Multicommodity Distribution System Design by Benders Decomposition * ^{† ‡}

Abstract

A commonly occurring problem in distribution system design is the optimal location of intermediate distribution facilities between plants and customers. A multicommodity capacitated single-period version of this problem is formulated as a mixed integer linear program. A solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones. An essentially optimal solution was found and proven with a surprisingly small number of Benders cuts. Some discussion is given concerning why this problem class appears to be so amenable to solution by Benders’ method, and also concerning what we feel to be the proper professional use of the present computational technique.

Reprinted by permission, A. M. Geoffrion, G. W. Graves: Multicommodity Distribution System Design by Benders Decomposition, Management Science 20(5), 822–844, 1974. Copyright 1974, the Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 310, Hanover, MD 21076 USA.

Received August 15, 1973.

An earlier version of this paper was presented at the NATO Conference on Applications of Optimization Methods for Large-Scale Resource Allocation Problems, Elsinore, Denmark, July 5–9, 1971. This research was partially supported by the National Science Foundation under Grant GP-36090X and the Office of Naval Research under Contract N00014-69-A-0200-4042. Reproduction in whole or in part is permitted for any purpose of the United States Government.

We wish to express our gratitude to Mr. Steven M. Niino, Manager of Operations Research at Hunt-Wesson Foods, Inc., for his outstanding contribution to the success of the practical application reported in this paper. We also want to thank Mr. Shao-Ju Lee of California State University at Northridge for his invaluable assistance in carrying out a difficult computer implementation.