The Earliest Due Date rule is when jobs are scheduled according to the earliest due date given, this is supposed to minimize the total tardiness of the whole jobs.
But the earliest due date rule is not supposed to be optimal, ie it does not guarantee the minimal tardiness possible.
Can someone help me understand why this is the case, if not can someone provide a simple example where scheduling via the Earliest Due Date does not give the minimum tardiness
Here is a somewhat extreme example:
One big job, takes 4 days but is unfortunately already due in 2 days, and one small job that takes just 1 day but is due in 3 days. The big job is due first, but if you do that first then both jobs are 2 days late. If you do the small job first then it is in time, and the big job is 3 days late.
So the total amount of tardiness is less by not following EDD (assuming both jobs have the same weight), even though the maximum tardiness is more.