots and
slaughterhouses within the state. The optimal timing and loca-
tion of each activity -- backgrounding, feeding, and slaugh-
tering/processing -- is determined.
The specific objectives are as follows.

(1) Calculate the cost of backgrounding and subsequently fat-
tening calves in a feedlot within Florida.
(2) Determine the cost of establishing and utilizing slaugh-
terhouses locally for slaughtering and processing Florida-
fed cattle.
(3) Calculate the cost of transporting live animals and fin-
ished beef between selected backgrounding, feedlot/slaugh-
terhouse, and final distribution locations.
(4) Using the results of objectives 1 through 3, determine the
optimum feedlot/slaughterhouse locations in Florida by
minimizing total costs, beginning with backgrounding and
continuing through processing until the final product
(boxed beef) reaches final destinations.
(5) Using variable lengths of time for backgrounding and feed-
lot production, determine the optimal production required







each quarter to provide consumers with constant supplies of
beef.


The Spatiotemporal Optimization Model

The model used in this study integrates a standard plant
location model with a scheduling model. The study thereby
characterizes a spatiotemporal optimization problem. The tem-
poral dimension provides varying lengths of time a calf is
backgrounded and fed in a feedlot. Although there is a seasonal
supply of calves, the temporal aspect of the model provides a
means for maintaining continuous availability of processed
beef. This study focuses exclusively on the Florida cattle
industry. The optimization model provides intraregional results
for Florida, which, when compared to other cattle producing
regions in the United States, can provide a better understanding
of the Florida cattle industry. This study is not designed to
investigate the aspects of interregional competition.

Static Plant Location Model
To illustrate a standard plant location model, consider a
model which includes I supply points, J possible plant loca-
tions, and K final demand points. This gives I x J x K possible
routes through the system. The cost of each route is cal-
culated. The mathematical statement of the model is



minimize z E E Ci.. Xi.. + E F.P.
i j k k k


subject to Z E X. = S. (i = )
j k 1 '
SE X jk CAP. P. (j = 1,*. J)
ujk J 3



SE Xijk = Dk (k = 1,.--,K),
ij
where Xijk = number of units of product shipped from supply
i to plant j to final demand k;
Cijk = unit cost of transporting the product from
supply point i through plant j to final
demand point k;
Pj = 1 if a plant is located at point j
(j = . J),
= 0 otherwise;
F = fixed cost incurred if a plant is built at
location j (j = 1,...,J);
Si = supply at location i (i = 1,...,I);
CAPj = capacity of plant located at point j; and
Dk = demand at location k (k = 1,...,K).







This model minimizes the total cost of shipping the avail-
able supply (ES.) through plant j to meet total
demand (ED ) and includes the fixed cost of establishing a plant
at point j. The constraints ensure that (1) total shipments
from point i do not exceed availability, (2) utilization of
plant j is less than or equal to the capacity at plant j, and
(3) the amount sent to final demand point k satisfies the amount
required at that point. Feasibility of the model is assured if
total supply equals total demand (ES = EDk) and sufficient
plant capacity is available (ECAP. ES.).
Certain assumptions must accompany the model. A simplified
list of assumptions include the following:

(1) Supply, plant, and demand points are separated into a
finite number of locations and represented by single
discrete points.
(2) Supplies and demands are known and fixed.
(3) There is no storage of product.
(4) All production units are the same quality and measured in
comparable units.
(5) Total plant processing costs are a linear function of plant
volume and have a positive intercept.

Spatiotemporal Model
The model used in this study is a modification of the
transshipment model. The model includes three intermediate
points: backgrounding, finishing in a feedlot, and slaughter-
ing. A nontemporal route in the model would start at one of
four supply points, pass through one of four backgrounding
points, then through one of three feedlot/slaughterhouse points
which include two possible slaughterplant sizes, and end at one
of five demand points. Thus, without considering the temporal
dimension, there are 480 (4 x 4 x 3 x 2 x 5) possible routes
through the model.
The scheduling portion of the model includes paths of three
different lengths: (1) two quarters of backgrounding plus two
quarters in a feedlot, totaling to a four-quarter path; (2) four
quarters of backgrounding plus one quarter in a feed-lot,
totaling five quarters; and (3) five quarters of backgrounding
plus one quarter in a feedlot, totaling six quarters.1 Each of




1The four-, five-, and six-quarter combinations of back-
grounding and feedlot finishing were selected after numerous
trials of the simulation models for backgrounding feeder cattle
and beef gain (feedlot finishing). For example, in order to
produce a five-quarter gain from 400 pounds to 1,050 pounds,
only four quarters of backgrounding and one quarter of feeding
were feasible. Three quarters of backgrounding and two quar-
ters of feeding produced feeder cattle in excess of the target
weight of 1,050 pounds. Thus, these four-, five-, and six-
quarter combinations of backgrounding and feeding were selected
because they produced the desired weight gain results.







these three paths can begin in any one of the four quarters of
the year. Thus, the static model with 480 paths is expanded to
include 12 possible timing paths, totaling 5,760 possible paths
through the model. The model also includes alternative
options: (1) placing only one slaughterhouse per location but
offering two different size options and (2) placing multiple
feedlots per location but offering only one size feedlot. Three
feedlot locations and two possible slaughterplant sizes at three
locations yields nine integer variables.
In order for the model to reflect the seasonal supply of
calves, quarterly data are used. The year is divided into
quarters rather than months in order to reflect the seasonal
supplies without incurring an excessively large model. If each
of the three weight gain paths began in any of the 12 months,
the model would be expanded from 5,760 paths to 17,280 paths
(480 x 3 x 12). It would require extensive computer time to
solve a mixed integer programming problem with 17,280 continuous
variables and 9 integer variables.
The temporal dimension of the model allows for a continuous
supply of beef throughout the four quarters of the year. The
supply of Florida calves is seasonal, with marketing peaking in
the fall quarter. By allowing different lengths of time for
maturing weaned calves to reach slaughterweight, there is an
opportunity to make beef available to the consumer throughout
the four quarters of the year. The following example
illustrates this scheduling technique.
Suppose during the first and second quarter of the year
there are no calves available. There are, however, 100 calves
available in each of the third and fourth quarters. By using
appropriate combinations of the four-, five-, and six-quarter
weight gain programs, 50 carcasses can be available to consumers
in each quarter of the year. For example: (1) Fifty calves
available during the third quarter are placed on a four-quarter
path, making 50 carcasses available in the following third
quarter. (2) Fifty calves remaining from the third quarter
supply are placed on a five-quarter path, making 50 carcasses
available during the fourth quarter. (3) Fifty calves available
during the fourth quarter are placed on a five-quarter path,
making 50 carcasses available during the first quarter of the
year. (4) Finally, the remaining 50 calves available during the
fourth quarter are placed on a six-quarter path, making 50
carcasses available in the second quarter. Thus, all four
quarters have a constant amount available, although the original
supply was available only during two quarters.
The empirical problem is to determine the optimal number,
size, and location of feedlot/slaughterhouse combinations and
determine optimal locations for backgrounding weaned calves,
given spatially dispersed and separated patterns of weaned-calf
supply and processed-beef demand. The fixed cost associated
with the establishment of feedlot and slaughterhouse facilities
represents the cost of opening a plant of given capacity. The
fixed cost is independent of the actual plant volume and is
explicitly recognized in the model. In addition, there are unit
variable costs for feedlot, slaughtering, and processing;
transportation costs for weaned calves transported between







supply, backgrounding, and feedlot/slaughterhouse stages; and
transportation costs for processed beef transported from
slaughterplant to final demand points.

Spatiotemporal Model Assumptions
The Florida beef cattle industry and marketing network are
complex. Therefore, the following simplifying assumptions are
necessary to reduce the size, scope, and intent of the spatio-
temporal model:

(1) Weaned-calf supply, backgrounding pastures, feedlot/
slaughterplant facilities, and final demand may be
separated into a finite number of regions in space and
represented by single discrete points.
(2) Only Florida-weaned calves are considered for weight gain
programs.
(3) Regional calf supplies and beef demand are known and fixed.
(4) There is no storage of beef; however, there is a "storage"
on-the-hoof via different lengths of time for backgrounding
and feeding.
(5) All beef units are the same quality and weight (weaned calf
= 400 pounds; finished feedlot calf = 1,050 pounds; boxed
beef carcass = 555 pounds; meat cutup percentages are known
and constant).
(6) Feedlots and slaughterplants are located in tandem; for
example, if a slaughterplant is built at location number 2,
at least 1 feedlot (and no more than 10 feedlots) will also
be built at location number 2.
(7) There is no transportation possible between different
locations of feedlots and slaughterhouses; both facilities
at the same location handle the same animals.
(8) Total slaughtering and processing costs are a linear
function of plant volume and have a positive intercept.
(9) Total transportation costs include loading and receiving
costs and are a linear function of volume, with an
intercept at the origin.
(10) There is no constraint associated with acreage available
for backgrounding weaned calves.
(11) Corn, used as the primary portion of the feedlot diet, has
a fixed price which is known and constant. The price of
corn varies among north, central and south Florida due to
higher transportation costs for shipments to central and
south Florida.
The mathematical formulation of the spatiotemporal
model is

6
minimize Z Z E E C ijkm X.jk
i j k Z m s p=4
(1)
+ E FkYk + E G k Zk
k k S







subject to I E r E Z Xijkmsp = S.
j k mp msp

i = 1,**,4
s = 1,**- ,4



i jEm ijkim24 Xijkkm34 + ijkiml5 + Xijk.m46)


SCAPl Y
k1 k



S (Xijkim34 +Xijkim44 + ijkim25 + Xijkml6)


SCAPk2 Yk




i i(X + X + X + Xjkm26
i j m E(Xijkim14 ijktm44 ijkim35 ijkim26
i j i


SCAPk3 k
k3 k


TE ( X. + X. + X + X )
i j m 1(Xijkim14 Xijkim24 + 1ijkim45 + XijkZm36


< CAPk4 k





k = 1, 2, 3


E X X C
E E E E Xijkimsp
i j kmps







E E E Xijkimsp = Dmt
i j k ps


AP Z
t k = 1,2,3
= 1,2
t = 1,. .,4





m = 1,.**,5
t = 1,*.. ,4







Z11 Z 12 Y1


Z21 + 22 2 Y2 (10)


Z31 + 32 Y3 (11)

where, 0 Y Yk 5 10,

0 Z Zki : 1, and

Yk, Zk are integers.




