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Combinatorial approximation algorithms for the robust facility location problem with penalties

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  • Fengmin Wang
  • Dachuan Xu
  • Chenchen Wu

Abstract

In this paper, we consider the robust facility location problem with penalties, aiming to serve only a specified fraction of the clients. We formulate this problem as an integer linear program to identify which clients must be served. Based on the corresponding LP relaxation and dual program, we propose a primal–dual (combinatorial) 3-approximation algorithm. Combining the greedy augmentation procedure, we further improve the above approximation ratio to 2. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Fengmin Wang & Dachuan Xu & Chenchen Wu, 2016. "Combinatorial approximation algorithms for the robust facility location problem with penalties," Journal of Global Optimization, Springer, vol. 64(3), pages 483-496, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:483-496
    DOI: 10.1007/s10898-014-0251-6
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    References listed on IDEAS

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    1. Jiawei Zhang & Bo Chen & Yinyu Ye, 2005. "A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 389-403, May.
    2. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    3. Gaidi Li & Yu Li & Jia Shu & Dachuan Xu, 2013. "A cross-monotonic cost-sharing scheme for the concave facility location game," Journal of Global Optimization, Springer, vol. 56(4), pages 1325-1334, August.
    4. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    5. Hyunwoo Jung & Mohammad Khairul Hasan & Kyung-Yong Chwa, 2009. "A 6.55 factor primal-dual approximation algorithm for the connected facility location problem," Journal of Combinatorial Optimization, Springer, vol. 18(3), pages 258-271, October.
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    Cited by:

    1. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    2. Mehdi Karimi & Somayeh Moazeni & Levent Tunçel, 2018. "A Utility Theory Based Interactive Approach to Robustness in Linear Optimization," Journal of Global Optimization, Springer, vol. 70(4), pages 811-842, April.
    3. Chenchen Wu & Dachuan Xu & Dongmei Zhang & Peng Zhang, 2018. "Approximation algorithms for the robust/soft-capacitated 2-level facility location problems," Journal of Global Optimization, Springer, vol. 70(1), pages 207-222, January.

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