Delayed Purchase Options in Single-Leg Revenue Management

Many airline reservation systems offer the commitment option to their potential passengers. This option allows passengers to reserve a seat for a fixed duration before making a final purchase decision. In this study, we develop single-leg revenue management models that consider such contingent commitment decisions. We start with a dynamic programming model of this problem. This model is computationally intractable as it requires storing a multi-dimensional state space due to book-keeping of the committed seats. To alleviate this difficulty, we propose an alternate dynamic programming formulation that uses an approximate model of how the contingent commitments behave and we show how to extract a capacity allocation policy from the approximate dynamic programming formulation. In addition, we present a deterministic linear programming model that gives an upper bound on the optimal expected revenue from the intractable dynamic programming model. As the problem size becomes large in terms of flight capacity and the expected number of arrivals, we demonstrate an asymptotic lower bound for the deterministic linear programming model. Our extensive numerical study indicates that offering commitment options can noticeably increase the expected revenue even though offering a contingent commitment option may not always be in the best interest of the airline. Also, our results show that the proposed approximate dynamic programming model coordinates capacity allocation and commitment decisions quite well.