This paper examines a supply planning problem for multilevel serial production systems under lead time uncertainties. 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 evaluate the influence of the planned lead times on the total cost. An exact performance evaluation technique is developed to calculate the total cost as a function of the planned lead times when the actual lead times are random discrete variables. The sum of the average component holding and tardiness costs at each level, plus the average finished product backlogging cost is considered. Several properties of this function are proven. A numerical example is reported.