Abstract: We consider on-line scheduling on a parallel batching machine where the jobs come with the nonincreasing-processing times. In this paper online means that jobs arrive over time. The objective is to minimize the maximum flow time of these jobs.  The flow-time of a job means that its completion time minus its arrival time.  It reflects the time of the job staying in the system. For the bounded model, we give a best possible algorithm with competitive ratio $\frac{1+\sqrt{5}}{2}$. For the unbounded model, we also give a best possible algorithm with competitive ratio $\sqrt{2}$.

Key words: on-line scheduling, parallel batching, maximum flow-time, competitive ratio