OPTIMAL ORDER POLICIES IN ASSEMBLY SYSTEMS WITH RANDOM DEMAND AND RANDOM SUPPLIER DELIVERY

In this paper we consider an assembly problem where two critical compo nents are required for assembly of the final product, the demand for w hich is stochastic. The components can be ordered separately from indi vidual suppliers or in a set (a set refers to the components in the re quired ratio) from a joint supplier. We consider the case where the as sembly stage is free, i.e., the firm procures and stores the component s and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor i ndustries). We assume that a supplier, with probability beta (say), su pplies 100% of the order quantity in the current period, and with prob ability (1-beta) supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexi ty of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no or der is placed with the joint supplier, the order quantities from the i ndividual suppliers follows an order-up-to policy structure with ident ical order levels. However, it is optimal to diversify (i.e., order fr om the joint supplier as well) when the inventory level is below a cer tain threshold (determined in this paper). With lower initial inventor y levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain condi tions on the cost and delivery parameters of the suppliers, we show th at the policy structure for the multi-period problem is similar to tha t of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra compone nts for use in the future. This is a direct consequence of the uncerta inty in the delivery timing of the suppliers. Finally we conduct a com putational study of the two-period problem and determine the effect of supplier costs and the probability of delivery on the optimal order p olicy. The policies are intuitive and offer a better understanding of the effect of supply and demand uncertainty on the assembly problem.