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

This paper examines a two-tier assemble-to-order system. Customer orders for various products must be filled within the product-specific target lead time, or become lost sales. A product can be assembled instantaneously if its required components are in stock at the assembly facility. The production facility for each component is geographically distant from the assembly facility, and the transportation lead time is deterministic. Each shipment of components incurs a fixed cost and a variable cost per unit. The system manager must initially commit to the production capacity for each component. Then, in response to customer orders, he must dynamically manage production (expediting and salvaging) and shipping for each component, and the sequence of customer orders for assembly (how scarce components are allocated to outstanding orders). The objective is to minimize expected discounted costs for lost sales, production, and shipping. This discounted formulation accounts for financial inventory holding costs but not physical inventory holding costs. The main result is that as the order arrival rate for each product becomes large and the discount rate becomes small, a simple threshold policy with independent control of each component is asymptotically optimal. The policy is parameterized by five numbers for each component. Expressions for these parameters, the expected discounted cost, and the long-run average rates of salvaging and expediting are obtained by solving an approximating Brownian control problem. In a numerical example from the computer industry, the Brownian approximation is remarkably accurate.