Comments on “A Suggested Computation for Maximal Multi-Commodity Network Flows”

Abstract

This article comments on the paper 'A Suggested Computation for Maximal Multi-Commodity Network Flows,' by L. R. Ford Jr. and D. R. Fulkerson. It was said that the paper is a foundation study for two important developments in the management sciences. The basic theory for single-commodity network flows was developed primarily by Ford, Fulkerson, and Dantzig and documented in a series of publications in the late 1950s and two famous books, 'Flows in Networks and Extensions' by Dantzig. This 'Management Science' 1958 manuscript introduced the concept of multiple commodities sharing the same capacitated network. In the introduction, the major differences between the multicommodity version and its single-commodity cousin was stated. The multicommodity network flow problem has become an important model in the management sciences with numerous applications in the area of distribution networks and telecommunication design. Some of the first applications served by the KORBX linear programming system based on the interior point algorithm of Narendrea Karmarkar of AT& amp;T were large multicommodity network problems for military airlift applications. In recent years, multicommodity models regularly appear in the telecommunication design literature. All the work on this family of problems traces its roots to the 1958 'Management Science' issue.