Using multiple objective programming in a dairy cow breeding program.

Multiple-objective programming was used to examine the effects various objectives had on the optimal portfolio of sires chosen for a given breeding problem in a Jersey cow dairy herd. It was assumed that the dairy producer had the following three objectives in the breeding decision: to maximize Net Merit, to minimize inbreeding, and to minimize total expenditure on semen. Integer programming models of these three single objectives were estimated to provide the ideal and anti-ideal values for use in several multiple-objective programming models. The integer multiple-objective models examined the interactions and costs of tradeoffs between the three single objectives in a model framework designed to minimize the maximum deviations from the single-objective optima. A model with equal weights on each objective resulted in a decrease of 3% in average inbreeding but also reduced average Net Merit by $170 from the single-objective optima. A second model, where the weight on Net Merit was twice that of inbreeding and semen cost, decreased Net Merit by $100 and reduced inbreeding by 2% from the single objective optima. The results of the multiple-objective programming models show that reducing the inbreeding coefficient for a group of sires purchased will decrease the Net Merit. However, the results generated also demonstrate that the weights placed on each objective by the dairy producer substantially affect the optimal levels of each objective within the multiple-objective model.