Optimal and heuristic policies for assemble-to-order systems with different review periods

We study an assemble-to-order (ATO) system with a single end product assembled from two components. The inventory levels of the components are reviewed periodically. One component is expensive and has a long lead time and short review period, whereas the other component is relatively cheap with a shorter lead time and longer review period. The lead times are deterministic and review periods are determined exogenously. Stochastic customer demand occurs for the end product only and unsatisfied customer demands are backordered. The system incurs holding costs for component inventories and penalty costs for backorders. Assuming an infinite planning horizon, our objective is to identify the optimal component ordering policy to minimize the long-run average cost. Under specific demand distributions we identify the properties of the optimal component ordering policy and observe that the optimal policy has a complex state-dependent structure. Motivated by the complexity of the optimal policy, we introduce a heuristic component ordering policy for more general demand distributions. Given that the heuristic performs well, we use it to measure the effects of various system parameters on the total cost.