Distance‐constrained multifacility minimax location problems on tree networks

We consider the problem of locating new facilities with respect to existing facilities on a tree network. The objective is to minimize the maximum of the weighted distances between existing and new facilities and between pairs of new facilities. There are upper bounds on the distances between pairs of new facilities and between new and existing facilities. We give a polynomial order, binary search algorithm, based on rational representation of data. We also present a strongly polynomial order algorithm employing a parameteric approach and exploiting parallelism.