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On-line and semi-online scheduling for flow shop problems on two machines

We investigate the on-line and semi-online scheduling for flow shop problems on two machines with the objective to minimize the makespan. Several lower bounds for the problems with and without preemption are derived. For some special cases of semi-online version, we provide two on-line algorithms with a competitive ratio of . Finally we give a lower bound for the problem with unavailable time interval on the first machine. And for the problem with the interval on the second machine, we show that no on-line algorithm has a constant competitive ratio.