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A new cut-based algorithm for the multi-state flow network reliability problem

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  • Yeh, Wei-Chang
  • Bae, Changseok
  • Huang, Chia-Ling

Abstract

Many real-world systems can be modeled as multi-state network systems in which reliability can be derived in terms of the lower bound points of level d, called d-minimal cuts (d-MCs). This study proposes a new method to find and verify obtained d-MCs with simple and useful found properties for the multi-state flow network reliability problem. The proposed algorithm runs in O(mσp) time, which represents a significant improvement over the previous O(mp2σ) time bound based on max-flow/min-cut, where p, σ and m denote the number of MCs, d-MC candidates and edges, respectively. The proposed algorithm also conquers the weakness of some existing methods, which failed to remove duplicate d-MCs in special cases. A step-by-step example is given to demonstrate how the proposed algorithm locates and verifies all d-MC candidates. As evidence of the utility of the proposed approach, we present extensive computational results on 20 benchmark networks in another example. The computational results compare favorably with a previously developed algorithm in the literature.

Suggested Citation

  • Yeh, Wei-Chang & Bae, Changseok & Huang, Chia-Ling, 2015. "A new cut-based algorithm for the multi-state flow network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 1-7.
    • Handle: RePEc:eee:reensy:v:136:y:2015:i:c:p:1-7
    DOI: 10.1016/j.ress.2014.11.010
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    References listed on IDEAS

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    1. Joseph C. Hudson & Kailash C. Kapur, 1985. "Reliability Bounds for Multistate Systems with Multistate Components," Operations Research, INFORMS, vol. 33(1), pages 153-160, February.
    2. Yan, Zhou & Qian, Meng, 2007. "Improving efficiency of solving d-MC problem in stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 30-39.
    3. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, December.
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