A mixed integer program solves for profit-maximizing forage and beef enterprises. Dry matter, total digestible nutrients, and crude protein characterize livestock nutritional needs and production of warm and cool season forages.Livestock Production/Industries,

Doye, Damona G.

Epplin, Francis M.

Kletke, Darrel D.

Lalman, David L.

Smith, Karen

English

Research Papers in Economics

An Alternative Method for Analyzing Forage/Livestock Systems
Damona Doye, Karen Smith, Francis Epplin, Darrel Kletke, and David Lalman
1
Abstract
A mixed integer program solves for profit-maximizing forage and beef enterprises.  Dry
matter, total digestible nutrients, and crude protein characterize livestock nutritional
needs and production of warm and cool season forages.
Paper presented at the Western Agricultural Economics Association Annual Meetings,
Vancouver, British Columbia, June 29-July 1, 2000.
Copyright 2000 by Damona Doye, Karen Smith, Francis Epplin, Darrel Kletke, and
David Lalman.  All rights reserved.  Readers may make verbatim copies of this document
for non-commercial purposes by any means, provided that this copyright notice appears
on all such copies.
                                               
1 Author’s affiliations and e-mail addresses are respectively Oklahoma State University,
ddoye@okstate.edu; University of Tennessee, kesmith@ext1.ag.utk.edu; Oklahoma State
University, epplin@okstate.edu; Oklahoma State University, dkletke@okstate.edu; and
Oklahoma State University, dlalman@okstate.edu.  Support for this project was provided
by The Noble Foundation, Inc. and a Southern Region Sustainable Agriculture Research
and Education (SARE) grant.  Oklahoma State University Department of Agricultural
Economics AEP-0003.1
The “Freedom to Farm” bill has enabled Oklahoma producers to consider use of
traditional cropland for the production of alternative crops, including forage.  In many
areas, environmental conditions limit crop alternatives.  Forage rather than grain might be
more profitable.  Cool season grasses such as fescue are increasingly being promoted as a
component of a forage system to lower costs of beef production.  Cool season forages are
capable of providing nutrients at a lower cost than purchased supplements at times when
warm season forages such as tall grass prairie, bluestem, and bermuda are not growing or
are poor quality. The objective of this paper is to identify profit-maximizing enterprise
combinations for alternative scenarios for a given resource base using a new framework
for matching beef cows and stockers’ nutritional needs to forage production using crude
protein (CP), dry matter (DM) and total digestible nutrients (TDN).
Data and Methods
Animal unit months (AUMs) have traditionally been used to define the carrying
capacity of pasture.  But, the quantity produced and quality of different forages vary
significantly over a year.  Forage data were collected from various experiment station
reports authored by agronomists and animal scientists, from personal contacts with
faculty in both departments, from Natural Resource Conservation Service (NRCS) files
and contacts, and from Noble Foundation reports and scientists.  Monthly averages of
forage total digestible nutrients (TDN) and crude protein (CP) were estimated along with
monthly dry matter (DM) production for wheat for forage, dual purpose wheat, bluestem,
bermuda, fescue, and native pasture.
Livestock nutritional needs depend on the type, size and gender of the animal.2
For breeding livestock, timing of peak needs depends on the breeding season for cows.
National Research Council (NRC) equations were used to estimate beef cattle nutrient
requirements, specifically TDN, CP, and DM, and bounds on livestock intake.
A mixed integer program was developed to determine the profit-maximizing use
of the land resource (Smith).  Initial acreage (cropland, improved pasture, native range) is
specified by the user, but additional blocks of land may be rented.  Rental rates are
specified by type of land. Product price, operating costs (excluding cost of livestock
