Dynamic Pricing for Nonperishable Products with Demand Learning

A retailer is endowed with a finite inventory of a non-perishable product. Demand for this product is driven by a price-sensitive Poisson process that depends on an unknown parameter, θ; a proxy for the market size. If θ is high then the retailer can take advantage of a large market charging premium prices, but if θ is small then price markdowns can be applied to encourage sales. The retailer has a prior belief on the value of θ which he updates as time and available information (prices and sales) evolve. We also assume that the retailer faces an opportunity cost when selling this non-perishable product. This opportunity cost is given by the long-term average discounted profits that the retailer can make if he switches and starts selling a different assortment of products. 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 non-perishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the non-perishable product at any time to switch to a different menu of products. In both cases, the retailer’s pricing policy trades-off immediate revenues and future profits based on active demand learning. We formulate the retailer’s problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution which we use to propose a simple approximated solution. This solution combines a pricing policy and a stopping rule (if stopping is an option) depending on the inventory position and the retailer’s belief about the value of θ. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed solution.