Optimal Policies for an Assemble-to-Order N-System

We consider an assemble-to-order (ATO) N-system, in which there are two components and two products. One product requires only component-1, while the other product requires both components. The components are kept in stock and are procured from outside suppliers with fixed leadtimes. The final products are assembled only after customer orders are realized. Using a hybrid approach that combines sample-path analysis, linear programming, and the tower property of conditional expectation, we characterize the optimal component replenishment policy and common component allocation rule. To our knowledge, this is the first full characterization of the optimal policies for ATO systems with non-identical leadtimes. The optimality results require a certain symmetry in the cost parameters. In the absence of this symmetry, the optimal policies have no clear structure. For these latter systems, we develop heuristic policies and show their effectiveness. Finally, we present comparative statics of the optimal policy parameters and show that some commonly used heuristic policies can lead to significant optimality loss.