The goal of this paper is to determine the importance of
considering heterogeneity of animal growth in making herd replacement
decisions. As a first step, the net returns of basing the optimal
slaughter age on the herd average growth curve are compared with results
obtained when basing the optimal slaughter age on the heterogeneous
growth curves in the herd. For comparability, the entire herd is
marketed on a single day in both the average growth and heterogeneous
growth cases. In addition, revenues in both cases are calculated on the
basis of the true heterogeneous weights of the animals at slaughter. As
a second step, it is demonstrated that marketing animals in truckload
batches over time rather than on a single day, corresponding to common
producer practice in the industry, can further increase profit. The
advantage of this approach is that faster growing animals can be
marketed earlier than slower growing animals, potentially avoiding some
discounts for overweight and underweight animals that occur when
marketing on a single day.
Heterogeneity is particularly important in the swine industry where
packer payment programs frequently include significant price discounts
for over- and under-weight animals, and where the majority of producers
with over 100 animals empty an entire production unit for cleaning
before replacing the animals with a new herd under a system called
All-In/All-Out production (USDA 2005). The present analysis focuses upon
the replacement decision for a hog producer using an All-In/All-Out
(AIAO) grow/finish production system in which animals are fed from age
50 days to slaughter in a barn with a capacity of 1,000 head. As per the
AIAO system, all pigs must be marketed and the barn cleaned and
disinfected before the next group of animals can be brought in. It is
further assumed that animals are marketed through a cash based carcass
merit payment system. Under this system, packers set prices that are
transparent and known prior to delivery. As is common in practice, this
study assumes that the packer applies price discounts to animals whose
weight and/or percent leanness is outside a desired range with larger
discounts for weights/lean percentage further from the desired range. An
important aspect of these discounts is that they are (discontinuous)
step functions of live weight and leanness.
Traditional analysis of the livestock replacement problem has
focused on a representative animal or the mean of a group of animals as
the unit of analysis. For example, Chavas, Kliebenstein, and Crenshaw
(1985) apply this type of analysis to the evaluation of nutrition and
marketing decisions. With a few exceptions, within-herd heterogeneity of
animal growth has been ignored in the production literature. Some
exceptions include Greer and Trapp (2000) who examine the impact of
alternative pricing grids on the optimal feeding period for groups of
animals. Lusk et al. (2003) evaluate the use of ultrasound technology to
choose the marketing method for cattle, but they do not consider the
optimal timing of marketing. Brorsen et al. (2002) evaluate the economic
impact of banning the use of antibiotics at sub-therapeutic levels in
swine production, accounting for the decrease in ending weight variation
with antibiotics.
This paper goes beyond previous research in two important ways that
lead to new insights. First, we follow common industry practice wherein
swine are marketed in semi-tractor trailer loads. We evaluate the
strategy of optimally marketing the herd over time, with the potential
to ship some truckload batches of animals to slaughter several days
before the rest of the herd is shipped, and taking into account that the
entire herd must be shipped before a new herd of feeder pigs can be
brought into the facilities.
Models
A simulation model was developed that incorporates an algorithm to
determine the optimal slaughter weights of pigs that are raised in a
large (1,000 head) barn, and are potentially marketed in truckload
groups on different days. The purpose of this analysis is to consider
herd replacement in a fixed capacity facility, and consequently the
objective is to maximize average daily returns to the facility and
operator labor. In order to assess the economic outcomes of the
alternative approaches to analyzing marketing decisions, three variants
of the model are developed. These models are presented below, followed
by a discussion of the model parameters.
Homogeneous Herd
In this model, the producer bases the shipping decision upon a
"mean animal" whose growth curve is equal to the average of
the growth curves of all animals in the herd. It is assumed that all
animals will be shipped on one day, and that the selected day will be
the one for which the discounted average daily profit generated by this
mean animal is maximized (Dillon and Anderson 1990). As profits received
by the producer are based on actual weights rather than on the mean
animal's weight, the heterogeneous herd information is used to
determine actual profits on the selected shipping date.
This model can be written as
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where t + k denotes the number of days the production facility is
in use for the production cycle (animal growth and finishing, t, plus
turnover time, k), [beta] denotes the discount factor used to convert
future revenue to present value, [[bar.W].sub.t] is the herd average hot
carcass weight on day t, [[bar.L].sub.t] denotes the herd average
leanness (%), n denotes total number of individual pigs (n = 1,000),
[[bar.VC].sub.t] denotes the present value of average cumulative
variable production costs per pig on day t, P denotes the base hot
carcass weight price ($/kg), and d([[bar.W].sub.t][[bar.L].sub.t])
denotes the price discount for the herd average hot carcass weight and
leanness ($/kg).
Heterogeneous Herd with a Single Shipping Decision
Similar to the homogeneous herd model, this model optimizes the day
on which all animals are marketed. This analysis differs, however, in
that this model explicitly recognizes the effect of herd heterogeneity
on revenues; here the shipping decision independently considers each
animal's weight and its associated discounted price. This model can
thus be specified as
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where i indexes the animals in the herd, [L.sub.it] denotes the
leanness of pig i on day t, [W.sub.it] denotes the hot carcass weight of
pig i on day t, [VC.sub.it] denotes the present value of cumulative
variable production costs for pig i on day t, and d([W.sub.it],
[L.sub.it]) denotes the price discount for the hot carcass weight of pig
i on day t ($/kg).
