An exact algorithm for the service network design problem with hub capacity constraints.

The service network design problem is commonly used to represent the tactical decisions encountered by a consolidation carrier operating a hub-and-spoke network: what transportation services to operate between hubs and how to route commodities from their origin to their destination through the network. In most settings, the capacity at hubs is not a limiting factor and can safely be ignored. However, in the context of city logistics networks, where space is limited and expensive, hub capacities typically have to be taken into account. The presence of hub capacity (and time) constraints implies that, contrary to traditional service network design problems, the existence of a feasible solution is no longer guaranteed. We present an exact dynamic discretization discovery algorithm for a variant of the service network design problem in which the number of vehicles that can be loaded and unloaded simultaneously at a hub is restricted. Novel techniques are introduced in the algorithm to handle the hub capacity constraints. A computational study using instances derived from real-world data shows the potential of dynamic discretization discovery for this class of problems: integer program sizes are reduced by a factor of up to one thousand and small to mid size instances can be (optimally) solved in an acceptable amount of time.