Interfering job set scheduling on two-operation three-machine flowshop

This paper considers three machine flowshop scheduling problem with two agents. The jobs of first agent have two operations executed in the same order, on M-1 and then on M-2 respectively. According to the second agent, the jobs should be executed on M-2 and then on M-3. Thus, the second machine M-2 has to be shared to perform all of jobs. The objective is to minimize at the same time the makespan of each job set. The epsilon-constraint approach is utilized, i.e. the maximum completion time of the one agent has to be minimized while the maximum completion time of the other is bounded. This scheduling problem was proved as binary NP-hard. In this study, a pseudo-polynomial algorithm is proposed.