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An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

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  • André Berger
  • Alexander Grigoriev
  • Andrej Winokurow

Abstract

The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. $$\ell _1$$ ℓ 1 or $$\ell _\infty $$ ℓ ∞ . We develop an exact combinatorial algorithm running in time $$O(n\log ^c n)$$ O ( n log c n ) for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.

Suggested Citation

  • André Berger & Alexander Grigoriev & Andrej Winokurow, 2017. "An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions," Computational Optimization and Applications, Springer, vol. 68(3), pages 661-669, December.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:3:d:10.1007_s10589-017-9935-4
    DOI: 10.1007/s10589-017-9935-4
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    References listed on IDEAS

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    1. Stefan Nickel & Justo Puerto & Antonio M. Rodriguez-Chia, 2003. "An Approach to Location Models Involving Sets as Existing Facilities," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 693-715, November.
    2. S. Nickel & J. Puerto & A. M. Rodríguez-Chía & A. Weissler, 2005. "Multicriteria Planar Ordered Median Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 657-683, September.
    3. J. Brimberg & G.O. Wesolowsky, 2002. "Minisum Location with Closest Euclidean Distances," Annals of Operations Research, Springer, vol. 111(1), pages 151-165, March.
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    Cited by:

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    2. Wei-jie Cong & Le Wang & Hui Sun, 2020. "Rank-two update algorithm versus Frank–Wolfe algorithm with away steps for the weighted Euclidean one-center problem," Computational Optimization and Applications, Springer, vol. 75(1), pages 237-262, January.

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