Feature-based profitability evaluation for newsvendor-type products

Abstract

We study how firms selling newsvendor-type products determine order quantities to maximize the probability of achieving a target profit, referred to as profitability. Unlike existing literature, we assume decision-makers have access to historical demand data and related feature data. To integrate feature information into the optimization model, we propose a weighted sample average approximation method that resolves the inherent inconsistency of traditional SAA approaches. This feature-based model is reformulated as a mixed integer programming for efficient solution. We further prove the consistency and asymptotic optimality of the ordering policy derived from our method. For high-dimensional feature settings with irrelevant features, we develop a decision-based feature selection method within the nonparametric optimization framework. Additionally, we introduce a nonparametric bootstrap method to estimate conservative profitability, mitigating overestimation risks caused by sampling errors. Numerical experiments using both synthetic and real data are conducted to demonstrate the effectiveness of our proposed methods. Notably, as the sample size increases, our feature selection method consistently identifies all relevant features, meaning the probability of correctly selecting the model approaches 1. Furthermore, in real-data experiments, our feature-based method improves profitability by more than 50% compared to the SAA method.