SOEN 341
week 5
Project planning 2
Project scheduling activities
From Textbook, Chapter 23 Project Planning.
• Split project into tasks and estimate time and
resources required to complete each task.
• Organize tasks concurrently to make optimal
use of workforce.
• Minimize task dependencies to avoid delays
caused by one task waiting for another to complete.
• Dependent on project managers’ intuition and
experience.
2
Activity label
Duration
ES
Activity description
LS
EF
LF
Float
3wks
3
Activity label
Duration
ES
Activity description
LS
EF
LF
Float
3wks
4
Update graph as project progresses
• Make adjustments to the graph as the project
progresses.
• As the project unfolds, the estimated times can be
replaced with actual times.
• In cases where there are delays, additional resources
may be needed to stay on schedule
– the chart may be modified to reflect the new situation.
• A new critical path may emerge, and structural changes
may be made in the graph if project requirements
change.
5
Critical path method
• We can use activity network diagram to find the critical
path(s)
– AKA critical path method / critical path analysis
• The significance of the critical path is that the activities
that lie on it cannot be delayed without delaying the
project.
• Because of its impact on the entire project, critical path
analysis is an important aspect of project planning.
• To accelerate the project it is necessary to reduce the
total time required for the activities in the critical path.
6
Schedule compression
• Shorten the project schedule by:
– resource allocation
– task duration reduction
– schedule optimization
• Focus on critical path activities
7
Compression techniques
Crashing $
Fast tracking
Reducing scope
Negotiating with
stakeholders
Optimize resource
allocation
8
Schedule compression notes
• Schedule compression is
applied when project
deadlines are at risk
• Requires careful planning
and management to
mitigate potential risks
• Remember, be hard on
the date, but flexible on
features
9
Program Evaluation and Review
Technique (PERT)
• Based on the idea that estimates are uncertain
– Usually, people apply critical path method and
PERT at the same time
• Uses ranges and probability and an expected value of
the duration of a project
• E.g. The most likely completion time is 4 weeks but it
could be anywhere between 3 weeks and 8 weeks
10
Probabilistic Time Estimates
• Beta distribution
– a probability distribution traditionally
used in CPM/PERT
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Probabilistic Time Estimates
• The Beta distribution is best for representing a probabilistic
distribution of probabilities—the case where we don't know
what a probability is in advance—but we have some
reasonable guesses.
• Variance 𝜎 2 : a measure of the difference between the
observed value of a variable and the mean
• Standard Deviation 𝜎: is essentially the square root of the
variance. In PERT, standard deviation provides a more
interpretable measure of uncertainty than variance
because it's in the same unit as the original data (e.g.,
days, hours).
• The three-point estimation approximates the probability
distribution representing the outcome of future events, based
on very limited information.
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Activity-on-node Network with
Probabilistic Time Estimates: Example
13
Activity Time Estimates
TIME ESTIMATES (WKS)
MEAN TIME
VARIANCE
ACTIVITY
a
m
b
t
б2
1
2
3
4
5
6
7
8
9
10
11
6
3
1
2
2
3
2
3
2
1
1
8
6
3
4
3
4
2
7
4
4
10
10
9
5
12
4
5
2
11
6
7
13
8
6
3
5
3
4
2
7
4
4
9
0.44
1.00
0.44
2.78
0.11
0.11
0.00
1.78
0.44
1.00
4.00
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Earliest, Latest, and Float
activity
ES, EF
t
LS, LF
2 0
6 0
8 9
7 9
6
6
5 6
3 6
9
9
16
16
11 16 25
9 16 25
 =  (t2, t5, t8, t11)
 = 25, which is the
duration of the
project.
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Activity Early, Late Times,
and Float
ACTIVITY
1
2
3
4
5
6
7
8
9
10
11
t
б
ES
EF
LS
LF
F
8
6
3
5
3
4
2
7
4
4
9
0.44
1.00
0.44
2.78
0.11
0.11
0.00
1.78
0.44
1.00
4.00
0
0
0
8
6
3
3
9
9
13
16
8
6
3
13
9
7
5
16
13
17
16
1
0
2
16
6
5
14
9
12
21
16
9
6
5
21
9
9
16
16
16
25
25
1
0
2
9
0
2
11
0
3
9
0
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Compute the uncertainty or variability
associated with each activity's duration
estimate.
2 = 22 + 52 + 82 + 112
2 = 1.00 + 0.11 + 1.78+ 4
2 = 6.89
 = 2.62 weeks
Notice that we only consider the activities in the critical path
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Probabilistic Network Analysis
Determine probability that project is
completed within specified time
Z=
where
x-

 = tp = project mean time
 = project standard deviation
x = proposed project time
Z = number of standard deviations x
is from mean
Notice that for tp we are only consider the sum. of t for the
activities in the critical path, as we did for 
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Probability of Completion Time
What is the probability that the project is completed
within 30 weeks?
P(x  30 weeks)
 = 25 x = 30
Time (weeks)
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Probability of Completion Time
What is the probability that the project is completed
within 30 weeks?
P(x  30 weeks)
 2 = 6.89 weeks
 =
6.89
 = 2.62 weeks
Z=
=
x-

30 - 25
2.62
= 1.91
 = 25 x = 30
Time (weeks)
From Z scores Table, a Z score of 1.91 corresponds to a probability
0.9719.
20
21
Z values
Probability of Completion Time
What is the probability that the project is completed
within 22 weeks?
x-
2
Z=
 = 6.89 weeks
P(x  22 weeks)

 =
6.89
 = 2.62 weeks
=
22 - 25
2.62
= -1.14
x = 22  = 25
Time
(weeks)
From Z scores Table, a Z score of -1.14 corresponds to a probability of
0.1271
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Z values
Limitations of PERT/CPM
• Assumes clearly defined, independent
activities
• Activity times (PERT) follow beta
distribution
• Subjective time estimates
• CPM only focuses on time and does not
incorporate cost variations
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Exercise
•
•
Activity ID
Duration
Dependency
A
1,3,5
B
2,6,10
A
C
12,15,24
A
D
2,10,12
B,C
E
2,4,6
B
F
1,3,11
D
G
2,5,20
E,F
Find the critical path?
What is the probability of finishing the project within 45, or 50 weeks?
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Exercise
t
2
3
0.44
A
6
1.78
12,15,24
A
16
4
D
2,10,12
B,C
9
2.78
E
2,4,6
B
4
0.44
F
1,3,11
D
4
2.78
G
2,5,20
E,F
7
9
Activity ID
Duration
A
1,3,5
B
2,6,10
C
Dependency
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Conclusion
• While PERT and CPM are useful for
project scheduling, their limitations make
them less effective for dynamic, resourceconstrained, or highly uncertain projects.
• Combining them with modern project
management tools (like Agile or Monte
Carlo simulations) can improve
effectiveness.
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Review Quiz
https://forms.office.com/r/s0iWTFLuvn
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References
• Ch. 23.2-23.3 Sommerville, Ian. Software
Engineering. 10th edition. Pearson, 2016.
• Hughes, B., and Cotterell, M. (1999) Software
Project Management, 2nd edition, McGraw-Hill.
(slides)
• Pfleeger, S.L. (1998) Software Engineering:
Theory and Practice, Prentice Hall.
• Roberta Russell & Bernard W. Taylor, III (2006)
Operations Management - 5th Edition, John Wiley
& Sons (slides)
• Normal Tables. http://miha.ef.unilj.si/_dokumenti3plus2/195166/norm-tables.pdf
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