On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan. Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while in the non-clairvoyant on-line model, this processing requirement is not known until the job is processed and completed. In both models, scheduling of a job is irrevocable. We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5=4 (preemptive) and 3=2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3=2 (preemptive and non-preemptive).