Multiple-objective (goal) programming model for feed formulation: an example for reducing nutrient variation

A multiple-objective programming (MOP) model was applied to the feed formulation process with the objectives of minimizing nutrient variance and minimizing ration cost. A MOP model was constructed for a broiler grower ration (3 to 6 wk) and formulated with a Microsoft Excel solver. Twenty-one ingredients with 17 nutrients were included in the formulation. Amino acids were based on digestible values. The following objectives were considered as soft constraints: (1) meeting the nutrient requirements; (2) meeting the ingredient restrictions; and (3) meeting nutrient ratios, including calcium to phosphorus and the relationship of amino acids to lysine (ideal amino acid ratios). Hard constraints considered were (1) a least-cost ration and (2) minimal nutrient variances for protein, methionine, and lysine. It was found that (1) the MOP model was more flexible in providing a compromise solution than a traditional feed formulation with a linear program, (2) the MOP model was able to handle several conflicting objectives simultaneously as compared to the traditional linear programming approach that could handle only one objective, and (3) the MOP model gave the best compromise solution that would satisfy multiple decision makers when trade-offs were made between the ration cost and minimum variances of protein and methionine. The MOP model is an efficient tool to assist the decision-making process through solving a series of linear/nonlinear programs and by interacting with decision-makers.