Customers know best: Pricing policies for products with heterogeneous quality

This article studies the pricing problem of a seller given an initial inventory of products with heterogeneous quality, facing uncertain customer arrivals over a finite selling season. We consider various regimes depending on whether the seller inspects the inventory to assess the quality levels of the products, and whether customers examine the inventory themselves and pick their specific item of choice among the available products. We formulate the problem under each regime as a stochastic optimization model which maximizes the seller's expected profits, capturing the salient problem features such as stochastic customer arrivals, customers' choice behavior, and uncertain product qualities. As obtaining closed-form solutions or structural properties for the optimal prices is quite difficult, we explore the full information solution to the problem as an upper bound, as well as solution approaches that approximate some key problem characteristics. Finally, we substantiate our results through an extensive numerical study, focusing on the performance of the proposed pricing policies and approximations.