This document discusses project management and the critical path method technique. It defines project management as planning, directing, and controlling resources to meet time, cost, and technical constraints. The critical path method allows project managers to identify the critical activities and completion time of a project by determining the earliest and latest times of each activity. The document provides examples of constructing critical path networks and calculating key timing metrics to schedule and control a project.

1. CHAPTER 6
PROJECT MANAGEMENT
(PM)

2. Chapter Outline
6.1 Definition of project management
6.2 Three stages of project management
6.3 Project management technique- Critical
Path Method

3. 6.0 WHAT IS PROJECT?
A series of related jobs that are usually
directed toward some major output and
require a significant period of time to
perform

4. The planning, directing and controlling
resources (i.e. people, equipment,
material) to meet the technical, cost
and time constraints of the project.
6.1 WHAT IS PROJECT MANAGEMENT?

5. 6.2 Three Stages of Project Management
a) Project Planning – Developing a course of action about a specific
project. It involves with the activities such as description of the goal,
specification of the final output, resources, completion time, results
and priority, team organization need to be formed, project manager,
forecast and budget.
b) Project Scheduling – establishes the times for each activity in a
project and it also involves with tying the resources the resources to
specific activities and related to each other.
c) Project Controlling – monitor the resources , costs, quality and
budgets to compare the actual and planned progress of each activity.
It is able to identify the activities either behind or ahead schedule. It
also includes revising and changing plans, as well as shifting
resources to meet time, cost and quality demand.

6. Objectives of PM
1. Avoid unnecessary delay and costs
2. Complete projects successfully
according to time and costs

7. THREE PROJECT MANAGEMENT
TECHNIQUES
1. Project Evaluation and Review
Technique (PERT)
- Never performed project; can handle
uncertainties and able to estimate activity
time probability.

8. THREE PROJECT MANAGEMENT
TECHNIQUES
2. Critical Path Method (CPM)
- Most activities are similar to previous
projects. Activities times known.
3. Gantt Chart
- showing activity to perform at the time;
which activity is on schedule or behind
schedule

9. 1. When will the entire project be
completed?
2. What are the critical activities or tasks in
the project?
3. Which are the noncritical activities?
4. What is the probability the project will be
completed by a specific date?
Questions PERT & CPM Can Answer

10. A Simple Gantt Chart
Time
J F M A M J J A S
Design
Prototype
Test
Revise
Production

11. APPLICATION of PM (CPM )
Step 1 : Defining the project and WBS
Step 2 : Develop precedences
Step 3 : Draw CPM network
Step 4 : Compute the completion time
Step 5 : Use the network to plan,
schedule and control the project.

12. Step 3 : Draw CPM network
Methods of drawing:
1. Activity-On-Node (AON)
- use circles to represent project activity with arrow linking
them together to show the sequence in which they are to be
performed.
1. Activity-On-Arrow (AOA)
- use arrow to represent the project activity with circles
connecting predecessor and successor activities.

13. A Comparison of AON and AOA
Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
1 2 3 4
A comes before
B, which comes
before C.
(a) A B C
BA C
3 4
1
2
A and B must both
be completed before
C can start.
(b)
A
C
C
B
A
B
1 2
3
4
B and C cannot
begin until A is
completed.
(c)
B
A
C
A
B
C

14. Activity-On-Node (AON)
ACTIVITY
PRECEEDING
ACTIVITY
DURATION
(Days)
A - 1
B A 4
C A 3
D A 7
E B 6
F C,D 2
G E,F 7
H D 9
I G,H 4

15. a) Construct the network for this project
A
B
1
4
C
D
3
F
4
9
7E
7
6
2
G
H
I

16. b) Calculate the Earliest Start (ES), Earliest Finish (EF), Latest
Start (LS), Latest Finish (LF) and Slack time for each activity.
A
B
1
C
D
3
F
4
9
7E
7
6
2
G
H
I
0
0
1
1
1
1
5
5
5
5
11
11 11
11
18
18
1
6
4
9
1
2
8
9
8
9
10
11
8
9
17
18
18
18
22
22
4
Yellow- Earliest Start & Earliest
Finish
Red- Latest Start & Latest Finish

17. 1) ES - all predecessor activities must be able to
complete before and activity can be start.
2) EF – the earliest time activity can be completed
3) LS – all following activity must be completed
without delaying the entire project.
4) LF – the latest time and activity can be
completed and still maintain the project critical
path time.
ES EF
LS LF

18. Slack Time - activity that can be delayed without
affecting completion time activities
that is not the critical path
C
1
6
4
9
Slack = LF – EF @ LS - ES
Slack = 9 – 4 = 5 days
D
1
2
8
9 Slack = 9 – 8 = 1 day
Slack (H) = 18 – 17 = 1 day
Slack (F) = 11 – 10 = 1 day

19. c) Identify the Critical Path
A B E G I
0
0
1
1
1
1
5
5
5
5
11
11
11
11
18
18
18
18
22
22
Take out all the available path from the diagram;
1) A,B,E,G,I = 22 days- ‘CHOOSE THE HIGHEST TIME’
2) A,C,F,G,H,I = 17 days
3) A,D,F,G,H = 21 days
4) A,D,H,I = 21 days

