Theoretical Results
In the particular machine case, several theoretical results are identified or can be derived:
(a) If each operation can be scheduled such that everyone is ended before its due date, then EDD achieves this;
(b) If the schedule that is produced by EDD is such that only one operation ended late, then EDD minimizes the mean tardiness T_{max};
(c) If all arrival times a_{j} or all operation times o_{j} are equivalent, then EDD minimizes the maximal tardiness T_{max};
(d) If all due date t_{dj} are equivalent, then SPT minimizes T_{mean} and FIFO minimizes T_{max};
(e) If all operations are inevitably ended late, then SPT also minimizes T_{mean }since it minimizes the mean throughput time;
(f) If only two operations exist that have the same arrival time, then MOD minimizes T_{mean}. It is no longer valid for three or more operations in the queue.
These results merely hold for static difficulties where a fixed queue has to be ordered and no latest jobs arrive. Nevertheless, they offer interesting indications in usual for the usual situation:
(a) Along with respect to T_{mean } and T_{max} , ODD or same rules can be expected to offer good results for a condition where most of the work can be finished in time (low load);
(b)Along with respect to T_{mean}, SPT and rules that employ SPT for urgent jobs can be expected to offer good results for results where more of the work is ended late.