Achieving an Optimal Lower Bound for Two Stage Supply Chain Scheduling with Regard to the Different Setup Time

Abstract

In this paper, a two-stage supply-chain scheduling problem including manufacturers and distributors will be investigated and modeled. The objective function is to minimize the makespan, which is equivalent to the completion time of the last job to leave the system. A minimum makespan usually implies a good utilization of the machine(s). In this research, serial batching machines do jobs processing and then the jobs will deliver to customers (in the next stage) for further processing. The capacity of each batch is limited. Delivery unit cost of each batch is fixed and independent of the number of jobs in the batch. Processing and setup time of jobs are varying according to jobs types. The setup time is determined according to jobs type within each batch. The problem has been formulated as a mixed integer-programming model. Finally, a lower bound will be provided. Computational experiments demonstrate the performance of new lower band.