Least Cost Poultry Rations with Nutrient Variability: A Comparison of Linear Programming with a Margin of Safety and Stochastic Programming Models

Abstract

A common feed formulation problem is the variability of nutrients in ingredients coming from different sources. Linear programming (LP) models require the variability of ingredients to be disregarded or to be estimated and linearized. However, stochastic programming (SP) can incorporate nutrient variability to provide least cost rations that meet each nutritional requirement at specified confidence levels. This study evaluated the ability of LP, LP with a margin of Safety (LPMS), and SP models to formulate poultry rations at least cost, with a given probability to meet nutrient requirements as set by the National Research Council in 1984. Rations formulated by LP were least cost, but did not take nutrient variability into account. The LPMS and SP models met various poultry nutritional requirements at confidence levels ranging from P≥.5 to P≥.90. The SP model consistently produced lower cost rations than LPMS.