Subscripts are used to indicate weaned-calf supply, back-
grounding, feedlot/slaughter locations, facility size, final
demand locations, time paths through the system, and quarters of
the year.
Let
Sis weaned-calf supply at location i in quarter s
(i = 1,...,4; s = 1,...,4)
j = backgrounding locations (j = 1,...,4)
Dmt = final demand located at point m in quarter t (m
= 1,...,5; t = 1,... 4)
s = quarter when weaned calves begin backgrounding
(s = 1,...,4)
p = path used for fattening weaned calves to
slaughterweight (p = 4, 5, or 6 quarters)
t = quarter when animals are slaughtered and
processed beef is subsequently available at
final demand points mod4(s+p) = t
C. = cost of entire route beginning with a calf at
ijmsp supply point i, transported to and backgrounded
at point j, transported to and fattened at
feedlot at point k, slaughtered and processed
in slaughterplant size %, and transported to
demand point m. The calf begins in quarter s
and follows time path p. This cost includes
variable costs associated with backgrounding,
feeding, slaughtering, and transportation.
Xijkmsp = the number of animals following route ijkmsp
ij kjmsp



2For example, if an animal begins backgrounding in quarter
1 (s=1) and follows a five-quarter path, it will be ready for
slaughter in quarter 6, which is the second quarter of next
year.







Fk = the fixed cost of establishing a feedlot at
location k (k = 1,...,3)
G = the fixed cost of establishing a slaughterplant
of size at location k (k = 1,...3; 2 = 1,2)
Yk= number of feedlots built at location k (k
1,.... 3)
Z = 1 when a slaughterplant of size Z is built at
location k (k = 1,...,3; R = 1,2)
0 otherwise
CAPks = capacity of feedlot at location k during quar-
ter s (k = 1,...,3; s = 1,...,4)
CAP = capacity of slaughterhouse of size 2 at loca-
S tion k during quarter t (k = 1,...3; 1 = 1,2;
t = 1,...,4)

The spatiotemporal model minimizes the total cost of (1)
assembly of weaned calves in region i during quarter s, (2)
backgrounding calves at location j, (3) feeding calves at loca-
tion k, (4) slaughtering the animals in slaughterplant
size 2, (5) meeting total demand at location m during quarter t,
(6) beginning in quarter s, and (7) following one of three
weight gain programs (p = 4, 5, or 6). Total system cost also
includes the fixed cost of establishing a feedlot at point k and
establishing a slaughterplant of size i at location k. Since a
feedlot and slaughterplant are located in tandem, point k
indicates the location of both facilities and 2 indicates the
size of the slaughterplant. The constraints ensure that total
shipments from point i during quarter s do not exceed
availability (equation 2); utilization of feedlots at point k
during the first quarter (equation 3), second quarter (equation
4), third quarter (equation 5), and fourth quarter (equation 6)
is less than or equal to capacity of feedlots at that location
during that particular quarter; utilization of a slaughterplant
of size 2 at location k during time period t is less than or
equal to capacity of that size plant at that location during
that particular quarter (equation 7); the amount of boxed beef
sent to final demand point m during quarter t satisfies the
amount required at that location and time period (equation 8);
and a slaughterplant is built at a particular location only if a
feedlot is built at that location (equation 9, equation 10, and
equation 11).
There are four feedlot capacity constraints which corre-
spond to the capacity required during any given quarter. An
animal following a four-quarter weight gain program requires two
quarters of feedlot capacity, whereas an animal on a five- or
six-quarter program only requires one quarter of feedlot
capacity. In order to allow for this difference in feedlot
utilization, each feedlot capacity constraint specifically
identifies each beginning quarter and weight gain program which
would require feedlot capacity during a specific quarter.
Another way of illustrating the 5,760 paths of the spatio-
temporal model is by means of a tableau. The simplified tableau
presented in Figure 1 indicates only the temporal dimensions of
the model. Each column represents a possible temporal path.
The numeral "1" indicates the stage of production for an animal










Figure 1. Simplified

Stages of
Production QTRa

Backgrounding 1


Feedlot




5 Slaughterplant




Demand


2
3
4

1
2
3
4

1
2
3
4

1
2
3
4


Tableau Indicating the Temporal Dimension.


Four-Quarter Path

i(S)b 1(E)c
1(E) 1(S)
1(E) 1(S)
1(E) 1(S)

1(E) 1(S)
1(E) 1(S)


Five-Quarter

1(S) 1(E) 1
1 1(S) 1(E)
1 1 1(S)
1(E) 1 1

1(E)


Path

1
1
1 (E)
1(S)


Six-Quarter Path

1(S,E)d 1 1
1 1(S,E) 1
1 1 1(S,E)
1 1 1


1(E)


1 (E)

1


a QTR = Quarter
b (S) = Starting Quarter

0 (E) = Ending Quarter
d(S,E) = Starting Quarter and Ending Quarter (1 year later)


1
1
1
1(S,E)

1(E)





1


--


---







during any given quarter. In the backgrounding and feedlot
sections, the numeral "1" followed by an "S" in parentheses
indicates the starting quarter, an "E" in parentheses indicates
the ending quarter, and both an "S" and an "E" in parentheses
indicate the starting and ending quarter (1 year later) for a
six-quarter path which includes five quarters of backgrounding.

Identification of Specific Locations
One step in constructing the model is delineating regions
and identifying finite points for supply, backgrounding,
feedlot/slaughterplant, and demand. Region delineation is
always mapped along official county lines.
Supply and backgrounding points fall into four major areas
based upon general forage conditions and state geography. The
four regions are north, central, southeast, and southwest
Florida. The general delineation was based on the areas north
and west of the Suwannee River in north Florida, between the
Suwannee River and U.S. Interstate 4 in central Florida, and
east and west of U.S. Highway 27 in south Florida. Forage or
pasture conditions are a combination of available dry matter and
quality of dry matter. Geographic and seasonal differences in
forage production were accounted for by varying the quality and
quantity of forage assumed to be available by region and month.
Centralized locations within the state were selected for
feedlots and slaughterhouses. The three locations are (1)
Tallahassee, representing north Florida, (2) Ocala, represent-
ing central Florida, and (3) Okeechobee, representing south
Florida.
Demand regions were selected according to major metropoli-
tan areas. (These regions are not necessarily of equal popula-
tion density.) Demand, therefore, was divided into five re-
gions: two for north Florida and three for central and south
Florida. North Florida is delineated via the Suwannee River.
The northeast region includes the Jacksonville/Gainesville area,
with Marion and Volusia counties separating north and central-
south Florida. U.S. Highway 27 and Florida State Road 60 divide
central and south Florida into three demand regions. Panama
City and Hollywood were chosen because each approximates the
geographic center of the region.
Figures 2, 3, and 4 indicate the regions described
previously. Supply and backgrounding points include
Tallahassee, Ocala, Wauchula, and Belle Glade. Demand locations
include Hollywood, Jacksonville, Orlando, Tampa, and Panama
City.

Empirical Specification of the Model

In the spatiotemporal model the cost of feeding a 400-
pound weaned steer calf to 1,050 pounds slaughterweight and
subsequently slaughtering and delivering boxed beef to the
supermarket has been formulated as one continuous path with cost
components calculated at each stage of production. There are
five stages: (1) supplying a 400-pound weaned calf, (2)
backgrounding the calf to an average of 725 pounds, (3) fat-
tening in a feedlot to 1,050 pounds, (4) slaughtering the animal
























1-North Florida-Tallahassee
2-Central Florida-Ocala
3-Southwest Florida-Wauchula
4-Southeast Florida-Belle Glade











Figure 2. Delineation of Supply and Backgrounding Regions.


.,I3-'..*





















1-North Florida-Tallahassee
2-Central Florida-Ocala
3-South Florida-Okeechobee











Figure 3. Delineation of Feedlot/Slaughterplant Regions.






















1-Northwest Florida-Panama City
2-Northeast Florida-Jacksonville
3-Central Florida-Orlando
4-Southwest Florida-Tampa
5-Southeast Florida-Hollywood








Figure 4. Delineation of Demand Regions.







and providing 555 pounds of boxed beef, and (5) transporting the
boxed beef to the final destination. At each stage
transportation charges are incurred if the animal is transported
between locations.

Supply
In 1982, the Florida cattle industry produced 1,150,000
calves (Florida Crop and Livestock Reporting Service, 1983). To
determine the number of available feeder calves, the number of
heifer calves used as beef and dairy cow replacements must be
subtracted from the total calf crop. Beef and dairy cow re-
placements for 1982 totaled 188,000 and 45,000, respectively
(Florida Crop and Livestock Reporting Service). Thus, in 1982
there were 917,000 calves available for feeder calf production.
Table 1 indicates feeder calf availability in 1982.

Table 1. Feeder Calf Availability.

1982 Florida Calf Crop 1,150,000
1982 Beef Cow Replacements 188,000
1982 Dairy Cow Replacements 45,000
1982 Calves Available as Feeder Cattle
(Calf Crop minus Replacements) 917,000

Source: Florida Crop and Livestock Reporting Service.


Feeder calf availability by quarters was estimated using
1980-82 average quarterly marketing from several local Florida
auction markets (Florida Crop and Livestock Reporting Service,
unpublished). Auction markets were grouped by supply region.
Total cattle inventory for 1982 for all counties in each supply
region was divided by total cattle inventory in Florida, giving
a percentage of calves marketed in each region for the year.
North Florida had 15.04 percent of total cows; central Florida
had 22.96 percent of total cows; southwest Florida had 33.32
percent of the total cows; southeast Florida had 28.68 percent
of the total cows. Average quarterly marketing by region
determined the quarterly calf supply by region. This data is
presented in Table 2.

Backgrounding
A growth simulation model for stocker cattle (Spreen et.
al.) provided the means to estimate the cost of backgrounding a
400-pound calf to a weight sufficient (average of 725 pounds) to
be fed to 1,050 pounds in a feedlot. The cost of a 400-pound
calf was assumed to be $60 per hundredweight, a representative
price for 1982 (United Stated Department of Commerce, 1982a).
Calf prices change depending on seasonal availability. Feeder
calves available in the fall are priced lower than calves
available during the spring, because more calves are marketed
during the fall. The spatial price differential between Kansas
City prices and Florida prices for "choice" feeder steers














Table 2. Quarterly Feeder Calf Supply by Region.