Assumptions concerning producer information and prices are the same
as those described in the homogeneous herd model above. The net returns
for the homogeneous herd model are calculated as in (2) despite (1)
being used as the objective function for the optimization. Thus, the
homogeneous herd model is optimizing with respect to the wrong objective
due to the assumption that it is adequate to analyze the mean animal. By
taking the heterogeneity of animal weights into account when evaluating
revenue, the heterogeneous herd with a single shipping decision model
uses a more accurate measure of the price discounts.
Heterogeneous Herd with Multiple Shipping Decisions
The heterogeneous herd with a multiple shipping decision model also
treats the herd as a heterogeneous group. In this model, however, the
artificial restriction that the entire herd of animals must be shipped
on the same day is relaxed. Thus in the heterogeneous herd with a
multiple shipping decision model, truckload batches of animals may be
shipped on multiple shipping dates, with the possibility that more than
one batch will be shipped on any given day. For each herd of 1,000
animals, it is assumed that truckloads are shipped full (170 head), with
the exception of the final, sixth load which contains the remaining 150
head. Changes in animal growth due to reduced crowding following
shipments are not considered in this analysis; as such, the benefits of
multiple shipment dates are likely understated.
While producers are assumed to have perfect knowledge of animal
weights, they are not assumed to have knowledge concerning the leanness
of each animal. (Only a small fraction of producers use ultrasound
imaging to assess carcass leanness at the farm, and even those producers
do not evaluate every market hog.) Because an important reason for early
shipments is to reduce discounts due to animal weight and/or leanness,
lack of carcass quality information limits producer ability to optimally
market their animals. Thus, we model the producer's selection of
animals for shipment within a load by the simple rule that they will opt
to ship the heaviest animals first.
As argued by Burt (1965, 1993) and Dillon and Anderson (1990), the
decision of the length of the complete production cycle should reflect
the opportunity cost of the facility. However, when multiple shipping
dates are optimal, this opportunity cost only plays a role in the choice
of the final shipping date. Shipments on earlier dates should be chosen
so as to maximize the net return to the load. A flow chart which
describes the algorithm for determining the optimal shipping dates for
each load is presented in figure 1.
[FIGURE 1 OMITTED]
The algebraic statement of this model is
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [s.sub.1] denotes the marketing day for load l, and
[B.sub.l]([s.sub.l]) denotes the subset of size 170 (150 for l = 6) of
the remaining animals that are heaviest on day [s.sub.l]. This
formulation does not exclude the possibility of shipping multiple loads
on a single day. Thus, the optimal objective value for this model will
always be at least as great as for the heterogeneous herd with a single
shipping decision model.
Production Characteristics and Assumptions
The following discussion provides details concerning the parameters
and assumptions that were used in developing this model.
Swine Herd
This analysis uses a stochastic model of swine herd compositional
growth that has been estimated as a mixed effects model based on animal
feeding trials (Schinckel et al. 2003a). The portion of the model
focused on live weight growth is briefly described below as a function
of time:
(4) [BW.sub.it]
= (C + [C.sub.i])(1 - exp(-exp (M + [m.sub.i])[t.sup.A])) + b +
[e.sub.it]
where [BW.sub.it] denotes the body weight of ith pig at time t; C,
M, and A denote fixed population parameters; [c.sub.i] and [m.sub.i]
denote the random effects for the ith pig; t denotes the age of the pig;
and b denotes body weight at birth (a constant equal to 1.4 kg).
The portion of the model focused on feed consumption is as follows:
(5) [PA.sub.it] = (E + [e.sub.i])[1 - exp([delta] + [delta]
[BW.sub.it]
+ [[delta].sub.2] [BW.sup.2].sub.it)] - (E + [e.sub.i])
x [1 - exp([delta] + [[delta].sub.1] BW i,t-1
+ [delta].sub.2] [BW.sup2].sub. i, t-1)]
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(7) [FI.sub.it] = [[PHI].sub.t][BW.sup.[eta].sub.it] +
[[phi].sub.it] + [[PSI].sub.t][FA.sub.it]
where [PA.sub.it] denotes the protein accretion for ith pig at time
t; [FA.sub.it] denotes fat accretion for ith pig at time t; [FI.sub.it]
denotes feed intake for ith pig at time t; E, [[delta].sub.0],
[[delta].sub.1], and [[delta].sub.2] denote fixed population parameters
for protein accretion; [e.sub.i] denotes a random effect parameter for
ith pig's protein accretion (correlated with
[C.sub.i]);[[alpha].sub.1], [[alpha].sub.2], [[gamma].sub.1], and
[[gamma].sub.2] are parameters for fat accretion; and [[PHI].sub.t],
[[phi].sub.t], and [[PSI].sub.t] are parameters for feed intake (these
are indexed by t because these constants change with the feed rations to
reflect different energy densities).
Because this model focuses on the growth of individual animals in
the herd, and reflects the most important determinants of revenue (body
weight and the relative proportions of fat and lean) and costs (feed
intake), it is ideal for the evaluation of the impacts of heterogeneity
on optimal marketing decisions. Details of the biological growth model
may be found in Schinckel et al. (2003, 2003a).
Using this model, 100 herds of 1,000 gilts were generated, and body
weight and feed intake were recorded daily from the age of 50 to 200
days; this time span is sufficiently large to cover any reasonable cycle
length for the grow-finish stage of production. The alternative
marketing models were applied to each of the 100 herds.
