WSPT
If the important weights W_{i} were to be considered the WSPT could be used to minimise the Weighted Flow Time (WMFT) to yield the sequence 3-4-8-2-7-6-5-1. This results by first choosing job with t_{i}/W_{i} in the table. The respective flow time of jobs in this sequence are 6, 9, 12, 21, 28, 42, 58. Mean flow time is hours
12=27.85 hours “>
Example 7.2. Eight jobs A, B, C, D, E, F, G arrive at one time to be processed on a single machine. Find out the optimal job sequence. when their operation time is given in the table below.
Job (n) |
Operation time in minutes |
A |
16 |
B |
12 |
C |
10 |
D |
8 |
E |
7 |
F |
4 |
G |
2 |
H |
1 |
Sol. For determining the optimal sequence, the jobs are selected in a non-descending operation time as follows.
Non-decreasing operation time sequence is H → G → F → E → D → C → B → A
Total processing time
H= 1
G=1+2=3
F = 1+2 + 4 =7
E = 1 + 2 + 4 + 7 = 14 .
D = 1 + 2 + 4 + 7 + 8 = 22
C = 1 + 2 + 4 + 7 + 8 + 10 = 32
B = 1 + 2 + 4 + 7 + 8 + 10 + 12 = 44
A = 1 + 2 + 4 + 7 + 8 + 10 + 12 + 16 = 60
Average processing time = Total time/number of jobs = 183/8 = 23 minutes.
In case the jobs are processed in the order of their arrival i.e. A→ B → C → D → E →F → G → H the total processing time would have been as follows :
A= 16
B = 16 + 12 =28
C=16+12+10=38
D= 16+ 12 + 10 + 8 = 46
E= 16+ 12+ 10+8+7=53
F=16+ 12+10+8+7+4=57
G = 16 + 12 + 10 + 8 +7 + 4 + 2 = 59
H=16+ 12+10+8+7+4+2+ 1=60
Average processing time = 357/8 = 44.6, which is much more than the previous time.
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