By Quarter:
Percentage of Total Feeder Quarterly Marketing Percentage, Total Calves
Region Population Calves 1 2 3 4

North 19.7a 23.2% 31.7% 25.4%
Florida 15.04% 137,947 27,176b 32,004 43,728 35,039

Central 19.0% 19.9% 33.4% 27.7%
Florida 22.96% 210,552 39,926 41,799 70,373 58,454

Southwest 20.5% 25.4% 30.1% 24.0%
Florida 33.32% 305,479 62,623 77,592 91,949 73,315

Southeast 18.9% 28.6% 30.4% 22.1%
Florida 28.68% 263,022 49,711 75,224 79,959 58,128

aPercentage of feeder calves marketed during a specific quarter in a particular region.
bTotal feeder calves marketed during a specific quarter in a particular region.







contains a seasonal component characterized by larger than
average differentials in the heavy marketing season of August
through November and smaller differentials in January, April,
and July (Shonkwiler and Spreen). With feedlots located in
Florida, seasonal calf price fluctuations would be reduced. The
cost estimates used in the initial specification of the
spatiotemporal model do not reflect seasonal calf prices.
Numerous combinations of forages can be used for back-
grounding weaned calves. However, in executing the growth
simulation model for stocker cattle, three programs were util-
ized. First, in north Florida rye-ryegrass is grazed October
through March, and pensacola bahia is grazed from April through
September. Second, in central Florida rye-ryegrass is grazed
from December through March, and pensacola bahia is grazed from
April through November. Third, in south Florida digitgrass can
be grazed from February through November, and hay is used as the
primary feed during the months of December and January.
Heat stress is an important factor in backgrounding calves,
due to the reduction in weight gain possible during the hot
summer months. The weight gain of all calves backgrounded
during the third quarter is reduced to account for heat
stress. In addition, the weight gain of all calves backgrounded
south of Interstate 4 (southeast and southwest Florida) during
the third quarter is reduced to account for more severe heat
stress encountered in south Florida than in north and central
Florida.
The backgrounding simulation model requires data for the
quality and quantity of pasture forages and cost information for
these forages. Land rental charges are explicitly included in
the model for pastureland. These charges are an attempt to
reflect the opportunity cost of land used for backgrounding.
Fixed and variable costs for pastures of rye-ryegrass, pensacola
bahia, hay (Hewitt), and digitgrass (Prevatt and Mislevy), and
the cost of corn (Santa Fe Feed) as a feed supplement are
required as inputs for the simulation model. Corn is estimated
to cost $7.30/cwt in north Florida, $7.48/cwt in central
Florida, and $7.66/cwt in south Florida. The price
differentials across regions represent approximate additional
transport costs for corn shipped in from the eastern Corn Belt
(Central State Enterprises). Forage quantity is determined by
the dry matter (DM) yield, which estimates the amount of forage
available for consumption. Forage quality is determined by
Total Digestible Nutrients (TDN)3, and Forage Quality Index
(FQI) is based on a scale developed by Moore (1981). Tables 3,
4, and 5 list the forage quality and quantity data for north,
central, and south Florida, respectively, and show the
respective forage budgets.





Nutrient accounting in the backgrounding simulation model
is based upon the net energy system. The backgrounding model
converts Total Digestible Nutrients into net energy.












Table 3. North Florida Forage Quality and Quantity.

Variable
Months Fixed cost per
Forage Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec cost season

Rye-ryegrass $30.00 $107.04

TDN 66 64 62 68 68 67
FQI 1.8 1.8 1.7 2.1 2.0 1.9
DM 1000 1000 1000 585 1000 1000


Pensacola
bahiagrass $20.00 $78.50

TDN 64 64 62 58 54 50
FQI 1.9 1.9 1.7 1.4 1.2 0.9
DM 800 1164 1600 1330 800 400

TDN = Total Digestible Nutrients
FQI = Forage Quality Index
DM = Dry Matter
Adapted from Spreen et al.










Table 4. Central Florida Forage Quality and Quantity.

Variable
Months Fixed cost per
Forage Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec cost season

Rye-ryegrass $20.00 $107.04

TDN 66 64 62 68
FQI 2.0 1.9 1.8 2.1
DM 1170 1820 1430 650




Pensacola
bahiagrass $26.50 $78.50

TDN 63 64 60 54 50 52 56 50
FQI 1.8 1.9 1.7 1.4 1.2 1.3 1.5 1.0
DM 1645 1600 2000 1680 1040 480 240 240

TDN = Total Digestible Nutrients
FQI = Forage Quality Index
DM = Dry Matter
Adapted from Spreen et al.










Table 5. South Florida Forage Quality and Quantity.

Variable
Months Fixed cost per
Forage Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec cost season

Digitgrass $10.00 $85.90

TDN 70 68 68 67 63 58 55 55 58 58
FQI 2.2 2.0 2.0 2.0 1.9 1.5 1.4 1.4 1.6 1.6
DM 390 910 1560 2080 2340 2080 1560 1040 650 260




Hay NAa

TDN 55 55
FQI 1.0 1.0
DM NA NA

TDN = Total Digestible Nutrients
FQI = Forage Quality Index
DM = Dry Matter
NA = Not Applicable
aHay cost $40.00 per ton.

Adapted from Spreen et al.







Output from the backgrounding simulation model includes
predicted ending weight and breakeven price per hundredweight.
The breakeven price is the price required to cover all costs
incurred due to the weight gain program. The ending weight and
breakeven price per hundredweight obtained from the background-
ing model are used as initial input in the feedlot simulation
model.
Weight gain can be controlled in order to meet timing
requirements. In the backgrounding model, animals needing to
gain weight quickly (only two quarters of backgrounding) are fed
corn to supplement the pasture forage; animals needing to gain
weight slowly can be more heavily stocked on pasture forage
thereby reducing forage intake per animal. In the feedlot
simulation model, animals needing to gain weight quickly are fed
diets that have maximum amounts of corn as a proportion of the
ration; animals needing to gain weight more slowly have reduced
proportions of corn and increased proportions of roughage
(sorghum silage).

Fattening in a Feedlot
The feedlot simulation model (Fox, et al.) requires the
entry weight and price of the animal (the ending weight and
breakeven price from the backgrounding model), feed costs,
ration consumption, nutritional values for each component of the
feedlot diet, and feedlot yardage cost. The spatiotemporal
model also requires the fixed cost of establishing a feedlot.
The feedlot ration is assumed to consist of corn, sorghum
silage, and sufficient supplementary vitamins and minerals to
provide a balanced weight gain diet. The cost of corn shipped
to Florida in 1982 and 1983 averaged approximately $7.00 per
hundredweight or $3.92 per bushel (Santa Fe Feed). To account
for additional transport costs, corn was priced at $7.18/cwt. in
central Florida and $7.36/cwt in south Florida.5 The cost of
sorghum silage was estimated at $.013 per pound ($26 per ton)
(Hewitt).
Backgrounded animals fattened using the feedlot simulation
model gained from 1.9 to 2.5 pounds per day, depending on the
ration fed. An 882-pound steer requires at least 9.4 percent
protein in its daily feed ration if it gains 2.2 pounds per
day. Feedlot steers averaging 725 pounds and gaining 1.5 to 2.2
pounds per day require 9 to 9.5 percent protein in the feedlot
ration to maintain a balanced diet (National Academy of
Sciences). Rations used in the feedlot simulation program
provided at least 9.2 percent and as much as 9.5 percent




Feedlot yardage cost (feedlot variable cost) is the daily
cost for overhead. Overhead includes the cost of labor, ma-
chinery, repairs, facilities use, and bedding.

5Corn was priced slightly higher in the backgrounding
phase versus the feedlot phase in an attempt to account for
increased efficiency in handling.







protein, there y meeting protein requirements necessary for a
balanced diet.
In making weight gain projections, the feedlot simulation
model accounts for net energy of the feedlot diet, heat stress,
and backgrounding location. Weight gain projections are influ-
enced by these three factors. The net energy an animal can
obtain from a particular feedlot diet influences weight gain
potential. Net energy has two components. Net energy for
maintenance is the minimum amount of feed intake necessary for
an animal to maintain current weight. Net energy for gain is
the amount of intake, over and above minimum maintenance re-
quirements, which increases current weight (Fox and Black).
Different diets provide different proportions of net energy.
Animals subject to heat stress have limited weight gain poten-
tial because heat stress restricts the amount of feed or forage
that an animal will consume. Heat stress affects net energy
requirements and is incorporated by the model if the animal is
fed during the third quarter.
In order to determine the cost of feeding calves trans-
ported from different backgrounding locations, the number of
days to regain shrinkage lost during transport was varied ac-
cording to the distance the animal was transported. Number of
days to regain in-transit shrink adjusts for days required to
regain weight lost from purchase weight (breakeven price from
the backgrounding program) to arrival at the feedlot. An
average would be 14 to 21 days (Fox, et al.). An animal
traveling between adjacent regions required 10 days to regain
weight lost in transit (north Florida to central Florida;
central Florida to south Florida and vice versa). An animal
transported from north Florida backgrounding to feeding in a
south Florida feedlot (and vice versa) required 15 days to
regain weight loss. Animals remaining in the same region for
backgrounding and feeding required 5 days to regain shrinkage
due to relocation.
The backgrounding simulation model determines the stocking
rate, the number of acres per head, for each forage pasture.
Rye-ryegrass and pensacola bahia are the winter and summer
forages, respectively, used in north and central Florida back-
grounding programs. As can be seen in Tables 3 and 4, pensacola
bahia does not consistently produce as much quality dry matter
as rye-ryegrass. This affects the stocking rate because the
month with the least amount of dry matter determines the
stocking rate for the entire grazing period. Therefore, the




yellow corn and sorghum silage, used in the feedlot ra-
tion, are 10 and 7.2 percent protein, respectively. There are
four feedlot rations: (1) 70 percent corn and 30 percent sor-
ghum silage, providing 9.3 percent protein, (2) 75 percent corn
and 25 percent sorghum silage, providing 9.3 percent protein,
(3) 78 percent corn and 22 percent sorghum silage, providing
9.4 percent protein, and (4) 81 percent corn and 19 percent
sorghum silage, providing 9.5 percent protein.







