PREEMPTIVE SCHEDULING IN A 2-STAGE MULTIPROCESSOR FLOW-SHOP IS NP-HARD

In 1954, Johnson gave an efficient algorithm for minimizing makespan i n a two-machine flow shop; there is no advantage to preemption in this case. McNaughton's wrap-around rule of 1959 finds a shortest preempti ve schedule on identical parallel machines in linear time. A similarly efficient algorithm is unlikely to exist for the simplest common gene ralization of these problems. We show that preemptive scheduling in a two-stage flow shop with at least two identical parallel machines in o ne of the stages so as to minimize makespan is NP-hard in the strong s ense.