Assembly systems with one type of finished product and several types of components are studied. The lead times of components are random variables, and the finished product demand is constant. The criterion considered is the sum of the average holding cost for the components and the average backlogging cost for the finished product. The decision variables are the planned lead times of components. A model that gives the optimal values for the planned lead times is proposed. From a practical point of view, this model can be used to calculate the safety lead time on assembly systems under supply uncertainty, and from a theoretical point of view, it is a generalization of the well-known discrete newsboy model.