Optimal Statistical Estimation and Dynamic Adaptive Control of Airline Seat Protection Levels for Several Nested Fare Classes under Parametric Uncertainty of Customer Demand Models

Assigning seats in the same compartment to different fare classes of passengers is a major problem of airline seat allocation. Airlines sell the same seat at different prices according to the time at which the reservation is made and other conditions. Thus the same seat can be sold at different prices. The problem is to find an optimal policy that maximizes total expected revenue. To solve the above problem, this paper presents the novel computational approach to optimization and dynamic adaptive prediction of airline seat protection levels for multiple nested fare classes of single-leg flights under parametric uncertainty. It is assumed that time T (before the flight is scheduled to depart) is divided into h periods, namely a full fare period and h-1 discounted fare periods. The fare structure is given. An airplane has a seat capacity of N. For the sake of simplicity, but without loss of generality, we consider (for illustration) the case of nonstop flight with two fare classes (business and economy). The proposed airline's inventory management policy is based on the use of the proposed computational models. These models emphasize pivotal quantities and ancillary statistics relevant for obtaining statistical predictive limits for anticipated quantities under parametric uncertainty and are applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. The proposed technique is based on a probability transformation and pivotal quantity averaging. It is conceptually simple and easy to use. Finally, we give illustrative examples, where the proposed analytical methodology is illustrated in terms of the two-parameter exponential distribution. Applications to other log-location-scale distributions could follow directly.