Working out the critical path
AS 91576
Critical Paths
Having drawn the network diagram from the precedence table will look like this
A
B
C
E
G
D
I
H
F
J
Critical Paths
Now replace each vertex with a box of six parts
Critical Paths
The boxes are the following
Looking at the top row the middle box is the duration of the task
The top left box is the earliest start time for the task (ie the first task starts at time 0)
The top right box is the earliest finish time for the task (is the early start time plus duration)
Critical Paths
Fill in the duration times
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Now starting on the left hand side fill in the start times of task A, B and C as zero. The finish times can also be filled in
Critical Paths
Now Task E can only start after task A and B are finished. Task A finishes after 7 days and Task B finishes after 2 days so the earliest Task E can start is after 7 Days.
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Keep filling in the boxes. Notice that Task F can only start after Task G and D have finished (so day 25) but Task H can start as soon as Task G has finished.
Critical Paths
There are two end points. Task H and Task J. Task J finishes after task H so the shortest possible finish time is after 32 days.
Critical Paths
Back to the boxes now looking at the bottom row.
The bottom right box is the latest finish time (ie for end tasks the longest duration of path through the diagram)
The bottom left box is the latest finish time minus the duration
The float is the difference between the early and late time
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There are two end points. Task H and Task J both their late finish times are 32 because that was the finish time of the latest task
Critical Paths
Task G must finish before the two events that follow it. One needs to be finished by day 24 and the other by day 25, so the latest Task G can finish is Day 24.
Critical Paths
Keep working backwards until you get to the beginning.
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Now work out the difference between top left and bottom left and put that as the float.
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The critical path will all have zeros in the float time.
In this case the Critical path is A,E,D,F,I,J. Any delay on any of those tasks will delay the delay the whole project