Online Scheduling on Two Uniform Unbounded Parallel-Batch Machines to Minimize Makespan

We study an online (over time) scheduling problem on two uniform unbounded parallel-batch machines with processing speed 1 and \(v (0online algorithm can have a competitive ratio less than \(1+ \alpha _L\), where \(\alpha _L= (\sqrt{5}-1)/2\approx 0.618\) if \(0online algorithm with a competitive ratio at most \(\min \{(\sqrt{5}+1)/2,\; \sqrt{2}/v\}\). When the jobs have the same processing times, we present the best possible online algorithm with a competitive ratio \(1+ \alpha _L\).