Mathematical Model for Supply Planning of Multi-Level Assembly Systems with Stochastic Lead Times

The deal for industrial companies is to satisfy their customers with the best quality, the most reliable lead times, and the lowest costs. One of the keys to achieve it is in the inventory control in the Supply Chain. Moreover, it is mandatory to possess necessary components in order to produce the requested products by the due date. But, as the components lead time is an unpredictable parameter, it is difficult to take it into account correctly. In this paper we deal with this question considering that each component has a fixed unit inventory cost; the finished product has an inventory cost and a backlogging cost per unit of time. Then, a general mathematical model for supply planning of multilevel assembly system is presented to calculate the expected value of the total cost which equals to the sum of the inventory holding costs for the components, the backlogging and the inventory holding costs for the finished product.