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A novel multi-distribution multi-state flow network and its reliability optimization problem

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  • Yeh, Wei-Chang
  • Chu, Ta-Chung

Abstract

The traditional multi-state flow network (MFN) reliability problem is a well-known NP-hard problem, and has been an active area of research for the past four decades. In the MFN reliability problem, the state distribution, i.e. the states and the occurrence probabilities of each arc, is known and fixed. However, the notations used in the MFN problems never considered the state distribution. In addition, each arc has only one state distribution, and this limits the application of the MFN. Thus, the notations relating to the state distribution are added or redefined in this study, and a novel budget-allocation multi-distribution MFN reliability problem is defined and proposed by considering networks with more than one state distribution under different budget allocations. Furthermore, a new algorithm is proposed to solve the proposed novel NP-Hard problem. The correctness and time complexity of the proposed algorithm are analyzed, and one benchmark example is given to demonstrate how to optimize the budget-allocation multi-distribution MFN reliability under different budget constraints.

Suggested Citation

  • Yeh, Wei-Chang & Chu, Ta-Chung, 2018. "A novel multi-distribution multi-state flow network and its reliability optimization problem," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 209-217.
    • Handle: RePEc:eee:reensy:v:176:y:2018:i:c:p:209-217
    DOI: 10.1016/j.ress.2018.04.006
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    Cited by:

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    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. Wu, Baichao & Sun, Long, 2024. "A novel layer-by-layer recursive decomposition algorithm for calculation of network reliability," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    6. Ding-Hsiang Huang & Cheng-Fu Huang & Yi-Kuei Lin, 2019. "Reliability Evaluation for a Stochastic Flow Network Based on Upper and Lower Boundary Vectors," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    7. Lin, Shuai & Jia, Limin & Zhang, Hengrun & Zhang, Pengzhu, 2022. "Reliability of high-speed electric multiple units in terms of the expanded multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    8. Hao, Zhifeng & Yeh, Wei-Chang & Zuo, Ming & Wang, Jing, 2020. "Multi-distribution multi-commodity multistate flow network model and its reliability evaluation algorithm," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Peng Su & Guanjun Wang, 2022. "Reliability analysis of network systems subject to probabilistic propagation failures and failure isolation effects," Journal of Risk and Reliability, , vol. 236(2), pages 290-306, April.
    10. Zhang, Hanxiao & Sun, Muxia & Li, Yan-Fu, 2022. "Reliability–redundancy allocation problem in multi-state flow network: Minimal cut-based approximation scheme," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    11. Ping-Chen Chang, 2022. "Reliability evaluation and big data analytics architecture for a stochastic flow network with time attribute," Annals of Operations Research, Springer, vol. 311(1), pages 3-18, April.
    12. Cui, Huixia & Chen, Xiangyong & Guo, Ming & Jiao, Yang & Cao, Jinde & Qiu, Jianlong, 2023. "A distribution center location optimization model based on minimizing operating costs under uncertain demand with logistics node capacity scalability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    13. Yeh, Wei-Chang & Hao, Zhifeng & Forghani-elahabad, Majid & Wang, Gai-Ge & Lin, Yih-Lon, 2021. "Novel Binary-Addition Tree Algorithm for Reliability Evaluation of Acyclic Multistate Information Networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
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