A two-level facility location and sizing problem for maximal coverage

Abstract

This paper presents a two-stage hierarchical location problem for systems where the lower level facilities act as the first points contact for the customers while the upper level facilities act as suppliers of the lower level facilities that either serve them or provide advanced services to customers. Furthermore, more recent and realistic coverage constructs such as gradual and cooperative covering are included in our setting. Although our problem can be applicable in various settings, the most fitting application is in wireless telecommunication networks to determine the location of base stations and mobile switching centers. We have developed two competing formulations for the problem, each of which involve nonlinear components that are difficult to deal with. We then develop their respective linearizations and tested their performances. These formulations are solved by commercial optimizers for a set of reasonably large problem instances and it is found that majority of the problems can be solved within a maximum of 10% optimality gap within a short time.