Optimal airline seat allocation with fare classes nested by origins and destinations

Previous research in the optimal allocation of airline seats has followed one of two themes: marginal seat revenue or mathematical programming. Both approaches capture important elements of the revenue management problem. The marginal seat revenue approach accounts for the ‘nesting’ of fare classes in computer reservation systems, but can only control seat inventory by bookings on legs. The mathematical programming approach will handle realistically large problems and will account for multiple origin-destination itineraries and side constraints, but it does not account for fare class nesting in the reservation systems. This paper combines both approaches by developing equations to find the optimal allocation of seats when fare classes are nested on an origin-destination itinerary and the inventory is not shared among origin-destinations. These results are applicable to seat allocation in certain reservations systems, point-of-sale control, and acceptance of groups over their entire itinerary. A special case of the analysis produces the optimal booking limits for leg-based seat allocation with nested fare classes.