Multi-period hub network design problems with modular capacities

In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. For each case, a mixed-integer linear programming formulation is proposed and a set of valid inequalities is derived for enhancing the corresponding model. The results of a set of computational tests performed using the formulations proposed and their enhancements are reported. The value of the multi-period solution is discussed as a measure for evaluating the relevance of considering a multi-period model instead of a static counterpart.