Error Propagation in Asymptotic Analysis of the Data-Driven (s , S) Inventory Policy.

This article focuses on the asymptotic analysis of the data-driven \((s, S)\)-inventory policy in multiperiod stochastic inventory control, where ordering decisions are based solely on historical demand data without knowledge of the demand distribution. The authors address the key challenge of backward error propagation arising from recursively estimated empirical cost-to-go functions, which leads to complex dependencies and multi-sample U-processes rather than independent and identically distributed sums. They develop novel multi-sample U-process theory to fully characterize the influence functions of the estimated reorder points and order-up-to levels, establishing joint asymptotic normality and providing consistent estimators for the optimal expected cost and its variance. The work extends to settings with dependent demand by proposing a consistent sample average approximation (SAA) estimator for the optimal base-stock policy and compares its efficiency with the empirical dynamic programming (EDP) estimator under independence assumptions. Numerical experiments validate the accuracy of confidence intervals derived from their asymptotic results and demonstrate the practical implications for sample size determination and hypothesis testing in inventory management.