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On Two Commodity Network Flows

Author

Listed:
  • B. Rothschild

    (Yale University, New Haven, Connecticut)

  • A. Whinston

    (University of Virginia, Charlottesville, Virginia)

Abstract

The paper considers the problem of two-commodity network flows and generalizes a result of Hu on integral flows in networks with integral capacities. The main result of the paper is a max-flow min-cut theorem for two commodity networks. The method of proof involves a particular type of separation process. This leads to an algorithm for finding the maximal flows. Several counterexamples to certain possible generalizations are given at the end of the paper.

Suggested Citation

  • B. Rothschild & A. Whinston, 1966. "On Two Commodity Network Flows," Operations Research, INFORMS, vol. 14(3), pages 377-387, June.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:3:p:377-387
    DOI: 10.1287/opre.14.3.377
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    Citations

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    Cited by:

    1. Lin, Yi-Kuei, 2007. "Generate upper boundary vectors meeting the demand and budget for a p-commodity network with unreliable nodes," European Journal of Operational Research, Elsevier, vol. 183(1), pages 253-262, November.
    2. Lin, Yi-Kuei, 2006. "A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 923-929.
    3. Lin, Yi-Kuei, 2007. "Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 646-652.
    4. Lin, Yi-Kuei, 2007. "Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 572-580, June.
    5. A. Sedeño-Noda & C. González-Martín & S. Alonso-Rodríguez, 2010. "A new strategy for the undirected two-commodity maximum flow problem," Computational Optimization and Applications, Springer, vol. 47(2), pages 289-305, October.
    6. Sedeno-Noda, A. & Gonzalez-Martin, C. & Gutierrez, J., 2005. "The biobjective undirected two-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 164(1), pages 89-103, July.
    7. Lin, Yi-Kuei, 2007. "On a multicommodity stochastic-flow network with unreliable nodes subject to budget constraint," European Journal of Operational Research, Elsevier, vol. 176(1), pages 347-360, January.
    8. Costa, Marie-Christine & Letocart, Lucas & Roupin, Frederic, 2005. "Minimal multicut and maximal integer multiflow: A survey," European Journal of Operational Research, Elsevier, vol. 162(1), pages 55-69, April.
    9. Lin, Yi-Kuei, 2010. "A stochastic model to study the system capacity for supply chains in terms of minimal cuts," International Journal of Production Economics, Elsevier, vol. 124(1), pages 181-187, March.

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