  This paper introduces a new hierarchical facility location model with three
levels: first-level facilities which manufacture different products,
second-level facilities which act as warehouses and a third-level consisting of
the clients who demand the products that have been manufactured in the first
level and stored in the second level. In this model, called multi-product
maximal covering second-level facility location problem (SL-MCFLP), the aim is
to decide the location of the second-level facilities and the products to be
stored in each of them maximizing the overall clients' satisfaction with
respect their coverage. To deal with this model, we introduce a Mixed Integer
Linear Program (MILP) which is reinforced by some families of valid
inequalities. Since some of these families have an exponential number of
constraints, separation algorithms are proposed. In addition, three variants of
a matheuristic procedure are developed. Computational studies are included,
showing the potentials and limits of the formulation and the effectiveness of
the heuristic.