stocking rate for pensacola bahia is usually higher than rye-
ryegrass because more acres of pensacola bahia are required to
graze fewer animals during low production months. For example,
animals grazing pensacola bahia in north Florida from April
through September can be stocked at .75 acres per animal; corn
supplement must be added in September in order to meet mainte-
nance requirements. Animals grazing pensacola bahia in central
Florida from April through November can only be stocked at 1.92
acres per animal and require corn supplement each month in order
to meet net energy requirements. By comparison, animals grazing
rye-ryegrass never exceeded .73 acres per animal and smaller
amounts of corn supplement are used.
Variable costs for feedlot production are calculated
through feedlot yardage costs estimated to be 20 cents per
day. Feedlot yardage costs vary, depending on what the charges
include. A feedlot in central Florida charges 18 cents per day
as yardage cost. Davis Feedlot in Balm, Florida charges 30 to
32 cents per day, but this includes both fixed and variable
costs as well as a margin of profit. Without including profit
and excluding fixed costs, the 20-cent yardage charge is an
approximate statewide average.
The fixed cost of establishing a feedlot with an annual
capacity of 50,000 head was calculated at an investment cost of
$155.15 per head of capacity (Gee). This fixed cost totals to
$7,757,500. This facility is assumed to have an average in-
vestment life of 10 years, since different equipment and con-
struction have varying years of investment life. Thus, in a
given year, the fixed cost of a feedlot with 50,000-head annual
capacity is $775,750. An interest rate of 13.0 percent is
calculated on all operating costs in both the backgrounding and
feedlot simulation models.
All calves reach 1,050 pounds in the feedlot. The total
cost for backgrounding and feeding is reflected in the total
cost obtained from the feedlot simulation model, because the
cost per hundredweight obtained from the backgrounding model was
used as the calf cost initially entered in the feedlot model.
There are a total of 144 backgrounding/feedlot costs,
considering four backgrounding locations, three feedlot loca-
tions, four quarters of the year, and three different lengths of
time a calf can be backgrounded and fed (four, five, or six
quarters). These costs, backgrounding forage stocking rates,
feedlot entry weight, and cost per pound of gain for the back-
grounding and feeding program are shown in Tables 6A, 6B, 6C,
7A, 7B, 7C, 8A, 8B, and 8C. All information found in these
tables was acquired from the backgrounding simulation model
(Spreen, et al.) and the feedlot simulation model (Fox, et
al.). Cost per pound of gain is calculated by subtracting
weaned calf cost, $240 (a 400-pound calf at $60 per hundred-
weight), from the total cost and then dividing by 650 pounds,
the total weight gain from 400 pounds to 1,050 pounds.
Although south Florida has two supply regions, background-
ing and feeding costs are identical for southwest and southeast
Florida. South Florida was divided into separate supply regions
due to the large quantity of cattle available from this area of
the state. Thus, the backgrounding and feeding costs shown in













Table 6A. Backgrounding and Feeding Costs for a Four-Quarter Weight Gain Program, North Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.45 .54 North Florida 1 $635.27 $.61 648
--- .66 North Florida 2 $693.16 $.70 553
.59 .54 North Florida 3 $670.01 $.66 598
.35 --- North Florida 4 $657.57 $.64 598

.45 .54 Central Florida 1 $649.66 $.63 648
--- .66 Central Florida 2 $708.02 $.72 553
.59 .54 Central Florida 3 $684.38 $.68 598
.35 --- Central Florida 4 $671.22 $.66 598

.45 .54 South Florida 1 $638.41 $.61 648
--- .66 South Florida 2 $707.73 $.72 553
.59 .54 South Florida 3 $681.76 $.68 598
.35 --- South Florida 4 $668.85 $.66 598

*Stocking Rate = Acre per Head
RRG = Rye-Ryegrass
PG = Pensacola Bahiagrass












Table 6B. Backgrounding and Feeding Costs for a Four-Quarter Weight Gain Program, Central Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.43 .40 North Florida 1 $643.77 $.62 652
--- .71 North Florida 2 $698.85 $.71 597
.70 1.35 North Florida 3 $755.92 $.79 601
.66 1.20 North Florida 4 $699.11 $.71 650

.43 .40 Central Florida 1 $642.35 $.62 652
--- .71 Central Florida 2 $696.91 $.70 597
.70 1.35 Central Florida 3 $752.08 $.79 601
.66 1.20 Central Florida 4 $702.63 $.71 650

.43 .40 South Florida 1 $642.62 $.62 652
--- .71 South Florida 2 $697.54 $.70 597
.70 1.35 South Florida 3 $754.61 $.79 601
.66 1.20 South Florida 4 $697.91 $.70 650

*Stocking Rate = Acre per Head
RRG = Rye-Ryegrass
PG = Pensacola Bahiagrass














Table 6C. Backgrounding and Feeding Costs for a Four-Quarter Weight Gain Program, South Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
Digitgrass Location Quarter per Head Pound of Gain Weight (Pounds)

.50 North Florida 1 $637.27 $.61 629
.33 North Florida 2 $651.26 $.63 600
1.29 North Florida 3 $743.96 $.78 585
1.25 North Florida 4 $696.72 $.70 600

.50 Central Florida 1 $636.81 $.61 629
.33 Central Florida 2 $652.69 $.64 600
1.29 Central Florida 3 $744.81 $.78 585
1.25 Central Florida 4 $694.63 $.70 600

.50 South Florida 1 $627.21 $.60 629
.33 South Florida 2 $636.53 $.61 600
1.29 South Florida 3 $728.20 $.75 585
1.25 South Florida 4 $684.76 $.68 600

*Stocking Rate = Acre per Head












Table 7A. Backgrounding and Feeding Costs for a Five-Quarter Weight Gain Program, North Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.53 .79 North Florida 1 $643.91 $.62 857
.61 .66 North Florida 2 $634.71 $.61 849
.50 .59 North Florida 3 $615.14 $.58 872
.45 .92 North Florida 4 $661.30 $.65 857

.53 .79 Central Florida 1 $656.02 $.64 857
.61 .66 Central Florida 2 $648.80 $.63 849
.50 .59 Central Florida 3 $625.53 $.59 872
.45 .92 Central Florida 4 $674.01 $.67 857

.53 .79 South Florida 1 $661.52 $.65 857
.61 .66 South Florida 2 $655.91 $.64 849
.50 .59 South Florida 3 $629.59 $.60 872
.45 .92 South Florida 4 $675.05 $.67 857

*Stocking Rate = Acre per Head
RRG = Rye-Ryegrass
PG = Pensacola Bahiagrass













Table 7B. Backgrounding and Feeding Costs for a Five-Quarter Weight Gain Program, Central Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.44 1.92 North Florida 1 $798.24 $.86 858
.73 1.61 North Florida 2 $789.94 $.85 847
.56 .97 North Florida 3 $706.62 $.72 872
.62 1.03 North Florida 4 $707.59 $.72 845

.44 1.92 Central Florida 1 $791.03 $.85 858
.73 1.61 Central Florida 2 $789.48 $.85 847
.56 .97 Central Florida 3 $700.73 $.71 872
.62 1.03 Central Florida 4 $700.47 $.71 845

.44 1.92 South Florida 1 $797.62 $.86 858
.73 1.61 South Florida 2 $789.25 $.85 847
.56 .97 South Florida 3 $705.99 $.72 872
.62 1.03 South Florida 4 $706.90 $.72 845

*Stocking Rate = Acre per Head
RRG = Rye-Ryegrass
PG = Pensacola Bahiagrass













Table 7C. Backgrounding and Feeding Costs for a Five-Quarter Weight Gain Program, South Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
Digitgrass Location Quarter per Head Pound of Gain Weight (Pounds)

1.13 North Florida 1 $773.30 $.82 855
.62 North Florida 2 $740.83 $.77 844
.85 North Florida 3 $680.12 $.68 852
1.65 North Florida 4 $664.62 $.65 855

1.13 Central Florida 1 $772.75 $.82 855
.62 Central Florida 2 $733.64 $.76 844
.85 Central Florida 3 $675.34 $.67 852
1.65 Central Florida 4 $659.59 $.65 855

1.13 South Florida 1 $759.32 $.80 855
.62 South Florida 2 $722.14 $.74 844
.85 South Florida 3 $662.72 $.65 852
1.65 South Florida 4 $646.99 $.63 855

*Stocking Rate = Acre per Head













Table 8A. Backgrounding and Feeding Costs for a Six-Quarter Weight Gain Program, North Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.45 .58 North Florida 1 $658.70 $.64 847
.42 .61 North Florida 2 $668.82 $.66 852
.59 .79 North Florida 3 $705.88 $.72 852
.47 .75 North Florida 4 $670.44 $.66 850

.45 .58 Central Florida 1 $672.70 $.67 847
.42 .61 Central Florida 2 $679.60 $.68 852
.59 .79 Central Florida 3 $714.30 $.73 852
.47 .75 Central Florida 4 $681.06 $.68 850

.45 .58 South Florida 1 $677.70 $.67 847
.42 .61 South Florida 2 $683.23 $.68 852
.59 .79 South Florida 3 $716.95 $.73 852
.47 .75 South Florida 4 $684.31 $.68 850

*Stocking Rate = Acre per Head
RRG = Rye-Ryegrass
PG = Pensacola Bahiagrass












Table 8B. Backgrounding and Feeding Costs for a Six-Quarter Weight Gain Program, Central Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
RRG PG Location Quarter per Head Pound of Gain Weight (Pounds)

.39 1.55 North Florida 1 $745.91 $.78 851
.43 .83 North Florida 2 $691.33 $.69 850
.44 1.24 North Florida 3 $782.55 $.84 850
.69 1.98 North Florida 4 $869.90 $.97 847

.39 1.55 Central Florida 1 $739.49 $.77 851
.43 .83 Central Florida 2 $689.30 $.69 850
.44 1.24 Central Florida 3 $778.10 $.83 850
.69 1.98 Central Florida 4 $862.73 $.96 847

.39 1.55 South Florida 1 $745.23 $.78 851
.43 .83 South Florida 2 $690.64 $.69 850
.44 1.24 South Florida 3 $781.88 $.83 850
.69 1.98 South Florida 4 $869.21 $.97 847


*Stocking Rate
RRG
PG


= Acre per Head
= Rye-Ryegrass
= Pensacola Bahiagrass













Table 8C. Backgrounding and Feeding Costs for a Six-Quarter Weight Gain Program, South Florida.

Stocking Rate* Feedlot Beginning Total Cost Cost per Feedlot Entry
Digitgrass Location Quarter per Head Pound of Gain Weight (Pounds)

1.89 North Florida 1 $710.27 $.72 832
1.69 North Florida 2 $624.29 $.59 846
1.28 North Florida 3 $710.43 $.72 840
1.12 North Florida 4 $782.51 $.84 833

1.89 Central Florida 1 $703.72 $.71 832
1.69 Central Florida 2 $619.71 $.58 846
1.28 Central Florida 3 $705.43 $.72 840
1.12 Central Florida 4 $775.37 $.82 833

1.89 South Florida 1 $692.09 $.70 832
1.69 South Florida 2 $608.03 $.57 846
1.28 South Florida 3 $691.23 $.69 840
1.12 South Florida 4 $763.29 $.81 833

*Stocking Rate = Acre per Head







Tables 6, 7, and 8 total to 108 costs instead of 144, due to the
duplication of costs for southwest and southeast Florida.
Amounts of corn and sorghum silage fed in the feedlot
program in north, central, and south Florida are shown in Tables
9, 10, and 11, respectively. Note the following:

(1) Animals can be backgrounded in any of three locations
(north, central, and south Florida) and subsequently
transported to feedlots in one of these three locations.
Transportation between regions affects the number of days
required to regain weight lost during transport. Thus, the
amount of feed fed in the feedlot varies, depending on
backgrounding location.
(2) Animals fed in central Florida show identical amounts of
corn and sorghum silage intake if they were backgrounded in
north or south Florida, because these two regions require
the same number of days for an animal to regain in-transit
shrink when transported to central Florida.
(3) There are four feedlot diets: (a) 70 percent corn and 30
percent sorghum silage, (b) 75 percent corn and 25 percent
sorghum silage, (c) 78 percent corn and 22 percent sorghum
silage, and (d) 81 percent corn and 19 percent sorghum
silage, where the percentages are based on dry matter. The
following tables indicate the amount of corn and sorghum
silage fed on an "as fed basis," which includes the
moisture content in the total poundage. It appears that
more sorghum silage is fed than corn, but sorghum silage is
70.6 percent moisture, whereas corn is only 11 percent
moisture.
(4) Four-quarter weight gain programs require approximately
twice as much corn and silage than five- and six-quarter
programs, because four-quarter paths include two quarters
of feedlot fattening, whereas five- and six-quarter paths
include only one quarter of feedlot fattening. All
information for these tables originates from the feedlot
simulation program (Fox, et al.).

