时 间：2021年12月13日（周一）11：00-12：00
地 点：腾讯会议：966 255 549
题 目：Asymptotic Analysis of Data-Driven Multi-Stage Inventory Policies
报告人：叶志盛 新加坡国立大学副教授
主持人：唐炎林 研究员
主 办：统计学院
摘 要：
We study periodic review stochastic inventory control in the data-driven setting, in which the retailer makes ordering decisions based only on historical demand observations without any knowledge of the probability distribution of the demand. Since an (s, S)-policy is optimal when the demand distribution is known, we investigate the statistical properties of the data-driven (s, S)-policy obtained by recursively computing the empirical cost-to-go functions (called DP-based estimator). This estimator is inherently challenging to analyze because the recursion induces propagation of the estimation error backward in time. In this work, we establish the asymptotic properties of this data-driven policy by fully accounting for the error propagation. First, we rigorously show the consistency of the estimated parameters by filling in some gaps (due to unaccounted error propagation) in the existing studies. On the other hand, empirical process theory cannot be directly applied to show asymptotic normality since the empirical cost-to-go functions for the estimated parameters are not i.i.d. sums, again due to the error propagation. Our main methodological innovation comes from an asymptotic representation for multi-sample U-processes in terms of i.i.d. sums. This representation enables us to apply empirical process theory to derive the influence functions of the estimated parameters and establish joint asymptotic normality. Based on these results, we also propose an entirely data-driven estimator of the optimal expected cost and we derive its asymptotic distribution. Beyond deriving the asymptotic distribution of our DP-based estimators, we further investigate the semiparametric efficiency of the proposed estimators. We show that the asymptotic variances of DP-based estimators match the statistical lower bound and so the proposed estimators are asymptotically efficient. The extensions to dependent demand are also investigated in this work, where we propose an SAA type estimator to estimate the optimal expected cost under base stock policies. We demonstrate some useful applications of our asymptotic results, including sample size determination, as well as interval estimation and hypothesis testing on vital parameters of the inventory problem. The results from our numerical simulations conform to our theoretical analysis.
报告人简介：
叶志盛博士本科毕业于清华大学材料科学与工程系，博士就读于新加坡国大工业与系统工程系。现在为新加坡国大工业系统工程与管理系副教授。他的主要研究方向包括剩余寿命预测，可靠性建模，及数据驱动的运营决策。