Multi-product maximal covering second-level facility location problem.

Resumen

In this work, we consider a hierarchical facility framework consisting in three levels. The first-level is composed by a set of facilitieswhich manufacture certain products, the second-level facilities act aswarehouses, and finally, the clients demanding some of these productscompose the third-level. The products must be supplied to the clientsby using the second-level facilities. It should be noted that, in order tosatisfy the customers’ demand, there must be a double coverage: the client must be covered by a second-level facility, and this, in turn, by a first-level facility. This kind of problem can be identified in several applications as healthcare systems, telecommunication networks or ecommerce. The aim of the proposed model, denoted as SL-MCFLP, is to determine the location and product configuration of second-levelfacilities in such a way that the overall client satisfaction with respect their coverage is maximized. We propose a mixed integer linear programming formulation, and we introduce several valid inequalities to improve its performance time. In some cases, the number of valid inequalities is exponential and, consequently, separation algorithms are developed. In addition, several variants of a matheuristic approach are introduced.