Slaughtering Fed Cattle
A slaughterplant cost analyzer (Nelson) determined the
fixed and variable costs for two sizes of slaughterplant facil-
ities. The small slaughterplant can slaughter and process 120
head of cattle per hour or 225,000 head annually at a fixed cost
of $26.358 per head or $5,930,550 per year. The variable costs
for a small plant are $53.046 per head. The large slaughter-
plant can process 300 head of cattle per hour operating two
shifts daily. Thus, annual capacity is 1,125,000 head at a
fixed cost of $11.5816 per head or $13,029,300 per year. The
variable costs for a large slaughterplant are $49.383 per
head. Fixed costs are costs associated with establishing the
facility. Variable costs are costs incurred with respect to
slaughtering the animals and processing the meat.
Decreasing cost aspects of the slaughter industry are
reflected via small and large plant possibilities. The variable
costs of slaughtering beef are considered by the model to be
linear. The per unit variable costs would increase by










Table 9. Amount of Corn and Sorghum Silage Fed Per Animal in the Feedlot Program, North Florida.

Beginning Length of Feeding Corn Sorghum Silage
Quarter in Quarters NF CF SF NF CF SF

- - - - - - - Pounds* - - - - - - -
1 4 2650 2722 2899 3438 3531 2475
2 4 3264 3333 3404 2318 2367 2417
3 4 3004 3082 3199 2565 2631 2271
4 4 3053 3124 3246 2607 2667 2305

1 5 1503 1591 1679 1283 1359 1434
2 5 1559 1654 1749 1331 1412 1494
3 5 1444 1516 1586 1233 1294 1355
4 5 1449 1528 1650 1880 1982 1665

1 6 1574 1669 1797 1344 1425 1277
2 6 1610 1680 1753 1141 1193 1245
3 6 1480 1598 1739 1920 1613 1316
4 6 1531 1643 1737 1545 1403 1314

*Pounds = "As fed basis"
Sorghum silage = 70.6 percent moisture
Corn = 11 percent moisture
NF = North Florida
CF = Central Florida
SF = South Florida










Table 10. Amount of Corn and Sorghum Silage Fed Per Animal in the Feedlot Program, Central Florida.

Beginning Length of Feeding Corn Sorghum Silage
Quarter in Quarters NF CF SF NF CF SF

- - - - - - - Pounds* - - - - -
1 4 2693 2693 2693 3494 3424 3494
2 4 3081 3011 3081 2631 2571 2631
3 4 3071 2993 3071 2623 2555 2623
4 4 2831 2684 2831 2856 3483 2856

1 5 1512 1432 1512 1961 1858 1961
2 5 1669 1518 1669 1425 1969 1425
3 5 1516 1444 1516 1294 1233 1294
4 5 1677 1590 1677 1432 1358 1432

1 6 1638 1560 1638 1399 1332 1399
2 6 1678 1583 1678 1192 1351 1192
3 6 1615 1479 1615 1630 1918 1630
4 6 1659 1572 1659 1417 1342 1417

*Pounds = "As fed basis"
Sorghum silage = 70.6 percent moisture
Corn = 11 percent moisture
NF = North Florida
CF = Central Florida
SF = South Florida











Table 11. Amount of Corn and Sorghum Silage Fed Per Animal in the Feedlot Program, South Florida.

Beginning Length of Feeding Corn Sorghum Silage
Quarter in Quarters NF CF SF NF CF SF

- - - - - - - Pounds* - - - - - - -
1 4 3021 2921 2821 2286 2494 2846
2 4 3189 3068 2997 2264 2620 2559
3 4 3274 3155 3083 2325 2693 2632
4 4 3231 3156 3057 2294 2241 2610

1 5 1723 1553 1447 1223 1828 1878
2 5 1814 1715 1606 1288 1218 1371
3 5 1753 1680 1607 1245 1193 1141
4 5 1667 1527 1447 1682 1981 1878

1 6 1886 1794 1684 1339 1274 1437
2 6 1787 1715 1643 1269 1218 1167
3 6 1809 1692 1605 1285 1445 1371
4 6 1863 1773 1658 1323 1259 1416

*Pounds = "As fed basis"
Sorghum silage = 70.6 percent moisture
Corn = 11 percent moisture
NF = North Florida
CF = Central Florida
SF = South Florida






approximately $1 per head for each 100,000 head below maximum
capacity.
Slaughtering costs include fabrication of each carcass into
boxed beef. Carcass weight, which is 638 pounds, is assumed to
be 60.8 percent of live weight (1,050 pounds). Fat and bone
(carcass by-products) per carcass unit are 83 pounds for regular
boxed beef (Duewer). A 638-pound carcass thus yields 555 pounds
of boxed beef.
Waste products salvaged when an animal is initially
slaughtered, becoming a 638-pound carcass, can be utilized for
various industrial purposes. These by-products can be sold to
manufacturers, which reduces slaughtering costs. The estimated
by-product allowance is $5.96 per hundredweight of live weight
(1,050 pounds) or $62.58 per animal (United States Department of
Agriculture).

Demand
In order to determine the quantity of beef consumed in each
region, the percentage of population relative to state
population was determined for each region using county popula-
tion statistics (United States Department of Commerce, 1983).
All population estimates are 1980-82 full-time equivalents which
includes calculations for tourist fluctuations. The model
assumes that consumption is directly proportional to
population. Since just over 1 million head of fed cattle were
consumed in Florida in 1980 (Spreen), this means that the
available feeder calf supply (917,000) cannot totally meet
demand requirements. The deficit is assumed to be met by beef
imports.
Regional population was determined by summing the appro-
priate counties' population in each region. Each regional
population was divided by total Florida population to determine
the regional percentage of state population.
The total number of feeder cattle available for supply
(917,000) was distributed in each demand region according to the
region's percentage of state population. For example, northwest
Florida, with 10 percent of the state's population, would
require 10 percent of available supply of 91,700 head. This
number was equally divided among the four quarters of the year
in order to determine demand requirements for each region during
each quarter. Table 12 indicates demand regions by population
and quarterly regional demand. Florida population in 1982
totaled 11,261,769 (United States Department of Commerce, 1983).

Transportation
Transportation costs are incurred between (1) supply and
backgrounding locations if these two stages of production occur
in different regions, (2) backgrounding and feedlot operations
if these occur in different regions, and (3) slaughterplant
facilities and demand locations. L.T. Manning Trucking Company
charges $1.70 per mile for any size truckload for all trips out
of the Ocala, Florida area. Each truck can carry 49,000 pounds
of live animals. A full truckload of 400-pound calves would
contain 123 animals. At $1.70 per mile, this would cost $.014
per animal per mile for transporting between supply and
















Table 12. Population by Demand Region and Quarterly Regional Demand.

Percentage State
Region Population Population Beef Demand Quarterly Demand

Northwest Florida 1,102,247 10% 91,700 22,925

Northeast Florida 1,158,109 10% 91,700 22,925

Central Florida 2,040,577 18% 165,060 41,265

Southwest Florida 3,245,778 29% 265,928 66,482

Southeast Florida 3,715,058 33% 302,612 75,653

Source: United States Department of Commerce, 1983.







backgrounding regions. A full truckload of 725-pound calves
(the average weight of an animal after backgrounding) would
contain 68 animals. At $1.70 per mile, the cost to transport an
animal between backgrounding and feedlot locations would be
$.025 per mile. The cost per animal per trip between supply and
backgrounding locations is shown in Table 13. The cost per
animal per trip between backgrounding and feedlot locations is
shown in Table 14.
The cost of shipping 555 pounds of boxed beef is estimated
at $.01 per hundredweight per mile (Duewer). Shipment of 555
pounds of boxed beef costs $.0555 per mile. Table 15 indicates
the cost per animal per trip between the slaughterplant and
demand regions.


Empirical Results

The results obtained from the spatiotemporal optimization
model identify (1) the total minimum cost of feeding Florida
feeder calves to slaughterweight and slaughtering the calves,
(2) the size and location of slaughterplant facilities, and (3)
the number and location of feedlot facilities. Presented herein
are the results of the optimal solution.

Optimal Solution
The optimal solution results in a total cost of
$668,958,771. By-products of hide and offal are sold to manu-
facturers for industrial purposes. The value of hide and offal
for 1983 averaged $5.96 per hundredweight of live weight (United
States Department of Agriculture, 1983). The total value of
hide and offal for 917,000 feeder calves equals $57,385,860.
Deducting the revenue received from the sale of hide and offal
by-products results in a total minimum cost of $611,572,911.
When this total is divided by the total number of feeder calves,
the cost per animal is $666.93. The cost per animal divided by
the carcass weight of 638 pounds results in a carcass price of
$1.045 per pound. In 1983, boxed beef cutout, equivalent to
carcass price (Omaha, Nebraska basis), averaged $102.26 per
hundredweight (United States Department of Agriculture, 1983),
or $1.022 per pound.
The optimal solution is to build one large slaughterplant
and six feedlots in north Florida. The slaughterplant is oper-
ated at an annual capacity of 81.5 percent. Feedlots are
operated at 95.3 percent capacity during the first quarter, 76.4
percent capacity during the second quarter, 77.9 percent
capacity in the third quarter, and 94.5 percent capacity during
the fourth quarter.
All animals are backgrounded in north Florida. These
calves are backgrounded and fed primarily using five-quarter
weight gain programs. Five-quarter paths constitute 87.4
percent of the optimal solution. Four-quarter paths are 12.6
percent, and there are no six-quarter paths in the optimal
solution.














Table 13. Cost per Animal per Trip between Supply and Backgrounding Regions.