nutrients) and operating capital are entered for each enterprise, as are labor requirements
by month.  Maximums on owner-supplied capital and borrowed capital are needed along
with an interest rate.  Available owner/operator hours are specified by month; a
maximum number of hired labor hours per month can be entered.
A minimum number of acres of a specific forage type may be specified.  Annual
forage production levels are specified and used with monthly distributions developed
from data collected.  Harvest efficiencies as well as the percentage of dry matter retained
in month-to-month transfers of unused forage may be specified by the user. Unused
native pasture and bermuda can be baled and sold.  Solutions allow cropland to be
transferred to pasture.
Fall and spring calving cows and up to six stocker enterprises are included.  For
the cow/calf enterprise, average cow weight, body condition score, milk production, calf
birth weight, month calves are born and sold, percent calf crop, percent kept for
replacements, and weaning weights for steers and heifers must be specified.  For each of
six potential stocker activities, the user may specify the purchase date and weight, sale3
date, expected average daily gain, death loss, and shrink percentage. Livestock nutritional
requirements may be met either through forage utilization or purchased supplements.
Base Case
For analysis purposes, a case study representing a typical ranch in northwest
Oklahoma was developed.  The ranch consists of 150 acres of cropland, 200 acres of
improved pasture, and 650 acres of native range.  In the base scenario, rental tracts were
150-acre blocks of cropland, improved pasture, and native range with rental rates of $30
per acre, $11 per acre, and $7 per acre respectively.  Harvest efficiency for forage was
assumed to be 45 percent for wheat, 35 percent for bermuda and fescue, 25 percent for
bluestem, and 20 percent for native pasture.  Month-to-month transfers were set at 75
percent, except for winter months for bermuda, bluestem, and native pasture where they
were 60 or 65 percent, and in August when fescue was at 65 percent.
Cows were 1000 pounds with average body condition scores of 5, milking 11
pounds per day.  Calf birth weight was 80 pounds.  An 85 percent calf crop and 15
percent replacement heifer percentage was assumed.  Spring calving cows weaned calves
in November; fall calving cows weaned calves in July.  All stocker enterprises had 2
percent death losses and 2 percent shrink.
All capital was borrowed at 10.5 percent interest; the maximum borrowing was
set at $150,000.  The owner/operator provided up to 200 hours of labor per month; labor
was hired at $6.50 per hour up to 200 hours per month.  Twenty percent range cubes
could be purchased for 8 cents per pound; 38 percent range cubes could be purchased for
11 cents per pound.  Other enterprise assumptions are listed in Table 1.4
Results
For the base case, the profit-maximizing solution used 1,300 acres: 183 acres of
cropland for wheat for grain plus forage and 117 acres of wheat for forage only (150
acres of owned and 150 acres of rented cropland), 350 acres of fescue on the improved
pasture land (200 acres owned, 150 acres rented), and 650 acres of owned native pasture
(Table 2).  The livestock enterprises were 139 fall-calving cows plus 252 November-May
stockers and 274 March to July stockers.  To meet livestock nutritional needs, 40 tons of
20% cubes were purchased.  The owner/operator supplied 1,717 hours of labor and hired
an additional 102 hours of help.  Borrowed capital reached its limit of $150,000.  Net
returns to land and management before tax was $34,247.  The stocking rate seemed high,
but otherwise the solution seemed reasonable in selection of enterprises and returns to the
operation.
To test the sensitivity of the results to assumptions and robustness of the model, a
variety of scenarios were developed.  Minimum acreages of other improved forages
(bermuda and bluestem) were specified to model an owner’s preference for an existing
