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Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts

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  • Lin, Yi-Kuei

Abstract

This paper proposes a performance index to measure the quality level of a stochastic-flow network in which each node has a designated capacity, which will have different lower levels due to various partial and complete failures. The performance index is the probability that the maximum flow of the network equals the demand d without exceeding the budget b. A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for (d, b), and then the probability that the maximum flow is less than or equal to d can be calculated in terms of such points. The upper boundary point for (d, b) is a maximal vector representing the capacity of each arc such that the maximum flow of the network under the budget b is d. The performance index can be calculated by repeating the proposed algorithm to obtain all upper boundary point for (d−1, b). A benchmark example is shown to illustrate the solution procedure.

Suggested Citation

  • Lin, Yi-Kuei, 2006. "Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts," Reliability Engineering and System Safety, Elsevier, vol. 91(5), pages 539-545.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:5:p:539-545
    DOI: 10.1016/j.ress.2005.03.018
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    References listed on IDEAS

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    1. Ravindra K. Ahuja & Dorit S. Hochbaum & James B. Orlin, 2003. "Solving the Convex Cost Integer Dual Network Flow Problem," Management Science, INFORMS, vol. 49(7), pages 950-964, July.
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    Cited by:

    1. Kozyra, Paweł Marcin, 2023. "The usefulness of (d,b)-MCs and (d,b)-MPs in network reliability evaluation under delivery or maintenance cost constraints," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Esha Datta & Neeraj Kumar Goyal, 2017. "Sum of disjoint product approach for reliability evaluation of stochastic flow networks," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1734-1749, November.
    3. 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.
    4. Chin‐Chia Jane & Yih‐Wenn Laih, 2012. "Evaluating cost and reliability integrated performance of stochastic logistics systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 577-586, October.

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