Multifacility Ordered Median Problems on Networks: A Further Analysis

In this paper, we address the ordered p-median problem, which includes as special cases most of the classical multifacility location problems discussed in the literature. Finite dominating sets (FDS) are known for particular instances of this problem: p-median, p-center, and p-centdian. We find an FDS for the ordered p-median problem. This set allows us to gain a better insight into the general FDS structure of network location problems. This FDS is later used to present the first polynomial time algorithm for p-facility ordered median problems on tree networks. This result is combined with some approximation algorithms to give an O(log M log log M) approximate solution of these problems on general networks, where M is the number of vertices.