Encyclopedia of Operations Research and Management Science

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

Multicommodity network flows

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

INTRODUCTION

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 x jk denotes the flow of commodity k through arc j, and the vector of all flows of commodity k is denoted by xv k = [ x 1k,..., x mk]. The unit cost of flow of commodity k through arc j is denoted by c jk and the corresponding vector of costs by cv k = [ c 1k,..., c mk]. The total capacity of arc j is denoted by b j with corresponding vector bv = [ b 1,..., b m]. Mathematically, the multicommodity minimal cost network flow problem may be defined as follows:
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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Bala Shetty
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA