Transfer batch scheduling for a two-matching flow shop with attached and separate setup times

This paper considers the transfer batch scheduling problem for a two-machine flow shop with setup times consisting of attached setup time and separate setup time. The attached setup is attached to the processing and cannot be done while the job is somewhere else. The separate setup is unattached to the processing and can be scheduled in anticipation of arriving work. Two cases of the separate setup are addressed. One is the case that the separate setup can be done only when a machine is idle. The other is the case that the separate setup can be done even though the machine is operating. A scheduling rule similar to Johnson's rule is suggested to minimize makespan. The scheduling rule developed can be applied to most of the two-machine flow shop scheduling problems if some parameters are adjusted. A numerical example is presented to illustrate the scheduling rule.