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QUALITY FEED
FORMULATION WITH
STOCHASTIC NONLINEAR
PROGRAMMING
William B. Roush
Associate Professor
Poultry Science
Nutritionists face the problem of
nutrient variability in feed ingre
dients when formulating rations
to animals. This variability can
come from many sources and may
cause the diet to have inconsistent
nutrient levels.
Some sources of nutrient varia
bility include differences in crop
varieties, weather, locality, and
soil conditions. Other sources of
error associated with nutrient var
iability come from sampling,
weighing, mixing, transporting,
and feeding.
A common procedure used by
nutritionists to overcome variabili
ty is to subtract a specified level
from the average amount of nutri
ents in the ingredient, usually a
half of a standard deviation. This
correction method has become
known as the margin-of-safety
method.
This approach underestimates
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the nutrient; therefore, it increases
the amount of ingredient to insure
the specific nutrient requirement is
met.
The margin-of-safety has been
used for the last 40 years along
with the well-established proce
dure of linear programming for
feed formulation. The ideal situa
tion would be to evaluate and
account for variability to guarantee
desired nutrient compositions in
feeds.
Because of the nonlinear nature
of variability, linear programming
is inadequate for this kind of opti
mization. Fortunately, stochastic
nonlinear programming is emerg
ing as a promising feed formula
tion approach to help solve the
nutrient variability problem.
The word “stochastic” refers to
the uncertainty in a process or
problem. Uncertainty is usually
described by variance, which is
nonlinear.
The nonlinear nature of variance
cannot be adequately incorporated
in a linear feed formulation prog
ram. There have been many proce
dures proposed for linearizing die
problem. However, there are non
linear algorithms available for
computers which will allow nutri
ent variability to be effectively
incorporated in the feed formula
tion process.
In comparing rations formulated
by linear programming with a
margin-of-safety and stochastic
nonlinear programming, it has
been found that the stochastic
program more accurately meets
the requested guaranteed analysis.
For example, if the nutritionist
is requesting that the protein level
be met at least 69 percent of the
time, this level will be more accu
rately met with stochastic prog
ramming than with the margin-of
safety method.
Theoretically, the subtraction of
a half of a standard deviation from
the average provides a 69 percent
statistical probability. In reality,
the margin-of-safety method con
sistently overformulates the nutri
ent requirement
One feed formulation example
using the margin-of-safety method
showed the protein requirement
was overformulated from a
requested probability of 69 percent
to a level of 77 percent
Ovcrformulation of nutrients is
costly. One commercial feed com
pany has shown the economic dif
ference in accurately meeting the
requested nutrient guarantee with
stochastic programming has been
an average of $2 per ton over the
margin-of-safcty method.
Studies at Penn State have
shown there was no difference in
performance of layers and broilers
fed rations formulated with sto
chastic or margin-of-safety
methods. The rations formulated
by stochastic programming were
consistently lesser cost than the
margin-of-safcty method.
A side benefit of more accurate
feed formulation is the reduction
of nutrient waste to the environ
ment This is a great concern in
FEEDER PIG OPERATION
many Pennsylvania farming com
munities, particularly for nitrogen
and phosphorus.
Most feed mills have quality
control programs. In many mills,
the nutrient information is used
primarily as a protection against
litigation.
Stochastic nonlinear program-
Animal
Student
Fellowship
NEWARK, Del. Douglas R.
Korver, University of Delaware
master's degree student has been
awarded a Purina Research Fel
lowship Award for the 1992-1993
school year.
The fellowship carries with it a
sl2,soostipend. Only four fellow
ships are awarded annually in the
U.S.
A native of Lethbridge, Alberta,
Canada, Korver was chosen from a
group of 42 applicants.
The awards are intended to
assist in training for leadership in
the nutritional sciences of food and
companion animals. Recipients
must be qualified for graduate
study in a land-grant agricultural
college.
Korver came to the university in
fall of 1990 for graduate study in
animal science in the College of
Agricultural Sciences. He holds a
bachelor’s degree in poultry sci
ence from the University of
Saskatchewan.
The graduate student’s research
at Delaware has focused on nutri
tion and its effect on the poultry
POULTRY OPERATION
LanettUr fmnino. Situßiiy, June 8. IW2-E5
ming now offcn an effective
method to use the statistical infor
mation produced in quality control
programs for feed formulation. As
a result, stochastic nonlinear prog
ramming is a promising bridge
between quality control programs
and quality least cost feed
formulation.
Science
Garners
immune system. Korver, under the
direction of his advisor. Dr. Wil
liam W. Saylor, has been investi
gating how the oxidation ofdietary
fats affects feed quality and, ulti
mately, the chicken’s ability to
resist diseases.
“During manufacturing and
storage of feed, fat oxidation can
occur,” Korver said. "This can
result in a buildup of products such
as peroxides that can damage
nutrients essential for normal
immune function. The addition of
antioxidants to feeds can prevent
but not reverse damage.”
In addition to his research, the
graduate student has assisted in
several courses including livestock
nutrition, animal physiology, and
beef and sheep production. Korver
plans to complete a Ph.D. in ani
mal science.