An Online Mirror Descent Learning Algorithm for Multiproduct Inventory Systems

• 成果类型: Article; Early Access
• 署名作者: Guo, Sichen; Shi, Cong; Yang, Chaolin; Zacharias, Christos
• 署名单位: University of Miami; Shanghai University of Finance & Economics; University of Miami
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2024.0982
• 发表日期: 2026
• 关键词: lost-sales; policies

摘要

We study a canonical inventory control problem: a multiproduct, periodicreview, lost-sales inventory system with a warehouse-capacity constraint. We study this well-researched problem under the lens of demand learning from censored data. Unlike the traditional literature, we do not assume that demand distributions are known a priori. Instead, the decision maker only has access to observed sales data, whereas the lost-sales quantity remains unobserved. Existing online learning algorithms bear limitations in providing good-quality solutions to inventory systems offering a large variety of products. We employ and innovate mirror descent with cyclic update techniques to address the challenge of high dimensionality in product menus. We prove theoretically that our algorithm's regret bound exhibits a logarithmic dependence on the number of products. This constitutes a significant improvement compared with the square-root regret bound established in the existing literature. Using empirical data, we implemented our methods to assess their practical merit and expose additional managerial insights. Our numerical study confirms that our methodology indeed produces inventory policies superior to existing state-of-the-art solutions, especially when managing a large menu of products. Drawing from our numerical observations and theory-informed insights, we provide clear guidelines for practical implementation along with fine-tuning recommendations.