A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems

This paper presents a new approach to determining the optimal facility locations for uncapacitated location problems in two stages. First, it is shown that a subset of all solutions to the uncapacitated public facility location problem can be obtained by considering a closely related private location problem. The exact nature of the problem is established using the Generalized Lagrange Multiplier results given by Everett. In the second section of the paper a particularly efficient parametric decomposition algorithm, which is based on the results of the first section, is presented. Computational results are given which summarize the current level of experience with the algorithm.