A Duality Based Approach for Network Revenue Management in Airline Alliances

In this paper, we develop a revenue management model for airline alliances. In particular, our model allows the members of the alliance to decide how to share the revenues from itineraries spanning flight legs operated by multiple airlines and how to coordinate their capacity allocation decisions. We start with a deterministic linear programming approximation to the revenue management problem that takes place over the whole alliance network. This linear program models the decisions made by a central planner. In the linear program, we relax the constraints that link the decisions for different airlines by associating dual multipliers with them, in which case, the linear program decomposes by the airlines into smaller linear programs. We extract a booking control policy from the smaller linear programs that allows each airline to make its booking control decisions autonomously. Furthermore, the dual multipliers indicate how to share the revenues from itineraries that span flight legs operated by multiple airlines. We prove that the revenue sharing scheme provided by our approach has a number of intuitively appealing features. Computational experiments indicate that our model and our revenue sharing scheme coordinate the decisions of the alliance members quite well.