New formulations for two location problems with interconnected facilities

This paper studies two location problems with interconnected facilities. In the first problem, all customers need to be served by open facilities, and in the second (covering) variant a penalty is imposed for customers that cannot receive the service. Compared to the standard facility location setting, an additional constraint is imposed asking that all open facilities are interconnected, i.e., all open facilities need to be within a given radius of each other. These problems combine classical facility location aspects with network design, and we exploit this link to derive new mixed integer programming models. The strength of these models is investigated both theoretically and empirically. An extensive computational study is conducted on a set of benchmark instances from the literature, in which branch-and-cut, Benders decomposition and compact models are assessed in terms of the runtime and the resulting gaps.