Location problems with grouped structure of demand: Complexity and algorithms

Location problems with grouped structure of demand: Complexity and algorithms

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Article ID: iaor20022152
Country: United States
Volume: 31
Issue: 2
Start Page Number: 81
End Page Number: 92
Publication Date: Mar 1998
Journal: Networks
Authors: ,
Keywords: networks
Abstract:

We study generalizations of classical multifacility location problems, where customers' demand has a hierarchial structure, i.e., the set of local customers is partitioned into categories (global customers), each having its own requirements for quality of service. For the case of identical facilities, we prove that the categorized coverage, covering, p-center, and p-median problems are strongly NP-hard on trees, in contrast with their classical noncategorized versions (which are polynomially solvable on trees). Some of the problems are shown to be NP-hard even on paths. For the case of distinguishable facilities, we provide polynomial and strongly polynomial algorithms for the categorized covering, multicenter, and multimedian problems with mutual communication on a tree.

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