Location problems with grouped structure of demand: Complexity and algorithms

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 NPhard 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. q 1998 John Wiley & Sons, Inc. Networks 31: 81–92, 1998