‫كلية العلوم والدراسات االنسانية بالغاط‬
Chapter 2: Project Management
(PERT/CPM)
‫محمــد الــحداد‬
mhaddad@mu.edu. sa
http://tel.archives-ouvertes.fr/tel00411282/fr/
1
Project Planning

Given:

Statement of work




written description of goals
work & time frame of project
Work Breakdown Structure
Be able to: develop precedence relationship
diagram which shows sequential relationship
of project activities
2
Project

“A project is a series of activities directed to
accomplishment of a desired objective.”
Plan your work first…..then work
your plan
Network analysis
Introduction
Network analysis is the general name given to certain specific
techniques which can be used for the planning, management and
control of projects.
History



Developed in 1950’s
CPM by DuPont for chemical plants
PERT by U.S. Navy for Polaris missile
CPM was developed by Du Pont and the emphasis was on the
trade-off between the cost of the project and its overall
completion time (e.g. for certain activities it may be possible
to decrease their completion times by spending more money how does this affect the overall completion time of the
project?)
PERT was developed by the US Navy for the planning and control of
the Polaris missile program and the emphasis was on completing the
program in the shortest possible time. In addition PERT had the
ability to cope with uncertain activity completion times (e.g. for a
particular activity the most likely completion time is 4 weeks but it
could be anywhere between 3 weeks and 8 weeks).
CPM - Critical Path Method

Definition: In CPM activities are shown as a network of
precedence relationships using activity-on-node network
construction
 Single estimate of activity time
 Deterministic activity times
USED IN : Production management - for the jobs of repetitive
in nature where the activity time estimates can be predicted
with considerable certainty due to the existence of past
experience.
PERT Project Evaluation & Review Techniques

Definition: In PERT activities are shown as a network of precedence
relationships using activity-on-arrow network construction
 Multiple time estimates
 Probabilistic activity times
USED IN : Project management - for non-repetitive jobs (research
and development work), where the time and cost estimates tend
to be quite uncertain. This technique uses probabilistic time
estimates.
The Network construction

Use of nodes and arrows
 An arrow leads from tail to head directionally
Indicate ACTIVITY, a time consuming effort that is required to perform
a part of the work.
Arrows

 A node is represented by a circle
Indicate EVENT, a point in time where one or more activities start
and/or finish.
Nodes
-
-
A dummy shows precedence for two activities with same start & end
nodes
Activity on Node & Activity on Arrow
Activity on Node
Activity on Arrow
Gantt Chart


A Gantt chart is a type of bar chart, that
illustrates a project schedule.
Gantt charts illustrate the start and finish
dates of a project. Gantt charts can be used
to show current schedule status using
percent-complete shadings and a vertical
"TODAY" line as shown here.
Gantt Chart




Popular tool for project scheduling
Graph with bar representing time for each
task
Provides visual display of project schedule
Also shows slack for activities

(amount of time activity can be delayed without
delaying project)
11
Gantt Chart (continued)
Gantt chart
Originated by H.L.Gantt in 1918
Advantages
Limitations
-
Gantt charts are quite commonly used.
-
They provide an easy graphical
representation of when activities
(might) take place.
- Do not clearly indicate details regarding
the progress of activities
-
easy to maintain and read.
- Do not give a clear indication of
interrelation ship between the separate
activities
The Project Network
Network consists of branches & nodes
Node
1
2
3
Branch
14
Concurrent Activities
Lay foundation
2
3
Order material
Incorrect
precedence
relationship
3
Lay
foundation
Dummy
2
4
Order material
Correct
precedence
relationship
15
Consider the following table which describes the
activities to be done to build a house and its
sequence
Activity
predecessors Duration
A Design house and obtain financing
3
B Lay foundation
A
2
C Order and receive materials
A
1
D Build house
B,C 3
E Select paint
B,C 1
F Select carpet
E
1
G Finish work
D,F 1
16
Project Network For A House
3
Lay foundation
1
3
Design house
and obtain
financing
2
2
0
1
Order and
receive
materials
Dummy
4
Select
paint
Build
house
1
3
5
6
Finish
work
1
7
1 Select
carpet
17
Critical Path

A path is a sequence of connected activities
running from the start to the end node in a
network

The critical path is the path with the longest
duration in the network

A project cannot be completed in less than
the time of the critical path (under normal
circumstances)
18
All Possible Paths
path1:
1-2-3-4-6-7
3 + 2 + 0 + 3 + 1 = 9 months; the critical path
path2:
1-2-3-4-5-6-7
3 + 2 + 0 + 1 + 1 + 1 = 8 months
path3:
1-2-4-6-7
3 + 1 + 3 + 1 = 8 months
path4:
1-2-4-5-6-7
3 + 1 + 1 + 1 + 1 = 7 months
19
Forward and Backward Pass



