Problem definition: This paper investigates a periodically reviewed distribution inventory system where a central warehouse replenishes multiple retailers facing uncertain demand. Only moment information about demand at each retailer is available, and unmet demand is backlogged. Methodology/results: We develop a robust multiperiod inventory model for the system based on the central limit theorem–based uncertainty set and transform the inventory planning problem into a transportation problem. We characterize two conditions under which a Monge sequence exists for the transportation problem and derive the optimal ordering decisions for the robust inventory model. Building on the robust optimal policy structure, we propose a priority-based inventory policy with look-up-to-k-period reservation. Under this policy, each retailer maintains both an order-up-to level and a reservation target based on the number of periods each retailer looks ahead. Managerial implications: Numerical experiments show that our policy outperforms the other benchmark policies from the literature. The advantage is particularly pronounced under robust performance measures and with real-world demand data that exhibit high variability, skewness, and tail risk. This highlights the strong ability of our policy to handle extreme cases in real-world data sets. Funding: L. Wang is supported by the Humanities and Social Science Research Project of Anhui Educational Committee Grant 2024AH052105. C. Yang is partially supported by the National Natural Science Foundation of China (NSFC) Grants NSFC-72531005, 72122012, and 72071126 and the Program for Innovative Research Team of Shanghai University of Finance and Economics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0502 .
Wang et al. (2026) studied this question.