Gradual location set covering with service quality

Abstract

Location set covering models were first described in the early 1970s. In their simplest form,
they minimize the number of facilities necessary to completely cover a set of customers in
some given space, where covering means providing service within a predetermined
distance. This paper considers extensions of the basic model that soften the covered/not
covered dichotomy and replace it with gradual covering. The models discussed in this
work include the quality of service as a criterion. The models are formulated and compared
with each other with respect to their size and features. A small series of computational
tests concludes the paper.