Question

The processing times and the due dates of 4 independent jobs processed by a single machine in a shop are given in the table.

Job	Processing time  (days)	Due date  (in days)
1	4	6
2	7	9
3	2	18
4	8	15

 

The average lateness of the job (in days) following the shortest processing time (SPT) rule is _____.

Answer 1

Concept:

In the SPT rule, jobs are sequenced in increasing order of their processing time i.e. minimum time first and maximum time in last.

Note: If two jobs have the same process time then job having less due date will be processed first.

Calculation:

In this question, arranging the jobs according to SPT rule.

Jobs	Processing time	Due date	Completion time	Lateness
3	2	18	0 + 2 = 2	0
1	4	6	2 + 4 = 6	0
2	7	9	6 + 7 = 13	4
4	8	15	13 + 8 = 21	6

Total lateness = 10 

\(Average\;lateness = \frac{{10}}{4} = 2.5\;days\;per\;job\)