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

The nestedness property has become an increasingly important means for devising effcient algorithms for network location problems. In this paper we prove that the nestedness property holds for the tactical continuous, and strategic discrete and continuous subtree location problems in a tree network with the ordered median objective, where the λ-weights take at most two different values. These results extend some existing results in the literature. With these nestedness results, we solve the problems in polynomial time. Finally we pose an open problem on identifying the nestedness property for the (k1; k2)-trimmed problem.