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On multi-state two separate minimal paths reliability problem with time and budget constraints

Author

Listed:
  • Majid Forghani-Elahabad
  • Nezam Mahdavi-Amiri
  • Nelson Kagan

Abstract

In a stochastic-flow network, a (d, T, b, P1, P2)-MP is a system state vector for which d units of flow can be transmitted through two separate minimal paths (SMPs) P1 and P2 simultaneously from a source node to a sink node satisfying time and budget limitations T and b, respectively. Problem of determining all the (d, T, b, P1, P2)-MPs, termed as the (d, T, b, P1, P2)-MP problem, has been attractive in reliability theory. Here, some new results are established for the problem. Using these results, a new algorithm is developed to find all the (d, T, b, P1, P2)-MPs, and its correctness is established. The algorithm is compared with a recently proposed one to show the practical efficiency of the algorithm.

Suggested Citation

  • Majid Forghani-Elahabad & Nezam Mahdavi-Amiri & Nelson Kagan, 2020. "On multi-state two separate minimal paths reliability problem with time and budget constraints," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 37(4), pages 479-490.
    • Handle: RePEc:ids:ijores:v:37:y:2020:i:4:p:479-490
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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. Yeh, Wei-Chang, 2023. "Novel recursive inclusion-exclusion technology based on BAT and MPs for heterogeneous-arc binary-state network reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    3. 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).
    4. 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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