Page 249 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Figure 12.16: Critical Path of the Project
5 10 10 15
4 9
T T 1 5 T T
E L E L
0 0 2 4 9 7 22 22
15 15
4
2 10
1 5
1 7
8
1 8 1
6
3 5 4 6 17 17

1 1 7 7 11 16

The critical path is 1-3-5-7-8-10 (shown in double line in Figure 12.16) with the project duration
of 22 days.

Example: The following Table 12.6 gives the activities in construction project and time
duration.

Table 12.6: Project Schedule with Time Duration

Activity Preceding Activity Normal time (days)
1-2 - 20
1-3 - 25
2-3 1-2 10
2-4 1-2 12
3-4 1-3,2-3 5
4-5 2-4,3-4 10

1. Draw the activity network of the project.
2. Find the total float and free float for each activity.
Solution:
1. From the activity relationship given, the activity network is shown in Figure 12.17 below:

Figure 12.17: Activity Network Diagram

2
12
20
10
1 4 5
10
25 5
3

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