Perishable Inventory Systems: Convexity Results for Base-Stock Policies and Learning Algorithms Under Gel loured Demand

作     者：Zhang, Huanan Chao, Xiuli Shi, Cong 

作者机构：Penn State Univ Harold & Inge Marcus Dept Ind & Mfg Engn University Pk PA 16802 USA Univ Michigan Ind & Operat Engn Ann Arbor MI 48105 USA 

出 版 物：《OPERATIONS RESEARCH》 (Oper Res)

年 卷 期：2018年第66卷第5期

页      面：1276-1286页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation (NSF) [CMMI-1362619, CMMI-1634505, CMMI-1634676] NSF [CMMI-1362619, CMMI-1634505, CMMI-1634676] 

主　　题：inventory perishable products base-stock policy censored demand learning algorithms 

摘      要：We develop the first nonparametric learning algorithm for periodic-review perishable inventory systems. In contrast to the classical perishable inventory literature, we assume that the firm does not know the demand distribution a priori and makes replenishment decisions in each period based only on the past sales (censored demand) data. It is well known that even with complete information about the demand distribution a priori, the optimal policy for this problem does not possess a simple structure. Motivated by the studies in the literature showing that base-stock policies perform near optimal in these systems, we focus on finding the best base-stock policy. We first establish a convexity result, showing that the total holding, lost sales and outdating cost is convex in the base-stock level. Then, we develop a nonparametric learning algorithm that generates a sequence of order-up-to levels whose running average cost converges to the cost of the optimal base-stock policy. We establish a square-root convergence rate of the proposed algorithm, which is the best possible. Our algorithm and analyses require a novel method for computing a valid cycle subgradient and the construction of a bridging problem, which significantly departs from previous studies.