On properties of optimal schedules in the flow shop problem with preemption and an arbitrary regular criterion

We investigate the properties of optimal solutions of the NP-hard flow shop scheduling problem with preemption and an arbitrary regular objective function. It is shown that for any instance of the problem its optimal solution can be found by choosing appropriate job priority orders on each machine. The number of preemptions in such schedule is estimated from above. It is also shown that the length of the optimal schedule (for a specified regular criterion) is always equal to the total length of operations from a certain subset. The results of the paper significantly extend previously known results established for the flow shop problem with the minimum makespan objective. Il. 5, bibl. 10.