IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v91y2006i5p539-545.html
   My bibliography  Save this article

Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts

Author

Listed:
  • Lin, Yi-Kuei

Abstract

This paper proposes a performance index to measure the quality level of a stochastic-flow network in which each node has a designated capacity, which will have different lower levels due to various partial and complete failures. The performance index is the probability that the maximum flow of the network equals the demand d without exceeding the budget b. A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for (d, b), and then the probability that the maximum flow is less than or equal to d can be calculated in terms of such points. The upper boundary point for (d, b) is a maximal vector representing the capacity of each arc such that the maximum flow of the network under the budget b is d. The performance index can be calculated by repeating the proposed algorithm to obtain all upper boundary point for (d−1, b). A benchmark example is shown to illustrate the solution procedure.

Suggested Citation

  • Lin, Yi-Kuei, 2006. "Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts," Reliability Engineering and System Safety, Elsevier, vol. 91(5), pages 539-545.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:5:p:539-545
    DOI: 10.1016/j.ress.2005.03.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832005001080
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2005.03.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ravindra K. Ahuja & Dorit S. Hochbaum & James B. Orlin, 2003. "Solving the Convex Cost Integer Dual Network Flow Problem," Management Science, INFORMS, vol. 49(7), pages 950-964, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Chin‐Chia Jane & Yih‐Wenn Laih, 2012. "Evaluating cost and reliability integrated performance of stochastic logistics systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 577-586, October.
    3. 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.
    4. Lin, Yi-Kuei, 2010. "A stochastic model to study the system capacity for supply chains in terms of minimal cuts," International Journal of Production Economics, Elsevier, vol. 124(1), pages 181-187, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nathan Atkinson & Scott C. Ganz & Dorit S. Hochbaum & James B. Orlin, 2023. "The Strong Maximum Circulation Algorithm: A New Method for Aggregating Preference Rankings," Papers 2307.15702, arXiv.org, revised Jan 2024.
    2. Bürgy, Reinhard & Bülbül, Kerem, 2018. "The job shop scheduling problem with convex costs," European Journal of Operational Research, Elsevier, vol. 268(1), pages 82-100.
    3. Carlo Mannino & Alessandro Mascis, 2009. "Optimal Real-Time Traffic Control in Metro Stations," Operations Research, INFORMS, vol. 57(4), pages 1026-1039, August.
    4. Thomas W. M. Vossen & R. Kevin Wood & Alexandra M. Newman, 2016. "Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing," Operations Research, INFORMS, vol. 64(4), pages 771-793, August.
    5. Dorit S. Hochbaum, 2004. "50th Anniversary Article: Selection, Provisioning, Shared Fixed Costs, Maximum Closure, and Implications on Algorithmic Methods Today," Management Science, INFORMS, vol. 50(6), pages 709-723, June.
    6. Dorit S. Hochbaum & Erick Moreno-Centeno & Phillip Yelland & Rodolfo A. Catena, 2011. "Rating Customers According to Their Promptness to Adopt New Products," Operations Research, INFORMS, vol. 59(5), pages 1171-1183, October.
    7. David Wu & Viet Hung Nguyen & Michel Minoux & Hai Tran, 2022. "Optimal deterministic and robust selection of electricity contracts," Journal of Global Optimization, Springer, vol. 82(4), pages 993-1013, April.
    8. Bachelet, Bruno & Duhamel, Christophe, 2009. "Aggregation approach for the minimum binary cost tension problem," European Journal of Operational Research, Elsevier, vol. 197(2), pages 837-841, September.
    9. Dorit S. Hochbaum & Asaf Levin, 2006. "Methodologies and Algorithms for Group-Rankings Decision," Management Science, INFORMS, vol. 52(9), pages 1394-1408, September.
    10. Mehdi Ghiyasvand, 2019. "An $$O(n(m+n\log n)\log n)$$O(n(m+nlogn)logn) time algorithm to solve the minimum cost tension problem," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 957-969, April.
    11. Dorit Hochbaum, 2007. "Complexity and algorithms for nonlinear optimization problems," Annals of Operations Research, Springer, vol. 153(1), pages 257-296, September.
    12. Mehdi Ghiyasvand, 2017. "A faster strongly polynomial time algorithm to solve the minimum cost tension problem," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 203-217, July.
    13. Garaix, Thierry & Artigues, Christian & Feillet, Dominique & Josselin, Didier, 2010. "Vehicle routing problems with alternative paths: An application to on-demand transportation," European Journal of Operational Research, Elsevier, vol. 204(1), pages 62-75, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:91:y:2006:i:5:p:539-545. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.