Mathematical programming for network revenue management revisited

Mathematical programming models for airline seat inventory control provide booking limits and bid-prices for all itineraries and fare classes. E.L. Williamson [Airline network seat inventory control: methodologies and revenue impacts, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992] finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics. We argue that this phenomenon is due to a booking process that includes nesting of the fare classes, which is ignored in the modeling phase. The differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case. Our study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.