A heuristic for scheduling two-machine no-wait flow shops with anticipatory setups

We consider a problem of scheduling jobs in two-machine no-wait flow shops for which the objective is to minimize the makespan. Each job, upon completion of its processing on the first machine, must be transferred immediately to the second machine due to a no-wait in process constraint. Every job requires a setup time on each machine before it is processed. The setup on the second machine is anticipatory, since it can be performed in advance of an arriving job, and consists of two parts. During the first part of the setup, the job should not be present in the machine, while the second part of setup can be done in the presence or absence of the job. A heuristic algorithm is proposed, and its worst-case performance ratio of 4/3 is established.