Discrete cooperative coverage location models with alternative facility types in a probabilistic setting

In this paper, we discuss discrete location problems where the objective is to locate a given number of facilities of different types in order to appropriately cover a given set of demand points. The coverage provided to each demand point is the result of the cooperation among the located facilities. The different types of facility refer to the coverage radius or quality of coverage that each type may provide. We present a non-linear formulation of the problem where the objective is to maximize the percentage of demand points that are appropriately covered. We then show how the model can be linearized based on a representation of probabilities through a network structure. To address large instances of the problem, we introduce a genetic algorithm (GA) that is based on the representation of the solution by two chromosomes. Computational experiments over a wide range of randomly generated problems indicate the GA clearly outperforms CPLEX, especially in larger instances.