MIP Modeling of Incremental Connected Facility Location

We consider the incremental connected facility location problem, in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of customers to be served, the assignment of these customers to the open facilities, and a network that connects the open facilities. Once a customer is served, it must also be served in subsequent periods. Furthermore, in each time period the total demand of all customers served must be at least equal to a given minimum coverage requirement for that period. The objective is to maximize the net present value of the network, which is given by the discounted revenues of serving the customers and by the discounted investments and maintenance costs for the facilities and the network. We study different MIP models for this problem, discuss some valid inequalities to strengthen these formulations, and present a branch and cut algorithm for finding its solution. Finally, we report (preliminary) computational results of our implementation of this algorithm. Ashwin Arulselvan, Andreas Bley and Olaf Maurer Technische Universität Berlin, e-mail: {arulsel,maurer,bley}@math.tu-berlin.de, Straße des 17. Juni 136, 10623 Berlin, Germany Stefan Gollowitzer Department of Statistics and Operations Research, e-mail: stefan.gollowitzer@univie. ac.at, University of Vienna, Austria Ivana Ljubić Institute of Computer Graphics and Algorithms, e-mail: [email protected], Vienna University of Technology, Austria