The multimode covering location problem

In this paper we introduce the Multimode Covering Location Problem. This is a generalization of the Maximal Covering Location Problem that consists in locating a given number of facilities of different types with a limitation on the number of facilities sharing the same site.The problem is challenging and intrinsically much harder than its basic version. Nevertheless, it admits a constant factor approximation guarantee, which can be achieved combining two greedy algorithms. To improve the greedy solutions, we have developed a Variable Neighborhood Search approach, based on an exponential-size neighborhood. This algorithm computes good quality solutions in short computational time. The viability of the approach here proposed is also corroborated by a comparison with a Heuristic Concentration algorithm, which is presently the most effective approach to solve large instances of the Maximal Covering Location Problem. HighlightsWe present a multimode generalization of the Maximal Covering Location Problem.We propose two greedy approximation algorithms for the new problem.We develop a Variable Neighborhood Search approach, whose local search procedure is based on Very Large Scale Neighborhood Search.We compare this approach with a basic VNS approach based on a polynomial sized neighborhood and with a Heuristic Concentration approach, which exploit general purpose exact solvers.