Production System
The present analysis assumes the use of an AIAO production system.
This widely used system accounts for 80% of pigs currently produced in
the United States, and has been the focus of work by several authors
including Conner and Lowe (2002). Briefly, under this system, all pigs
must be marketed and the barn must be cleaned and disinfected before the
barn is refilled with young feeder pigs. This does not imply that all
pigs must be marketed on the same day, but rather that the barn must be
cleaned and disinfected before it is refilled. It is assumed that this
cleaning and herd restocking process takes seven days.
This analysis further assumes that the production facilities are a
sunk expense, and have no alternative uses. Labor to operate the
production facility is subsumed in the production facility cost and is
assumed not to vary with either the herd or herd size. As such, both the
facility and associated operator labor are considered fixed expenses;
the objective to be optimized is thus equivalent to annual returns to
these fixed facilities and operator labor. Given low interest rates and
the relatively short period it takes a herd to cycle through a barn
(less than four months), the discount rate reflecting the time value of
money was set to zero.
Production Inputs
Feeder pigs, feed, transportation costs, and a small number of
other inputs are explicitly taken into account in calculating the return
to fixed facilities and operator labor. Each of these inputs and their
costs are detailed below.
Feeder pigs. It was assumed that pigs were purchased from another
(nursery) site at fifty days of age. A ten year average (1991-2000)
feeder pig price of $42.00 (Li 2003) was used in this analysis.
Feed. As feed is the largest component of cost in the swine
grower-finisher production process. To approximate an economically
optimal nutrition program, this analysis assumed that pigs would be fed
a total of five diets over their growth and finishing phases. The model
simulated that animals were fed diets 1-3 during the growth phase, and
diets 4-5 during the finishing phase. Feed composition was based on a
standard corn-soybean meal diet that included synthetic lysine, a
vitamin-mineral premix. Calculation of feed composition and feed cost
followed the cost minimization research work by Hill et al. (1998).
Decisions concerning the day on which each diet was started were based
on Li (2003), and Schinckel (2005). The content for each of these diets
is presented in table 1. In addition to feed ingredients, the cost per
kg of each diet includes $12/ton for grinding, mixing, and feed
transportation (Richert 2005).
Corn. Industry standard nutrient values were used for the corn used
in this analysis (yellow grain, National Research Council 1998). Corn
prices were calculated by Li (2003) and were based on a ten-year
(1991-2003) price average.
Soybean meal Industry standard nutrient values for soybean meal
were used in this analysis (dehulled, 48% crude protein soybean meal,
National Research Council 1998). The soybean meal price used in this
analysis was based upon the same ten-year price average (Li 2003).
Lysine. As dietary lysine is available to hogs through a number of
common feeds, producers may mix feed ingredients to obtain the lowest
cost of desired lysine levels. Lysine is the first limiting essential
amino acid in corn-soybean meal based swine diets (National Research
Council 1998). In this instance, corn and soybean meal provided the
major sources of lysine and other essential amino acids. Following the
Purdue recommended swine diets (Purdue University 2003), it was assumed
that 0.15% synthetic Lysine-HCL containing 78% L-Lysine was added
throughout the feeding period.
Other feed ingredients. While the relative soybean meal and corn
content of diets was adjusted to meet minimum lysine requirements, and
varied with the relative prices of these ingredients, other feed
ingredients were assumed to be included in fixed quantities. The
quantity and composition of other diet ingredients that help ensure that
the swine nutrient requirements are met at each growth/finishing stage
are presented in table 1 and were based upon the Purdue University
recommended standard swine diets (Purdue University 2003).
Transportation. The cost of feeder pig transportation to the
production facility is assumed to be included in the feeder pig purchase
price. Transportation costs for marketing are based upon ten-year
transportation cost averages (1991-2000), and were determined to be
$2/head (Li 2003). It is assumed that transportation costs per head are
the same whether the entire barn is marketed at once or truckload
batches are marketed over time.
In order to most efficiently market a herd, it is assumed that,
where possible, animals are shipped in full-truckload batches. Shipping
in this manner requires five full truckloads of 170 head/truck, and one
partial truckload of the remaining 150 head. It is further assumed that,
in shipping, animals are ordered by weight at the time the load is
shipped with the heaviest animals shipped first.
Other inputs. For the purposes of this analysis, a variety of
other, relatively small, inputs and expenses are included. These
expenses are for veterinary services, medication, death loss, and
miscellaneous, and the cost of these items are estimated to be $0.09/day
(Li 2003).
Marketing
To encourage the delivery of more homogeneous animals, swine
processors discount base prices for animals that are outside a desired
range of weight and carcass leanness. Hog base price and discount
schedules are based on the individual animal's hot carcass weight
(head and skin removed) rather than their live weight. This model
assumes that the producer has perfect knowledge of the individual
pig's live weight and the corresponding hot carcass weight, and it
is assumed that the producer can sort animals without error.
Two types of carcass-based payment schemes are commonly used in
industry. The first scheme assigns a price ($/cwt) to the animal equal
to a base price adjusted by a discount based on live weight. The
discount is typically a step function--that is, it is constant over
several live weight ranges. The second scheme is more commonly used.
Under the second scheme, the price ($/cwt) is again equal to a base
price adjusted by a discount (or premium) that is based not only on live
weight range, but also on carcass leanness. The present study considers
only the second type of payment scheme. A ten-year average live weight
price (1991-2000) of $43.00/cwt was used as the base price (Li 2003). It
is assumed that the market for live hogs is competitive, that the
producer cannot influence the price or discount schedule for either
finished hogs or feeder pigs, and that producers face no price risk.
