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COBRA: A New Formulation of the Classic p-Median Location Problem

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  • Richard Church

Abstract

The p-median problem was first formulated as an integer-linear programming problem by ReVelle and Swain (1970) and further revised by Rosing, ReVelle and Rosing-Vogelaar (1979). These two forms have withstood the test of time, as they have been used by virtually everyone since then. We prove that a property associated with geographical proximity makes it possible to eliminate many of the model variables through a substitution process. This new substitution technique has resulted in the elimination of up to 60% of the variables needed in either of these classic model formulations. Copyright Kluwer Academic Publishers 2003

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  • Richard Church, 2003. "COBRA: A New Formulation of the Classic p-Median Location Problem," Annals of Operations Research, Springer, vol. 122(1), pages 103-120, September.
    • Handle: RePEc:spr:annopr:v:122:y:2003:i:1:p:103-120:10.1023/a:1026142406234
    DOI: 10.1023/A:1026142406234
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    Citations

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    Cited by:

    1. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    2. Sergio García & Martine Labbé & Alfredo Marín, 2011. "Solving Large p -Median Problems with a Radius Formulation," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 546-556, November.
    3. Sourour Elloumi, 2010. "A tighter formulation of the p-median problem," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 69-83, January.
    4. Deniz Aksen & Nuray Piyade & Necati Aras, 2010. "The budget constrained r-interdiction median problem with capacity expansion," 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. 18(3), pages 269-291, September.
    5. Amir Khakbaz & Ali Nookabadi & S. Shetab-bushehri, 2013. "A Model for Locating Park-and-Ride Facilities on Urban Networks Based on Maximizing Flow Capture: A Case Study of Isfahan, Iran," Networks and Spatial Economics, Springer, vol. 13(1), pages 43-66, March.
    6. Wangshu Mu & Daoqin Tong, 2020. "On solving large p-median problems," Environment and Planning B, , vol. 47(6), pages 981-996, July.
    7. Feng, Xin & Murray, Alan T. & Church, Richard L., 2021. "Drone service response: Spatiotemporal heterogeneity implications," Journal of Transport Geography, Elsevier, vol. 93(C).
    8. 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.
    9. Irawan, Chandra Ade & Salhi, Said & Scaparra, Maria Paola, 2014. "An adaptive multiphase approach for large unconditional and conditional p-median problems," European Journal of Operational Research, Elsevier, vol. 237(2), pages 590-605.
    10. Weiping Zeng & Ignacio Castillo & M. Hodgson, 2010. "A Generalized Model for Locating Facilities on a Network with Flow-Based Demand," Networks and Spatial Economics, Springer, vol. 10(4), pages 579-611, December.
    11. Kenneth Carling & Mengjie Han & Johan Håkansson, 2012. "Does Euclidean distance work well when the p-median model is applied in rural areas?," Annals of Operations Research, Springer, vol. 201(1), pages 83-97, December.
    12. Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.

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