Optimal Control Assemble-to-Order Systems with Delay Guarantees

Consider a high-volume assemble-to-order system with multiple products and components in which component production can be expedited at some additional cost. The objective is to maximize expected discounted profit subject to assembling orders within a guaranteed maximum leadtime. We show that optimal product pricing and component production balances customer demand with component supply, meaning the system is in “heavy traffic”. In this regime, the system exhibits a reduction in problem dimensionality. In particular, the limiting diffusion approximation has dimension equal to the number of components (rather than the number of components PLUS the number of products). We use this insight to derive an easily implementable dynamic control policy for sequencing product orders for assembly and expediting components that is optimal in heavy traffic. We finish by recommending a non-basestock inventory policy which accounts for dependencies amongst components and is based on the solution to a singular diffusion control problem.