Gradual location set covering with service quality

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.