Tractable open loop policies for joint overbooking and capacity control over a single flight leg with multiple fare classes

Official URL: http://legacy.orie.cornell.edu/~huseyin/publications/overbooking_emsr.pdf

In this paper, we consider the joint overbooking and capacity control problem over a single flight leg with multiple fare classes. The objective is to maximize the expected profit, which is given by the difference between the expected revenue from the accepted requests and the expected penalty cost from the denied reservations. We study a class of open loop policies that accept the requests for each fare class with a fixed acceptance probability. In this case, the challenge becomes that of finding a set of acceptance probabilities that maximize the expected profit. We derive a simple expression that can be used to compute the optimal acceptance probabilities, despite the fact that the problem of finding the optimal acceptance probabilities is a high dimensional optimization problem. We show that the optimal acceptance probabilities randomize the acceptance decisions for at most one fare class, indicating that the randomized nature of our open loop policies is not a huge practical concern. We bound the performance loss of our open loop policies when compared with the optimal policy. Computational experiments demonstrate that open loop policies perform remarkably well, providing expected pro¯ts within two percent of the optimal expected profits on average.