A Stackelberg hub arc location model for a competitive environment

In this paper, we consider the design of large-scale multiple allocation hub-and-spoke transportation networks in a competitive environment. We adopt a generic hub arc location model that locates arcs with discounted transport costs connecting pairs of hub facilities. Two firms compete for customers in a Stackelberg framework where the leader firm locates hub arcs to maximize its revenue, given that the follower firm will subsequently locate its own hub arcs to maximize its own revenue. We present an optimal solution algorithm that allocates traffic between the two firms based on the relative utility of travel via the competing hub networks. Results for each competing firm with up to three hub arcs show the important role of competition in designing hub-based transportation systems.