Profit Estimation Error in the Newsvendor Model Under a Parametric Demand Distribution

We consider the newsvendor model in which uncertain demand is assumed to follow a probabilistic distribution with known functional form but unknown parameters. These parameters are estimated, unbiasedly and consistently, from data. We show that the classic maximized expected profit expression exhibits a systematic expected estimation error. We provide an asymptotic adjustment so that the estimate of maximized expected profit is unbiased. We also study expected estimation error in the optimal order quantity, which depends on the distribution: (1) if demand is exponentially or normally distributed, the order quantity has zero expected estimation error; (2) if demand is log-normally distributed, there is a nonzero expected estimation error in the order quantity that can be corrected. Numerical experiments, for light- and heavy-tailed distributions, confirm our theoretical results. This paper was accepted by Vishal Gaur, operations management.