The General N-Location Distribution Problem

Abstract

This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. Specifically, it is shown that there is a correspondence between the optimal policies and the extreme points, edges, faces etc. of the dual feasible region. This method is not directly suitable for the solution of large problems but the exact solution for small problems can be obtained. It is shown that the three location case involves 37 policies as compared to seven for the two location case. For the numerical solutions of large problems, the problem has been formulated as a linear program with column generation. This latter approach is quite robust in the sense that it is easily extended to incorporate capacity constraints and the multiproduct case. Extensions of this work are briefly discussed.