Semi-online scheduling with known maximum job size on two uniform machines

In this paper, we investigate the semi-online scheduling problem with known maximum job size on two uniform machines with the speed ratio s≥1. The objective is to minimize the makespan. Two algorithms are presented, where the first is optimal for $1s\sqrt{2}$ , and the second is optimal for 1.559≤s≤2 and $s\ge \frac{3\sqrt{17}}{2}$ . In addition, the improvement on lower bounds is made for $\mathrm{s}\frac{3\sqrt{17}}{2}$