A note on the subtree ordered median problem in networks based on nestedness property

Abstract

The nestedness property has become an increasinglyimportant means for devising efficient algorithms for networklocation problems. In this paper we prove that the nestednessproperty holds for the tactical continuous, and strategic discrete and continuous subtree location problems in a tree network with the ordered median objective, where the$\lambda$-weights take at most two different values. These resultsextend some existing results in the literature. With thesenestedness results, we solve the problems in polynomial time. Finallywe pose an open problem on identifying the nestedness property forthe $(k_1,k_2)$-trimmed problem.