This study makes use of two payment schedules which were
established and used by a major U.S. packer. These schedules (schedules
1 and 2) are presented in table 2. Schedule 1 is currently in use by the
packer, while schedule 2 is an older schedule.
In examining these schedules it is clear that the strategy of the
packer has changed over time. In schedule 2, animals with carcass
weights of 170 to 208 lbs and leanness of 51 to 53% were considered to
be the "baseline" for which no discount or premium was
applied. Animals that were lighter or heavier than this range, and/or
that had a lower percent carcass leanness ("fatter" carcasses)
were penalized; premiums were awarded for animals that had a higher
percent leanness than this range. The more recent payment schedule 1
follows a similar pattern of discounts and premiums. In this instance,
the "baseline" no-discount range is applied to animals with
carcass weights of 170 to 223 lbs and who have a carcass leanness of 49
to 51%. Thus, the baseline weight range became nearly 40% wider due to
an increase in the upper bound of the desired weight range, and the
baseline carcass leanness range shifted downward by 2%. While the
pattern of discounts beyond this baseline grid region is similar to the
one used for schedule 2, the penalties and premiums imposed are notably
larger. Comparing these schedules suggests that, over time, the packer
has become willing to accept a wider range of live weights that was
extended to include heavier animals. At the same time, the steeper
discounts provide additional incentive to producers to deliver animals
within the desired range.
Results and Discussion
Animal heterogeneity is important from the perspectives of both
producers and packers. Herd heterogeneity has an impact not only on when
producers should market their animals, but also on which animals to
market in a multiple batch marketing setting. For packers, the
heterogeneous quality of the animals received as inputs to their
production processes has an impact on the mix of products they can
produce, and thus their profit potential. Understanding producer
responses to payment schemes may help packers design discount/premium
schedules that encourage delivery of animals which better suit the
demand for final pork products.
Results from a Producer Perspective
For producers, animal heterogeneity will affect the optimal
shipping strategy and thus affect the potential returns which may be
realized by producers. The following discussion presents results of
shipping animals under the three alternative marketing strategies. This
analysis makes use of the more recently available carcass payment
schedule (schedule 1 in table 2).
Single day shipment strategies. Analyses of swine shipping
decisions have historically been based on a representative animal. In
this analysis, the homogeneous herd and heterogeneous herd with a single
shipping decision models were used to determine the difference in the
optimal shipping decision when herd heterogeneity is taken into account.
The results of this analysis are displayed in the first two columns of
table 3.
The first column in table 3 displays the results when the analysis
is based on the representative animal, but revenues are calculated based
on the true, heterogeneous animal weights. Based on 100 randomly sampled
herds, the expected annual return for a 1,000 head barn was $97,247 with
a standard deviation of $586, and the observed range is from about one
and a half percent below the mean to about one percent above the mean.
The average number of days on feed was quite stable with a range of 111
to 113 days.
The second column of table 3 displays results when herd
heterogeneity is explicitly recognized (the heterogeneous herd with a
single shipping decision model). The average number of days on feed is
reduced by two days, and the average return to fixed facilities and
operator labor increased by over 0.3%. In addition, the standard
deviation of returns is reduced by about 0.4%. The range of optimal
shipping dates is slightly wider with this approach to analysis--six
days as opposed to two days with the analysis based on the
representative animal.
Multiple shipment strategies. The results for the analysis that
explicitly recognizes that the herd is heterogeneous and allows
truckload shipments on multiple dates are displayed in columns 3 through
5 in table 3. Because multiple shipment dates are permitted, but not
required, one feasible strategy is to market all animals on the same
day. This was not optimal for any of the 100 randomly generated herds.
In a majority of cases (91% of the time), it was optimal to ship one
truckload of animals on one day and ship the rest of the animals on
another day. These cases are summarized in the fourth column of table 3.
For the remainder of the herds (9%), a shipping strategy in which the
two single loads were shipped on different days, with the remainder of
the animals shipped on a third day was determined to be optimal. These
cases are summarized in the fifth column of table 3. The average of the
of these multiple shipment strategies are presented in column three of
this table.
The multiple shipment strategy offers the potential to increase
returns to fixed facilities and operator labor. When the overall impact
of a multiple shipment strategy is compared with the homogeneous herd
model results, an increase of 1.6% in profit was realized. This strategy
also reduces the standard deviation of returns (-2.2%), providing a
modest benefit in terms of risk management. The optimal date for
shipping the final load is only slightly changed by the multiple
shipment strategy. It increases by about four days on average,
reflecting the fact that the marketing of an early truckload or two
removes the heaviest animals from the herd, thereby reducing the
incidence of discounts for heavy animals in the final shipment. However,
the fact that the increase in the shipping date for the final load is
small indicates that the opportunity cost of the facility continues to
dominate that decision.
Impact of packer schedule on shipping strategy. Packer payment
schedules change over time. Two payment schedules used by the same
packer at two different points in time were obtained and compared from
the perspective of a producer. Results obtained using the most recent
payment schedule (schedule 1) are provided in table 3 and are discussed
above. Table 4 describes the results when the three marketing models are
evaluated with schedule 2 (table 2).
In general, the differences between results for the alternative
marketing models are even greater than with discount/premium schedule 1.
