We study the problem of managing inventory in an assemble-to-order environment under service level requirements. The main feature of the system is that multiple components are produced and kept in inventories to be assembled to final products according to customer orders. Customer service level is measured by the fill rate, which is the proportion of orders filled within a target delivery lead-time. The question we address is how to set the base-stock levels for each component to minimize the total inventory holding cost of the system while satisfying a high fill rate requirement.

The difficulty with the problem is that generally there is no analytical expression for the fill rate and even checking the feasibility of an inventory policy typically involves (rare event) simulation, a hard problem. We derive closed form solutions to the problem based on an approximate formulation, where the original fill rate requirement is replaced by a more stringent, but asymptotically tight surrogate. To illustrate the effectiveness of our closed form solution, we compare its performance with that of the true optimal one obtained from exclusive search.