We consider a parallel machine scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on m identical machines, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its processing time becomes known at its arrival. We deal with the problem of minimizing the makespan, which is the time by which all jobs have been finished. We propose and analyze the following on-line LPT algorithm: At any time a machine becomes available for processing, schedule an available job with the largest processing time. We prove that this algorithm has a performance guarantee of 3/2, and that this bound is tight. Furthermore, we show that any on-line algorithm will have a performance bound of at least 1.3473. This bound is improved to (5 – √(5))/2 ≈ 1.3820 for m = 2.