A data-driven distributionally robust newsvendor model with a Wasserstein ambiguity set

Abstract

In this paper, we derive a closed-form solution and an explicit characterization of the worst-case distribution for the data-driven distributionally robust newsvendor model with an ambiguity set based on the Wasserstein distance of order $p\in [1,\infty ).$ We also consider the risk-averse decision with the Conditional Value-at-Risk (CVaR) objective. For the risk-averse model, we derive a closed-form solution for the p = 1 case, and propose a tractable formulation to obtain an optimal order quantity for the p > 1 case. We conduct numerical experiments to compare out-of-sample performance and convergence results of the proposed solutions against the solutions with other distributionally robust models. We also analyze the risk-averse solutions compared to the risk-neutral solutions.

Keywords:

• Newsvendor Model
• distributionally robust optimization
• Wasserstein distance

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT and Future Planning (MSIT) [NRF-2019R1A2C2084616].