A New Dynamic Programming Decomposition Method for the Network Revenue Management Problem with Customer Choice Behavior

In this paper, we propose a new dynamic programming decomposition method for the network revenue management problem with customer choice behavior. The fundamental idea behind our dynamic programming decomposition method is to allocate the revenue associated with an itinerary among the different flight legs and to solve a single-leg revenue management problem for each flight leg in the airline network. The novel aspect of our approach is that it chooses the revenue allocations by solving an auxiliary optimization problem that takes the probabilistic nature of the customer choices into consideration. We compare our approach with two standard benchmark methods. The first benchmark method uses a deterministic linear programming formulation. The second benchmark method is a dynamic programming decomposition idea that is similar to our approach, but it chooses the revenue allocations in an ad hoc manner. We establish that our approach provides an upper bound on the optimal total expected revenue, and this upper bound is tighter than the ones obtained by the two benchmark methods. Computational experiments indicate that our approach provides significant improvements over the performances of the benchmark methods.