  This paper introduces a general modeling framework for a multi-type maximal
covering location problem in which the position of facilities in different
metric 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 metric 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, 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
on. The data consists of up to 920 demand nodes using real geographical and
demographic data.
