A Stochastic Program Based Lower Bound for Assemble-to-Order Inventory Systems

In this paper we develop a multi-stage stochastic program that provides a lower bound on the long-run average inventory cost of general assemble-to-order (ATO) inventory systems. The stochastic program also motivates a replenishment policy for these systems. Our lower bound generalizes a previous result of Dogru et al. (2010) for systems with identical component replenishment lead times to those with general deterministic lead times. We prove that the cost of our replenishment policy reaches the lower bound in single-product ATO systems. We also prove that in such systems, our policy reduces to the optimal policy of Rosling (1989) and is thus an extension of the latter scheme to multi-product ATO systems.