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The p-median problem under uncertainty

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  • Berman, Oded
  • Drezner, Zvi

Abstract

Consider the need to currently locate p facilities but it is possible that up to q additional facilities will have to be located in the future. There are known probabilities that 0 [less-than-or-equals, slant] r [less-than-or-equals, slant] q facilities will need to be located. The p-median problem under uncertainty is to find the location of p facilities such that the expected value of the objective function in the future is minimized. The problem is formulated on a graph, properties of it are proven, an integer programming formulation is constructed, and heuristic algorithms are suggested for its solution. The heuristic algorithms are modified to reduce the run time by about two orders of magnitude with minimal effect on the quality of the solution. Optimal solutions for many problems are found effectively by CPLEX. Computational results using the heuristic algorithms are presented.

Suggested Citation

  • Berman, Oded & Drezner, Zvi, 2008. "The p-median problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 189(1), pages 19-30, August.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:1:p:19-30
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    References listed on IDEAS

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    Cited by:

    1. Murali, Pavankumar & Ordóñez, Fernando & Dessouky, Maged M., 2012. "Facility location under demand uncertainty: Response to a large-scale bio-terror attack," Socio-Economic Planning Sciences, Elsevier, vol. 46(1), pages 78-87.
    2. Amir Hossein Sadeghi & Ziyuan Sun & Amirreza Sahebi-Fakhrabad & Hamid Arzani & Robert Handfield, 2023. "A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design," Logistics, MDPI, vol. 7(1), pages 1-24, March.
    3. Qianli Zhang & Haijun Mao, 2022. "An Integrated Method for Locating Logistic Centers in a Rural Area," Sustainability, MDPI, vol. 14(9), pages 1-19, May.
    4. Chen, Xudong & Fujita, Tsuyoshi & Hayashi, Yoshitsugu & Kato, Hirokazu & Geng, Yong, 2014. "Determining optimal resource recycling boundary at regional level: A case study on Tokyo Metropolitan Area in Japan," European Journal of Operational Research, Elsevier, vol. 233(2), pages 337-348.
    5. Guerriero, Francesca & Miglionico, Giovanna & Olivito, Filomena, 2016. "Location and reorganization problems: The Calabrian health care system case," European Journal of Operational Research, Elsevier, vol. 250(3), pages 939-954.
    6. Li, Xin & Pan, Yanchun & Jiang, Shiqiang & Huang, Qiang & Chen, Zhimin & Zhang, Mingxia & Zhang, Zuoyao, 2021. "Locate vaccination stations considering travel distance, operational cost, and work schedule," Omega, Elsevier, vol. 101(C).
    7. Simon Blanchard & Daniel Aloise & Wayne DeSarbo, 2012. "The Heterogeneous P-Median Problem for Categorization Based Clustering," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 741-762, October.
    8. N Görmez & M Köksalan & F S Salman, 2011. "Locating disaster response facilities in Istanbul," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1239-1252, July.
    9. T Drezner & Z Drezner & P Kalczynski, 2011. "A cover-based competitive location model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 100-113, January.
    10. Shahzad Bhatti & Michael Lim & Ho-Yin Mak, 2015. "Alternative fuel station location model with demand learning," Annals of Operations Research, Springer, vol. 230(1), pages 105-127, July.
    11. Sonmez, Ayse Durukan & Lim, Gino J., 2012. "A decomposition approach for facility location and relocation problem with uncertain number of future facilities," European Journal of Operational Research, Elsevier, vol. 218(2), pages 327-338.

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