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An Optimal Control Problem of Dynamic Pricing

An optimal control problem of dynamic pricing is studied. In the model, prices are chosen to sell multiple products to multiple customer classes over time. The products share a number of scarce resources. All parameters, such as the arrival rates of customers, their purchasing probabilities, their cancellation rates, and the cancellation refunds, are allowed to be time dependent. A solution method for the problem is developed, and is tested with some numerical examples. ∗Supported, in part, by the National Science Foundation under grant DMI-9875400.