Abstract: In a assembly system with uncertain demand time, suppliers' uncoordinated deliver times can heavily bring down the manufacturer's and the supply chain's performances. Under such a circumstance, manufacturer has to use some inventory control policies (e.g., VMI) to reduce his inventory cost, while the supplier tries to deliver at the most appropriate time. In this paper, the supplier optimal deliver time and the manufacturer's best inventory holding period in an assemble system with uncertain demand time are studied. To this end, two different models are conducted in N-1 setting: the Nash game among the multi-suppliers, and the Stacklberg game between the manufacturer and the suppliers. The manufacturer's optimal limited inventory holding period under two different conditions is also discussed. One is the manufacturer that sets the same inventory holding period to all the suppliers, and the other is the manufacturer that can choose different inventory holding periods to the different suppliers. The result identifies the suppliers' optimal deliver time and shows that the manufacturer can effectively improve his and the channel's profit by either means. In other words, traditional VMI policy isn't good for neither the manufacturer nor the supply chain. By numerical analysis, the sensitivities of the supplier heterogeneity are identified, and it is shown that the supply chain efficiency increases when the manufacturer is able to choose different inventory holding periods. Moreover, the essential condition for the supply chain coordination is concisely provided.

Key words: assembly system, on-time delivery, inventory sharing policy, sequential process