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Evaluating the reliability of a stochastic distribution network in terms of minimal cuts

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  • Niu, Yi-Feng
  • Gao, Zi-You
  • Lam, William H.K.

Abstract

This paper presents a d-minimal cut based algorithm to evaluate the performance index Rd+1 of a distribution network, defined as the probability that a specified demand d+1 can be successfully distributed through stochastic arc capacities from the source to the destination. To improve the efficiency of solving d-minimal cuts, a novel technique is developed to determine the minimal capacities of arcs. Also, two new judging criteria are proposed to detect duplicate d-minimal cuts. Both theoretical and computational results indicate that our algorithm outperforms the existing methods. Furthermore, a real case study is provided to illustrate the application of the algorithm.

Suggested Citation

  • Niu, Yi-Feng & Gao, Zi-You & Lam, William H.K., 2017. "Evaluating the reliability of a stochastic distribution network in terms of minimal cuts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 100(C), pages 75-97.
    • Handle: RePEc:eee:transe:v:100:y:2017:i:c:p:75-97
    DOI: 10.1016/j.tre.2017.01.008
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    Cited by:

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    3. 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).
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    5. Yi-Feng Niu & Can He & De-Qiang Fu, 2022. "Reliability assessment of a multi-state distribution network under cost and spoilage considerations," Annals of Operations Research, Springer, vol. 309(1), pages 189-208, February.
    6. Paweł Marcin Kozyra, 2020. "Analysis of minimal path and cut vectors in multistate monotone systems and use it for detection of binary type multistate monotone systems," Journal of Risk and Reliability, , vol. 234(5), pages 686-695, October.
    7. Niu, Yi-Feng & Wan, Xiao-Yu & Xu, Xiu-Zhen & Ding, Dong, 2020. "Finding all multi-state minimal paths of a multi-state flow network via feasible circulations," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Niu, Yi-Feng, 2021. "Performance measure of a multi-state flow network under reliability and maintenance cost considerations," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. 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).
    10. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    11. Xu, Xiu-Zhen & Niu, Yi-Feng & Song, Yi-Fan, 2021. "Computing the reliability of a stochastic distribution network subject to budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    12. Yeh, Cheng-Ta & Lin, Yi-Kuei & Yeng, Louis Cheng-Lu & Huang, Pei-Tzu, 2021. "Reliability evaluation of a multistate railway transportation network from the perspective of a travel agent," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    13. Niu, Yi-Feng & Zhao, Xia & Xu, Xiu-Zhen & Zhang, Shi-Yun, 2023. "Reliability assessment of a stochastic-flow distribution network with carbon emission constraint," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
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