Stochastic Programming Model in Least Cost Feed Formulation for Lactating Cattle

Abstract

A conventional linear programming model (LPM) for feed formulation of lactating cattle will overlook the variation in feed components. LPM only considers the mean composition of feed values, regardless of variations, the confidence in satisfying the nutrient need falls to 50%. Whereas the stochastic model (SM), which takes into account both the mean and variation of feed composition and provides 90-99% confidence in meeting the nutrient need. In present work, we have proposed SM for least-cost feed formulation of lactating cattle where the variation in the composition of nutrients like crude protein (CP), Calcium (Ca) and Phosphorus (P) in the feedstuff are considered. Data provided by the National Research Council (2001) are the basis for the current analysis. These SMs are resolved using M.S. Excel's Generalized Reduced Gradient (GRG) nonlinear and LINGO's Nonlinear solver, and the results are compared to LPM; the feed formulated by SM (90 % and 99 %) has the lowest cost when compared to LPM. Nutrients estimated by LPM, SM by GRG nonlinear, and SM by Nonlinear solver utilized for feed formulation had no significant differences as (p>0.05). When compared to LPM, the stochastic model is a better technique, particularly when dealing with nutrient variation.

Keywords

• feed formulation
• generalized reduced gradient
• linear programming model
• lingo's nonlinear solver
• stochastic model