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The Stochastic Location-Assignment Problem on a Tree

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  • Ting Zeng
  • James Ward

Abstract

In the assignment problem units of supply are assigned on a one-to-one basis to units of demand so as to minimize the sum of the cost associated with each supply-to-demand matched pair. Defined on a network, the supplies and demands are located at vertices and the cost of a supply-to-demand matched pair is the distance between them. This paper considers a two-stage stochastic program for locating the units of supply based upon only a probabilistic characterization of demand. The objective of the first-stage location problem is to minimize the expected cost of the second-stage assignment problem. Principal results include showing that the problem is NP-hard on a general network, has a simple solution procedure on a line network, and is solvable by a low order polynomial greedy procedure on a tree network. Potential applications are discussed. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Ting Zeng & James Ward, 2005. "The Stochastic Location-Assignment Problem on a Tree," Annals of Operations Research, Springer, vol. 136(1), pages 81-97, April.
    • Handle: RePEc:spr:annopr:v:136:y:2005:i:1:p:81-97:10.1007/s10479-005-2040-6
    DOI: 10.1007/s10479-005-2040-6
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    References listed on IDEAS

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    1. Louveaux, F. & Thisse, J.-F., 1984. "Production and location on a network under demand uncertainty," LIDAM Discussion Papers CORE 1984001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Gilbert Laporte & François V. Louveaux & Luc van Hamme, 1994. "Exact Solution to a Location Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 28(2), pages 95-103, May.
    3. Oded Berman & Richard C. Larson & Samuel S. Chiu, 1985. "Optimal Server Location on a Network Operating as an M / G /1 Queue," Operations Research, INFORMS, vol. 33(4), pages 746-771, August.
    4. Margaret L. Brandeau & Samuel S. Chiu, 1989. "An Overview of Representative Problems in Location Research," Management Science, INFORMS, vol. 35(6), pages 645-674, June.
    5. Donald Erlenkotter, 1978. "A Dual-Based Procedure for Uncapacitated Facility Location," Operations Research, INFORMS, vol. 26(6), pages 992-1009, December.
    6. 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.
    7. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
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    Cited by:

    1. Zuo-Jun Max Shen & Roger Lezhou Zhan & Jiawei Zhang, 2011. "The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 470-482, August.
    2. Kannan Viswanath & James Ward, 2010. "Stochastic Location-assignment on an Interval with Sequential Arrivals," Networks and Spatial Economics, Springer, vol. 10(3), pages 389-410, September.
    3. Liming Yao & Zhongwen Xu & Ziqiang Zeng, 2020. "A Soft‐Path Solution to Risk Reduction by Modeling Medical Waste Disposal Center Location‐Allocation Optimization," Risk Analysis, John Wiley & Sons, vol. 40(9), pages 1863-1886, September.

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