Error Propagation in Asymptotic Analysis of the Data-Driven (<i>s</i>, <i>S</i>) Inventory Policy

Estimating Optimal Inventory Policies: Moving Beyond SAA and Empirical Process Theory In “Error Propagation in Asymptotic Analysis of the Data-Driven (s,S) Inventory Policy,” Zhang, Ye, and Haskell dive into the class multiperiod stochastic inventory control in a data-driven setting. They investigate the statistical properties of the data-driven $(s, S)$-policy obtained by recursively computing the empirical cost-to-go functions. In this setting, the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums because of the error propagation. They establish a novel asymptotic representation for multi-sample $U$-processes in terms of i.i.d. sums. This representation enables them to apply empirical process theory to derive the influence functions of the estimated parameters and to establish joint asymptotic normality. Based on these results, they also propose an entirely data-driven estimator of the optimal expected cost and derive its asymptotic distribution. They demonstrate some useful applications of their asymptotic results, including sample size determination and interval estimation.