Title: VC Theory for Inventory Policies

We adopt the supervised learning approach and analyze the learning complexity of several well-known classes of inventory policies, including base-stock and (s, S) policies, by leveraging the celebrated Vapnik-Chervonenkis (VC) theory. Specifically, we apply the concepts of the Pseudo-dimension and Pseudo_gamma-dimension from VC theory to distinguish between inventory policies in terms of their generalizability, that is, the difference between an inventory policy’s performance on training data and its expected performance on unseen data. We prove that the generalization error of (s, S) policies is an order of magnitude higher than that of base-stock policies. This result conveys important managerial insights into the principle of "learning less is more" in inventory management: depending on the amount of data available, learning a base-stock policy with one parameter may be preferable to learning an (s, S) policy with two parameters. That being said, the "learning less is more" principle can be milder in other settings: the generalization error of {S^t} policies, which have non-stationary base-stock levels, is in fact of the same order as base-stock policies despite having linearly many parameters. This translates to the insight that not many samples are needed before it is preferable to learn the more complex policy.

This is joint work with Yaqi Xie (Booth second-year PhD student) and Will Ma (Columbia GSB).

Linwei Xin is an associate professor of operations management at the University of Chicago Booth School of Business. He specializes in inventory and supply chain management, where he designs cutting-edge models and algorithms that enable organizations to effectively balance supply and demand in various contexts with uncertainty. Xin's research using asymptotic analysis to study stochastic inventory theory is renowned and has been recognized with several prestigious INFORMS paper competition awards, including First Place in the George E. Nicholson Student Paper Competition in 2015 and the Applied Probability Society Best Publication Award in 2019. His research on implementing state-of-the-art multi-agent deep reinforcement learning techniques in Alibaba's inventory replenishment system was selected as a finalist for the INFORMS 2022 Daniel H. Wagner Prize, with over 65% algorithm-adoption rate within Alibaba's own supermarket brand Tmall Mart. His research on designing dispatching algorithms for robots in JD.com's intelligent warehouses was recognized as a finalist for the INFORMS 2021 Franz Edelman Award, with estimated annual savings in the hundreds of millions of dollars. Xin currently serves as an associate editor for Operations Research, Management Science, Manufacturing & Service Operations Management, and Naval Research Logistics.