Dynamic Learning, Pricing, and Ordering by a Censored Newsvendor

We address the problem of determining optimal ordering and pricing policies in a finite-horizon newsvendor model with unobservable lost sales. The demand distribution is price-dependent and involves unknown parameters. We consider both the cases of perishable and non-perishable inventory. A very general class of demand functions is studied in this paper. We derive the optimal ordering and pricing policies as unique functions of the stocking factor (which is a linear transformation of the safety factor). An important expression is obtained for the marginal expected value of information. As a consequence, we show when lost sales are unobservable, with perishable inventory the optimal stocking factor is always at least as large as the one given by the single-period model; whereas, if inventory is non-perishable, this result holds only under a strong condition. This expression also helps to explain why the optimal stocking factor of a period may not increase with the length of the problem. We compare this behavior with that of a full information model. We further examine the implications of the results to the special cases when demand uncertainty is described by additive and multiplicative models. For the additive case, we show that if demand is censored, the optimal policy is to order more as well as charge higher retail prices when compared to the policies in the single-period model and the full information model. We also compare optimal and myopic policies for the additive and multiplicative models.