Optimization for supply planning in multi-level assembly systems with stochastic lead-times

We are interested in a supply planning for multilevel assembly systems under uncertainty of components lead times, more precisely to determinate planned lead times when the component procurement times are independent and identically distributed discrete random variables. The finished product demand, for a given due date, is supposed to be known. The optimization is made for only single-period demand. The developed model is for an infinite capacity assembly system. This study proposed a Branch and Bound (B&B) method to obtain the optimal values of planned lead times which minimize the expected value of the total cost which equals to the sum of the average inventory holding cost for components and the average backlogging and inventory holding costs for the finished product. We also developed a Genetic Algorithm (GA) to overcome the computational difficulty of the B&B method.