A multilevel assembly system with one type of finished product and several types of components is considered in this paper. The component lead times at each level are discrete independent random variables, and the finished product demand is fixed. The assembly of the components at each level is carried out as soon as the components necessary are available. The demand of finished product should be satisfied by the end of each period. Otherwise a backlogging cost is incurred. Components necessary to assemble the same semi-finished product that are delivered not at same time will cause holding cost. The objective is to find the optimal release dates for the components in order to minimize the total expected costs composed of the finished product backlogging cost and the component holding cost. We propose a model that gives the optimal release dates values for the components. From a theoretical point of view, it is a generalization of the well known discrete Newsboy Model