A problem of inventory control for assembly systems is considered where the component lead times are random. A periodic "lot-for-lot" policy for component supply is studied. The decision variables are component planned lead times. The aim is to minimize the average holding cost for components while keeping a high customer service level for the finished product. When the lead times of the different types of components follow the same distribution probability, and unit holding costs are identical for all components, an efficient algorithm is proposed. For a more general case with arbitrary distribution and holding costs, some properties and a lower bound on the cost function are proved. These results can be useful for the development of efficient exact optimization algorithms as Branch and Bound. This article's models can be employed for MRP parameterization, more precisely for safety lead time or safety stock calculation for each component under component lead time uncertainty.