Results of the homogeneous herd model are found in column 1 of table 4.
This strategy offers the lowest average annual return to the facility
and has highest standard deviation of returns. Results of the
heterogeneous herd with a single shipping decision model, which
considers animal heterogeneity and ships animals on a single day, are
displayed in column 2 of table 4. Expected annual returns with the
heterogeneous herd with a single shipping decision model are more than
1% greater than with the homogeneous herd model, and the standard
deviation of annual returns is decreased by about 1%. This income
improvement over the homogeneous herd model is largely due to a
reduction in the barn turn-over period by four days. Consideration of
herd heterogeneity and use of multiple shipment dates (the heterogeneous
herd with a multiple shipping decision model; presented in column 3)
offer producers the highest potential average return by increasing
expected annual returns by over 1% and decreasing the standard deviation
of annual returns by 10%, relative to the heterogeneous herd with a
single shipping decision model.
While the differences in the distributions of annual returns
appears to be larger across the three models under schedule 2 than under
schedule 1, the differences in shipping patterns are more pronounced.
Under schedule 2 with multiple shipping dates, the vast majority (80%)
of herds were shipped in three batches, one early truckload followed by
another truckload about a week later, and the rest of the animals
shipped about one day later.
Results from the Packer Perspective
The fundamental goal of discount/premium schedules is to influence
the distribution of the attributes of the animals packers procure. The
following sections explore the impact of herd heterogeneity and choice
of payment schedule on packer procurement costs and the distribution of
animals received as inputs.
Price Paid for Hogs
In table 5, the average packer payments as well as producer costs
and producer net returns are examined under each model. The top half of
the table displays results for schedule 1, while the bottom half of the
table displays results for schedule 2. Producer revenue is the base
price less discounts plus premiums, and represents the packer payment to
producer on average. Under schedule 1, discounts and premiums are of
similar magnitude, and so producer revenue is near the base price. (The
exception to this rule is with multiple shipments where premiums are
near twice discounts.) The situation under the older schedule 2 was
quite different with discounts ranging from 7.5 to over 16 times larger
than premiums.
Composition of Inputs
Because packer payment schedules affect the marketing decisions of
producers, payment schedules will, as a consequence, influence the
composition (weight/leanness characteristics) of inputs which packers
receive. Table 6 displays the distributions of animals marketed for 100
simulations of herds of 1,000 hogs using the heterogeneous herd with a
multiple shipping decision model under payment schedules 1 and 2. The
distributions under each of these schedules are quite heterogeneous with
carcass weights ranging from 164-170 to over 238 pounds under schedule 1
and 149-156 to over 237 pounds under schedule 2. Similarly, the lean
percentages range from 43-45 to 5557 for both schedules. Despite their
wide range, these distributions are quite peaked with over 37% of the
distribution falling in the 215223 carcass weight range and 49-51%
leanness range for schedule 1, and over 30% of the distribution in the
208-215 carcass weight range and 49-51% leanness under schedule 2.
Over 55% of the distribution of animals falls in the base price
categories (170-223 pounds carcass weight and 49-51% leanness) for
schedule 1. Over 28% of the animals receive premiums, and nearly 17%
receive discounts under schedule 1. The situation is quite different
with schedule 2 where about 19% of the distribution receives the base
price, less than 2% receives a premium, and over 79% receive discounts.
Examining the marginal distributions (labeled total in table 6) reveals
that in moving to the newer schedule 1 from schedule 2 there is a shift
toward animals with a lower lean percentage and toward animals with
heavier carcass weights.
Conclusions
This paper extends the standard approach to the livestock
replacement model to the situation where the unit of analysis is a herd,
and the growth of animals within the herd is heterogeneous. Based on
simulation results for a swine production unit, we find that explicit
recognition of heterogeneous animal growth allows us to evaluate the
strategy of marketing at multiple points in time. In the context of a
swine producing unit where marketing is typically done in truckload
batches, producers can increase expected returns to facilities and
operator labor by marketing a batch or two of the heaviest animals, and
then waiting a few days before marketing the rest of the herd. By
marketing these heavier animals early, the producer is able to avoid
some discounts for heavy animals. In addition to increasing mean
returns, this strategy resulted in a decrease in the variability of
returns as well.
The results presented here are based on an estimated herd-level
swine growth model where the original data comes from herds with good
genetics, above average growth rates, and above average health status.
Thus, the variability of live weight within the herd was at the low end
of what is achievable for an average commercial producer. Additional
work should focus on evaluating the multiple marketing strategy under a
greater within herd variability and for alternative packer payment
programs.
[Received March 2004; accepted February 2006.]
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Bowers, D. Kelly, M. Cobb, and D. Bundy. 1999. "Effects of Fiber
Addition (10% Soybean Hulls) to a Reduced Crude Protein Diet
Supplemented with Synthetic Amino Acid versus a Standard Commercial Diet
on Pig Performance, Pit Composition, Odor, and Ammonia Levels in Swine
Buildings." Dept. Animal Science. Purdue University 1999 Swine Day
Report, Purdue University.
Kirstein, D. 2001. "Tools to Evaluate the Use of Animal Fats
in Livestock and Poultry Rations." Paper presented at AMENA
Congress, Puerto Vallarta, Mexico, 31 October.
Li, N. 2003. "Economic Analysis of Optimal Production and
Marketing Management Strategies for Swine Production Operations with
Paylean." Ph.D dissertation, Purdue University.
