If assignments get tossed on your desk at unpredictable moments, the optimal strategy for minimizing maximum lateness is still the preemptive version of Earliest Due Date—switching to the job that just came up if it’s due sooner than the one you’re currently doing, and otherwise ignoring it. Similarly, the preemptive version of Shortest Processing Time—compare the time left to finish the current task to the time it would take to complete the new one—is still optimal for minimizing the sum of completion times.
