数学科学学院学术报告[2024] 108号

(高水平大学建设系列报告988号)

报告题目: Optimal Policies and Balance Equations in Inventory Control

报告人： 胡奇英  教授（ 复旦大学）

报告时间：2024年11月1日（周五）上午10:00-11:30

报告地点： 汇星楼702会议室

报告内容：In practical inventory control problems, the surplus cost function is often non-convex. However, certain convexity assumptions are typically required in the literature to demonstrate optimal (s,S) policies. This paper explores the structure of optimal policies in a periodic review inventory control system with fixed setup costs for the finite horizon problem, as well as the discounted and average criteria in infinite horizons. It is demonstrated that, for each criterion, there exists an optimal piecewise (s1,s2,S) policy without requiring convexity: The inventory level set is divided into several intervals, and within each interval there exists s1 ≤ s2 ≤ S such that it is optimal to order up to S if x ≤ s1, order nothing if x > s2, and either order up to S or order nothing otherwise. Furthermore, this policy can be simplified to have better structures under additional assumptions on the surplus cost function. When the surplus cost function is d increasing on the right-hand side (or decreasing on the left-hand side) of its global minimum point for some d > 0, the optimal policy has only one piece (or s1 = s2). Interestingly, the quasi-convexity of the surplus cost function is separated into two parts with different roles. Finally, two equations representing balances among the fixed setup cost, holding cost, and shortage cost under optimality are provided. Our approach can address both backlog and lost-sales cases, as well as all three criteria.

报告人简历：胡奇英，复旦大学管理学院教授。先后从事现代供应链、商业模式、商务人工智能、动态决策与控制、金融工程、道德经等领域的研究与教学工作；先后承担国家自然科学基金项目14项，在DCDS, ECRA, EJOR, IJPE, JMAA, MSOM, NRL, POM，管理科学学报等国内外学术期刊上发表论文200余篇；在Springer出版社、科学出版社等出版著作19部。享受国务院政府特殊津贴，曾获霍英东高校青年教师壹等奖、省部级科技进步奖2项。兼任中国运筹学会常务理事、金融工程与风险管理分会理事长。

欢迎师生参加！

邀请人：孙晓丽

                                            数学科学学院

                                       2024年月10月28日