Lusk, J., R. Little, A. Williams, J. Anderson, and B. McKinley.
2003. "Utilizing Ultrasound Technology to Improve Livestock
Marketing Decisions." Review of Agricultural Economics 25:203-17.
National Research Council (NRC). 1998. Nutrient Requirements of
Swine, 10th revised ed. Washington, DC: National Academic Press.
Purdue University. 2003. "Purdue University Standard Swine
Diets for the Research and Teaching Center. Revised 11.18.2003."
Purdue University.
Richert, B. 2005. Personal Communication with Authors. West
Lafayette, IN, March.
Schinckel, A. 2005. Personal Communication with Authors. West
Lafayette, IN, March.
Schinckel, A., N. Li, P. Preckel, M. Einstein, and D. Miller.
2003a. "Development of a Stochastic Pig Compositional Growth
Model." Professional Animal Scientist 19:255-60.
Schinckel, A., N. Li, B. Richert, P. Preckel, and M. Einstein.
2003. "Development of a Model to Describe the Compositional Growth
and Dietary Lysine Requirements of Pigs Fed Ractopamine." Journal
of Animal Science 81:110619.
U.S. Department of Agriculture. 2005. Changes in the U.S. Pork
Industry, 1990-2000. USDA: APHIS:VS,CEAH, National Animal Health
Monitoring System, #N428.0405, Fort Collins, CO, April.
Kathryn A. Boys is a graduate research assistant and Paul Preckel
and Kenneth Foster are professors in the Department of Agricultural
Economics, Purdue University, 403 West State Street, West Lafayette, IN
47907. Ning Li is senior risk modeler, Consumer Analytics and Modeling
Unit, Citigroup, 30 Arbor Road, Syosset, NY 11791. Allan Schinckel is
professor, Department of Animal Sciences, Purdue University, Lilly Hall
of Life Sciences, West Lafayette, IN 47907.
Assistance in generating simulated heterogeneous herd growth
results by Mark Einstein and feed cost information provided by Dr. Brian
Richert are gratefully acknowledged. The helpful comments of three
anonymous reviewers and the Managing Editor Wade Brorsen are also
gratefully acknowledged.
Table 1. Composition of Phase Feeding Diets Used during
the Growth and Finishing Stages
Diet (a) 1 2
Diet Phase Grower 1 Grower l
Days Diet Fed
(start-finish) 50-75 76-102
Days on Diet 25 26
Metabolizable
Ingredient Energy (kcal/kg)
Corn ($0.0992/kg (b)) 3420 (c) 71.60 77.10
Soybean meal, 48% 3380 (c) 24.70 19.30
crude protein
($0.2106/kg (b))
Lysine HCL ($1.2125/kg (d)) 701 (e) 0.15 0.15
Supplement containing: (f)
Dical. Phosphate 0 1.08 1.08
Limestone 0 0.75 0.75
Salt 0 0.35 0.35
Choice white grease 0 1.00 1.00
Swine vit. premix 0 0.15 0.15
Swine TM premix 0 0.0875 0.0875
Selinium 600 premix 0 0.05 0.05
OTC or CTC (50 g/lb) 0 0.10 0.10
Tylan 40 0 0.00 0.00
Phytase (600 PU/g) 0 0.075 0.075
Supplement cost ($/kg(g)) 0.012907 0.012907
Calculated analysis
Crude protein, % 18.40 17.00
Lysine, % 1.10 1.10
Diet (a) 3 4 5
Diet Phase Grower 2 Finisher 1 Finisher 2
Days Diet Fed
(start-finish) 102-116 117-129 130-Market
Days on Diet 14 13 Variable
Ingredient Ingredient %
Corn ($0.0992/kg (b)) 80.80 83.80 86.90
Soybean meal, 48% 15.70 13.10 10.20
crude protein
($0.2106/kg (b))
Lysine HCL ($1.2125/kg (d)) 0.15 0.15 0.15
Supplement containing: (f)
Dical. Phosphate 0.92 0.74 0.54
Limestone 0.78 0.81 0.83
Salt 0.35 0.25 0.25
Choice white grease 1.00 1.00 1.00
Swine vit. premix 0.15 0.10 0.10
Swine TM premix 0.0875 0.05 0.05
Selinium 600 premix 0.05 0.025 0.025
OTC or CTC (50 g/lb) 0.10 0.10 0.00
Tylan 40 0.00 0.00 0.05
Phytase (600 PU/g) 0.075 0.075 0.05
Supplement cost ($/kg(g)) 0.012343 0.011438 0.013561
Calculated analysis
Crude protein, % 14.90 12.90 11.50
Lysine, % 1.10 1.10 1.10
(a) Corn and soybean meal percentage content was optimized
based on market prices and lysine requirements. Percentage
content of all other ingredients was based on the Purdue
University Standard Diets for Research and Teaching Center
(Revised 11.18.2003).
(b) Source: Li (2003).
(c) Source: National Research Council (1998).
(d) Source: Kendall et al. (1999).
(e) Source: Kirstein (2001).
(f) Assumes no dietary energy content for supplementary ingredients.
(g) Source: Richert (2005).
