Optimal multicommodity network flows with resource allocation

J. E. Cremeans, R. A. Smith and G. R. Tyndall

Naval Research Logistics Quarterly, 1970, vol. 17, issue 3, 269-279

Abstract: The problem of determining multicommodity flows over a capacitated network subject to resource constraints may be solved by linear programming; however, the number of potential vectors in most applications is such that the standard arc‐chain formulation becomes impractical. This paper describes an approach—an extension of the column generation technique used in the multicommodity network flow problem—that simultaneously considers network chain selection and resource allocation, thus making the problem both manageable and optimal. The flow attained is constrained by resource availability and network capacity. A minimum‐cost formulation is described and an extension to permit the substitution of resources is developed. Computational experience with the model is discussed.

Date: 1970
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