Optimal and approximate control policies for airline booking with sequential nonmonotonic fare classes

This paper addresses the question of when to refuse discount bookings from airline passengers to reserve seats for potential future passengers who are willing to pay a higher fare. When passengers arrive in sequential fare classes, the optimal policy will be to accept reservation requests as long as the cumulative seats booked does not exceed a given booking limit. This paper relates the probability of filling the plane, under the optimal policy, with the ratios of the current to the highest remaining fare classes. In addition, it extends the solution from monotonically increasing fares to fares occurring in arbitrary order. Finally, it demonstrates how Monte Carlo integration is easy to use to get arbitrarily close approximations to the optimal policy.