On-line two-machine job shop scheduling with time lags

We consider the on-line two-machine job shop scheduling problem with time lags so as to minimize the makespan. Each job consists of no more than two operations and time lags exist between the completion time of the first and the start time of the second operation of any two-operation job. We prove that any greedy algorithm is 2-competitive. For the non-clairvoyant variant of the problem, no on-line algorithm can do better. For the clairvoyant variant, no on-line delay algorithm has a competitive ratio better than , and a greedy algorithm is still the best on-line non-delay algorithm. We also show that the same results hold for the two-machine flow shop problem with time lags.