Web Summary The primary objective of feed formulation is to generate a formula that meets the specifications set for it at the lowest possible cost. The inherent variability in nutrient composition of feed ingredients represents a major risk factor in formula optimization. The risk with nutrient variability in formulated diets is that the diets may not fully meet the nutrient requirements of the animal. The risk associated with nutrient variability must be handled diligently by feed manufacturers. While under-delivery of nutrients is detrimental to feed performance, over-formulating, i.e. specifying nutrients in excess of requirements is wasteful and expensive. Furthermore, reduction of variance to deliver consistent quality finished goods is expected in modern manufacturing industries. It has been suggested that nutrient variability in the feed formulation process could be managed by providing a margin of safety for the nutrients. The recommendation is to adjust the nutrient means by subtracting 0.5 of the nutrient standard deviation (SD). For example, soybean meal with a mean protein value of 44.5% and an SD of 1.4 would have an adjusted protein value of 43.8% [(44.5)-(1.4÷2) = 43.8]. These margins of safety values would then make up the ingredient database for the linear program. However, nutrient adjustments (margins of safety) are not appropriate for a linear program. Technically, it is assumed that the input values (e.g., nutrient levels, animal requirements and ingredient cost) in a linear program are linear and are known with certainty. Because the variance of nutrients used in the formulation algorithm is the square of the standard deviation (i.e., variance = (standard deviation)2), the formulation process becomes a nonlinear problem. Therefore, nutrient variation as a nonlinear input variable violates the assumptions of uncertainty and linearity for the linear program. The resulting consequence of a linear program formulation with an adjusted nutrient matrix is a costly over-formulation of the diet. A more appropriate diet formulation method is the use of stochastic programming (also referred to as chance-constrained programming). Stochastic programming is a nonlinear approach to feed formulation and it is a refinement in providing margins of safety for feed formulation. Stochastic refers to the variability of nutrients and the probability of meeting the nutrient requirement. Stochastic programming is, therefore, a method of feed formulation that can effectively incorporate nutrient variability into the formulation process to meet animal requirements with a measured level of certainty. Full Paper
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