Optimal Control of a Single-Product Assemble-to-Order System With Multiple Demand Classes and Backordering

We analyze the optimal control problem for a continuous-review assemble-to-order (ATO) system with multiple demand classes and backordering. The objective is to minimize total discounted cost over an infinite horizon. It remains an open question of the production control literature what optimal policy structure of such a system is. Using the concept of $L^{\natural}$-convexity and following the recent developments in the inventory theory literature, we characterize the structure of the optimal policy. Our approach appears to significantly simplify the structural analysis for similar problems.