Anti-covering Problems

In covering location models, one seeks the location of facilities optimizing the weight of individuals covered, i.e., those at the distance from the facilities below a threshold value. Attractive facilities are wished to be close to the individuals, and thus the covering is to be maximized, while for repulsive facilities the covering is to be minimized. On top of such individual-facility interactions, facility-facility interactions are relevant, since they may repel each other. This chapter is focused on models for locating facilities using covering criteria, taking into account that facilities are repulsive from each other. Contrary to the usual approach, in which individuals are assumed to be concentrated at a finite set of points, we assume the individuals to be continuously distributed in a planar region. The problem is formulated as a global optimization problem, and a branch and bound algorithm is proposed.

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