Some reverse location problems

The general location problem in a network is to find locations of facilities in a given network such that the total cost is minimum. It is very common to have its reverse case, in which the facilities have already been located on the network, and the problem is how to improve the network within a given budget so that the improved network is as efficient as possible. In this paper we present a strongly polynomial algorithm for a reverse location problem in tree networks. The method can be extended to solve reverse two- or more-location problems.