Abstract
This paper investigates two different semi on-line scheduling problems on a two-machine system. In the first case, we assume that all jobs have their processing times in between p and rp\((p>0, r\geq1)\). In the second case, we assume that the largest processing time is known in advance. We show that one has a best possible algorithm with worst case ratio 4/3 while LS is still the best possible for the other problem with ratio \((r+1)/2\) which is still \(3/2\) in the worst case \(r=2\).
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