Data-Driven Newsvendor with Profit Risk Consideration

Abstract

We study a risk-averse newsvendor problem where demand distribution is unknown. The focal product is new, and only the historical demand information of related products is available. The newsvendor aims to maximize its expected profit subject to a profit risk constraint. We develop a model with a value-at-risk constraint and propose a data-driven approximation to the theoretical risk-averse newsvendor model. Specifically, based on the covariate information, we use machine learning methods to weight the similarity between the new product and the previous ones. The sample-dependent weights are then embedded to approximate the expected profit and the profit risk constraint. Afterward, we show that the data-driven risk-averse newsvendor solution entails a closed-form quantile structure and can be efficiently computed. Finally, we prove that this data-driven solution is asymptotically optimal. Experiments based on real data and synthetic data demonstrate the effectiveness of our approach. We find that under data-driven decision making, contrary to that in the theoretical risk-averse newsvendor model, the average realized profit may benefit from a stronger risk aversion. It further reveals that under data-driven decision making, even a risk-neutral newsvendor can benefit from incorporating a risk constraint, which plays a regularizing role in mitigating issues of data-driven decision making such as sampling error and model misspecification. The above effects however diminish as the size of the training data set increases, as the asymptotic optimality result implies.