Exactly solving a two-level location problem with modular node capacities

In many telecommunication networks, a given set of client nodes must be served by different sets of facilities—providing different services and having dif- ferent capabilities—which must be located and dimen- sioned in the design phase. Network topology must be designed as well, by assigning clients to facilities and facilities to higher level entities, when necessary. We tackle a particular location problem, where two sets of facilities have to be located, and in which different devices can be installed at each site, providing different capacities at different costs. We optimize location and dimensioning of these facilities simultaneously. We intro- duce a compact formulation of that problem, we use dis- cretization and Dantzig–Wolfe reformulation techniques to improve models, and we design an exact optimization algorithm. We test our approach on a set of instances derived from existing literature on facility location.