Stochastic Feed Formulation
The purpose of commercial feed formulation is
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 formula.
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 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
