Semi on-line scheduling for maximising the minimum machine completion time on two machines with available time

In this paper, we consider two semi on-line scheduling problems on two machine systems. In the first case, if the machines are uniform ones with available time, we assume that the total processing time is known in advance. In the second case, if the machines are two identical ones with available time, we assume that the largest processing time is known in advance. For each case, we propose a semi on-line algorithm and investigate its competitive ratio.