A Stochastic Approximation Method for the Revenue Management Problem on a Single Flight Leg with Discrete Demand Distributions

We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is well-known that the optimal policy for this classical problem is characterized by a set of protection levels. In this paper, we propose a stochastic approximation method to compute the optimal protection levels under the assumption that the demand distributions are not known and we only have access to the samples from the demand distributions. The novel aspect of our method is that it works with the nonsmooth version of the problem where the capacity can only be allocated in integer quantities. We show that our method obtains valid stochastic subgradients of the value functions without computing expectations explicitly and discuss applications to the case where the demand information is censored by the seat availability. Numerical experiments indicate that our method is especially advantageous when the total expected demand exceeds the capacity by a significant margin.