## Theoretical results-conventional priority rules, Mechanical Engineering

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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 Tmax;

(c) If all arrival times aj or all operation times oj are equivalent, then EDD minimizes the maximal tardiness Tmax;

(d) If all due date tdj are equivalent, then SPT minimizes Tmean and FIFO minimizes Tmax;

(e)  If all operations are inevitably ended late, then SPT also minimizes Tmean since it minimizes the mean throughput time;

(f) If only two operations exist that have the same arrival time, then MOD minimizes Tmean. It is no longer valid for three or more operations in the queue.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 Tmean   and Tmax  , 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 Tmean, 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.

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