Multi-type maximal covering location problems: Hybridizing discrete and continuous problems

Abstract

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different normed spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous normed spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, by taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported. Apart from a synthetic dataset, the different approaches are tested on a real geographical and demographic data with up to 920 demand nodes.