On the price of demand censoring in the newsvendor problem

We consider a repeated newsvendor problem where the decision-maker (DM) does not have access to the underlying distribution of discrete demand. We analyze three informational settings: i.) the DM observes realized demand in each period; ii.) the DM only observes realized sales ; and iii.) the DM observes realized sales but also a lost sales indicator that records whether demand was censored or not. We provide a characterization of the best achievable performance in each of these cases, where we measure performance in terms of regret: the worst case difference between the cumulative costs of any policy and the optimal cumulative costs with knowledge of the demand distribution. In particular, we show that for both the first and the third settings, the best achievable performance is bounded (i.e., does not scale with the number of periods) while in the second setting, it grows logarithmically with the number of periods. The results enable one to quantify the performance degradation stemming from demand censoring and identifies minimal information through the lost sales indicator that mitigates some of this degradation.