Algorithmic approaches for network design with facility location: A survey

We consider a family of problems that combine network design and facility location. Such problems arise in many practical applications in different fields such as telecommunications, transportation networks, logistic, and energy supply networks. In facility location problems, we want to decide which facilities to open and how to assign clients to the open facilities so as to minimize the sum of the facility opening costs and client connection costs. These problems typically do not involve decisions concerning the routing of the clients’ demands to the open facilities; once we decided on the set of open facilities, each client is served by the closest open facility. In network design problems, on the other hand, we generally want to design and dimension a minimum-cost routing network providing sufficient capacities to route all clients’ demands to their destinations. These problems involve deciding on the routing of each client’s demand. But, in contrast to facility location problems, demands’ destinations are predetermined. In many modern day applications, however, all these decisions are interdependent and affect each other. Hence, they should be taken simultaneously. The aim of this work is to survey models, algorithmic approaches and methodologies concerning such combined network design facility location problems.