The Longest Processing Time first (LPT) rule assigns at t = 0 the m longest jobs to the m machines. After that, whenever a machine is freed the longest job among those not yet processed is put on the machine. This heuristic tries to place the shorter jobs more towards the end of the schedule, where they can be used for balancing the loads.

Consider P2|| Cmax. Consider instances with 4 jobs. Either argue that LPT is always optimal in this case, or give an example which shows that it is not.