Suppose that five jobs have processing times
and due dates as given below:
| Job |
A |
B |
C |
D |
E |
| Processing Time |
4 |
7 |
6 |
2 |
3 |
| Due Date |
15 |
16 |
8 |
21 |
9 |
|
Find the flow time, tardiness and lateness for
each job if they are processed in
a) order A-B-C-D-E
b) order of Shortest processing Time
c) Order in Earliest Due Date
a) Jobs processed in the order A-B-C-D-E
| Job |
A |
B |
C |
D |
E |
| Processing Time |
4 |
7 |
6 |
2 |
3 |
| Flow time |
4 |
4+7=11 |
11+2=13 |
13+6=19 |
19+3=22 |
| Due Date |
15 |
16 |
8 |
21 |
9 |
| Tardiness |
0 |
0 |
5 |
0 |
13 |
| Lateness |
-11 |
-5 |
5 |
-2 |
13 |
|
Average Flow time =( 4+11+13+19+22)/5=69/5 =13.8
Average Tardiness =(0+0+5+0+13)/5 = 18/5=3.6
Average Lateness = (-11-5+5-2+11)/5 =0/5=0
(b) Order according to SPT. The sequence will
be C-E-A-D-B
| Job |
A |
B |
C |
D |
E |
| Processing Time |
2 |
3 |
4 |
6 |
7 |
| Flow time |
2 |
2+3=5 |
5+4=9 |
9+6=15 |
15+7=22 |
| Due Date |
8 |
9 |
15 |
21 |
16 |
| Tardiness |
0 |
0 |
0 |
0 |
6 |
| Lateness |
-8 |
-4 |
-6 |
-6 |
6 |
|
Average Flow time = (2+5+9+15+22)/5= 53/5=10.6
Average Tardiness =(0+0+0+0+6)/5 = 6/5=1.2
Average Lateness = (-6-4-6-6+6)/5 =-16/5=-3.2
Note here the maximum tardiness is 6 and maximum lateness is
also 6.
c) Order according to earliest due date is C-E-A-B-D
| Job |
A |
B |
C |
D |
E |
| Processing Time |
2 |
3 |
4 |
7 |
6 |
| Flow
time |
2 |
2+3=5 |
5+4=9 |
9+7=16 |
16+6=22 |
| Due Date |
8 |
9 |
15 |
16 |
21 |
| Tardiness |
0 |
0 |
0 |
0 |
1 |
| Lateness |
-6 |
-4 |
-6 |
0 |
1 |
|
Average Flow time = (2+5+9+16+22)/5= 54/5=10.8
Average Tardiness =(0+0+0+0+1)/5 = 1/5=0.2
Average Lateness = (-6-4-6+0+1/5 =-15/5=-3.0
Note here the maximum tardiness is 1 and maximum lateness is
also 1. However, the average lateness is worse than SPT rule.
|
|
