Managing inventory and supply performance in assembly systems with random supply capacity and demand

We consider stock positioning in a pure assembly system controlled using installation base-stock policies. When component suppliers have random capacity and end-product demand is uncertain, we characterize the system's inventory dynamics. We show that components and the end product play convex complementary roles in providing customer service. We propose a decomposition approach that uses an internal service level to independently determine near-optimal stock levels for each component. Compared with the optimal, the average error of the decomposition approach is 0.66% across the tested instances. Compared with current practice, this approach has the potential to reduce the safety-stock cost by as much as 30%. Our computational analysis on two-echelon systems also illustrates several managerial insights: We observe that the cost reduction from improving supply performance is high when demand variability or the number of components or target customer service is high, or when the end product is more expensive relative to components. On average, (i) reducing the lead time of the more expensive component yielded higher benefit than reducing the lead time for the less expensive component, and (ii) the benefit of improving one of the supply parameters (service level or lead time) was higher when the value of the other parameter was already more favorable (lower lead time or higher service level, respectively). Finally, we analytically show how a multi-echelon pure assembly system may be converted into an equivalent two-echelon assembly system to which all our results apply.