Forward pass is a technique to move forward
through a diagram to calculate activity duration.
Backward pass is its opposite.
Early Start (ES) and Early Finish (EF) use the
forward pass technique.
Late Start (LS) and Late Finish(LF) use the
backward pass technique.
20
Early Times
(House building example)



ES - earliest time activity can start
Forward pass starts at beginning of network
to determine ES times
EF = ES + activity time




ESij = maximum (EFi)
EFij = ESij + tij
ES12 = 0
EF12 = ES12 + t12 = 0 + 3 = 3 months
i
j
21
Computing Early Times
-ES23 = max (EF2) = 3 months
- ES46 = max (EF4) = max (5,4) = 5 months
- EF46 = ES46 + t46 = 5 + 3 = 8 months
- EF67 =9 months, the project duration
22
Late Times



LS - latest time activity can be started
without delaying the project
Backward pass starts at end of network to
determine LS times
LF - latest time activity can be completed
without delaying the project


LSij = LFij - tij
LFij = minimum (LSj)
23
Computing Late Times







If a deadline is not given take LF of the project
to be EF of the last activity
LF67 = 9 months
LS67 = LF67 - t67 = 9 - 1 = 8 months
LF56 = minimum (LS6) = 8 months
LS56 = LF56 - t56 = 8 - 1 = 7 months
LF24 = minimum (LS4) = min(5, 6) = 5 months
LS24 = LF24 - t24 = 5 - 1 = 4 months
24
Project cost analysis:ES=5, EF=5
ES=3, EF=5
LS=3, LF=5
1
3
ES=0, EF=3
LS=0, LF=3
2
3
2
LS=5, LF=5
0
1
ES=3, EF=4
4
ES=5, EF=8
ES=8, EF=9
LS=5, LF=8
LS=8, LF=9
LS=4, LF=5
1
ES=5, EF=6
LS=6, LF=7
3
1
5
6
1
7
ES=6, EF=7
LS=7, LF=8
25
Activity Slack

Slack is defined as the LS-ES or LF-EF
Activities on critical path have ES = LS & EF
= LF (slack is 0)

Activities not on critical path have slack




Sij = LSij - ESij
Sij = LFij - EFij
S24 = LS24 - ES24 = 4 - 3 = 1 month
26
Total slack/float or Slack of an activity



Total slack/ float means the amount of time that
an activity can be delayed without affecting the
entire project completion time.
The activity on a given
path share the
maximum possible slack of the activity along
that path according to its share.
Sum of the possible slacks of the activities can
not exceed the maximum slack along that path.
27
Free slack of an activity
This is the maximum possible delay of
an activity which does not affect its
immediate successors.
 This is evaluated as
 FSij = ESj – EFij

28
Activity Slack Data
Activity
1-2*
2-3
2-4
3-4*
4-5
4-6*
5-6
6-7*
ES
0
3
3
5
5
5
6
8
LS
0
3
4
5
6
5
7
8
EF
3
5
4
5
6
8
7
9
LF
3
5
5
5
7
8
8
9
Slack (S)
0
0
1
0
1
0
1
0
Free slack
0
0
1
0
0
0
1
0
* Critical path
29
Probability of completing the project
within given time:0

