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Local search algorithm for universal facility location problem with linear penalties

Author

Listed:
  • Yicheng Xu

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

  • Donglei Du

    (University of New Brunswick)

  • Chenchen Wu

    (Tianjin University of Technology)

Abstract

The universal facility location problem generalizes several classical facility location problems, such as the uncapacitated facility location problem and the capacitated location problem (both hard and soft capacities). In the universal facility location problem, we are given a set of demand points and a set of facilities. We wish to assign the demands to facilities such that the total service as well as facility cost is minimized. The service cost is proportional to the distance that each unit of the demand has to travel to its assigned facility. The open cost of facility i depends on the amount z of demand assigned to i and is given by a cost function $$f_i(z)$$ f i ( z ) . In this work, we extend the universal facility location problem to include linear penalties, where we pay certain penalty cost whenever we refuse serving some demand points. As our main contribution, we present a ( $$7.88+\epsilon $$ 7.88 + ϵ )-approximation local search algorithm for this problem.

Suggested Citation

  • Yicheng Xu & Dachuan Xu & Donglei Du & Chenchen Wu, 2017. "Local search algorithm for universal facility location problem with linear penalties," Journal of Global Optimization, Springer, vol. 67(1), pages 367-378, January.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-015-0394-0
    DOI: 10.1007/s10898-015-0394-0
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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. Eric Angel & Nguyen Kim Thang & Damien Regnault, 2015. "Improved local search for universal facility location," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 237-246, January.
    3. Guang Xu & Jinhui Xu, 2009. "An improved approximation algorithm for uncapacitated facility location problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 424-436, May.
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