Robust Inventory Management: A Cycle-Based Approach

Problem definition: We study the robust formulation of an inventory model with positive fixed ordering costs, where the unfulfilled demand is either backlogged or lost, the lead time is allowed to be positive, the demand is potentially intertemporally correlated, and the information about the demand distribution is limited. Methodology/results: We propose a robust cycle-based policy that manages inventory by dividing the planning horizon into nonoverlapping inventory cycles, where an order is placed at the beginning of each cycle. Our policy selects the lengths and order quantities for all inventory cycles to minimize the worst-case total cost incurred over the planning horizon. When the uncertain demand belongs to a general polyhedral uncertainty set, the decisions in our policy can be computed by solving linear programs (LPs) for the backlogging model with any lead time and the lost-sales model with zero lead time; however, the number of LPs that need to be solved grows exponentially in the length of the planning horizon. In the special case where the uncertain demand belongs to a box uncertainty set, the decisions in our policy can be computed using a dynamic programming (DP) recursion whose complexity grows polynomially in the length of the planning horizon. We also propose a one-cycle look-ahead heuristic to handle large problem instances with a general polyhedral uncertainty set. This heuristic can be applied for both the backlogging and lost-sales models with any lead time, and it only requires solving LPs whose number grows quadratically in the length of the planning horizon. Results from extensive computational experiments clearly show that both a rolling-cycle implementation of our policy and the one-cycle look-ahead heuristic have very strong empirical performance. Managerial implications: Our robust cycle-based policy and the one-cycle look-ahead heuristic are conceptually simple and can accommodate multiple realistic features in inventory management problems. They provide a very effective approach to robust inventory management, especially in the lost-sales setting. Funding: Y. Chen was supported by a start-up grant from Nanyang Technological University. C. Wang was supported by the National Natural Science Foundation of China [Grant 71802115] and the Tsinghua University Initiative Scientific Research Program. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1168 .