4
6
8
10
Activity

Design house and
obtain financing

Lay foundation


Order and receive
materials

Build house

Select paint

Select carpet

Finish work

2
1
3
5
7
9
30
Probabilistic Time Estimates

Reflect uncertainty of activity times

Beta distribution is used in PERT
a + 4m + b
Mean (expected time): t =
6
2
b
a
Variance: s = (
)
6
2
where,
a = optimistic estimate
m = most likely time estimate
b = pessimistic time estimate
31
P (time)
P (time)
Example Beta Distributions
a
b
a
t
m
b
P (time)
m
t
a
m=t
b
32
Activity Information
Activity
1–2A
1–3B
1–4C
2–5D
2-6 E
3-5 F
4–5G
4–7H
5–8I
5–7J
7–8K
6–9L
8–9M
Time estimates (wks)
a
m
b
6
3
1
0
2
2
3
2
3
2
0
1
1
8
6
3
0
4
3
4
2
7
4
0
4
10
Mean Time
t
Variance
s2
10
9
5
0
12
4
5
2
11
6
0
7
13
33
Activity Information
Activity
1 – 2A
1 – 3B
1 – 4C
2 – 5D
2 – 6E
3-5F
4 – 5G
4 – 7H
5 – 8I
5 – 7J
7 – 8K
6 – 9L
8 – 9M
Time estimates (wks)
a
m
b
6
3
1
0
2
2
3
2
3
2
0
1
1
8
6
3
0
4
3
4
2
7
4
0
4
10
10
9
5
0
12
4
5
2
11
6
0
7
13
Mean Time
t
8
6
3
0
5
3
4
2
7
4
0
4
9
Variance
s2
.44
1.00
.44
.00
2.78
.11
.11
.00
1.78
.44
.00
1.00
4.00
34
Network With Times
2
6
E
5
A 8
L
4
D0
1
3
B6
5
F
3
G4
C3
4
H
2
8
I
7
9
M
9
K
0
J
4
7
35
PERT Example
Equipment testing
and modification
2
Final
debugging
Dummy
Equipment
installation
1
6
System
development
3
Manual
Testing
Job
training
Position
recruiting
4
Orientation
5
System
Training
8
System
Testing
9
System
changeover
Dummy
7
36
Early And Late Times
Activity
t
s2
ES
1-2
1-3
1-4
2-5
2-6
3-5
4-5
4-7
5-8
5-7
7-8
6-9
8-9
8
6
3
0
5
3
4
2
7
4
0
4
9
0.44
1.00
0.44
0.00
2.78
0.11
0.11
0.00
1.78
0.44
0.00
1.00
4.00
0
0
0
8
8
6
3
3
9
9
13
13
16
EF
8
6
3
8
13
9
7
5
16
13
13
17
25
LS
1
0
2
9
16
6
5
14
9
12
16
21
16
LF
9
6
5
9
21
9
9
16
16
16
16
25
25
S
1
0
2
1
8
0
2
11
0
3
3
8
0
37
Network With Times
ES=8, EF=13
2
ES=0, EF=8
(LS=1, LF=9 )
( LS=16 LF=21 )
6
5
8
0
(LS=0, LF=6 )
6
(LS=9, LF=9 )
4
ES=9, EF=16
3
ES=0, EF=3
3
( LS=21 LF=25 )
ES=8, EF=8
ES=0, EF=6
1
ES=13, EF=17
(LS=2, LF=5 )
4
3
( LS=9, LF=16 )
5
ES=6, EF=9
(LS=6, LF=9 )
8
7
ES=9, EF=13
4
ES=3, EF=7
(LS=5, LF=9 )
( LS=12, LF=16)
2
ES=3, EF=5
( LS=14, LF=16)
0
9
ES=16, EF=25
( LS=16 LF=25 )
ES=13, EF=13
( LS=16 LF=16 )
4
9
7
38
Project Variance
Project variance is the sum of the variances
along the critical path
s2 = s2 13 + s2 35 + s2 58 + s2 89
= s 2 B + s2 F + s 2 I + s 2 M
= 1.00 +0.11 + 1.78 + 4.00
= 6.89 weeks
39
Probabilistic Network Analysis
Determine the probability that a project is
completed (project completion time is )
within a specified period of time
x-m
Z =
where
s
m = tp = project mean time
s = project standard deviation
x = project time (random variable)
Z = number of standard deviations of x from
the mean (standardized random variable) 
40
Normal Distribution Of Project Time
X ~ N (m ,s 2 )
z=
Probability
xm
s
Zs
m = tp
x
Time
41
Standard Normal Distribution Of
transformed Project Time
Probability
Z ~ N (0,1 )
Z
m =0
z
Time
42
Probabilistic Analysis Example
What is the probability that the project is
completed within 30 weeks?
P(X 30) = ?
s2 = 6.89 weeks
s = 6.89
= 2.62 weeks
Z = x - m =30 - 25 = 1.91
P(Z  s1.91) = ?2.62
43
Determining Probability
From Z Value
Z
0.00
..
1.1
.
..
0.3643
.
1.9
0.4713
0.01 ..
04
..
0.3665
0.3729
.
+0.4719
…
…
0.09
0.4767
P( x < 30 weeks) = 0.50+ 04719
= 0.9719
m = 25
x = 30
Time (weeks)
44
What is the probability that the project will
be completed within 22 weeks?
22 - 25 = -3
= -1.14
Z=
2.62
2.62
P(Z< -1.14) = 0.1271
x = 22 m = 25 x=28
Time (weeks)
P( x< 22 weeks) = 0.1271
45
Benefits of PERT/CPM






Useful at many stages of project
management
Mathematically simple
Uses graphical displays
Gives critical path & slack time
Provides project documentation
Useful in monitoring costs
46
Limitations of PERT/CPM





Assumes clearly defined, independent, &
stable activities
Specified precedence relationships
Activity times (PERT) follow
beta distribution
Subjective time estimates
Over-emphasis on critical path
47