We consider revenue management for a collection of parallel flights between a common origin and destination with dynamic customer choice among the flights. We cast the problem as an extension to the multi-period, single-flight "block demand" revenue management model. The formulation is computationally intractable, because of its multidimensional state space and the fact that the airline's inventory controls affect the joint demand distributions. We obtain computable bounds for the value function of our model, and propose simulation-based heuristics for solving the stochastic optimization problem.
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