Abstract
This paper investigates two preemptive semi-online scheduling problems to minimize makespan on two uniform machines. In the first semi-online problem, we know in advance that all jobs have their processing times in between p and rp $(p > 0,r\geq 1)$. In the second semi-online problem, we know the size of the largest job in advance. We design an optimal semi-online algorithm which is optimal for every combination of machine speed ratio $s\geq 1$ and job processing time ratio $r\geq 1$ for the first problem, and an optimal semi-online algorithm for every machine speed ratio $s\geq 1$ for the second problem.
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