Overbooking and Fare-Class Allocation with Limited Information

Overbooking and fare-class allocation are two central problems in revenue management. In this paper, we propose a distribution-free approach for coordinating these two sets of decisions for a single resource. The only information we use are upper and lower bounds of demand of each fare-class and upper and lower bounds of the no-show rate. We derive the optimal static overbooking levels and booking limits that (i) maximize the competitive ratio and (ii) minimize the maximum absolute regret. We provide closed-form solutions under either criteria. We also prove that the optimal booking limits under either criteria are nested. We provide extensive computational experiments and compare our methods to existing ones. Our computational results show that our proposed methods that use limited information are very effective and provide consistent and robust results. We also show that the optimal overbooking level determined using our distribution free method can be used to enhance the performance of the traditional fare-class allocation methods that assume no cancellations. This is of practical importance given the challenges associated with estimating the no-show rates and determining appropriate overbooking levels that are the main inputs for seat inventory control optimization in typical revenue management applications