Abstract
This paper deals with a two-machine open shop scheduling problem. The objective is to minimize the makespan. Jobs arrive over time. We study preemption-resume 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 Jj on the two machines M1 and M2, respectively. Bounded processing times mean that 1 ≤ pi, j ≤ α (i = 1, 2) for each job Jj, where α ≥ 1 is a constant number. We propose an optimal online algorithm with a competitive ratio \({\frac{5\alpha-1}{4\alpha}}\) .
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