Learning in Lost-Sales Inventory Systems with Stochastic Lead Times and Random Supplies

Supply uncertainty, characterized by stochastic lead times and random supply quantities, has attracted increasing attention from academia, industries, and governments, particularly in the aftermath of the COVID-19 pandemic. In this paper, we consider the problem of managing lost-sales inventory systems with general supply uncertainty: stochastic lead times and random supplies. Unlike the previous studies, we assume the decision maker has no prior information on the stochastic demand and supply. We propose the first provably effective learning algorithm for inventory management problems with censored demand and supply data under general supply uncertainty. Then, we establish a cumulative regret of $\tilde{\mathcal{O}}(L+\text{poly}(\overline{L})·\sqrt{T})$ for this learning algorithm compared with the best constant-order policy, where $\overline{L}$ is the upper bound of the random part, and L is the deterministic part of the stochastic lead times. We also conduct numerical experiments to demonstrate the effectiveness of our algorithm. Our approach lies in developing a new framework for transformed convexity. Furthermore, we address the unique challenges of our problem through new techniques, for example, estimating the long-run cost by establishing coupling and concentration results utilizing the system structures. These techniques are also of independent interest. Beyond our problem, our framework provides broad implications for other operations management (OM) problems exhibiting transformed convexity.

This paper was accepted by J. George Shanthikumar, data science.

Funding: J. Lyu and Y. Zhou are supported by the National Natural Science Foundation of China [Grant 52494974]. S. Yuan is supported by the National Natural Science Foundation of China [Grants 72588101, 72425008].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04203.