Computing Optimal Policies for the Dynamic Newsvendor Problem with Censored Demand

We address the problem of computing optimal policies for a finite-horizon newsvendor model with censored demand and perishable inventory. By combining an earlyperiod optimization based grid search with easily computable late-period bounds, we are able to handle a broad range of demand distributions and prior specifications. The grid-search is performed on a discretization of the demand-decision space and is demonstrated to work well on five interesting models: the exponential-gamma model, the one parameter Weibull-gamma model, the two parameter Weibull-gamma model, the normal model, and an infinite dimensional beta process model. Comparison with the exact answers, available for the exponential-gamma model, shows high accuracy of this discretized approximation scheme. We discuss, with a numerical illustration, that even for reasonable demand models that are not of the form of a one-parameter Weibull-gamma model, being forced to work with the latter model leads to stocking decisions that are inconsistent with the newsvendor’s true unknown demand distribution – a situation that can be avoided with our proposed algorithm. We conclude by showing that an application of the grid-search in the early periods leads to a substantial improvement in bounds obtained from substituting the end-period dynamic updates by easily implemented variants of the original newsvendor problem. While the no-update variant, which leads to an upper bound on the cost function, has been previously studied in the literature, our proposed lower bound through parameter collapsing appears a novel addition to inventory literature.