Locating semi-obnoxious facilities with expropriation: Minisum criterion

This paper considers the problem of locating semi-obnoxious facilities assuming that demand points within a certain distance from an open facility are expropriated at a given price. The objective is to locate the facilities so as to minimize the total weighted transportation cost and expropriation cost. Models are developed for both single and multiple facilities. For the case of locating a single facility, finite dominating sets are determined for the problems on a plane and on a network. An efficient algorithm is developed for the problem on a network. For the case of locating multiple facilities, a branch-and-bound procedure using Lagrangian relaxation is proposed and its efficiency is tested with computational experiments.