A location analysis of milk processing in Montana

Abstract

A mixed integer linear programming model is used to determine the number, size, and location of milk processing plants in Montana that minimizes total assembly, distribution, and processing costs. The model selected accounts for economies of size in the objective function and is based on the Stollsteimer location model. The minimum cost solution contained four plants of varying size located one each in Great Falls, Missoula, Bozeman, and Billings. The minimum cost solution was contrasted to the estimated present situation which includes eleven relatively large plants. Total costs for the present situation were 4.9 cents per gallon of milk higher than the least cost solution. A total cost curve with respect to plant numbers was estimated. The curve exhibited a wide range of relative flatness which infers that adjustment to fewer and larger plants will be relatively slow.