Abstract
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 inthe non-clairvoyant on-line model, this processing requirement is notknown 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).
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Chen, B., Vestjens, A.P. & Woeginger, G.J. On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time. Journal of Combinatorial Optimization 1, 355–365 (1998). https://doi.org/10.1023/A:1009786526733
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DOI: https://doi.org/10.1023/A:1009786526733