Asymptotically Optimal Control for an Assemble-to-Order System with Capacitated Component Production and Fixed Transport Costs

Consider a production system which rapidly assembles many different products from inventories of modular components. Customer orders for each product arrive according to a renewal process with known rate and variance. Orders are lost if not filled within the product-specific target leadtime. Production facilities for each component are geographically distant from the assembly facility, and the transportation leadtime is deterministic. Each shipment of components incurs a fixed cost and a variable cost per unit. The system manager must initially invest in production capacity for each component, and then dynamically control component production-expediting, salvaging and shipping, and the sequencing of customer orders for assembly. The objective is to minimize expected discounted costs for lost sales, production and shipping. We prove that as the order arrival rate becomes large, a simple policy with independent control of each component is asymptotically optimal. The policy is parameterized by 5 numbers for each component. We provide expressions for these 5 parameters and approximations for expected discounted cost and the long run average rates of salvaging and expediting, based on Harrison and Taksars (1983) solution of a singular diffusion control problem. For a PC assemble-to-order system, we implement the asymptotically optimal policy and find that the diffusion approximations are accurate.