forage type.  Both wheat and fescue forage production were halved to test the limits at
which other forages might be competitive.  Harvest efficiencies were lowered
dramatically across the board since the linear program assumes costless, perfectly
efficient movement of livestock to consume forage produced.  The minimum dry matter
requirement for livestock was raised to determine whether use of the relatively low
percent contributed to the seemingly high stocking rate.  The capital constraint was eased
to determine its impact on enterprises and net returns.  The size of rental tracts was5
increased.  Hay costs were halved, stocker and wheat prices were modified, and the
spring-calving cow enterprise costs were dramatically lowered.  Results are summarized
in Table 2.
Compared to the base case, constraining the owned improved pasture land to
either bluestem or bermuda lowered the net returns.  In both cases, additional cropland
and improved pasture (fescue) were rented.  More wheat was used for forage and stocker
numbers increased slightly.  With bluestem, cow numbers decreased slightly and
additional cubes were purchased; owner labor hours increased and hired labor hours
decreased slightly.  The bermuda solution was remarkably similarly to the base solution
in enterprises selected with some additional owner labor hours, but significantly lower
returns.
Halving the wheat forage produced by both the dual purpose wheat and wheat for
forage only results in most cropland (207 acres) being harvested for grain with the
remainder converted to improved pasture, specifically fescue.  The cow herd size is
reduced by approximately 1/3 of the base case.  Overall, stocker numbers increase--the
numbers of November-May stockers is roughly halved and March to July stockers
increase by 80 percent.  Fewer cubes are purchased, but more than 1/2 of the cubes
purchased are 38% cubes.  Net returns declined by 20 percent compared to the base.
If fescue forage production per acre is halved, some owned pasture land actually
goes unused.  Additional cropland is rented for wheat forage and all owned cropland is
devoted to wheat for forage.  Compared to the base case, the fall-calving cow herd is
approximately half the size, November to May stocker numbers are similar, and March to6
July stockers increase significantly.  Owner labor hours decrease.  Net returns are  26
percent lower than the base case.
If forage harvest efficiencies are reduced dramatically to 25% for wheat, 20% for
bermuda and fescue, 15% for bluestem, 12.5% for native, net returns fall dramatically as
well.  More than 2/3 of the wheat is harvested for grain and the cow/calf enterprise
shrinks to 41 cows, compared to 139 in the base case.  Stocker numbers decrease, but
only 13 percent, because of their profitability relative to the cow/calf enterprise.  The
borrowing maximum is not reached.
Increasing the minimum dry matter requirement for both cows and stockers to 2
percent of bodyweight leads to wheat being harvested for grain.  Three tons of native hay
is produced, cow numbers fall to a level similar to the reduced forage harvest efficiencies,
and stocker numbers increase greatly, with a shift to primarily March to July stockers.
Cube purchases decrease and hired labor increases relative to the base case.  Net returns
are 61 percent of the base case returns.
Easing the limit on borrowed capital primarily boosts the stocker enterprise and,
consequently, wheat for forage production relative to dual-purpose wheat.  November-
May stockers increase by 50 percent and March-July stockers increase by 45 percent.
Cube purchases increase by more than 50 percent as does hired labor.
Allowing rental of 300 acre tracts rather than 150 acre tracts shifts wheat to
entirely dual use as 350 acres of fescue are available for use in livestock production.
Cow numbers increase by 20 percent, November-May stockers increase by 27 percent,
March-July stockers decrease to 79 head from 274 head.  Net returns to management and7
