Survey of Data-driven Newsvendor: Unified Analysis and Spectrum of Achievable Regrets

In the newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high versus too low. In the data-driven version, the distribution is unknown, and one must work with samples from the distribution. The data-driven newsvendor problem has been studied under many variants: additive versus multiplicative regret, high-probability versus expectation bounds, and different distribution classes. This paper studies all combinations of these variants, filling many gaps in the literature and simplifying many proofs. In particular, we provide a unified analysis based on a notion of clustered distributions, which in conjunction with our new lower bounds, shows that the entire spectrum of regrets between $1/\sqrt{n}$ and $1/n$ is possible. Simulations on commonly used distributions demonstrate that our notion is the “correct” predictor of empirical regret across varying data sizes.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1348.