Continuous maximal covering location problems with interconnected facilities

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be linked by means of a given graph structure (provided that two facilities are allowed to be linked if a given distance is not exceed). We propose a mathematical programming framework for the problem and different resolution strategies. First, we provide a Mixed Integer Non Linear Programming formulation for the problem and derive some geometrical properties that allow us to reformulate it as an equivalent pure integer linear programming problem. We propose two branch-&-cut approaches by relaxing some sets of constraints of the former formulation. We also develop a math-heuristic algorithm for the problem capable to solve instances of larger sizes. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.