land increase to $38,286, approximately 12 percent.
Halving the hay costs relative to the initial assumptions leads to rental of all
available acreage, including native pasture from which 216 tons of native hay is produced
for sale.  Cow numbers decrease and stocker production shifts more to November-May
stockers and away from March-July stockers.
Lowering the sale price of purchased stockers by $5 per hundredweight and
increasing the sale price of raised stockers by $5 per hundredweight shifts livestock
production to primarily a cow/calf operation.  Native pasture is rented and all wheat is
dual-purpose.  No November-May stockers are used and only 53 March-July stockers are
included.
A lower wheat price of $2 per bushel results in slightly fewer overall livestock
numbers with relatively more November-May stockers.  A higher wheat price of $3 per
bushel leads to all wheat acreage being used for grain as well as forage.  Here, March-
July stocker numbers increase at the expense of cows and November-May stockers.
Assuming that the average daily gain is 2 pounds per day for all stocker
enterprises causes a very small increase in cow numbers and a reduction by half of
stocker numbers.  Dramatically lowering costs of production and operating capital costs
of spring-calving cows results in rental of native pasture, with both fall and spring-
calving cows in the solution (relatively more spring-calving cows).
Summary and Conclusions
The enterprises in the solution did not vary with changes in assumptions about
types of improved forage used, forage harvest efficiency, capital constraints, size of8
rental tracts, or changes in wheat price.  The maximum on available capital was
constraining in all scenarios except the low harvest efficiency scenario and most affected
the size of the stocker enterprise.  Easing the capital constraint and increasing the size of
rental tracts increased net returns relative to the base case.  Owner labor hours were not
constraining in any of the scenarios studied.
Fescue, because of its bimodal growth pattern plus volume and quality of
production, dominated improved pasture forage solutions despite its higher cost.  In all
scenarios, owned and rented pasture was fescue unless production is halved or acreage of
other forage was forced into the solution.  Some wheat was harvested as forage, except
when expected annual wheat forage production was halved or the dry matter minimum on
livestock consumption was raised.  Wheat was harvested for grain only when wheat
forage production was halved, harvest efficiency was dramatically lowered, or the dry
matter intake requirement raised.  Native pasture was used, but  additional acres were
rented only in the scenarios where hay costs were halved or spring-calving cow costs
were greatly reduced.  Bermudagrass and bluestem only came into the profit-maximizing
solution when forced.
Discussion
The model unrealistically assumes intermingling of livestock and costless
movement among forages.  Additional forages are expected to be added as is internal hay
use and modeling of forage use by calves not yet weaned off cows.  Deficiencies in
forage data forced reliance on expert opinion in many cases.  Differences in methods for
collecting data (both quantity and quality) by animal scientists and agronomists became9
apparent as the forage data base was being developed and discussed by the
interdisciplinary project team.
Several ideas for additional research have been generated.  Better documentation
of monthly production of forage and changes in forage quality over time under different
conditions (weather, precipitation, grazing management system) and for different soil
types is needed.  Likewise, more accurate measures of the ability of livestock to utilize
available forages are needed.   However, comparing the solutions using different
assumptions and resource bases has been insightful thus far.10
Table 1.  Enterprise Assumptions
Enterprise Operating
costs
($/unit)
Operating
capital
($/unit)
Production
per
Unit
Price
Wheat for
grain
50 25 35 bu. $2.50/bu.
