Page 244 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 12: Critical Path Method and PERT

Notes
Table 12.3: Activity Sequence for a Project
Activity A B C D E F G H I J K
Predecessor - - - A B B C D E H, I F, G

Solution:
The network diagram for the given problem is shown in Figure 12.14 with activities A, B and C
starting simultaneously.

Figure 12.14: Network Diagram

D H 8
5
2
J
A
I
E
B
1 3 6 9

C F
K
4
G 7

Task Draw a network diagram for a project given in Table.
Activity A B C D E F G H I J K L
Immediate - A B A D C, E D D H H F, H G, J
Predecessor

12.3 Critical Path Method (CPM)

The critical path for any network is the longest path through the entire network. Since all
activities must be completed to complete the entire project, the length of the critical path is also
the shortest time allowable for completion of the project. Thus if the project is to be completed
in that shortest time, all activities on the critical path must be started as soon as possible. These
activities are called critical activities. If the project has to be completed ahead of the schedule,
then the time required for at least one of the critical activity must be reduced. Further, any delay
in completing the critical activities will increase the project duration.

The activity, which does not lie on the critical path, is called non-critical activity. These
non-critical activities may have some slack time. The slack is the amount of time by which the
start of an activity may be delayed without affecting the overall completion time of the project.
But a critical activity has no slack. To reduce the overall project time, it would require more
resources (at extra cost) to reduce the time taken by the critical activities to complete.

LOVELY PROFESSIONAL UNIVERSITY 239