An optimal online algorithm for two-machine open shop preemptive scheduling with bounded processing times

This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemptionresume model, i.e., the currently processed job may be preempted at any moment in necessary and be resumed some time later. Let p1, j and p2, j denote the processing time of a job J j on the two machines M1 and M2, respectively. Bounded processing times mean that 1 ≤ pi, j ≤ α (i = 1, 2) for each job J j , where α ≥ 1 is a constant number. We propose an optimal online algorithm with a competitive ratio 5α−1 4α .