Dual-purpose
wheat
 68 34 30 bu.,
1000 lbs. forage
$2.50/bu.
Wheat for
forage
60 30 6300 lbs. forage
Bermudagrass 37 18.5 8,000 lbs. forage
Fescue 52 26 7000 lbs. forage
Bluestem 33 16.5 6,500 lbs. forage
Native pasture 4 2 5,000 lbs. forage
Bermuda hay 55 27.5 $60/ton
Native hay 25 12.5 $50/ton
Spring calving
cows
77 139 525 lb. steers,
475 lb. heifers
weaned
$90/cwt.
$80/cwt.
Fall calving
cows
79.5 159 630 lb. steers,
580 lb. heifers
weaned
$85/cwt
$78/cwt
Stocker 1
400 lbs.
Oct.-Mar.
63  175.05 2 lb. average daily
gain
Buy Oct. @ $100/cwt
Sell Mar. @$85/cwt
Stocker 2
400 lbs.
Nov.-May
69 245.42 2.2 lb. ADG Buy Nov. @ $100/cwt
Sell May @$80/cwt
Stocker 3
400 lbs.
Mar.-July
69 166.12 2.2 lb. ADG Buy Mar. @ $100/cwt
Sell July @$85/cwt
Stocker 4
400 lbs.
May-Aug.
63 136.78 2 lb. ADG Buy May @ $100/cwt
Sell Aug. @$80/cwt
Stocker 5
500 lbs.
May-Aug.
63 148.98 2 lb. ADG Buy May @ $100/cwt
Sell Aug. @$75/cwt11
Table 2.  Profit Maximizing Solutions under Alternative Scenarios
Base
Case
200 a. of
bluestem
200 a. of
bermudagrass
Wheat forage
halved
Fescue forage
halved
Harvest
efficiency
halved
DM minimum
increased
Borrowing
max increased
Acres Used 1,300 1,300 1,300 1,300 1,027 1,300 1,300 1,300
Owned 1,000 1,000 1,000 1,000 877 1,000 1,000 1,000
Rented 300 300 300 300 150 300 300 300
Wheat - Grain 207 235 300
Wheat - Dual 183 55 52 65 59
Wheat - Forage 117 245 248 300 241
Bermudagrass 200 77
Fescue 350 150 150 443 350 350 350
Bluestem 200
Native pasture 650 650 650 650 650 650 650 650
Cropland to pasture 93
Production
Hay (tons) 3
Wheat (bu.) 5,496 1,639 1,549 7,234 10,175 10,500 1,771
Spring Calving Cows
Fall Calving Cows 139 129 139 103 74 41 42 123
Stocker 2 (Nov.-May) 252 257 263 135 243 97 92 383
Stocker 3 (Mar.-July) 274 291 271 493 400 359 616 397
Purchases
20% cubes (tons) 40 48 40 11 48 26 13 68
38% cubes (tons) 2 1 13 4
Hired labor hours 102 87 86 140 103 13 168 332
Capital borrowed 150,000 150,000 150,000 150,000 150,000 108,316 150,000 200,000
Owner labor hours 1,717 1,733 1,762 1,638 1,584 1,363 1,610 1,831
Net Returns ($) 34,247 26,085 28,523 27,042 25,230 9,489 20,911 38,28612
Table 2 (continued).  Profit Maximizing Solutions under Alternative Scenarios
300 acre
rental blocks
Hay costs
halved
Lower stocker sale
price, higher raised calf
sale price
Wheat =
$2/bu.
Wheat =
$3/bu
ADG on all
stockers
= 2 lb.
Spring cow
w/much
lower cost
Acres Used 1,600 1,450 1,450 1,300 1,300 1,300 1,450
Owned 1,000 1,000 1,000 1,000 1,000 1,000 1,000
Rented 600 450 450 300 300 300 450
Wheat - Grain
Wheat - Dual 450 190 300 175 300 300 165
Wheat - Forage 110 125 135
Bermudagrass
Fescue 500 350 350 350 350 350 350
Bluestem
Native pasture 650 800 800 650 650 650 800
Cropland to pasture
Production
Hay (tons) 216
Wheat (bu.) 13,500 5,700 9,000 5,263 9,000 9,000 4,948
Spring calving cows 97
Fall calving cows 168 101 189 134 117 143 41
Stkr 2 (Nov.-May) 327 309 0 292 242 202 305
Stkr 3 (Mar.-July) 79 203 53 220 307 60 229
Purchases
20% cubes (tons) 44 56 7 52 56 36 54
38% cubes (tons) 1 3
Hired labor (hrs.) 121 75 86 99 121
Capital borrowed 150,000 150,000 63,837 150,000 150,000 102,950 150,000
Owner labor hours 1,833 1,621 1,249 1,695 1,683 1,415 1,718
Net Returns ($) 38,286 35,763 24,842 31,576 38,001 23,687 34,76213
References
National Research Council.  “Nutrient Requirements of Beef Cattle.”  Seventh Revised
Edition.  National Academy Press.  Washington, D.C.  1996.
Smith, Karen Elizabeth.  “Optimizing Forage Programs for Oklahoma Beef Production.”
MS. Thesis, Oklahoma State University.  December, 1999.15
An Alternative Method for Analyzing Forage/Livestock Systems
Abstract
A mixed integer program was developed to solve for profit-maximizing enterprise
combinations of forage and livestock.  Dry matter, total digestible nutrients, and crude
protein are used to depict livestock nutritional needs for beef enterprises and to
characterize forage production for several warm and cool season forages.

AN ALTERNATIVE METHOD FOR ANALYZING FORAGE/LIVESTOCK SYSTEMS

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