An Online Mirror Descent Learning Algorithm for Multiproduct Inventory Systems

We study a canonical inventory control problem: a multiproduct, periodic-review, 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.

Funding: C. Shi acknowledges support from Amazon [Amazon Research Award] and the University of Miami [Provost Research Award]. C. Yang acknowledges support from the National Natural Science Foundation of China [Grants 72531005, 72122012, and 72071126] and the Program for Innovative Research Team at Shanghai University of Finance and Economics.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0982.