- This article investigates an inventory control problem in a singlelevel multi-component assembly system. In this system, a product with random demand is assembled-to-order from a number of components. The assembler holds inventory at the component levels. We consider a periodic review inventory control system that uses an order-up-to policy for each component. Component safety stock is held to protect against the stock out risk during component replenishment lead times. We develop a linear approximation heuristic to minimise expected holding and backlog costs and show that this heuristic performs well in comparison to a previously proposed heuristic method in the literature called the equal-fractile heuristic. Copyright 2010 Inderscience Enterprises Ltd.