Backgrounding Region
Region I Region II Region III Region IV
Supply Region Tallahassee Ocala Wauchula Belle Glade

Region I --- $2.38 $4.00 $5.42
Tallahassee (170)a (286) (387)

Region II $2.38 --- $1.75 $3.05
Ocala (170) (125) (218)

Region III $4.00 $1.75 --- $1.64
Wauchula (286) (125) (117)

Region IV $5.42 $3.05 $1.64
Belle Glade (387) (218) (117)

Based on: $1.70 per mile per trip, L.T. Manning Trucking Company, Ocala, Florida.
aThe number in parentheses is the map mileage between the two locations.













Table 14. Cost per Animal per Trip between Backgrounding and Feedlot Regions.

Feedlot Region
Region I Region II Region III
Backgrounding Region Tallahassee Ocala Okeechobee

Region I --- $4.25 $8.53
Tallahassee (170)a (341)

Region II $4.25 --- $4.30
Ocala (170) (172)

Region III $6.70 $3.13 $1.80
Wauchula (268) (125) (72)

Region IV $9.68 $5.45 $1.15
Belle Glade (387) (218) (46)

Based on: $1.70 per mile per trip, L.T. Manning Trucking Company, Ocala, Florida.
aThe number in parentheses is the map mileage between the two locations.















Table 15. Cost per Animal per Trip between Slaughterplant and Demand Regions.

Demand Region
Region I Region II Region III Region IV Region V
Slaughterplant Region Panama City Jacksonville Orlando Tampa Hollywood

Region I $5.38 $9.05 $13.43 $13.26 $25.03
Tallahassee (97)a (163) (242) (239) (451)

Region II $14.54 $5.27 $4.00 $5.27 $15.71
Ocala (262) (95) (72) (95) (283)

Region III $24.03 $13.26 $5.83 $7.33 $6.16
Okeechobee (433) (239) (105) (132) (111)

Based on: $.01 per hundredweight per mile, (Duewer, 1985).
aThe number in parentheses is the map mileage between the two locations.







Optimal Routing Scheme
The optimal routing scheme chosen by the model includes 35
paths. The paths included in the optimal solution and the
number of animals following each path are shown in Table 16.
The seven-digit path identification number is interpreted as
follows:
(1) column 1 is one of four supply regions (1 = north Florida, 2
= central Florida, 3 = southwest Florida, and 4 = southeast
Florida);
(2) column 2 is one of four backgrounding locations (regional
numbers are the same as supply);
(3) column 3 is one of three feedlot/slaughterplant locations (1
= north Florida, 2 = central Florida, and 3 = south
Florida);
(4) column 4 indicates the slaughterplant size (1 = small
slaughterplant and 2 = large slaughterplant);

(5) column 5 is one of five demand locations (1 = northwest
Florida, 2 = northeast Florida, 3 = central Florida, 4 =
southwest Florida, and 5 = southeast Florida);
(6) column 6 is the quarter the animals begin backgrounding;
and
(7) column 7 is the quarter that boxed beef is available for
consumption.

Interpretation of Dual Information
The mixed integer programming model results in a solution
which indicated optimal primal variables, the 35 paths listed
previously, and corresponding dual variables. The spatiotem-
poral optimization model is a minimization problem with less-
than-or-equal-to supply constraints and greater-than-or-equal-
to demand constraints. Therefore, the dual variables for the
supply constraints are less than or equal to zero, meaning the
value of this dual variable indicates a reduction in total cost
if one additional animal is available for supply. The dual
variables for the demand constraints are greater than or equal
to zero, meaning the value of this dual variable indicates an
increase in total cost if one additional animal is needed to
meet consumption requirements.
The dual variables indicate the imputed marginal value of
availability (supply) and the imputed marginal cost of meeting
consumption requirements (demand). Dual variables (shadow
prices) are given for each quarter and location. The quarter in
which supply of additional animals produces the greatest
reduction in total cost is the first quarter. An additional
animal available in north Florida during the first quarter
reduces total cost by $51.21. If an additional animal is
available in north Florida during the first quarter, it could be
chosen to satisfy demand requirements, instead of an animal from
another, more costly location. An additional animal available
in central Florida during the first quarter reduces total cost
by $48.83. An additional animal from southwest and southeast
Florida during the first quarter reduces total cost by $47.21
and $45.70, respectively.










Table 16. Optimal Paths for Backgrounding, Feeding, and Slaughtering Florida Calves.

Optimal Path Number Optimal Path Number
S BA FL SP D B E of Calves S BA FL SP D B E of Calves

1 1 1 2 2 1 1 4,314 4 1 1 2 3 2 3 41,265
1 1 1 2 1 3 3 11,891 1 1 1 2 5 3 4 28,205
1 1 1 2 5 3 3 3,623 2 1 1 2 2 3 4 22,925
3 1 1 2 4 3 3 23,617 2 1 1 2 5 3 4 47,448
3 1 1 2 5 3 3 1,850 3 1 1 2 4 3 4 66,482
4 1 1 2 5 3 3 15,769 4 1 1 2 1 3 4 22,925
1 1 1 2 5 1 2 22,862 4 1 1 2 3 3 4 41,265
2 1 1 2 5 1 2 39,926 1 1 1 2 5 4 1 35,039
3 1 1 2 2 1 2 22,925 2 1 1 2 2 4 1 17,840
3 1 1 2 3 1 2 10,062 2 1 1 2 5 4 1 40,614
3 1 1 2 4 1 2 16,771 3 1 1 2 1 4 1 22,925
3 1 1 2 5 1 2 12,865 3 1 1 2 2 4 1 771
4 1 1 2 4 1 2 49,711 3 1 1 2 3 4 1 41,265
1 1 1 2 5 2 3 32,004 3 1 1 2 4 4 1 8,354
2 1 1 2 5 2 3 41,799 4 1 1 2 4 4 1 58,128
3 1 1 2 4 2 3 23,464 3 3 1 2 1 2 2 22,925
4 1 1 2 1 2 3 11,034 3 3 1 2 3 2 2 31,203
4 1 1 2 2 2 3 22,925


S = Supply Region
BA = Backgrounding Region
FL = Feedlot Location
SP = Slaughterplant Size


D = Demand Region
B = Beginning Quarter
E = Ending Quarter







The quarter which results in the smallest reduction in
total cost is the third quarter. Reduction in total cost for an
additional animal available during the third quarter from north,
central, and southwest Florida is $5.42, $3.04, and $1.42,
respectively. An additional animal available from southeast
Florida during the third quarter does not reduce total cost; the
shadow price is zero. The second most valued quarter for supply
is the second quarter, and the third most valued quarter is the
fourth quarter.
The imputed marginal value of availability is affected by
(1) the location of available feeder calf supplies, (2) the
location of feedlots and slaughterplant, (3) the cost of weight
gain programs, and (4) transportation costs. The greatest
reduction in total cost is in north Florida during the first
quarter; this is the location and quarter when the least number
of calves are available, feeding and slaughtering takes place in
this region, transportation costs are minimized, and weight gain
programs are generally less expensive than in other regions.
There is no reduction in total cost for calves available from
southeast Florida during the third quarter; several factors
affect this: (1) Only one other location has a greater number
of calves available. (2) This region is the most distant from
the feedlots and slaughterplant located in north Florida. (3)
Large transportation costs are incurred for transport between
south Florida and north Florida. (4) Weight gain programs are
generally more expensive in this region due to added heat stress
and low production forages. These four factors together affect
the imputed marginal values of availability. The imputed
marginal value for each supply region by quarter are presented
in Table 17.


Table 17. Imputed Marginal Value for Supply Regions by
Quarter.

Quarter
Region 1 2 3 4


North Florida $51.21 $40.71 $5.42 $25.19

Central Florida $48.83 $38.33 $3.04 $22.81

Southwest Florida $47.21 $36.71 $1.42 $21.19

Southeast Florida $45.79 $35.29 $0.00 $19.77



The imputed marginal cost of meeting consumption require-
ments indicates an increase to total cost incurred when an
additional animal is provided for consumption. The most expen-
sive quarter, or the quarter which increases total cost the
most, is the second quarter. The least expensive quarter is the
fourth quarter. The cost of providing an additional animal for







consumption during the second quarter in northwest Florida is
$749.88. During the second quarter in northeast, central,
southwest, and southeast Florida, providing an additional animal
for consumption increases total cost by $753.55, $757.93,
$757.76, and $769.53, respectively.
The imputed marginal cost of meeting consumption require-
ments is affected by three factors: (1) the cost of the weight
gain program, (2) location of the final demand point, and (3)
transportation costs. For example, having an additional animal
available for consumption during the second quarter in southeast
Florida increases total cost by $769.53; this location is the
most distant from the feedlot/slaughterplant facilities in north
Florida. In south Florida, a five-quarter weight gain program
ending in the second quarter is one of the most costly paths an
animal can follow (see Table 7C); transportation costs are most
expensive from the south Florida regions. The most costly time
of the year to provide an additional animal for consumption has
the largest imputed marginal cost. The imputed marginal values
for each demand region by quarter are shown in Table 18.



Table 18. Imputed Marginal Value for Demand Regions by
Quarter.

Quarter
Region 1 2 3 4

Northwest Florida $741.24 $749.88 $730.18 $675.32

Northeast Florida $744.91 $753.55 $733.85 $678.99

Central Florida $749.29 $757.93 $738.23 $683.37

Southwest Florida $749.12 $757.76 $738.06 $683.20

Southeast Florida $760.89 $769.53 $749.83 $694.97


Acreage Requirements for the Optimal Solution
One assumption of the model is that there is no constraint
associated with acreage available for backgrounding weaned
calves. In the optimal solution, paths chosen as optimal rout-
ing patterns require 669,239 acres of pensacola bahia forage and
519,160 acres of rye-ryegrass. Pensacola bahia is a summer
forage, and rye-ryegrass is a winter forage. Therefore, at
least 669,239 acres must be available for backgrounding pur-
poses. Over 2 million acres were available as crop and
pastureland in north Florida in 1982 (United States Department
of Commerce, 1982b). This assumption, therefore, remains valid.







Average Costs
In the optimal solution with 917,000 calves, the average
cost per animal is $666.93 or $1.045 per pound (carcass weight
basis). The model was executed for different levels of supply
to generate an average cost curve for the industry. Four levels
of supply fewer than 917,000 calves (200,000; 400,000; 600,000;
and 800,000) and three levels of supply greater than 917,000
(1,100,000; 1,300,000; and 1,500,000) are analyzed. Supply of
fewer than 917,000 calves is distributed by region and quarter
for supply and demand by the same methods used for the optimal
solution. The model assumes that all supply greater than
917,000 calves is provided from south Georgia and south Alabama,
and all animals in excess of 917,000 are available for supply
from the north Florida region. Transportation costs for
shipping animals from out-of-state locations is not calculated.
These additional computer executions provide a means to make
comparisons between different supply quantities, assuming
different levels are available within the state. The results of
the eight computer executions are shown in Tables 19 and 20.
The level of supply and number, size, and location of
facilities; total cost; and hide and offal value are indicated
in Table 19. The total minimum cost (total cost minus returns
from the sale of hide and offal), average cost per head, and
average cost per pound of boxed beef (carcass cutout price or
average cost per head divided by 638 pounds carcass weight) are
shown in Table 20.
Results obtained from assuming availability of different
levels of feeder calf supply indicate the respective average
cost associated with each level. Minimum average cost occurs
when 1.3 million calves are available for slaughter. Average
costs decline until 1.1 million animals are available for
slaughter, at which point a large slaughterplant is fully util-
ized. For production levels of 1.1 million head and greater,
average costs are approximately equal. The average cost per
pound of carcass weight is plotted for each level of feeder calf
supply in Figure 5.







