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Improving efficiency of solving d-MC problem in stochastic-flow network

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  • Yan, Zhou
  • Qian, Meng

Abstract

Solving d-MC problem is often a tedious process. Three ways are suggested to improve the efficiency of solving d-MC problem. The first way is to make the best use of some special properties of network. A property of Network with Joint Parallel Part, which is more common than series–parallel network, is illustrated. The second way is to reduce the number of d-MC candidates and then to reduce the cost of testing. Two theorems on how to find the d-MCs with only one element unsaturated and on how to set the Lower Capacity Limits (LCLs) of elements to some values higher than zero are proved. These two theorems will be helpful to reduce d-MC candidates without any loss of real d-MC. The third way is to efficiently remove the duplicated d-MCs. A theorem, elucidating which Minimal Cuts (MCs) the duplicated d-MCs will be generated from, is proved. Finally, an algorithm is proposed by adding a pre-numerating step to the algorithm presented in Yeh [A new approach to the d-MC problem. Reliab Eng Syst Safety 2002;77(2):201–6], and two examples are employed to illustrate the proposed algorithm, especially the pre-numerating step.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:1:p:30-39
    DOI: 10.1016/j.ress.2005.11.006
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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.
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    Cited by:

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    2. 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.
    3. Zhou, Yifan & Liu, Libo & Li, Hao, 2022. "Reliability estimation and optimisation of multistate flow networks using a conditional Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    4. Huang, Ding-Hsiang & Huang, Cheng-Fu & Lin, Yi-Kuei, 2020. "A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1107-1114.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
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    10. Yeh, Wei-Chang, 2024. "A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
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    12. 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).
    13. 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.

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