A supply planning for multilevel serial production systems under lead time uncertainties is considered. The techniques used in industry are often based on the assumption that the lead times are known. However, in a supply chain the lead times are often random variables. Therefore, it is necessary to find the best values of the planned lead times minimising the total cost. It is supposed that the demand for the finished product and its due date are known. It is assumed also that the component lead time at each level is a random discrete variable. No restrictive hypothesis is made on such random variables; only that one supposes that the distribution probabilities are known. Therefore, we develop an efficient model to aid in MRP parameterization under lead time uncertainties, more precisely to calculate planned lead times when the component procurement times are random. The aim is to find the values of planned lead times which minimize the total cost and satisfy customers. We consider the criterion to minimize the average holding and tardiness costs at each level while respect the customer service level. The proposed approach is based on a mathematical model of this problem with discrete decision variables. Several properties of the objective function are proven.