The Critical Path Method (CPM) is a project management technique used to identify essential tasks, their dependencies, and scheduling flexibility to ensure timely project completion. Developed in the late 1950s, CPM helps in efficient resource management and avoiding bottlenecks by breaking down projects into manageable activities, thereby facilitating better future planning. This document also elaborates on technical terms related to CPM, such as critical activities, float, and methods for calculating the critical path through examples and case studies.

1. CRITICAL PATH METHOD (CPM)
PRODUCTION MANAGEMENT
BY HIMANSHU KAKLOTAR (1920026)

2. WHAT IS CRITICAL PATH METHOD?
 The critical path method (CPM) is a technique to identify tasks that are necessary for project completion and
determine scheduling flexibilities.
 A critical path in project management is the longest sequence of activities that must be finished on time in
order for the entire project to be complete. Any delays in critical tasks will delay the rest of the project.
 CPM revolves around discovering the most important tasks in the project timeline, identifying task
dependencies, and calculating task durations.
 CPM was developed in the late 1950s as a method to resolve the issue of increased costs due to inefficient
scheduling.
 Since then, CPM has become popular for planning projects and prioritizing tasks.
 It helps you break down complex projects into individual tasks and gain a better understanding of the project’s
flexibility.

3. WHY TO USE CPM?
 Improves future planning: CPM can be used to compare expectations with actual progress. The data used
from current projects can inform future project plans.
 Facilitates more effective resource management: CPM helps project managers prioritize tasks, giving
them a better idea of how and where to deploy resources.
 Helps avoid bottlenecks: Bottlenecks in projects can result in lost valuable time. Plotting out project
dependencies using a network diagram, will give you a better idea of which activities can and can’t run in
parallel, allowing you to schedule accordingly.

4. TECHNICAL TERMS USED IN CPM
1. ACTIVITY
An activity is a part of the project denoted by an arrow on the network. The tail of the arrow indicates the start of
the activity whereas the head indicates the end of the activity.
2. DUMMY ACTIVITY
The activity which neither uses any resources nor any time for its completion is called dummy activity. It is
represented by a dotted arrow with zero time duration.
3. EVENT
An event represent the start or the completion of an activity. The beginning and end points of an activity are
events.
In a Network, a number of activities may terminate into single node called merge node and number of activities
may originate from a single node called burst node.
Tail event (i) Head event (j)
A
B
A
B
Merge Node Burst Node

5. 4. NETWORK
The diagrammatic representation of the activities of the entire project is called network of flow diagram.
5. PREDECESSOR AND SUCCESSOR ACTIVITY
All those activities, which must be completed for starting the activity under consideration are called its
predecessor activities.
All the activities which have to follow the activity under consideration are called its successor activities.
6. PATH
An unbroken chain of activities between two events is called path.
7. CRITICAL ACTIVITIES
The event which has no float, are called critical activities.
8. CRITICAL PATH
The path with the longest time sequence is called the critical path.
It is the longest path in the network from starting event to the ending event and defines the minimum time require
to complete the project.
If the activities on the critical path are delayed, the overall project time duration also delays.

6. 9. EARLY START TIME (E.S.)
The earliest possible time at which an activity may start, is called early start time.
10. EARLY FINISH TIME (E.F.)
The sum of the earliest start time of an activity and the time required for its completion is called early finish time.
11. LATE START TIME (L.S.)
The latest possible time at which an activity may start without delaying the date of the project, is called late start
time.
12. LATE FINISH TIME (L.F.)
The sum of the late start time of an activity and the time required for its completion is called late finish time.
13. SLACK
The slack of an event is the difference between the latest and the earliest time.
Slack (i) = L(i) – E(i)
14. FLOAT
Float is the amount of time that a task in a project network can be delayed without causing delay to subsequent
tasks project completion date.

7. TYPES OF FLOAT
1. TOTAL FLOAT
The amount of time by which the completion of an activity can be delayed beyond earliest expected Finish time
without affecting the overall project duration time.
Total float (TF) = LS – ES or LF – EF
2. FREE FLOAT
The amount of time by which the completion of an activity can be delayed beyond the earliest finish time without
affecting the earliest start of a subsequent activity.
Free Float (FF) = TF – Head slack
3. INDEPENDENT FLOAT
The amount of time by which the start of an activity can be delayed without affecting earliest start time of any
immediately following activities assuming that the preceding activity has finish at its latest finish time.
Independent float (IF) = FF – Tail Slack

8. HOW TO FIND CPM
NETWORK
Q.
1 2
3
A
B
C
D
E
F
4
5 6
3
5
7
10
5
4

9.  Now, to find the critical path, we have to find two values, Earliest Start Time (Es) and Latest Completion
Time (Lc).
 The process of determining the Es for all events is called a Forward Path Computation.
 The process of determining the Lc for all events is called a Backward Path Computation.
 Firstly, Divide the Circle into 3 parts as shown below:
 Left half section - Event.
 Top section of the right half - Earliest Start Time (Es)
 Bottom section of the right half – Latest Completion Time (Lc)

10. 1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
Network after dividing the circle in three sections:

11.  Forward Path Computation :
For Event 1, Earliest Start Time (Es1) is always zero.
Therefore, Es1 = 0
Es2 = Es1 + t1-2
= 0 + 3
Es2 = 3
Es3 = Es2 + t2-3
= 3 + 5
Es3 = 8
Es4 = Es2 + t2-4
= 3 + 7
Es4 = 10
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10

12. Es5 = max. (Es3 + t3-5 ,Es4 + t4-5 )
= max. (8 + 10, 10 + 5)
= max. (18,15)
Es5 = 18
Es6 = Es5 + t5-6
= 18 + 4
Es6 = 22
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
Therefore, Total Project Duration is 22 Weeks.

