Abstract: We consider the Newsvendor model where 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 lognormally distributed, there is a non-zero expected estimation error in the order quantity that can be corrected. Numerical experiments, for light and heavy-tailed distributions, confirm our theoretical results. Purely data-driven extensions are also provided.
Bio: Michael R. Wagner is an Associate Professor of Operations Management and a Neal and Jan Dempsey Endowed Faculty Fellow at the Foster School of Business, University of Washington. He is also an Amazon Scholar, working part-time on improving fast last-mile deliveries at Amazon. He received BS degrees in electrical engineering & computer science (EECS) and mathematics (’00), an M.Eng. degree in EECS (’01), and a Ph.D. degree in operations research (’06), all from MIT. His research interests include crowdsourcing, robust optimization, machine learning, and reinforcement learning.