Deterministic mathematical programming models that capture network effects play a predominant role in the theory and practice of airline revenue management. These models do not address important issues like demand uncertainty, nesting, and the dynamic nature of the booking process. Alternatively, the network problem can be broken down into leg-based problems for which there are satisfactory solution methods, but this approach cannot be expected to capture all relevant network aspects. In this paper, we propose a new algorithm that addresses these issues. Starting with any nested bookinglimit policy, we combine a stochastic gradient algorithm and approximate dynamic programming ideas to improve the initial booking limits. Preliminary simulation experiments suggest that the proposed algorithm can lead to practically significant revenue enhancements.

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