IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v31y2016i1d10.1007_s10878-014-9716-2.html
   My bibliography  Save this article

Minimax regret vertex 2-sink location problem in dynamic path networks

Author

Listed:
  • Hongmei Li

    (Sichuan University)

  • Yinfeng Xu

    (Sichuan University
    State Key Lab for Manufacturing Systems Engineering)

  • Guanqun Ni

    (Sichuan University)

Abstract

This paper considers the minimax regret vertex 2-sink location problem in a dynamic path network with positive edge lengths and uniform edge capacity. Let $$P$$ P be an undirected path graph of $$n$$ n vertices, and the weight (initial supply) of every vertex is known as an interval. The problem is to find two vertices $$x$$ x and $$y$$ y as two sinks on the path such that all the weights can evacuate to $$x$$ x and $$y$$ y with minimum regret of evacuation time in case of an emergency for any possible weight distribution. We present an $$O(n^3\log n)$$ O ( n 3 log n ) time algorithm.

Suggested Citation

  • Hongmei Li & Yinfeng Xu & Guanqun Ni, 2016. "Minimax regret vertex 2-sink location problem in dynamic path networks," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 79-94, January.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9716-2
    DOI: 10.1007/s10878-014-9716-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9716-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-014-9716-2?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. L. R. Ford & D. R. Fulkerson, 1958. "Constructing Maximal Dynamic Flows from Static Flows," Operations Research, INFORMS, vol. 6(3), pages 419-433, June.
    Full references (including those not matched with items on IDEAS)

    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. Yuya Higashikawa & Naoki Katoh, 2019. "A Survey on Facility Location Problems in Dynamic Flow Networks," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 163-208, October.
    2. Elisabeth Lübbecke & Marco E. Lübbecke & Rolf H. Möhring, 2019. "Ship Traffic Optimization for the Kiel Canal," Operations Research, INFORMS, vol. 67(3), pages 791-812, May.
    3. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    4. S. Khodayifar & M. A. Raayatpanah & P. M. Pardalos, 2019. "A polynomial time algorithm for the minimum flow problem in time-varying networks," Annals of Operations Research, Springer, vol. 272(1), pages 29-39, January.
    5. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    6. Anke Stieber & Armin Fügenschuh, 2022. "Dealing with time in the multiple traveling salespersons problem with moving targets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 991-1017, September.
    7. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    8. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
    9. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2007. "Fast, Fair, and Efficient Flows in Networks," Operations Research, INFORMS, vol. 55(2), pages 215-225, April.
    10. Hong Zheng & Yi-Chang Chiu, 2011. "A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 45(1), pages 121-137, February.
    11. Francisco Pérez‐Villalonga & Javier Salmerón & Kevin Wood, 2008. "Dynamic evacuation routes for personnel on a naval ship," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 785-799, December.
    12. Bretschneider, S. & Kimms, A., 2011. "A basic mathematical model for evacuation problems in urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 523-539, July.
    13. Bozhenyuk Alexander & Gerasimenko Evgeniya, 2013. "Algorithm for Monitoring Minimum Cost in Fuzzy Dynamic Networks," Information Technology and Management Science, Sciendo, vol. 16(1), pages 53-59, December.
    14. Koch, Ronald & Nasrabadi, Ebrahim, 2014. "Flows over time in time-varying networks: Optimality conditions and strong duality," European Journal of Operational Research, Elsevier, vol. 237(2), pages 580-589.
    15. Jian Li & Kaan Ozbay, 2015. "Evacuation Planning with Endogenous Transportation Network Degradations: A Stochastic Cell-Based Model and Solution Procedure," Networks and Spatial Economics, Springer, vol. 15(3), pages 677-696, September.
    16. Ryo Yamamoto & Atsushi Takizawa, 2019. "Partitioning Vertical Evacuation Areas in Umeda Underground Mall to Minimize the Evacuation Completion Time," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 209-225, October.
    17. Nazanin Abbasnezhad & Javad Mehri-Takmeh & Javad Vakili, 2020. "The domination over time and its discretisation," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 5-24.
    18. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    19. Bretschneider, S. & Kimms, A., 2012. "Pattern-based evacuation planning for urban areas," European Journal of Operational Research, Elsevier, vol. 216(1), pages 57-69.
    20. Lara Turner & Dwi Groß & Horst Hamacher & Sven Krumke, 2015. "Static and dynamic source locations in undirected networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 619-646, October.

    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:spr:jcomop:v:31:y:2016:i:1:d:10.1007_s10878-014-9716-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.