We consider the inventory management for the assembly system of one type of finished product from n different types of components. The components are supplied from n different and external suppliers. It is supposed that the component lead times and the finished product demand are random discrete variables. The company that handles the assembly operation must determine what are the optimal moments and optimal quantities to supply? The objective is to minimize the total cost consists of holding component costs, tardiness finished product cost, and finished product lost and surplus costs. We offer the one-period analytical modeling. Several properties of the objective function are shown. These properties are used for the development of Branch and Bound method. Several tests and different conclusions are presented. This study can be used for the parameterization of MRP software, specifically for calculating of safety stocks under uncertainties of both demand and lead times.