Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Multicommodity network flows

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_645


The multicommodity minimal cost network flow problem may be described in terms of a distribution problem over a network [V, E], where V is the node set with order n and E is the arc set with order m. The decision variable xjk denotes the flow of commodity k through arc j, and the vector of all flows of commodity k is denoted by xvk = [x1k,..., xmk]. The unit cost of flow of commodity k through arc j is denoted by cjk and the corresponding vector of costs by cvk = [c1k,..., cmk]. The total capacity of arc j is denoted by bj with corresponding vector bv = [b1,..., bm]. Mathematically, the multicommodity minimal cost network flow problem may be defined as follows:
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© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Texas A&M UniversityCollege StationUSA