ON STOCHASTIC LINEAR PROGRAMMING AND ITS APPLICATION IN AGRO-PASTORALISM

Abstract

Stochastic linear programming (SLP) is a robust method for optimization under uncertainty. This study applies SLP to livestock feed formulation, aiming to minimize costs while meeting nutritional requirements with probabilistic constraints. The model considers ten ingredients Ai with costs ci and five nutrients Jj. Minimum nutrient levels are set with given probabilities, and deterministic equivalents are derived using quantiles of three distribution laws: normal, uniform, and exponential. MATLAB analysis indicates that uniform and exponential distributions yield the most efficient input combinations for minimal cost. These results show how distributional assumptions affect optimal solutions and demonstrate the practical value of incorporating uncertainty into feed production. The study contributes to the literature on SLP in agriculture and economics, offering decision-makers strategies to balance cost efficiency with nutritional adequacy.