Table 19. Total System Costs and Optimal Plant Configura-
ations for Eight Different Levels of Supply.

Number, Size,
Level of and Location Hide & Offal
Supply of Facilities Total Cost($) Value ($)


200,000


1 Fl NFL
1 SSP NFL


400,000 1 Fl NFL
2 Fl SFL
1 SSP NFL
1 SSP SFL
600,000 4 Fl NFL
1 LSP NFL
800,000 5 Fl NFL
1 LSP NFL
917,000 6 Fl NFL
1 LSP NFL
1,100,000 7 Fl NFL
1 LSP NFL
1,300,000 6 Fl NFL


1,500,000


149,818,342

297,884,887




442,267,097

585,087,780

668,958,771

798,586,298

943,105,522




1,088,469,413


Fl = Feedlot NFL = North Florida
LSP = Large Slaughterplant SFL = South Florida
SSP = Small Slaughterplant



Table 20. Estimated Average cost for Eight Levels of Supply.
Level of Average Cost Average Cost
Supply Total Costa($) per Head($) per Poundb($)
200,000 137,302,342 686.51 1.076
400,000 272,852,887 682.13 1.069
600,000 404,719,097 674.53 1.057
800,000 535,023,780 668.78 1.048
917,000 611,572,911 666.93 1.045
1,100,000 729,748,298 663.41 1.040
1,300,000 861,751,522 662.89 1.039
1,500,000 994,599,413 663.07 1.039
"Adjusted for the value of hide and offal.
bCarcass weight basis.


12,516,000

25,032,000




37,548,000

50,064,000

57,385,860

68,838,000

81,354,000




93,870,000







1.100


1.090-


a3 1.080--


a)
x 1.070--
0

0


0
0 1.050-
0



a)





1
< 1.030-



1.020 260 460 660 860 97 1100 1300 1500

Supply in Thousands
Figure 5. Average Cost Curve for the Florida Feeding and Slaughtering Industry.







Sensitivity Analysis


In any analysis using a mathematical programming model, it
is useful to test the sensitivity of the model to alternative
specifications of exogenous variables. Two critical components
which determine the cost of producing high quality carcass beef
are the initial cost of the calf and the cost of feed fed in the
feedlot.
Due to the structure of the mixed-integer programming
model, coefficients which represent calf price or feed costs are
not isolated. These costs are added to transport, slaughter,
and other costs to give the cost of the entire path through the
system. Conducting sensitivity analysis on one of the cost
components requires recomputation of all path costs. These
considerations restricted sensitivity analysis to initial animal
cost and the price of corn. Regional costs of feeding and
slaughtering are also examined.

Regional Cost Differences
Three specifications of the model were formulated. Each
specification included paths in which feeding and slaughtering
could be done in one region: north, central, or south Florida.
Since the optimal solution to the base model located all feed-
lots and slaughterplants in north Florida, then the optimal
solution to the model which included only feeding and slaugh-
tering in north Florida is identical to the optimal solution of
the base model. The optimal solution for each of the three
restricted location models is summarized in Table 21.
Forcing all feedlots and slaughterplants to locate in a
single region has a minimal impact on total system cost. The
average cost for the base model is $1.045/lb. If all feeding
and slaughtering takes place in central Florida, average costs
increase to $1.052/lb. Average costs for a south Florida feed-
ing and slaughtering industry are $1.053/lb. The base model
chooses to build six feedlots and one large slaughterplant in
north Florida; six feedlots and one large slaughterplant is the
optimal configuration in central Florida; seven feedlots and one
large slaughterplant is the optimal configuration in south
Florida.
As shown in Table 21, when all feedlots are located in
central Florida, no backgrounding occurs in central Florida.
The restricted model chooses to background 82.7 percent of the
calves in north Florida and the remaining 17.3 percent in
southwest Florida for finishing and slaughtering. If all
feedlots are located in south Florida, 54.9 percent, 25.2
percent, and 19.9 percent of the calves are backgrounded in
north, southwest, and southeast Florida, respectively. Thus,
the assumptions regarding forage production and costs in the
four potential backgrounding regions place central Florida at a
disadvantage relative to the other regions.
The distribution of calves across paths of varying lengths
is somewhat affected by feedlot location. When all feedlots are
located in north Florida, a high proportion of calves are fed on
five-quarter weight gain programs, and no six-quarter programs
are utilized. When all feedlots are located in central Florida,













Table 21. Summary of Optimal Solutions for Restricted Location Model.

Distribution of Animals by Path Length and Backgrounding Location (Percentages)
Number of Four-quarter Five-quarter Six-quarter Average
Location Feedlotsa ND SWc SEd N SW SE N SW SE Total Coste Costf

North 6 6.7 5.9 87.4 $611,572,911 $1.045

Central 6 6.2 69.3 17.3 7.2 $615,544,837 $1.052

South 7 13.2 10.2 13.6 24.2 8.0 6.3 17.5 7.0 $615,853,673 $1.053

aEach solution included one large slaughterplant.
bNorth Florida.
cSouthwest Florida.
dSoutheast Florida.
eAdjusted for the value of hide and offal.

Per pound carcass weight basis.







five-quarter weight gain programs predominate and a small number
of cattle pass through six-quarter paths. When all feedlots are
located in south Florida, 37 percent of the cattle are fed on
four-quarter paths, 38.5 percent on five-quarter paths, and 24.5
percent on six-quarter paths. The higher number of animals on
four-quarter paths necessitates the construction of an
additional feedlot relative to north and central Florida.

Changes in Initial Animal Cost
In the base model, all weaned calves were priced at $60.00
per hundredweight. To test the sensitivity of the optimal
solution of the base model, the price of weaned calves was
varied from $55.00/cwt to $80.00/cwt in $5.00/cwt increments.
Variation in weaned calf prices had virtually no effect on
the optimal solution of the model, other than changing total
system cost. When weaned calves cost $55.00/cwt, all back-
grounding takes place in north Florida. All solutions required
six feedlots and one large slaughterplant to be built in north
Florida. The solutions for calf prices of $60.00, $65.00,
$70.00, $75.00, and $80.00 are identical. The relationship
between weaned calf prices and average cost per pound (carcass
weight) is shown in Figure 6.

Seasonal Calf Prices
Florida feeder calf prices currently exhibit a seasonal
pattern, with lower prices in the fall and higher prices in the
spring. Seasonal swings in feeder calf prices in Florida are
typically more pronounced than for the United States as a
whole. One plausible explanation for this wider seasonal price
swing is that, since most Florida feeder cattle are exported,
Florida prices are more depressed in the fall when there is a
surplus of feeder calves nationally. On the other hand, spring
prices are high because Florida is one of the few states which
has lightweight feeder cattle to market in the spring. It is
reasonable to hypothesize that the evolution of a large-scale
Florida feeding industry would tend to reduce seasonal
fluctuations in feeder calf prices, since it would possess a
year-round demand for feeder cattle. In formulating the base
model, a rather strong assumption that calf prices would have no
seasonal component was invoked. To test the impact of this
assumption, weaned calf prices were adjusted to account for
seasonal fluctuations. The fall quarter (quarter 3) was taken
as the base quarter and weaned calf were set to $60.00/cwt.
Using seasonal indices from Simpson and Alderman, weaned calf
prices for the other quarters were adjusted to $62.00/cwt in
quarter 1, $64.50/cwt in quarter 2, and $57.00/cwt in quarter 4.
The optimal solutions for the base model and seasonal calf
price model are summarized in Table 22. Introduction of sea-
sonal calf prices has virtually no impact on total system cost.
Seasonal calf prices do greatly alter the optimal location and
timing of backgrounding and slaughtering. Under seasonal calf
pricing, nine feedlots and one large slaughterplant are built in
south Florida. Timing of animals through the system is altered,
as 31.3 percent, 49.9 percent, and 18.8 percent, of the animals
pass through four-, five-, and six-quarter paths, respectively,





1.35-



1.30-



1.25-

c

) 1.20-



0
0 1.15-



0
S1.10-







.95






.95 60 65 70 75 80

Calf Price $/CWT
Figure 6. Estimated Relationship Between Weaned Calf Prices and Average Cost of Beef.
















Table 22. Summary of Optimal Solutions for Base and Seasonal Calf Price Models.

Number and Distribution of Animals by Path Length and Backgrounding Location (Percentages)
Price Location of Four-quarter Five-quarter Six-quarter Average
Structure Feedlots Nb SWc N SW SEd N SE Total Coste Costf

Constant 6-North 6.7 5.9 87.4 $611,572,911 $1.045

Seasonal 9-South 6.8 24.5 16.6 33.3 18.8 $611,958,248 $1.046

aEach solution included one large slaughterplant.
bNorth Florida.
cSouthwest Florida.
dSoutheast Florida.
eAdjusted for the value of hide and offal.
Per pound carcass weight basis.







compared to 12.6 percent and 87.4 percent through four- and
five-quarter paths, respectively, under constant calf prices.
There is no clear-cut explanation for the impact of sea-
sonal calf prices on the optimal solution. More calves are
available in quarter 2 in the two south Florida supply regions
when seasonal prices are high. The model chooses to background
these cattle for two quarters on south Florida digitgrass
pastures and place them in the feedlot in the first quarter when
pastures are dormant.

