ENGG 1865
Project Time, Cost and Resources
Week 3: Program Evaluation Review
Technique (PERT)
Presented by:
Dr. Mehdi Rajabi Asadabadi
Please find
your
groupmates,
before it is
too late…
Your Individual Assignment
has been published!
Your Individual Assignment
has been published!
ENGG1865 Schedule Overview
Weeks Topics
Week 1 Introduction
Week 2 CPM
Week 3 PERT
Week 4 Earned value management
Week 5 Project cost estimation
Week 6 Project scheduling & planning using MS Project (Basics)
Week 7 Project scheduling & planning using MS Project (Advanced)
Week 8 Common issues in project time, cost and resource planning
Week 9 Quiz I (Week 1, 2, 3, and 4)
Week 10 Resource planning
Week 11 Procurement planning
Week 12 Quiz II (Week 5, 6, 7, and 8)
Week 13 Class Presentations + Self Study Module
How long does it take you
to go home?
60 minutes
No traffic: How long does it
take you to go home?
30 minutes
Rush hours: How long does it
take you to go home?
120 minutes
PERT: Program Evaluation
Review Technique

PERT (expected
time) =
(30 + 4*60 + 120)/6
Expected time=65
minutes
Optimistic Estimate (O):
Estimate for all favourable
conditions with no risks or
changes
Pessimistic Estimate (P):
Estimate for all unfavourable
conditions with all negative risks
occurring and no mitigation of
negative risks
Most Likely Estimate (M):
Estimate for both favourable and
unfavourable conditions, with
some risks occurring.
Introduction to PERT
The Program Evaluation and Review Technique was developed
(in US Navy) in parallel to the Critical Path Method.
While CPM is a deterministic programming tool,
PERT is probabilistic or stochastic in nature.
Being a critical path technique, PERT has similarities to CPM
The fundamental aim of PERT is to track the progress of a project
and show, at different time intervals, the probability of
completing that project on time
Because no reliable
data is available to
evaluate a particular
PERT distribution, it is
generally assumed that
it falls on the beta
probability
distribution curve.
The Probability Concept In PERT
Three point Estimate
The fundamental aim of three point estimate is to capture the variability of activity completion estimates
and reflect these in the time forecasts for project completion.
The most likely time
duration of an activity, not
necessarily the mean.
The most optimistic
duration of an activity. The
shortest time interval the
activity might be
completed in.
The most pessimistic
duration estimate. The
longest time interval the
activity might be
completed in..
The mean te and standard deviation s of an activity can be calculated using the formulae
below:
a bm
= =
+ 4 + −
6 6
The Expected Project Duration and Z Value
Step 1: Calculate te and s at the activity level, for all activities.
= =
+ 4 + −
6 6
Step2: Calculate critical path using forward and backward pass using te as the
activity duration.
Step3: Calculate project duration by adding durations of critical activities.
= Σ() for critical activities
The expected project
duration is calculated
as a sum of durations of
critical activities on the
assumption of
independence among
activities.
The Expected Project Duration and Z Value
Step 4: Calculate 2 for the activities on the critical path
Step 5: Calculate for these critical activities
= √Σ2 for critical activities
Step 6: Calculate the number that allows you to look up a probability
−
=

The standard deviation
S of an expected project
duration is derived as
the square root of the
sum of the squares of
the standard deviations
of individual critical
activities.


Z = Ts−Te
S
The Probability Table
Step 7: The computed Z value is converted to a
probability value using the look-up table
Z = Ts−Te
S
The Probability Table
Step 7: The computed Z value is converted to a
probability value using the look-up table
89.25%
Z = 1.24
Z = Ts−Te
S
Example:
Z=1.24
The Probability Table
Step 7: The computed Z value is converted to a
probability value using the look-up table
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is ??
days. What is the probability of
this project being completed in
less than 140 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 10
days. What is the probability of
this project being completed in
less than 156 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 10
days. What is the probability of
this project being completed in
less than 156 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 10
days. What is the probability of
this project being completed in
less than 156 days?
94.52%
Z= 1.6
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 10
days. What is the probability of
this project being completed in
less than 156.5 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 10
days. What is the probability of
this project being completed in
less than 156.5 days?
95.05%
Z= 1.65
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 147 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 147 days?
72.91%
Z= 0.608 0.61
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 147 days?
72.91%
Z= 0.608 0.61
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 142 days?
Before you compute, will it be higher or
lower than completing project in 147
days???
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 142 days?
56.75%
Z= 0.173 0.17
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
more than 142 days?
100% - 56.75%
Z= 0.173 0.17
P=1-0.5675
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 140 days?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
more than 140 days?
50%
Z= 0.00
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 130 days?
??%
Z= - 0.869 -0.87
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 130 days?
??%
Z= - 0.869 -0.87
Will it be smaller or
larger than 50%?
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 130 days?
19.22%
Z= - 0.869 -0.87
P = 1- 0.8078
P= 0.1922
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 130 days?
??%
Z= - 0.869 -0.87
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 130 days?
Z= - 0.869 -0.87
P= 0.1922
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
more than 130 days?
Z= - 0.869 -0.87
P= 1- 0.1922
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 120 days?
Will it be higher or lower than
completing project in 130 days???
Z = Ts−Te
S
The Probability Table
A project expected completion
time is 140 days. The standard
deviation for this project is 11.5
days. What is the probability of
this project being completed in
less than 120 days?
Will it be higher or lower than
completing project in 130 days???


