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An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint

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  • Forghani-elahabad, Majid
  • Mahdavi-Amiri, Nezam

Abstract

Several researchers have worked on transmitting a given amount of flow through a network flow within fastest possible time, allowing flow to be transmitted through one or more paths. Extending this problem to the system reliability problem, the quickest path reliability problem has been introduced. The problem evaluates the probability of transmitting some given amount of flow from a source node to a sink node through a single minimal path in a stochastic-flow network within some specified units of time. Later, the problem has been extended to allow flow to be transmitted through two or more separate minimal paths (SMPs). Here, we consider the problem of sending flow through two SMPs with budget constraint. Presenting some new results, an efficient algorithm is proposed to solve the problem. The algorithm is illustrated through a benchmark ARPANET example. Computing complexity results, the algorithm is shown to be significantly more efficient than the existing ones. We also state how the optimal two SMPs with the best system reliability can be determined based on our proposed algorithm. Finally, testing on more than 10000 generated random test problems, the practical efficiency of our algorithm is demonstrated in comparison with a recently proposed algorithm.

Suggested Citation

  • Forghani-elahabad, Majid & Mahdavi-Amiri, Nezam, 2015. "An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 472-481.
    • Handle: RePEc:eee:reensy:v:142:y:2015:i:c:p:472-481
    DOI: 10.1016/j.ress.2015.06.012
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Forghani-elahabad, Majid & Yeh, Wei-Chang, 2022. "An improved algorithm for reliability evaluation of flow networks," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    2. Yi-Kuei Lin & Lance Fiondella & Ping-Chen Chang, 2022. "Reliability of time-constrained multi-state network susceptible to correlated component faults," Annals of Operations Research, Springer, vol. 311(1), pages 239-254, April.
    3. Forghani-elahabad, Majid & Kagan, Nelson & Mahdavi-Amiri, Nezam, 2019. "An MP-based approximation algorithm on reliability evaluation of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    4. 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).
    5. Majid Forghani-elahabad & Omar Mutab Alsalami, 2023. "Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    6. Yeh, Wei-Chang, 2022. "Novel direct algorithm for computing simultaneous all-level reliability of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    7. Esha Datta & Neeraj Goyal, 2023. "An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs," 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. 14(4), pages 1228-1246, August.

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    More about this item

    Keywords

    Stochastic quickest path problem; Transmission time; Budget constraint; Minimal paths (MPs); (d; T; b; P1; P2)-MP;
    All these keywords.

    JEL classification:

    • P1 - Political Economy and Comparative Economic Systems - - Capitalist Economies

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