Page 247 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Solution:
1. From the data given in the problem, the activity network is constructed as shown in
Figure 5.6.

Figure 12.15: Activity Network Diagram

1 5
2 4 9
7
4
10
5
1 7 2
1 8
8
1
1 6 4
3 5
6

2. To determine the critical path, compute the earliest, time T and latest time T for each of
E L
the activity of the project. The calculations of T and T are as follows:
E L
To calculate T for all activities,
E
T = 0
E1
T = T + t = 0 + 4 = 4
E2 E1 1, 2
T = T + t = 0 + 1 =1
E3 E1 1, 3
T = max (T + t and T + t )
E4 E2 2, 4 E3 3, 4
= max (4 + 1 and 1 + 1) = max (5, 2)

= 5 days
T = T + t = 1 + 6 = 7
E5 E3 3, 6
T = T + t = 7 + 4 = 11
E6 E5 5, 6
T = T + t = 7 + 8 = 15
E7 E5 5, 7
T = max (T + t and T + t )
E8 E6 6, 8 E7 7, 8
= max (11 + 1 and 15 + 2) = max (12, 17)
= 17 days
T = T +t = 5 + 5 = 10
E9 E4 4, 9
T = max (T + t and T + t )
E10 E9 9, 10 E8 8, 10
= max (10 + 7 and 17 + 5) = max (17, 22)

= 22 days

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