The aim of this paper is to propose models to adapt and parameterize the Material Requirement Planning (MRP) approach under lead time uncertainty. Multi-level assembly systems with one type of finished products and several types of components aer studied. 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 product 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.