A Robust Data-Driven Approach for the Newsvendor Problem with Nonparametric Information

Problem definition: For the standard newsvendor problem with an unknown demand distribution, we develop an approach that uses data input to construct a distribution ambiguity set with the nonparametric characteristics of the true distribution, and we use it to make robust decisions. Academic/practical relevance: Empirical approach relies on historical data to estimate the true distribution. Although the estimated distribution converges to the true distribution, its performance with limited data is not guaranteed. Our approach generates robust decisions from a distribution ambiguity set that is constructed by data-driven estimators for nonparametric characteristics and includes the true distribution with the desired probability. It fits situations where data size is small. Methodology: We apply a robust optimization approach with nonparametric information. Results: Under a fixed method to partition the support of the demand, we construct a distribution ambiguity set, build a protection curve as a proxy for the worst-case distribution in the set, and use it to obtain a robust stocking quantity in closed form. Implementation-wise, we develop an adaptive method to continuously feed data to update partitions with a prespecified confidence level in their unbiasedness and adjust the protection curve to obtain robust decisions. We theoretically and experimentally compare the proposed approach with existing approaches. Managerial implications: Our nonparametric approach under adaptive partitioning guarantees that the realized average profit exceeds the worst-case expected profit with a high probability. Using real data sets from Kaggle.com, it can outperform existing approaches in yielding profit rate and stabilizing the generated profits, and the advantages are more prominent as the service ratio decreases. Nonparametric information is more valuable than parametric information in profit generation provided that the service requirement is not too high. Moreover, our proposed approach provides a means of combining nonparametric and parametric information in a robust optimization framework.