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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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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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