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A retailer is endowed with a finite inventory of a nonperishable product. Demand for this product is driven by a price-sensitive Poisson process that depends on an unknown parameter that is a proxy for the market size. The retailer has a prior belief on the value of this parameter that he updates as time and available information (prices and sales) evolve. The retailer's objective is to maximize the discounted long-term average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the nonperishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the nonperishable product at any time and switch to a different menu of products. For both cases, we formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution, and suggest a simple and efficient approximated solution. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed policy.
Araman et al. (Thu,) studied this question.