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A new reformulation approach for the generalized partial covering problem

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  • Youngho Lee
  • Hanif D. Sherali
  • Ikhyun Kwon
  • Seongin Kim

Abstract

In this paper, we consider a situation in which a group of facilities must be constructed in order to serve a given set of customers, where the facilities might not be able to guarantee an absolute coverage to the different customers. We examine the problem of maximizing the total service reliability of the system subject to a budgetary constraint. We propose a new reformulation of this problem that facilitates the generation of tight lower and upper bounds. These bounding mechanisms are embedded within the framework of a branch‐and‐bound procedure. Computational results on problem instances ranging in size up to 100 facilities and 200 customers reveal the efficacy of the proposed exact and heuristic approaches. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Youngho Lee & Hanif D. Sherali & Ikhyun Kwon & Seongin Kim, 2006. "A new reformulation approach for the generalized partial covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 170-179, March.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:2:p:170-179
    DOI: 10.1002/nav.20130
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    References listed on IDEAS

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    1. Hanif D. Sherali & Seong‐In Kim & Edna L. Parrish, 1991. "Probabilistic partial set covering problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 41-51, February.
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    3. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
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    5. Egon Balas & Maria C. Carrera, 1996. "A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering," Operations Research, INFORMS, vol. 44(6), pages 875-890, December.
    6. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    7. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
    8. Marshall L. Fisher & Pradeep Kedia, 1990. "Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics," Management Science, INFORMS, vol. 36(6), pages 674-688, June.
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    Cited by:

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    2. Timothy C. Y. Chan & Derya Demirtas & Roy H. Kwon, 2016. "Optimizing the Deployment of Public Access Defibrillators," Management Science, INFORMS, vol. 62(12), pages 3617-3635, December.

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