Robust Inventory Management: A Cycle-Based Approach
33 Pages Posted: 10 Jun 2020 Last revised: 15 Feb 2022
Date Written: February 15, 2022
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 intertemporal demand is correlated, and the information about the demand distribution is limited. Computationally efficient policies for the robust inventory model with fixed ordering costs and the other aforementioned realistic features are highly relevant for practice; however, developing such policies has remained challenging. We propose a robust cycle-based policy that manages inventory by dividing the planning horizon into non-overlapping 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. We also propose a one-cycle look-ahead heuristic implementation for our policy in order to handle inventory problems with longer planning horizons. We show that the decisions in our robust cycle-based policy can be computed by solving only linear programs (LPs) in 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 for computing the policy decisions grows exponentially in the length of the planning horizon. On the other hand, the one-cycle look-ahead heuristic can be applied for both the backlogging and lost-sales models with any lead time, and the number of LPs required grows quadratically in the length of the planning horizon. Hence, this heuristic is computationally efficient even for large problem instances. Using extensive computational experiments, we show that both a rolling-cycle implementation of our policy and the one-cycle look-ahead heuristic outperform multiple strong benchmark policies. Our robust cycle-based policy is conceptually simple and can accommodate multiple realistic features in inventory management problems. This policy, particularly its one-cycle look-ahead heuristic implementation, provides a very effective approach to robust inventory management, especially in the lost-sales setting.
Keywords: inventory management, robust optimization, fixed ordering cost, lost sales
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