A Note on the Application of Linear Programming to a Distribution System Orientated Toward Service

A recent article by Marien developed a linear programming model for determining the minimum cost pattern for purchasing and shipping commodities subject to a constraint in the level of service provided. The approach taken is first to describe the problem in terms of network theory. Although this is theoretically correct it leads to an unnecessarily complex discussion of what is basically a very simple problem. More importantly it leads to a mathematical model for the sample problem presented that has 23 constraints when only 4 are needed. This fact can be extremely important to anyone who is considering using the model on a “real” problem involving many more product‐shipment combinations. Following is an alternate representation of the problem in a form which lends itself much more readily to extension to larger problems and to matrix generation.