Stochastic Feed Formulation
The purpose of commercial feed formulation is to balance nutrients
in diets to meet the nutritional requirements of animals at least
cost. Almost all commercial feed formulation software use Linear
Programming for feed formulation. In real life nutrient
composition is highly variable. This variation is associated with
variety of factors which include variation of nutrient content of
ingredients coming from different batches and sources and variation
attributed to the laboratory procedure and human error. For example
if a same sample of soybean is analyzed multiple times for protein
content, it is very likely that every time a slightly different
value will be obtained. Same sample analyses in different laboratories
or by different persons usually results in highly variable values.
In Linear Programming method a mean value of these analytical values
is used for formulation. Statistically, these mean values are associated
with only 50% confidence of meeting the requirements in prepared
Most feed manufacturers want to minimize the risk of not meeting
the nutrient requirements of the animal. The following two methods
have been proposed to minimize this risk.
- Application of safety margin in linear formulation
- Use of Stochastic Programming
In the first solution diets are formulated at 5-10% higher than
requirement. This is an unsatisfactory solution from quality control
and economic points of view because it does not account for variation
level. Nutrient variation could be higher enough to exceed safety
margin level. In case where variation level is low, the formulated
diet will be unnecessarily expensive. This will result in economical
loss of the Feed manufacturer or livestock farmer.
The second solution Stochastic Programming has been widely recommended
for feed formulation. The term Stochastic comes from the Greek word
meaning skilful at aiming. In modern terms, stochastic has become
a statistical word referring to variables that are random or uncertain.
The standard form of constraints in
linear programming is as follows.
If a user wishes to increase the success rate of meeting the
ith nutrient in the diet up to or to fall below the level bi, to
a probability of P > Øi, then both constraints will be
modified as follows
Because the above constraints are nonlinear so they could not
be solved using software that formulates least cost diets by linear
programming. This form of constraint is solved by stochastic programming.
Thus Stochastic Programming provides assurance of meeting the requirement
of animals to a grater probability.
WinFeed provides an excellent utility to solve Stochastic constraints.
It uses standard deviation of variability to meet required degree
of assurance, yet it is very simple to use.