A multi-objective programming approach to feed ration balancing and nutrient management

This paper examines the potential to use multiple objective programming to reduce nutrient excretion from dairy cows through incorporation of nutrient excretion functions into a ration formulation framework. In a typical ration formulation model, a ration is formulated to minimize cost while providing sufficient nutrients to meet the needs of the animal type being fed. To reduce the nutrient loading, rations can be formulated to minimize cost, and nitrogen and phosphorus excretion using multiple objective programming. Rations were initially formulated to minimize cost, nitrogen excretion and phosphorus excretion. Compromise programming was then utilized to examine the impacts on ration formulation of combining the three individual objectives. The multiple objective ration formulation reduced phosphorus excretion by 5% and marginally reduced nitrogen excretion with a small increase in ration cost compared to the single objective minimum cost ration. Multiple objective programming does have the potential to reduce nutrient excretion.