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A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network

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  • Lin, Yi-Kuei

Abstract

Both minimal paths and minimal cuts are important media to evaluate the performance indexes, the system reliability or unreliability, for a single-commodity stochastic-flow network. This paper concentrates on a multicommodity stochastic-flow network in which each arc has both the capacity and cost attributes. Different from the single-commodity case, the system capacity is a pattern for multicommodity case. Since the traditional performance indexes are not suitable for multicommodity case, we propose a new performance index, the probability that the system capacity is less than or equal to a given pattern under the budget constraint. A simple algorithm based on minimal cuts is presented to generate all (d,B)-MCs that are the maximal capacity vectors meeting the demand d and budget B. The proposed performance index can be evaluated in terms of (d,B)-MCs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:8:p:923-929
    DOI: 10.1016/j.ress.2005.09.006
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    References listed on IDEAS

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    1. B. Rothschild & A. Whinston, 1966. "On Two Commodity Network Flows," Operations Research, INFORMS, vol. 14(3), pages 377-387, June.
    2. B. Rothschild & A. Whinston, 1966. "Feasibility of Two Commodity Network Flows," Operations Research, INFORMS, vol. 14(6), pages 1121-1129, December.
    3. T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
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    Cited by:

    1. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.

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