Page 253 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Solution:
Calculate the time average t and variances of each activity as shown in Table 12.9.
a
2
Table 12.9: T &  Calculated
e
Activity To Tm Tp Ta  2
1-2 4 6 8 6 0.444
1-3 2 3 10 4 1.777
1-4 6 8 16 9 2.777
2-4 1 2 3 2 0.111
3-4 6 7 8 7 0.111
3-5 6 7 14 8 1.777
4-6 3 5 7 5 0.444
4-7 4 11 12 10 1.777
5-7 2 4 6 4 0.444
6-7 2 9 10 8 1.777

From the network diagram Figure 12.19, the critical path is identified as 1-4, 4-6, 6-7, with a
project duration of 22 days.
The probability of completing the project within 19 days is given by, P(Z< Z )
0
To find Z ,
0
 
  
  

  

 
   
  

  = -1.3416 days
 
we know, P (Z <Z ) = 0.5 –  (1.3416) (from normal tables, (1.3416) = 0.4099)
0
= 0.5 – 0.4099
= 0.0901
= 9.01%
Thus, the probability of completing the R&D project in 19 days is 9.01%. Since the probability of
completing the project in 19 days is less than 20%, we find the probability of completing if in 24
days.



    
=     = 0.8944 days
   

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