calculated either with network optimization tools or leg-based heuristics such as EMSR approaches. Talluri and van Ryzin (1999b) have done much work on network bid price control and identify the conditions under which this approach provides revenue optimality, while de Boer et al. (2002) compare the performance of deterministic and stochastic network formulations for O-D control. Until recently, relatively few airlines had implemented network optimization models for dynamic calculation of displacement costs and/or bid prices for O-D control. Because most reservations systems and, in turn, third-generation RM systems were developed on the basis of leg/fare class data, most airlines did not have access to the detailed historical ODIF booking data required by network optimization models. Use of large-scale network optimization models also raised technical and computational issues related to the solution times and frequency of reoptimization. However, with the development of airline databases designed to capture detailed ODIF historical data, along with advances in both solution algorithms and computational speeds, network revenue management has been implemented by over a dozen airlines in different parts of the world. The benefits of leg-based revenue management and incremental benefit of O-D controls over legbased fare class controls have been estimated by several researchers through simulation. For example, Williamson (1992) developed a network revenue management simulation approach that allowed different schemes for optimization and control of seat inventories to be tested. An even more realistic approach to simulating the impacts of different RM schemes in a full-scale, competitive airline network environment is that of the passenger origin-destination simulator (PODS). Developed originally by researchers at Boeing (Hopperstad 1997), PODShas been enhanced to realistically simulate large networks in which competing airlines generate RM forecasts and set seat inventory controls based on “historical” (i.e., previously simulated) data. At the same time, the simulated passengers in PODSchoose among alternative airlines, fares, restrictions, schedules, and seat inventory availability as established by each airline’s own RM system. PODShas been used to simulate the competitive impacts of RM (Belobaba and Wilson 1997), as well as the benefits of improved forecasting models and the impacts of RM on airline alliances.The simulations cited here along with others performed by academics and airlines have provided consistent estimates of the potential for revenue gains of 1%–2% from advanced network revenue management methods, above and beyond the 4%–6% gains realized from conventional leg-based fare class control.The potential to realize even 1% in additional revenue through network RM is substantial enough that many of the world’s largest airlines have implemented or are in the process of developing their O-D control capabilities. For a large airline with annual revenues of $5 to $10 billion or more, successful implementation of a network RM system can lead to total revenue increases of $50 to $100 million per year.3.5. Future Challenges Development of OR mod els for the “next generation”of airline revenue management is currently an extremely popular topic among academics and practitioners alike. The most obvious next steps in the further enhancement of airline revenue managementsystems is to integrate the pricing and seat inventory control decisions currently being made with different decision support tools and, at many airlines, in different parts of the organization. Clearly, the ability to relax the traditional RM assumption that fare structures are given and fixed has the potential to further increase the revenue gains of RM. Joint pricing and inventory optimization requires the incorporation of passenger choice and demand elasticity models, and promising OR work in this direction has been published by Weatherford (1997), Gallego and van Ryzin (1997), and Cote et al. (2003), among others. In a recent Ph.D. dissertation de Boer (2003) examines this problem in a network context and presents a variety of other modeling advances and insights.Looking ahead, it is apparent that information about the utilization of seat inventories and the response of passenger demand to different pricing strategies can and should provide useful feedback to fleet assignment and even scheduling of airline flight departure times. The integration of airline pricing and seat inventory decisions with those of the Transportation Science/Vol. 37, No. 4, November 2003 3