Table 2. Carcass Weight and Lean Discount/Premium
Grids as a Function of Weight and Lean-ness for Two
Alternative Schedules ($/cwt)
Hot Carcass Percent Carcass Lean (%)
Weight Range
(lbs) < 43% 43-45 45-47 47-49 49-51
Schedule 1 (a)
< 164 -23.50 -22.50 -18.50 -16.00 -13.50
164-170 -16.00 -15.00 -11.00 -8.50 -6.00
170-178 -10.00 -9.00 -5.00 -2.50 0.00
178-186 -10.00 -9.00 -5.00 -2.50 0.00
186-193 -10.00 -9.00 -5.00 -2.50 0.00
193-201 -10.00 -9.00 -5.00 -2.50 0.00
201-208 -10.00 -9.00 -5.00 -2.50 0.00
208-215 -10.00 -9.00 -5.00 -2.50 0.00
215-223 -10.00 -9.00 -5.00 -2.50 0.00
223-230 -13.00 -12.00 -8.00 -5.50 -3.00
230-238 -15.26 -14.26 -10.26 -7.76 -5.26
238-244 -26.00 -25.00 -21.00 -18.50 -16.00
> 244 -26.00 -25.00 -21.00 -18.50 -16.00
Schedule 2 (b)
< 141 -19.46 -16.96 -14.46 -11.96 -10.71
141-149 -19.46 -16.96 -14.46 -11.96 -10.71
149-156 -16.76 -14.26 -11.76 -9.26 -8.01
156-164 -14.05 -11.55 -9.05 -6.55 -5.30
164-170 -11.35 -8.85 -6.35 -3.85 -2.60
170-178 -10.00 -7.50 -5.00 -2.50 -1.25
178-186 -10.00 -7.50 -5.00 -2.50 -1.25
186-193 -10.00 -7.50 -5.00 -2.50 -1.25
193-201 -10.00 -7.50 -5.00 -2.50 -1.25
201-208 -10.00 -7.50 -5.00 -2.50 -1.25
208-215 -10.08 -8.18 -5.68 -3.18 -1.93
215-223 -12.03 -9.53 -7.03 -4.53 -3.28
223-230 -13.38 -10.88 -8.38 -5.88 -4.63
230-237 -16.08 -13.58 -11.08 -8.58 -7.33
> 237 -18.78 -16.28 -13.78 -11.28 -10.03
Hot Carcass Percent Carcass Lean (%)
Weight Range
(lbs) 51-53 53-55 55-57 57-59 59
Schedule 1 (a)
< 164 -13.50 -13.50 -13.50 -13.50 -13.50
164-170 -6.00 -6.00 -6.00 -6.00 -6.00
170-178 1.50 2.75 4.00 3.00 3.00
178-186 1.50 2.75 4.00 3.00 3.00
186-193 1.50 2.75 4.00 3.00 3.00
193-201 1.50 2.75 4.00 3.00 3.00
201-208 1.50 2.75 4.00 3.00 3.00
208-215 1.50 2.75 4.00 3.00 3.00
215-223 1.50 2.75 4.00 3.00 3.00
223-230 -1.50 -0.25 1.00 0.00 0.00
230-238 -3.76 -2.51 -1.26 -2.26 -2.26
238-244 -14.50 -13.25 -12.00 -13.00 -13.00
> 244 -16.00 -16.00 -16.00 -16.00 -16.00
Schedule 2 (b)
< 141 -9.46 -9.46 -9.46 -9.46 -9.46
141-149 -9.46 -9.46 -9.46 -9.46 -9.46
149-156 -6.76 -5.51 -4.26 -3.86 -4.76
156-164 -4.05 -2.80 -1.55 -1.15 -2.05
164-170 -1.35 -0.10 1.15 1.55 0.65
170-178 0.00 1.25 2.50 2.90 2.00
178-186 0.00 1.25 2.50 2.90 2.00
186-193 0.00 1.25 2.50 2.90 2.00
193-201 0.00 1.25 2.50 2.90 2.00
201-208 0.00 1.25 2.50 2.90 2.00
208-215 -0.68 0.57 1.82 2.22 1.32
215-223 -2.03 -0.78 0.47 0.87 -0.03
223-230 -3.38 -2.13 -0.88 -0.48 -1.38
230-237 -6.08 -4.83 -3.58 -3.18 -4.08
> 237 -8.78 -8.78 -8.78 -8.78 -8.78
(a) Source: Farmland Industries (2005).
(b) Source: Farmland Industries (1999).
Table 3. Annual Returns for All Models to Fixed
Facilities and Operator Labor with Live Weight
Pricing--Schedule 1
Heterogeneous
Herd
Homogeneous Single
(Average) Shipping
Item Herd (a) Decision
Expected return 97,247 97,554
($/yr.) (586) (584)
Minimum return 95,891 96,391
($/yr.)
Maximum return 98,319 98,848
($/yr.)
Average days 112 110
on feed (0.67) (1.32)
Minimum days 111 107
on feed
Maximum days 113 113
on feed
Number 100 100
of cases
Heterogeneous Herd
Multiple Shipping Decisions
Market Market
Item Overall Twice Thrice
Expected return 98,821 98,816 98,871
($/yr.) (574) (568) (625)
Minimum return 97,570 97,570 98,002
($/yr.)
Maximum return 100,008 99,880 100,008
($/yr.)
