Hub location under competition

Abstract

Hubs are consolidation and dissemination points in many-to-many flow networks. The 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 thesis, we propose a competitive hub location problem where the market is assumed to be a duopoly. Two decision-makers (or firms) sequentially decide the locations of their hubs and then customers choose the firm according to provided service levels. Each decision-maker aims to maximize his/her market share. Having investigated the existing studies in the field of economy, retail location and operation research, we propose two problems for the leader (former decision-maker) and follower (latter decision-maker): (r|Xp) hub-medianoid and (r|p) hub-centroid problems. After defining them as combinatorial optimization problems, the problems are proved to be NP-hard. Linear programming models are presented for these problems as well as exact solution algorithms for the (r|p) hub-centroid problem that outperform the linear model in terms of memory requirement and CPU time. The performance of models and algorithms are tested by the computational analysis conducted on two well-known data sets from the hub location literature.