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 It is no longer valid for three or more operations in the queue.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.