Computing time-dependent bid prices in network revenue management problems

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it naturally provides dynamic bid prices that depend on how much time is left until departure. We show that our method provides an upper bound on the optimal total expected revenue and that this upper bound is tighter than the one provided by the widely known deterministic linear programming approach. Furthermore, it is possible to use the bid prices computed by our method as a starting point in a dynamic programming decomposition-like idea to decompose the network revenue management problem by the flight legs and to obtain dynamic and capacity-dependent bid prices. Our computational experiments indicate that the proposed method improves on many standard benchmarks.