A problem of inventory control for assembly systems is considered where the component lead times are random. A periodic ldquolot for lotrdquo policy for component supplying 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. 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, for example. This articlepsilas models can be used for the following MRP parameterization: the calculation the planned lead time for each component under lead time uncertainties.