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The (beta)-Reliable Median on a Network with Discrete Probabilistic Demand Weights

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  • Jiamin Wang

    (College of Management, Long Island University, C. W. Post Campus, Brookville, New York 11548, and Center for Service Operations, School of Economics and Business Administration, Southwest Jiaotong University, Chengdu, China)

Abstract

This study extends the classical network median problem by considering the stochastic nature of demand. Assuming that the demand weights associated with nodes are independent discrete random variables, we introduce a chance-constrained programming model to define a (beta)-reliable median of the network. It is shown that the (beta)-reliable median problem is NP-hard. Exact solution procedures and a normal approximation algorithm are developed to search for the (beta)-reliable median. Their performance is evaluated by computational experiments.

Suggested Citation

  • Jiamin Wang, 2007. "The (beta)-Reliable Median on a Network with Discrete Probabilistic Demand Weights," Operations Research, INFORMS, vol. 55(5), pages 966-975, October.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:5:p:966-975
    DOI: 10.1287/opre.1070.0422
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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. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    3. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    4. H. Frank, 1966. "Optimum Locations on a Graph with Probabilistic Demands," Operations Research, INFORMS, vol. 14(3), pages 409-421, June.
    5. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
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    Cited by:

    1. Anand Deo & Karthyek Murthy, 2025. "The Scaling Behaviors in Achieving High Reliability via Chance-Constrained Optimization," Papers 2504.07728, arXiv.org.
    2. Wang, Lei & Liu, Qing & Dong, Shiyu & Guedes Soares, C., 2022. "Selection of countermeasure portfolio for shipping safety with consideration of investment risk aversion," Reliability Engineering and System Safety, Elsevier, vol. 219(C).

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