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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. 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.
    2. 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.
    3. 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.

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