Joint overbooking and seat allocation for fare families

Revenue management systems (RMS) traditionally solve overbooking and seat allocation separately. Overbooking is managed by inflating the physical capacity using a static overbooking model, followed by seat allocation (excluding overbooking) on the inflated capacity. This simplification, although not optimal, has been the practice since the birth of revenue management. In this paper, we solve the joint overbooking and seat allocation problem for fare families by invoking the Equivalence Charging Transformation of Subramanian et al. (Transp Sci 33(2):147–167, 1999) and the Marginal Revenue Transformation of Fiig et al. (J Revenue Pricing Manag 9(1):152–170, 2010). These transformations enable us to transform the high-dimensional dynamic programming (DP) model into an equivalent low-dimensional DP model that can readily be solved and implemented in existing RMS and inventory systems. We demonstrate that the DP model not only is able to incorporate factors that were previously ignored, such as the demand level, willingness to pay, and class-specific refund and cancellation rates, but importantly also provides significant revenue gains of 1 to 3 per cent at lower denied boarding levels compared with current industry practice.