This study considers a multi-level assembly system with several components in each sub-level. It is assumed that actual lead-time for all components is probabilistic; and Periodic order quantity (POQ) policy for ordering is utilized. If at a certain level, a job is not received at the expected time, a delay is incurred at the delivery of production at this level and this may result in backorders of the finished product. It is assumed in this case that a fixed percentage of the shortage is backlogged and other sales are lost. In the real situation, some but not all customers will wait for backlogged components during a period of shortage, such as for fashionable commodities or high-tech products with the short product life cycle. The objective of this study is to find the planned lead-time and periodicity for the total components in order to minimize the expected fixed ordering, holding and partial backlogging costs for the finished product. In this study, it is assumed that a percentage of components at each level are scrap. A general mathematical model is suggested and then finding the optimal solution for this model.
