Optimum Location, Number and Size of Processing Plants with Raw Product and Final Product Shipments

Abstract

The transhipment model of linear programming is utilized in this study to consider simultaneously the costs of shipping raw materials, processing, and shipping final product. The problem concerns the location and size of California cattle slaughtering plants given the location and quantity of slaughter animals and the final product demand. An iterative procedure is used to incorporate economies of scale in processing in addition to transfer costs in obtaining the minimum cost solution. Thirty-two regions in California plus two regions each for out-of-state animals and dressed beef shipments are considered. Slaughtering is indicated for 12 in-state regions with plants of varying scale, a solution which indicates the importance of assembly and distribution costs as well as economies of scale in processing in determining the optimum size of plant.