Critical Path Analysis

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Critical Path Analysis
Precedence Diagram Technique Precedence Networks
2
Critical Path Analysis

• why do it?
• what are the inputs?
• the process
• using the outputs
• PERT and uncertainty

3
the context

• identify tasks
• sequence
• estimate
• resources
• analysis
• scheduling
• optimisation

4
what are the benefits?

• critical path
• non-critical activities

5
what are the inputs?

• tasks
• sequence/dependencies
• durations

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Sequence

• the most common sequences / dependencies

Task B depends upon Task A B cannot start until
A is finished
Task A
Task B
Task B
Tasks B and C depend on Task A neither can start
until A is finished, but B and C are independent
of each other
Task A
Task C
Task A
Task C depends upon Task A and B C cannot start
until both A and B are finished
Task C
Task B
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rules and conventions

• just one start
• just one finish
• no danglers

slack
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the process - 2 stages

• draw
• analyse

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the process - forward pass
2
5
3

• Duration 18

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the process - backward pass
2
5
3
13
15
10
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more unusual links and relationships

• so far all links have been finish-start links...

3 days
Task B depends upon Task A, but with a 3 day
delay B cannot start until 3 days after A is
finished
Task A
Task B
Task A
The start of Task C depends on the start of Task
A this is a start-to-start link it may also
incorporate a delay
Task C
Task A
The finish of Task C depends upon the finish of
Task A
Task C
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using the outputs

• Gantt Charts
• resource histograms
• resource smoothing
• optimising the schedule

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Scheduling
task res. Duration Calendar

• task 1
• task 2
• task 3
• task 4
• task 5
• task 6
• task 7

2 days 3 days 1 day 2 days 7 days 4 days 1 day
Jane Bill Jane Jim Bill Jane Bill
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PERT and uncertainty - 1
The critical path looks like tasks 01-02-04
5
2
4
4
But what if you are not sure about the duration
for Task 03?
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PERT and uncertainty - 2
The better estimate for Task 03 might be its PERT
estimate, or Expected Value, EV)
5
2
4
EV O 4L P ___________ 6
O Optimistic estimate (say 2) L Most Likely
(say 4) P Pessimistic (say 12)
4
In this example the EV 6, which does, in fact
change the critical path
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PERT and uncertainty - 3
But how confident can we be in these results?
An durations spread is the degree to which
estimates of the duration differ from each other.
If every estimate of duration were about equal,
the estimate would have very little spread.
There are many measures of spread. The
distributions on this page have the same mean but
differ in spread the distribution on the bottom
is more spread out.
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PERT and uncertainty - 4
Standard deviation is used as a measure of
spread. In a normal distribution, about 68 of
estimates are within one standard deviation of
the mean and about 95 of the estimates are
within two standards deviations of the mean.
EV O 4L P ___________ 6
O Optimistic estimate (say 2) L Most Likely
(say 4) P Pessimistic (say 12)
SD (P O)/6
In our example SD (12-2)/6 1.666
So, we could say that, for task 03
With 68 certainty, the duration will be between
2.34 and 5.66 (4 SD) With 95 certainty the
duration will be between 0.68 and 7.32 (4 2SD)
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Classroom Practice - 1
4
2
Task 02
Task 03
3
Task 07
9
4
5
2
Task 04
Task 05
Task 09
Task 01
4
1
Task 08
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Classroom Practice - 2
4
2
Task 02
Task 03
5
Task 05
6
2
5
Task 01
Task 04
Task 07
4
Task 06
20
Classroom Practice - 3
2
2
Task 02
Task 03
3
Task 07
7
5
2
Task 01
Task 05
Task 09
4
4 days