Hubs are consolidation and dissemination points in many-to-many flow networks. Hub location problem is to locate hubs among available nodes and allocate non-hub nodes to these hubs. The mainstream hub location studies focus on optimal decisions of one decision-maker with respect to some objective(s) even though the markets that benefit hubbing are oligopolies. Therefore, in this paper, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide locations of their hubs and then customers choose one firm with respect to provided service levels. Each decision-maker aims to maximize his/her own market share. We propose two problems for the leader (former decision-maker) and follower (latter decision-maker): ( r | X p ) h u b − m e d i a n o i d and ( r | p ) h u b − c e n t r o i d problems, respectively. Both problems are proven to be NP-complete. Linear programming models are presented for these problems as well as exact solution algorithms for the ( r | p ) h u b − c e n t r o i d problem. The performance of models and algorithms are tested by computational analysis conducted on CAB and TR data sets. 
Hub location under competition