Multi-period hub location and hub network design problems with modular hub capacities

In this study, multi-period hub location and hub network design problems with modular hub capacities are considered. This problem decides on the locations and the capacities of hubs, the design of the hub network, the allocation of demand nodes to hubs and the routes of flow in each period. Mixed-integer linear programming formulations are developed for both the single and the multiple allocation versions of the problems. Furthermore, several sets of valid inequalities are proposed for enhancing the models. The objective of the models is to minimize total costs which consist of flow routing cost, hub operating cost, hub and hub link establishment costs, and capacity establishment cost. It is possible to establish a new hub and expand the capacity of an existing hub in each period during the planning horizon. It is assumed that capacities of the hubs are modular and at most one capacity module can be established for each hub in each period. Models are solved on test problems with 5-periods that are generated from the CAB data set with 15 and 25 nodes. In addition, computational performance of the proposed valid inequalities are analyzed. The value of the multi-period approach is determined using the proposed weak and strong value of the multi-period solution.