Contextual Data-Integrated Newsvendor Solution with Operational Data Analytics (ODA)

We study the data-integrated newsvendor problem in which the random demand depends on a set of covariates. Observing from the solutions analyzed in the existing studies, we identify the equivariant class of operational statistics (i.e., the mapping from the demand and covariate data to the inventory decision) to develop the operational data analytics (ODA) framework for the contextual newsvendor problem. The equivariant property is intuitively appealing, and it is justified by the fact that, regardless of the sample size, no other decision rule can uniformly dominate the optimal operational statistic within the equivariant class. We also demonstrate that nonequivariant solutions can produce unstable empirical performance with limited samples, where equivariant solutions exhibit robustness. When the distribution family of the demand is known but the coefficients of the demand function are unknown, we can directly validate the decision performance of operational statistics within the equivariant class, and derive the uniformly optimal solution. When the distribution family of the demand is unknown, we formulate the data-integration model as a subclass of equivariant operational statistics obtained through adaptively boosting some candidate solution. For decision validation, we project the validation data to the demand for the covariates of interests, and the projection is constructed by utilizing the structure of the candidate solution. We demonstrate the superior small-sample performance of adaptive boosting, and establish the consistency of the boosted operational statistics. Our ODA formulation, building on the inherent characteristics of the contextual newsvendor problem, highlights the importance of understanding structural properties in data-integrated decision making.