The Stochastic Location-Assignment Problem on a Tree (original) (raw)

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.

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Authors and Affiliations

1. Innovative Management Concepts, 21400 Ridgetop Circle, Dulles, VA, 20166
   Ting Zeng
2. Krannert Graduate School of Management, Purdue University, West Lafayette, IN, 47906
   James E. Ward

Authors

1. Ting Zeng
2. James E. Ward

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Zeng, T., Ward, J.E. The Stochastic Location-Assignment Problem on a Tree.Ann Oper Res 136, 81–97 (2005). https://doi.org/10.1007/s10479-005-2040-6

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• Issue date: April 2005
• DOI: https://doi.org/10.1007/s10479-005-2040-6

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