The gateway hub location problem

We introduce the Gateway Hub Location Problem (GHLP) to design global air transportation systems. Relying on a three-level hub network structure and on having nodes located in different geographic regions, the GHLP consists of locating international gateways and domestic hubs, activating arcs to induce a connected gateway and hub network, and routing flows within the network at minimum cost. Most previous studies focus on a typical hub-and-spoke network, in which local and global flows are not differentiated. Here to better represent a world wide air transportation system, global flows can only leave or enter a given geographic region by means of a gateway, while local flows can only use hubs within their respective region. As routing local or global flows involved different agents, this study presents a mixed integer programming formulation that exploits these differences to model both the local and global flows. Due to the formulation's characteristics, two algorithm variants based on Benders decomposition method are devised to solve the problem. A new repair procedure produces optimality Benders cuts whenever feasibility Benders cuts would rather be expected. While the monolithic version failed to solve medium size instances, our algorithms solved lager ones in reasonable time.