Average days 113 Load 1:106 Load 1:106 (1.60)
on feed (0.78) (1.48) Load 2: 115 (0.50)
Rest: 114 Rest: 116 (0.92)
(0.82)
Minimum days 102 Load 1:102 Load 1: 103
on feed Rest: 112 Load 2: 114
Rest: 115
Maximum days 118 Load 1:109 Load 1: 109
on feed Rest: 116 Load 2: 115
Rest: 118
Number 100 91 9
of cases
Note: Standard errors are reported in parentheses. These results are
based on 100 randomly generated herds of 1,000 animals for a finishing
operation. Calculations include a seven day period for marketing
animals, cleaning and restocking the facility.
(a) Actual revenues differ from expected; expected annual
revenues (std. dev.) $1116,698 (546).
Table 4. Annual Returns for All Models to Fixed
Facilities and Operator Labor with Live Weight
Pricing--Schedule 2
Heterogeneous
Herd
Homogeneous Single
Item (Average) Shipping
Herd (a) Decision
Expected return 87,162 88,241
($/yr.) (548) (532)
Minimum return 86,018 86,942
($/yr.)
Maximum return 88,420 89,508
($/yr.)
Average days 112 108
on feed (0.67) (0.73)
Minimum days 111 106
on feed
Maximum days 113 110
on feed
Number of cases 100 100
Heterogeneous Herd
Multiple Shipping Decisions
Item Market Market
Overall Twice Thrice
Expected return 89,242 89,337 89,218
($/yr.) (481) (427) (491)
Minimum return 88,241 88,458 88,241
($/yr.)
Maximum return 90,433 89,945 90,433
($/yr.)
Average days 109 Load Load 1:102 (0.97)
on feed (0.50) 1:103 (0.81) Load 2:110 (0.63)
Rest: Rest: 111 (0.52)
110 (0.40)
Minimum days 101 Load 1:102 Load 1: 101
on feed Rest: 110 Load 2: 108
Rest: 110
Maximum days 112 Load 1:105 Load 1: 104
on feed Rest: 111 Load 2: 111
Rest: 112
Number of cases 100 20 80
Note: Standard errors are reported in parentheses. These
results are based on 100 randomly generated herds of 1,000
animals for a finishing operation. Calculations include a
seven-day period for marketing animals, cleaning and
restocking the facility.
(a) Actual revenues differ from expected; expected annual
revenues (std. dev) $97,409 (529).
Table 5. Average Returns in per Pig Breakdown
for Three Models
Heterogeneous
Herd
Single Multiple
Homogeneous Shipping Shipping
Item ($) Herd Decision Decisions
Schedule 1
Base price 116.47 115.00 117.37
revenue
Discount 1.70 1.35 0.83
Premium 1.64 1.75 1.56
Revenue 116.41 115.40 118.10
Prod. costs 84.73 84.04 85.18
Total net 31.69 31.35 32.92
return
Schedule 2
Base price 116.47 112.84 114.05
revenue
Discount 3.56 2.31 1.80
Premium 0.22 0.30 0.24
Revenue 113.13 110.83 112.49
Prod. costs 84.73 83.04 83.62
Total net 28.40 27.78 28.88
return
Table 6. Distribution of Marketed Animals by
Weight and Lean Percentage--Schedule 1
Carcass
Weight Lean % Ranges
Ranges
(lbs) 43-45 45-47 47-49 49-51
Schedule 1
164-170 0.002
170-178 0.016
178-186 0.001 0.080
186-193 0.009 0.290
193-201 0.034 1.035
201-208 0.001 0.307 3.606
208-215 0.039 2.271 12.374
215-223 0.262 10.809 37.749
223-230 0.002 0.083 0.958 1.117
230-238 0.001 0.066 0.353 0.187
> 238 0.004 0.024 0.012 0.004
Total 0.007 0.475 14.754 56.459
Schedule 2
149-156 0.005
156-164
164-170 0.002
170-178 0.016
178-186 0.001 0.08
186-193 0.009 0.29
193-201 0.063 1.42
201-208 0.016 1.847 18.465
208-215 0.067 4.992 30.39
215-223 0.04 0.883 1.536
223-230 0.043 0.342 0.287
230-237 0.035 0.111 0.037
> 237 0.001 0.026 0.036 0.008
Total 0.001 0.227 8.284 52.536
Carcass
Weight Lean % Ranges
Ranges
(lbs) 51-53 53-55 55-57 Total
Schedule 1
164-170 0.034 0.019 0.055
170-178 0.144 0.075 0.003 0.239
178-186 0.444 0.142 0.003 0.671
186-193 0.920 0.235 0.005 1.458
193-201 2.242 0.308 0.002 3.621
201-208 3.496 0.267 0.001 7.677
208-215 6.210 0.271 21.165
215-223 12.995 0.358 62.173
223-230 0.123 0.002 2.285
230-238 0.006 0.613
> 238 0.044
Total 26.614 1.677 0.014
Schedule 2
149-156 0.002 0.001 0.008
156-164 0.016 0.006 0.022
164-170 0.034 0.019 0.055
170-178 0.143 0.077 0.003 0.239
178-186 0.444 0.143 0.003 0.671
186-193 0.925 0.232 0.005 1.461
193-201 2.503 0.334 0.002 4.322
201-208 15.136 0.918 0.001 36.383
208-215 16.937 0.769 0.001 53.156
215-223 0.275 0.003 2.737
223-230 0.019 0.691
230-237 0.001 0.184
> 237 0.071
Total 36.435 2.502 0.015
Note: Table represents the distribution of 100 herds of 1,000
animals shipped under the heterogeneous herd with multiple
shipping decisions marketing strategy.