Goal Programming for Supply Chain Optimization with Insufficient Capacity

Abstract : This article presents three different approaches to modeling and solving the classic transportation-location problem including the traditional cost-minimization mixed integer linear program. It is shown that modeling these problems as a profit maximization mixed integer program instead allows for the relaxation of a set of constraints. An alternative multi-objective optimization model using goal programming is also presented. A representative model of the fluid milk supply chain in the U.S. is developed to demonstrate the scenarios and solutions achieved by the three different models to conclude that the multi-objective model is a robust approach to solve these optimization problems even when there is only a single explicit objective.