Consider the network diagram shown in Figure. The time estimates in days along the arrows represents the activities. The project completion time in days based on critical path is
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The critical path may not be unique; there can be multiple paths with the same longest duration. Activities on the critical path are called critical activities, and any delay in these activities will directly impact the project completion time.
Step 1: Identify all possible paths from the start event to the end event.
We need to trace all the sequences of activities from node 1 (Start event) to node 6 (End event).
The possible paths are:
1. 1 $\rightarrow$ 2 $\rightarrow$ 3 $\rightarrow$ 5 $\rightarrow$ 6 (Activities A-B-D-F)
2. 1 $\rightarrow$ 2 $\rightarrow$ 4 $\rightarrow$ 5 $\rightarrow$ 6 (Activities A-C-E-F) Step 2: Calculate the total duration for each path by summing the time estimates of the activities along that path.
For Path 1 (A-B-D-F):
Duration = Time(A) + Time(B) + Time(D) + Time(F)
Duration = 3 days + 5 days + 10 days + 4 days = 22 days
For Path 2 (A-C-E-F):
Duration = Time(A) + Time(C) + Time(E) + Time(F)
Duration = 3 days + 7 days + 5 days + 4 days = 19 days Step 3: Identify the critical path.
The critical path is the longest path in the network diagram, as it determines the minimum project completion time. The path with the maximum duration is the critical path.
Comparing the durations of the two paths:
Path 1: 22 days
Path 2: 19 days
The longest duration is 22 days, which corresponds to Path 1 (A-B-D-F). Therefore, the critical path is 1 $\rightarrow$ 2 $\rightarrow$ 3 $\rightarrow$ 5 $\rightarrow$ 6.
Step 4: Determine the project completion time.
The project completion time based on the critical path is the duration of the critical path. In this case, it is 22 days.
