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Probabilistic partial set covering problems

Author

Listed:
  • Hanif D. Sherali
  • Seong‐In Kim
  • Edna L. Parrish

Abstract

In this article, we consider a situation in which a group of facilities need to be constructed in order to serve a given set of customers. However, the facilities cannot guarantee an absolute coverage to any of the customers. Hence, we formulate this problem as one of maximizing the total service reliability of the system subject to a budgetary constraint. For this problem, we develop and test suitable branch‐and‐bound algorithms and study the effect of problem parameters on solution difficulty. Some generalizations of this problem are also mentioned as possible extensions.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:1:p:41-51
    DOI: 10.1002/1520-6750(199102)38:13.0.CO;2-L
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    References listed on IDEAS

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    1. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    2. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
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    Cited by:

    1. Ojeong Kwon & Donghan Kang & Kyungsik Lee & Sungsoo Park, 1999. "Lagrangian relaxation approach to the targeting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 640-653, September.
    2. 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.
    3. 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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