Class Activity: Draw the Network Diagram
Activity Predecessors
A -
B A
C A
D A
E C
F E, B, D
0A
5 5
5
C
11 6
5
B
8 3
5
D
11 6
11
E
15 4
15
F
4
5
3
6
6
4
4
ES: Start from Zero
Compute ES and EF
ES ID LS
Float Description
EF Dur LF
Forward Pass
Forward Pass: Max
Class Activity: Do Forward Pass (ES and EF)
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 total duration ( = 20)
Floats???
0 0
A
5 5 5
5 5
C
11 6 11
5 12
B
8 3 15
5 9
D
11 6 15
11 11
E
15 4 15
15 15
F
19 4 19
5
3
6
6
4
4
ES: Start from Zero
Compute ES and EF
Backward Pass: Min
ES ID LS
Float Description
EF Dur LF
Backward Pass
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 total duration ( = 20)
Class Activity: Floats?
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
5
3
6
6
4
4
ES: Start from Zero
Compute ES and EF
Backward Pass: Min
ES ID LS
Float Description
EF Dur LF
Backward Pass
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 total duration ( = 20)

Standard deviations of tasks???
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
5
3
6
6
4
4
ES: Start from Zero
Compute ES and EF
Backward Pass: Min
ES ID LS
Float Description
EF Dur LF
Backward Pass
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 total duration ( = 20)
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 day total duration ( = 20)
Standard Deviation of the entire project?
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
ES: Start from Zero
Compute ES and EF
Backward Pass: Min
ES ID LS
Float Description
EF Dur LF
Backward Pass
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 day total duration ( = 20)
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
is computed based on s of critical activities (not all
activities):
= √ (0.110+0.110+0.110+0.444)
S=0.880
Standard Deviation of the entire project?
is computed based on s of critical activities (not all
activities):
= √ (0.110+0.110+0.110+0.444)
S=0.880
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 day total duration ( = 20)
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
??%
Z=
Z = Ts−Te
S
Class Activity 1: Floats? The probability of completion in less than 20 days?
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 day total duration ( = 20)
Class Activity 1: Floats?
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
??%
Z=1.14
Z = Ts−Te
S
The probability of completion in less than 20 days?
1. Calculate the total duration and critical path for the given project
2. Calculate the probability of completion for a 20 day total duration ( = 20)
Class Activity 1: Floats?
0 0
0 A
5 5 5
5 5
0 C
11 6 11
5 12
7 B
8 3 15
5 9
4 D
11 6 15
11 11
0 E
15 4 15
15 15
0 F
19 4 19
is computed based on s of critical activities (not all
activities):
= √ (0.110+0.110+0.110+0.444)
S=0.880
87.29%
Z=1.14
Z = Ts−Te
S
Class Ac ivity 1 n your own


ENGG1865 Schedule Overview
Weeks Topics
Week 1 Introduction
Week 2 CPM
Week 3 PERT
Week 4 Earned value management
Week 5 Project cost estimation
Week 6 Project scheduling & planning using MS Project (Basics)
Week 7 Project scheduling & planning using MS Project (Advanced)
Week 8 Common issues in project time, cost and resource planning
Week 9 Quiz I (Week 1, 2, 3, and 4)
Week 10 Resource planning
Week 11 Procurement planning
Week 12 Quiz II (Week 5, 6, 7, and 8)
Week 13 Class Presentations + Self Study Module