USA: +1-585-535-1023

UK: +44-208-133-5697

AUS: +61-280-07-5697

WSPT

WSPT

If the important weights Wi 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 ti/Wi 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.