Variation in Corn Price
In the base model, corn fed in the feedlot was priced at
$7.00/cwt ($3.92/bu) in north Florida, $7.18/cwt in central
Florida, and $7.36/cwt in south Florida. The price differences
across regions approximate additional transport costs for corn
shipped from the eastern Corn Belt. Corn fed as a supplemental
feed in the background phase was priced at $7.30/cwt, $7.48/cwt,
and $7.66/cwt for north, central, and south Florida, respec-
tively. Supplemental corn for backgrounding was priced higher
than feedlot corn to reflect quantity discounts. Sensitivity
analysis was conducted only on the cost of corn fed in the
feedlot.
The price of corn was varied from $5.00/cwt ($2.80/bu) to
$11.00/cwt ($6.16/bu) in $1.00/cwt increments. Calf prices were
$60.00/cwt over all quarters. The optimal solutions to these
runs are summarized in Table 23.
When corn prices are $6.00/cwt or less, nine feedlots and
one large slaughterplant are built in south Florida. Further-
more, four-quarter paths predominate. Over 84 percent of the
cattle follow four-quarter paths when corn costs $5.00/cwt, and
83.1 percent of the cattle are finished in four quarters, with
corn costing $6.00/cwt. When corn prices are increased to
$7.00/cwt, the percentage of four-quarter paths drops to 12.6
percent and all feedlots are located in north Florida. With
corn prices at $8.00/cwt and higher, only five feedlots in north
Florida are required, and most cattle follow five-quarter paths.
These results suggest that in a low-priced grain environ-
ment, the least cost system makes less use of forages. When
forage production is less important, south Florida has an ad-
vantage over north Florida. Lower transport costs for chilled
beef from a south Florida slaughterplant to the major popula-
tions in central and south Florida apparently offset higher
transport costs for corn. In a high-priced grain environment,
the least cost system includes those paths which involve less
feedlot feeding and more weight gain from grazing. When forage
production is a more important component, north Florida is the
least-cost region.
The emergence of south Florida as the preferred location
for feedlots and slaughterplants when corn prices are low is
similar to results under seasonal prices for weaned calves. To
further examine a system with seasonal feeder calf prices, corn
prices were varied for that model. The optimal solutions for a
seasonal calf price model are summarized in Table 24.
Under seasonal calf prices, all feedlots are located in
south Florida for corn prices less than or equal to $8.00/cwt.










Table 23. Summary of Optimal Solutions for Varying Corn Price Models.

Number and Distribution of Animals by Path Length and Backgrounding Location (Percentages)
Corn Location of Four-quarter Five-quarter Six-quarter Average
Pricea Feedlotsb Nc SWd SEe N SW SE N SW SE Total Costf Costg

5.00 9-South 42.0 28.8 13.6 8.7 .3 6.3 .3 $562,056,764 $ .961

6.00 9-South 41.3 28.8 13.0 8.0 1.0 6.3 .9 .7 $591,230,189 $1.011

7.00 6-North 6.7 5.9 87.4 $611,572,911 $1.045

8.00 5-North .3 94.3 5.4 $630,298,511 $1.077

9.00 5-North .3 94.3 5.4 $648,432,294 $1.108

10.00 5-North 87.8 12.2 $666,537,117 $1.139

11.00 5-North 87.8 12.2 $684,040,027 $1.169

aDollars per hundredweight.
bEach solution included one large slaughterplant.
CNorth Florida.
dSouthwest Florida.
eSoutheast Florida.

Adjusted for the value of hide and offal.
gPer pound carcass weight basis.









Table 24. Summary of Optimal Solutions for Seasonal Calf Prices and Varying Corn Prices.

Number and Distribution of Animals by Path Length and Backgrounding Location (Percentages)
Corn Location of Four-quarter Five-quarter Six-quarter Average
Pricea Feedlotsb NC SWd SEe N SW SE N SW SE Total Costf Costg

5.00 9-South 24.0 60.0 13.5 1.0 1.5 $557,920,144 $0.954

6.00 9-South 24.1 59.0 .9 1.4 1.6 $587,017,355 $1.003

7.00 9-South 6.8 24.5 16.6 33.3 18.8 $611,958,248 $1.046

8.00 9-South 6.8 24.5 25.3 24.6 18.8 $635,827,127 $1.087

9.00 5-North .3 2.3 72.9 16.8 7.7 $655,932,041 $1.121

10.00 5-North 2.3 68.9 14.3 14.5 $674,555,318 $1.153

11.00 5-North 86.9 6.4 6.7 $692,986,989 $1.185

aDollars per hundredweight.
bEach solution included one large slaughterplant.
CNorth Florida.
dSouthwest Florida.
eSoutheast Florida.

fAdjusted for the value of hide and offal.
gPer pound carcass weight basis.







With corn prices at $9.00/cwt ($5.04/bu.) and above, all
feedlots are located in north Florida. Under seasonal weaned
calf prices, south Florida retains a regional advantage over a
wider range of corn prices.
The relationship between corn prices and average cost per
pound (carcass weight) for both the constant calf price model
and seasonal calf price is shown in Figure 7.

Summary and Conclusions

With just over 1 million head of fed cattle consumed in
Florida in 1980 (Spreen, 1983) and transportation costs which
discriminate against regions most distant from major market
areas (Jordan, 1976), this study considers locally fattening
Florida-weaned calves to slaughterweight and slaughtering and
processing the finished beef within the state. The purpose of
this study is to estimate the total cost of feeding and slaugh-
tering an estimated Florida feeder cattle supply of 917,000
animals. A spatiotemporal optimization model is constructed to
determine the cost of (1) assembling, (2) backgrounding, (3)
finishing, (4) slaughtering, and (5) delivering boxed beef to
final destination points. The model built has special features;
the temporal dimension takes the seasonal supply of weaned
calves and makes a constant supply of boxed beef available to
consumers year-round. The spatial dimension allows animals and
subsequent boxed beef to be transported between different
regions of the state.
Costs have been estimated using simulation models for (1)
backgrounding Florida-weaned calves, (2) fattening calves in
Florida feedlots, and (3) locally slaughtering 1,050-pound cat-
tle. Transportation costs for delivering weaned calves, back-
grounded calves, slaughterweight calves, and boxed beef to
different regions of the state have also been included. The
results of the spatiotemporal model include the average cost per
head and the average cost per pound of boxed beef for eight
different levels of weaned calf supply.
In developing the model, production efficiency has been
considered. Feedlots can process up to 50,000 head at any given
time, and economies of scale are considered in slaughterplant
facilities (two different size options). The model considers
only costs incurred within the industry; there are no allowances
for returns to management or capital.

Conclusions
Results from the spatiotemporal model indicate the
following:

(1) Seasonal calf supplies can be smoothed out to provide a
continual supply of boxed beef.
(2) Considering feedlot and slaughterplant location
possibilities, north Florida has a slight advantage over
other regions of the state.
(3) The average cost of providing boxed beef to Florida
consumers is a downward sloping curve, becoming nearly flat
at production levels of 1.1 million animals annually.












































x Seasonal Calf Price
o Calf Price $60.00


2.80 3.36 3.2 4.48 5.b4
Corn Price $/Bushel


5.60 6.16


Figure 7. Estimated Relationship Between Corn Price and Average Cost of Beef for
Fixed and Seasonal Calf Price Models.


1.20,


1.17-


1.14-


1.11-



1.08-



1.05-



1.02-



.99--


.96







The results indicate that the Florida feeding and slaugh-
tering industry can be competitive with the Midwest industry.
Carcass price for the Midwest (Omaha) was $1.022 in 1982 (United
States Department of Agriculture, 1983). In order to provide
this beef to Florida consumers, additional transportation
charges are incurred for transportation from the Midwest back
into Florida. Adding approximately 5.5 cents per pound (White's
Packing Plant) for transportation back to Florida gives
$1.077. Thus, at current operating levels of less than 200,000
head annually, the cost of producing high quality carcass beef
in Florida is close to the national average plus transport
costs.

Outlook for the Future
Jordan (1976) concluded that calves could have been fed to
full slaughter weights within Florida and positive net returns
in all quarters could have been received. Now, nine years
later, this study concludes that the Florida feeding and
slaughtering industry can be competitive with the Midwest
industry. The question arises as to why there has been no
expansion in the Florida cattle industry, given these results.
One possible explanation is that the fixed investment to
construct the facilities required in the model's optimal
solution, with 917,000 head, is approximately $307 million.
Furthermore, the variable costs of the optimal solution are over
$651 million. Considering the capital required to finance the
system, other investment opportunities may produce greater
returns. In addition, this study has assumed an idealized
system where all stages of production fully cooperate in order
for the overall costs to be minimized. The Florida beef cattle
industry constitutes a large number of calf producers and
independent feedlot and slaughterplant owners. For these
reasons, the Florida cattle industry has not evolved into an
industry competitive with the Midwest.

Limitations
The model has also considered processing 1.3 and 1.5 mil-
lion animals. These two levels of processing are hypothetical
considerations used to indicate that full utilization of one
large slaughterplant is the most efficient production level.
Two important assumptions have been made for these two produc-
tion levels. First, it has been assumed that animals in excess
of 917,000 head come from south Georgia, Alabama, and Missis-
sippi and are available in north Florida, but no transportation
costs of relocating animals from these states has been included
in the model. Second, it has been assumed that all boxed beef
produced from these animals can be sold in Florida. It is
unlikely that over 1.1 million animals can actually be consumed
locally. However, these two production levels have been useful
in determining the most efficient level of production.
Although the spatiotemporal model minimizes total cost, the
simulation models were not executed for minimum costs. Thus,
the spatiotemporal model does not indicate the minimum costs
associated with each stage of production. For example, rye-
ryegrass and pensacola bahia are the two forages used in the







backgrounding program, but these are not necessarily the least
costly forages that can be used by forage producers. At the
same time, feedlot diets consisted of corn and sorghum silage,
which are not necessarily the least costly components of a
feedlot diet. Wheat, citrus pulp, and other locally produced
seasonal feeds could be utilized by Florida feedlot operators.

Implications for Future Research
Due to the size and scope of the spatiotemporal model, many
assumptions are required which additional research could
refine. Consumption levels are simply estimated without con-
sidering demographic differences in the population. Further
research by demographic specialists could determine consumption
requirements for beef products considering demographic differ-
ences between Cuban-Americans, retirees, tourists, and other
groups of Florida residents.
Pasture forage costs are apportioned on a monthly basis.
By apportioning costs in this manner, it is assumed that a
pasture grazed for only 3 months, for example, would have
animals available to graze for the remainder of the forage
growth period. Further research could determine the degree to
which this assumption is valid and to what degree forage costs
were underestimated.
The fall forage program (August, September, and October)
typically produces at reduced levels, thereby requiring corn
supplements during this period. The backgrounding simulation
model was executed many times before adequate corn supplements
were determined.
The lack of accurate transportation cost data hindered a
more complete analysis of projected changes in total system cost
due to regional price differentials for transporting live
animals and boxed beef.
The spatiotemporal model can now be used to investigate a
wide range of issues facing the Florida cattle industry: (1)
simulating different pasture forages, (2) varying the price of
weaned calves, (3) allowing for a minimum of 60 days in the
feedlot, (4) allowing for different U.S. Department of
Agriculture yield grades of beef, (5) simulating different
feedlot feed rations, (6) allowing for economies of scale in
grain handling, and (7) allowing for different sizes of
feedlots.







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