Exactly solving a two-level hierarchical 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 different capabilities, which must be located and dimensioned 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 in which two sets of facilities have to be located, and in which different devices can be installed in each site, providing different capacities at different costs. We optimize simultaneously location and dimensioning of these facilities. We introduce a compact formulation for that problem, we exploit discretization and Dantzig-Wolfe reformulation techniques to obtain better models, and we design an exact optimization algorithm. We test our approach on a set of instances derived from the facility location literature.