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
11
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.
12
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
14
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.
15
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
16
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
17
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
18
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)
19
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
22
23
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
24
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?
25
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
26
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.
27
Review Quiz
https://forms.office.com/r/s0iWTFLuvn
28
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
29