Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria

Abstract The traditionally used linear programming model for feed formulation has sought the least-cost combination of ingredients that satisfies a specific level of nutritional requirements. Together with the search for the lowest possible cost, other aspects such as maximising diet efficiency in relation to proposed production objectives and minimising any excess that may lead to unacceptable damage to the environment, are other factors that are gaining in importance in the world of animal nutrition. Taking into account all these factors forces us not only to bear in mind the individual concentrations of each of the nutrients in the feed but also the ratios of these with other nutrients. In this work we show how a multi-objective fractional programming model is better adapted to current needs in feed design than the traditionally used least cost linear model. We also show how the model can be solved using the interactive multi-goal programming method with existing linear optimisation software.