We develop a Markov decision process formulation of a dynamic pricing problem for multiple substitutable flights between the same origin and destination, taking into account customer choice among the flights. The model is rendered computationally intractable for exact solution by its multidimensional state and action spaces, so we develop and analyze various bounds and heuristics. We first describe three related models, each based on some form of pooling, and introduce heuristics suggested by these models. We also develop separable bounds for the value function which are used to construct value- and policy-approximation heuristics. Extensive numerical experiments show the value- and policy-approximation approaches to work well across a wide range of problem parameters, and to outperform the pooling-based heuristics in most cases. The methods are applicable even for large problems, and are potentially useful for practical applications
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