Locating a semi-obnoxious facility with expropriation

This paper considers the problem of locating semi-obnoxious facilities assuming that “too close” demand nodes can be expropriated by the developer at a given price. The objective is to maximize the minimum weighted distance from the facility to the non-expropriated demand nodes given a limited budget while taking into account the fact that customers do not want to be too far away from the facility. Two models of this problem on a network are presented. One is to minimize the difference between the maximum and the minimum weighted distances. The other one is to maximize the minimum weighted distance subject to an upper bound constraint on the maximum weighted distance. The dominating sets are determined and efficient algorithms are presented.