Multi-product Maximal Covering Second-level Facility Location Problem.

Abstract

In hierarchical facility location problems, the goal is to locate a set of interacting facilities at different levels of a hierarchical framework. Inthis context, we introduce a model which considers a first- (or highest-) level system of already established services (factories, product sources,etc.), a second-level system of facilities to locate, and a third- (or lowest-) level system of clients demanding di↵erent products produced in the first-level and provided by the second-level facilities. The set of clients has di↵erent product demands and distinct preferences depending on the first-level facility producing the product. The aim of this model is to locate a set of second-level facilities (warehouses, shops, etc.) in such a way that the covered clients’ demand is maximized. Therefore, in order to satisfy a customer’s demand, there must be double coverage, the customer must be covered by a secondlevel facility, and this, in turn, by a first-level facility. In this model, called multi-product maximal covering second-level facility location problem, there is a maximum number of di↵erent products that can be o↵ered at each second-level facility and also a budgetconstraint for the total cost of the facility locations. We derive a mixed integer formulation for this problem. Furthermore, we develop severalfamilies of valid inequalities to reinforce the model. In addition, we propose a heuristic procedure that provides good feasible solutions. Finally, we present several computational results that show the enhancement produced by the inclusion of valid inequalities in the formulation and the high-quality solution given by the heuristic algorithm.