The aim of this paper is to propose tools to adapt and parameterize the Material Requirement Planning (MRP) method under lead time uncertainty. We study multi - level assembly systems with one type of finished products and severa l types of components. We consider that each component has a fixed unit inventory cost and the finished product has a backlogging cost per unit of time. The lead times of components are discrete random variables, and the costumer's demand of the finished p roduct is known. A general mathematical model for supply planning of multi - level assembly systems is presented. A Genetic Algorithm (GA) method is proposed to minimize the sum of the average inventory holding cost for components and the average backlogging and inventory holding costs for the finished product .