Enhancing Pig Feed Mixture: Optimization Through Goal Programming

Abstract

Feed accounts for 70–75% of the total cost of pig production, so the composition of the feed mixture largely determines both the profitability of a farm and the growth performance of the animals. Conventional least-cost formulation treats the problem as a single-objective linear program and therefore ignores quality attributes of the mixture that decision makers care about in practice. This paper formulates pig feed design as a multicriteria problem in which three conflicting objectives are considered simultaneously: minimizing the cost of the mixture, maximizing its nutrient (digestibility) value, and minimizing its moisture content, the last being a proxy for shelf life and handling quality. Twelve locally available ingredients were considered for three growth phases of pigs (starter, up to 20 kg; grower, 20–50 kg; finisher, 50–100 kg), with nutritional bounds taken from Bureau of Indian Standards and NRC recommendations and ingredient compositions from the CVB feed tables. The marginal (single-objective) solutions and the resulting payoff matrix demonstrate that the objectives are strongly conflicting: relative to the minimum-cost ration for starter pigs, the nutrient-maximizing and moisture-minimizing rations are 62% and 81% more expensive, respectively. The multicriteria model is therefore converted into a lexicographic goal programming model in which the marginal optima serve as target values and positive and negative deviations from the targets are minimized under decision-maker priorities. Three priority scenarios are solved for each growth phase, and a fourth scenario introduces deviation variables on the crude protein constraint to control the protein oversupply observed in all earlier solutions. A weight-based sensitivity analysis implemented in Google Colab confirms that the model reallocates ingredient proportions predictably as priorities change while all scenarios remain feasible. The framework yields balanced, phase-specific rations and provides an interactive decision-support tool that can be extended to other livestock systems.