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The minmax regret gradual covering location problem on a network with incomplete information of demand weights

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  • Berman, Oded
  • Wang, Jiamin

Abstract

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only information on the range of these random variables, this study is aimed at finding the "minmax regret" location that minimizes the worst-case coverage loss. We show that under some conditions, the problem is equivalent to known location problems (e.g. the minmax regret median problem). Polynomial time algorithms are developed for the problem on a general network with linear coverage decay functions.

Suggested Citation

  • Berman, Oded & Wang, Jiamin, 2011. "The minmax regret gradual covering location problem on a network with incomplete information of demand weights," European Journal of Operational Research, Elsevier, vol. 208(3), pages 233-238, February.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:3:p:233-238
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    References listed on IDEAS

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    1. O Berman & J Wang, 2008. "The probabilistic 1-maximal covering problem on a network with discrete demand weights," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(10), pages 1398-1405, October.
    2. Igor Averbakh & Oded Berman, 2000. "Minmax Regret Median Location on a Network Under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 104-110, May.
    3. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    4. Averbakh, Igor & Berman, Oded, 2000. "Algorithms for the robust 1-center problem on a tree," European Journal of Operational Research, Elsevier, vol. 123(2), pages 292-302, June.
    5. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
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    Cited by:

    1. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.
    2. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. Ran Wei, 2016. "Coverage Location Models," International Regional Science Review, , vol. 39(1), pages 48-76, January.
    4. Vatsa, Amit Kumar, 2014. "Multi-Period Facility Location Problem with an Uncertain Number of Servers," IIMA Working Papers WP2014-02-06, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Baldomero-Naranjo, Marta & Kalcsics, Jörg & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2022. "Upgrading edges in the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 14-36.
    6. Vatsa, Amit Kumar & Ghosh, Diptesh, 2014. "Tabu Search for Multi-Period Facility Location: Uncapacitated Problem with an Uncertain Number of Servers," IIMA Working Papers WP2014-11-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    7. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    8. Vahid Hajipour & Parviz Fattahi & Hasan Bagheri & Samaneh Babaei Morad, 2022. "Dynamic maximal covering location problem for fire stations under uncertainty: soft-computing approaches," 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. 13(1), pages 90-112, February.
    9. Karatas, Mumtaz & Eriskin, Levent, 2021. "The minimal covering location and sizing problem in the presence of gradual cooperative coverage," European Journal of Operational Research, Elsevier, vol. 295(3), pages 838-856.
    10. Vatsa, Amit Kumar & Jayaswal, Sachin, 2021. "Capacitated multi-period maximal covering location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1107-1126.
    11. David Kik & Matthias G. Wichmann & Thomas S. Spengler, 2023. "Small- or Medium-Sized Enterprise Uses Operations Research to Select and Develop its Headquarters Location," Interfaces, INFORMS, vol. 53(4), pages 312-331, July.
    12. Bashiri, Mahdi & Chehrepak, Elaheh & Gomari, Saeed, 2014. "Gradual Covering Location Problem with Stochastic Radius," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 165-186, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.

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