The expropriation location problem

In this paper, we consider the location of a new obnoxious facility that serves only a certain proportion of the demand. Each demand point can be sought by the developer at a given price. An expropriation budget is given. Demand points closest to the facility are expropriated within the given budget. The objective is to maximize the distance to the closest point not expropriated. The problem is formulated and polynomial algorithms are proposed for its solution both on the plane and on a network.