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The probabilistic 1-maximal covering problem on a network with discrete demand weights

Author

Listed:
  • O Berman

    (University of Toronto)

  • J Wang

    (Long Island University)

Abstract

We discuss the probabilistic 1-maximal covering problem on a network with uncertain demand. A single facility is to be located on the network. The demand originating from a node is considered covered if the shortest distance from the node to the facility does not exceed a given service distance. It is assumed that demand weights are independent discrete random variables. The objective of the problem is to find a location for the facility so as to maximize the probability that the total covered demand is greater than or equal to a pre-selected threshold value. We show that the problem is NP-hard and that an optimal solution exists in a finite set of dominant points. We develop an exact algorithm and a normal approximation solution procedure. Computational experiment is performed to evaluate their performance.

Suggested Citation

  • O Berman & J Wang, 2008. "The probabilistic 1-maximal covering problem on a network with discrete demand weights," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(10), pages 1398-1405, October.
    • Handle: RePEc:pal:jorsoc:v:59:y:2008:i:10:d:10.1057_palgrave.jors.2602466
    DOI: 10.1057/palgrave.jors.2602466
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    References listed on IDEAS

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    1. H. Frank, 1967. "Letter to the Editor—Optimum Locations on Graphs with Correlated Normal Demands," Operations Research, INFORMS, vol. 15(3), pages 552-557, June.
    2. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    3. H. Frank, 1966. "Optimum Locations on a Graph with Probabilistic Demands," Operations Research, INFORMS, vol. 14(3), pages 409-421, June.
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    Cited by:

    1. Berman, Oded & Wang, Jiamin, 2011. "The minmax regret gradual covering location problem on a network with incomplete information of demand weights," European Journal of Operational Research, Elsevier, vol. 208(3), pages 233-238, February.
    2. Juan Yu & Mi Gan & Shaoquan Ni & Dingjun Chen, 2018. "Multi-objective models and real case study for dual-channel FAP supply chain network design with fuzzy information," Journal of Intelligent Manufacturing, Springer, vol. 29(2), pages 389-403, February.
    3. Correia, Isabel & Melo, Teresa, 2019. "Dynamic facility location problem with modular capacity adjustments under uncertainty," Technical Reports on Logistics of the Saarland Business School 17, Saarland University of Applied Sciences (htw saar), Saarland Business School.

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