| The subject of this study is the revenue management problem in hub-to-hub airline networks. The network consists of two hubs and a connecting flight between them with spoke cities expanding outwards. The airline produces various itineraries within the network, and its flights compete with each other for limited flight capacities during a fixed booking period. Although stochastic dynamic network revenue management has been theoretically established, in reality its implementation is still heavily dependent on linear programming-based heuristics. Simpson (1989) and Williamson (1992) proposed bid price control, which is now widely adopted by major airlines. Bertsimas and de Boer (2003) proposed certainty equivalent control, which has been little studied by RM researchers. In this thesis, bid price control is first explained, and then the structural properties of the hub-to-hub network are investigated. Using the Lagrange dual-function and the primal-dual relationship, it is shown that the threshold values used in bid price control have some monotone properties in the network's capacity states. The certainty equivalent control is then applied to the hub-to-hub network. By linking the network revenue management problem with a maximum-weight circulation problem in network flow, the optimal value function is shown to be supermodular in certain capacity dimensions, and submodular in other dimensions. This leads to the monotonicity of CEC thresholds on some short-haul itineraries. The notion of L ♮ concavity developed by Murota and Shioura (2005) is applied to this work, and it is shown that even the CEC thresholds on some two-leg or three-leg long-haul itineraries are monotonically increasing or decreasing in certain legs' capacities. It is hoped that the new structural properties found in this thesis can lead to a reduction of the computational work in the implementation of both the bid price control and the certainty equivalent control in the hub-to-hub airline network.;Keywords. Hub-to-hub network, bid-price control, certainty equivalent control, combinatorial optimization, structures, primal-dual, revenue management, airline network, monotone thresholds, supermodularity/submodularity, L♮ concavity, Lagrange dual. |
