Robust Allocation Policies for Distribution Inventory Systems with Replenishment

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 .