On Implications of Demand Censoring in the Newsvendor Problem

We consider a repeated newsvendor problem in which the decision-maker (DM) does not have access to the underlying demand distribution. The goal of the paper is to characterize the implications of demand censoring on performance. To that end, we compare the benchmark setting in which the DM has access to demand observations to a setting in which the DM may only rely on sales data. We measure performance in terms of regret: the difference between the cumulative costs of a policy and the optimal cumulative costs with knowledge of the demand distribution. Through upper and lower bounds, we characterize the optimal magnitude of the worst case regret for the two settings, enabling one to isolate the implications of demand censoring. In particular, the results imply that the exploration-exploitation trade-off introduced by demand censoring is fundamentally different in the continuous and discrete demand cases, and that active exploration plays a much stronger role in the latter case. We further establish that in the discrete demand case, the need for active exploration almost disappears as soon as a lost sales indicator (that records whether demand was censored or not) becomes available, in addition to the censored demand samples