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Minmax regret 1-facility location on uncertain path networks

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  • Wang, Haitao

Abstract

Let P be an undirected path graph of n vertices. Each edge of P has a positive length and a constant capacity. Every vertex has a nonnegative supply, which is an unknown value but is known to be in a given interval. The goal is to find a point on P to build a facility and move all vertex supplies to the facility such that the maximum regret is minimized. The previous best algorithm solves the problem in O(nlog2n) time and O(nlogn) space. In this paper, we present an O(nlogn) time and O(n) space algorithm, and our approach is based on new observations and algorithmic techniques.

Suggested Citation

  • Wang, Haitao, 2014. "Minmax regret 1-facility location on uncertain path networks," European Journal of Operational Research, Elsevier, vol. 239(3), pages 636-643.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:3:p:636-643
    DOI: 10.1016/j.ejor.2014.06.026
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    References listed on IDEAS

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    1. Conde, Eduardo, 2007. "Minmax regret location-allocation problem on a network under uncertainty," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1025-1039, June.
    2. 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.
    3. 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.
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    Cited by:

    1. Yuya Higashikawa & Naoki Katoh, 2019. "A Survey on Facility Location Problems in Dynamic Flow Networks," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 163-208, October.
    2. Li, Hongmei & Xu, Yinfeng, 2016. "Minimax regret 1-sink location problem with accessibility in dynamic general networks," European Journal of Operational Research, Elsevier, vol. 250(2), pages 360-366.
    3. Haitao Xu & Jingru Zhang, 2023. "The two-center problem of uncertain points on a real line," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-22, March.
    4. 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.

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