20. d) What would happen if activity F is revised
to take four days instead of two?
F
2
8
9
10
11
F
4
8
9
10
11
Revised time = 4 daysOriginal time = 2 days

21. d) What would happen if activity F is revised
to take four days instead of two?
F
4
9
7E
6
4
G
H
I
5
6
11
12 12
12
19
19
8
8
12
12
8
10
17
19
19
19
23
23
D
1
1
8
8
7

22. Exercise 1
ACTIVITY PRECEEDING ACTIVITY DURATION (Days)
A - 2
B - 3
C A,B 3
D C 3
E C 4
F C,E 3
G B 5
H E 3
I D 6
J D,F 4
K G,H 5
L I,J 3

23. a) Construct the network for this project
a) Calculate the Earliest Start (ES), Earliest Finish
(EF), Latest Start (LS), Latest Finish (LF) and Slack
time for each activity.
c) Identify the Critical Path

24. Activity-On-Arrow (AOA)
ACTIVITY
PRECEEDING
ACTIVITY
DURATION
(MONTH)
A - 2
B A 4
C A 3
D B 1
E C 3
F D,E 6

25. Drawing The Precedence Diagram
1 2
A,2 B,4 3
4
C,3 5
D,1
E,3
F,6
6

26. 4. Determine the Earliest Event Time
(EET) and Latest Event Time (LET)
1 2
A,2 B,4 3
4
C,3 5
D,1
E,3
F,6
6
0
0
2
2
6
5
8 14
7
5
8 14
8
7
3
2

27. Determine The Completion Time Of The Project
1 2
A,2 B,4 3
4
C,3 5
D,1
E,3
F,6
6
0
0
2
2
6
5
8 14
7
5
8 14
Completion time
= 14 months

28. Determine the Critical Path (the path whose
activities are expected to consume the most time in
which determines the completion time.
1 2
A,2 B,4 3
4
C,3 5
D,1
E,3
F,6
6
0
0
2
2
6
5
8 14
7
5
8 14
Critical Path =
1 2 4 5 6

29. Determine the Critical Activities (Activities on
the path of which if delayed will delay the completion
time.
1 2
A,2 B,4 3
4
C,3 5
D,1
E,3
F,6
6
0
0
2
2
6
5
8 14
7
5
8 14
Critical Activities =
A, C, E, F

30. DETERMINE THE SLACKS / FLOATS
1. Total Float
- Time can be delayed without affecting the
project completion time
2
B,4
3
2
2
6
7
TFB = 7 – 2 – 4
= 1 month

31. DETERMINE THE SLACKS / FLOATS
2. Free Float
- Time available if an activity start time is
delayed, without making it critical
2
B,4
3
2
2
6
7
FFB = 6 – 2 – 4
= 0 month

32. DETERMINE THE SLACKS / FLOATS
3. Independent Float
- Time available if an activity start time is
delayed at most and finish at earliest.
2
B,4
3
2
2
6
7
IFB = 6 – 2 – 4
= 0 month

33. QUESTION 2 (April 2011)
ACTIVITY
PRECEEDING
ACTIVITY
DURATION
(MONTH)
A - 3
B - 9
C - 7
D A 12
E B 10
F E 11
G D 10
H F 7
I G,H 14
J C 15
K I,J 9

34. a)Draw the appropriate PERT diagram
1
2
A,3
B,9
3 4
C,7
5
D,12
E,10 F,11
6
G,10
H,7
7
I,14
8
J,15
9
K,9
10

35. b) Calculate the earliest start and the latest
start time for each event
EVENT EET LET
1 0 0
2 3 29
3 9 9
4 19 19
5 15 41
6 30 30
7 37 37
8 7 45
9 51 51
10 60 60

36. c) Calculate the project completion time
d) Identify the critical activities.
c) 60 Months
d) B,E,F,H,I,K

37. e) Calculate the free float and the independent
float for activity D.
Free Float
2
D,12
5
3
29
15
41
FFD = 15 – 3 – 12
= 0 month
IFB = 15 – 29 – 12
= - 26 @ 0 month
2
D,12
5
3
29
15
41
Independent Float

38. f) Compute the project completion time if
activity I is delayed by 4 weeks..
Total Float
7
I,14
9
37
37
51
51
TFI = 51 – 37 – 14
= 0 month
If activity I is delayed by 4 weeks, the
project completion time will be delayed
by 4 weeks too.

39. A Comparison of AON and AOA
Network Conventions
Activity on Activity on
Node (AON) Arrow (AOA)
A
C
DB
A B
C
D
Dummy
activity
A
B
C
D

40. Dummy Activity
A fictitious activity that has no
completion time and use no resources.
It is created to show the relationship
with the predecessor.

41. September 2001
1
2a
b 3
4
c
5
d
e
f
6
7
g

42. IMPORTANT TERMS
 Activity
 Event
 Activity-On-Node Convention
 Activity-On-Arrow Convention
 Precedence Relationship
 Path
 Critical Path
 Slack/Float
 Dummy Activitiy