13.  Backward Path Computation :
For Event 6, Latest Completion Time (Lc6) is equal to Es6 .
Therefore, Lc6 = 22
Lc5 = Lc6 - t5-6
= 22 - 4
Lc5 = 18
Lc4 = Lc5 - t4-5
= 18 - 5
Lc4 = 13
Lc3 = Lc5 - t3-5
= 18 - 10
Lc3 = 8
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
22
18
13
8

14. 1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
0 22
18
13
8
3
Lc2 = min. (Lc4 - t2-4 , Lc3 - t2-3 )
= min. (13 – 7, 8 – 5)
= min. (6, 3)
Lc2 = 3
Lc1 = Lc2 - t1-2
= 3 - 3
Lc1 = 0

15.  Critical Path
1 2
3
4
5 6
A
B
C
D
E
F
3
5
7
10
5
4
0 3
8
10
18 22
0 22
18
13
8
3
To determine the critical path, following criteria needs to be satisfy.
Esj - Esi = tj-i
From the Network, we can see the activities that satisfy the above condition are:
1-2-3-5-6

16.  Float Table
Activity
Duration
(Week)
Earliest Latest Total float Free float Independent float
Start
time
Finish
time
Start
time
Finish
time
LS – ES /
LF – EF
TF – Head slack FF – Tail slack
1-2 3 0 3 0 3 0 0 0
2-3 5 3 8 3 8 0 0 0
2-4 7 3 10 6 13 3 0 0
3-5 10 8 18 8 18 0 0 0
4-5 5 10 15 13 18 3 3 0
5-6 4 18 22 18 22 0 0 0

17. CASE STUDY

18. 1 2
3
A
B
C
4
0
D
E F
G
H
5
6
7 8
12
12
4
9
31
17
55
NETWORK

19. 1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
 Forward Path Computation :
For Event 1, Earliest Start Time (Es1) is always zero.
Therefore, Es1 = 0
Es2 = Es1 + t1-2
= 0 + 0
Es2 = 0
Es3 = Es2 + t2-3
= 0 + 12
Es3 = 12
Es4 = Es2 + t2-4
= 0 + 12
Es4 = 12
0 0
12
12

20. Es5 = Es3 + t3-5
= 12 + 4
Es5 = 16
Es6 = max. (Es4 + t4-6 ,Es5 + t5-6)
= max. (12 + 0, 16 + 9)
= max. (12,25)
Es6 = 25
Es7 = max. (Es5 + t5-7 ,Es6 + t6-7 ,Es4 + t4-7)
= max. (16 + 31, 25 + 17, 12 + 0)
= max. (47,42,12)
Es7 = 47
Es8 = Es7 + t7-8
= 47 + 55
Es8 = 102
Therefore, Total project duration is 102 months
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102

21.  Backward Path Computation :
For Event 8, Latest Completion Time (Lc8) is equal to Es8 .
Therefore, Lc8 = 102
Lc7 = Lc8 – t7-8
= 102 - 55
Lc7 = 47
Lc6 = Lc7 - t6-7
= 47 - 17
Lc6 = 30
Lc5 = min. (Lc7 - t5-7 , Lc6 - t5-6 )
= min. (47 - 31, 30 – 9)
= min. (16, 21)
Lc5 = 16
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16

22. Lc4 = min. (Lc7 - t4-7 , Lc6 - t4-6 )
= min. (47 - 0, 30 – 0)
= min. (47, 30)
Lc4 = 30
Lc3 = Lc5 - t3-5
= 16 - 4
Lc3 = 12
Lc2 = min. (Lc4 - t2-4 , Lc3 - t2-4 )
= min. (30 - 12, 12 – 12)
= min. (18, 0)
Lc2 = 0
Lc1 = Lc2 - t1-2
= 0 - 0
Lc1 = 0
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16
30
0
0
12

23. From the Network, we can see the activities that are critical:
1-2-3-5-7-8
 Critical Path:
1 2
3
4
5
6
B
C
D
E F
7 8
G
H
A
0
12
12
4
9
31
17
55
0 0
12
12
16
25
47 102
102
47
30
16
30
0
0
12

24. Activity
Duration
(Months)
Earliest Latest Total float Free float
Independent
float
Start
time
Finish
time
Start
time
Finish
time
LS – ES /
LF – EF
TF – Head
slack
FF – Tail
slack
1-2 0 0 0 0 0 0 0 0
2-3 12 0 12 0 12 0 0 0
2-4 12 0 12 18 30 18 0 0
3-5 4 12 16 12 16 0 0 0
5-6 9 16 25 16 25 0 5 5
5-7 31 16 47 16 47 0 0 0
6-7 17 25 42 30 47 5 5 0
7-8 55 47 102 47 102 0 0 0
 Float Table:

25.  Conclusion:
1. Activity 2-4 and Activity 6-7 can be delayed by 18 months and 5 months
respectively beyond earliest expected finish time without delaying overall project
duration.
2. Both Activity 5-6 and Activity 6-7 can be delayed by 5 months beyond earliest start
time without delaying the early start of its successor activity.
3. Activity 5-6 starting or finishing of an activity can be delayed without affecting the
total float of its preceding or succeeding activity.
 Reference:
International Journal of Sciences
PROJECT PLANNING AND SCHEDULING, THE CRITICAL PATH METHOD
APPROACH. BUI POWER PROJECT AS A CASE STUDY.
Salifu Katara, S.K. Amponsah

26. THANK YOU