Critical Path Method (CPM) is a network diagramming technique used to predict total project duration and identify the critical path. The critical path is the longest sequence of activities with zero float - it determines the earliest project completion date. In the example network diagram, the critical path is activities A, B, C, F with a total length of 15 time units. Calculating early and late start/finish dates using forward and backward passes identifies float, which indicates how much delay activities on the critical path can experience before delaying the overall project end date.

1. Critical Path Method (CPM)

2. CPM is a network diagramming technique used
to predict total project duration.
CPM is an analysis technique with three main
purposes:
To calculate the project’s finish date
To indentify to what extent each activity in the
schedule can slip(float) without delaying the
project
To identify the activities with highest risk that
cannot slip without changing the project finish
date2

3. CPM
How does the Critical Path Method calculate the
project’s finish date?
o Forward pass calculation
 calculates Early Start and Early Finish dates
o Backward pass calculation
 calculates Late Start and Late Finish dates
3

4. Early Start (ES) is the earliest date a task can
start
Early Finish (EF) is the earliest date a task can
be completed
Late Start (LS) is the latest date a task can start
without delaying the project and date
Late Finish (LF) is the latest date a task can
finish without delaying the project end date
4

5. 5
Start
D
5
F
2
C
6
Finish
E
4
B
1
A
2
Forward Pass
0 0
0 1511652
550
1515
1111 13

6. • Early Start (ES) = Latest related early date of all
immediate predecessors
ES= immediate Predecessors’ ES max
Early finish (EF) = Early Start + Duration
EF= ES + D
6
Activity A
ES EF
ES=3
ES=9
ES=10
D

7. 7
Start
D
5
F
2
C
6
Finish
E
4
A
2
0
0
0
0
0
108
50
15
15
11
1165
1110
2
550
115
1515
1515
1111 13
B
1
1513
Backward Pass

8. Late Finish (LF) = Earliest related late date of all
immediate successors
LF= immediate Successors’ LF min
Late Start (LS) = Late Finish – Duration
LS= LF-D
8
Activity A
LS LF
LF=3
LF=9
LF=10D

9. The purpose of backward pass is to find the float.
Float is the amount of time an activity can be
delayed or lengthened. Also called slack.
Total float: the amount of time an activity can be
delayed or extended without extending the overall
project’s completion time
9

10. What is the total Float for activity A?
10
Start
D
5
F
2
C
6
Finish
E
4
A
2
0
0
0
0
0
108
50
15
15
11
1165
1110
2
550
115
1515
1515
1111 13
B
1
1513

11. 11
Total float = LF-ES-D
A
2
0
108
65
1110
2
B
1
LFLSEFES
10820
A
A
Float
Float

12. Total Float:
TF= LF - ES – D
TF= LF – (ES+D) = LF-EF
TF= LF-D-ES= LS-ES
12
Activity A
LS LF
ES EF

13. Free Float: the amount of time an activity can be
delayed without delaying the early start date of its
subsequent tasks
13
Activity A
LS LF
ES EF

14. What is the FF for activity A?
What would happen if A uses its max float?
(A)EF=LF=10 (B) ES=LS=10
IF the early finish date of activity A =5
the early start date of activity B=5
FF=5-2=3
14
A
2
0
108
65
1110
2
B
1

15. Free Float: the amount of time an activity can be
delayed without delaying the early start date of its
subsequent tasks
EF= ES(B) – EF(A)
EF= ES(earliest successor)- EF
15
Activity A
LS LF
ES EF

16. Why floats are important in the critical path
method?
If an activity has a TF=0, what does this mean?
Floats determine thee criticality of an activity
Critical activities have the least amount of Float
Floats determine the critical path
16

17. The critical path is made of activities that cannot
be delayed without delaying the final date of the
project
If an item is on critical path, it has a zero float
The critical path is the path with longest duration
It is possible to have more than one critical path
17

18. What is the critical path?
What is the length of the critical path?
18
Start
D
5
F
2
C
6
Finish
E
4
A
2
0
0
0
0
0
108
50
15
15
11
1165
1110
2
550
115
1515
1515
1111 13
B
1
1513

19. Critical Path Method (CPM)
CPM is a network diagramming technique used
to predict total project duration
A critical path for a project is the series of
activities that determines the earliest time by
which the project can be completed
The critical path is the longest path through the
network diagram and has the least amount of
slack or float
Slack or float is the amount of time an activity
may be delayed without delaying a succeeding
activity or the project finish date
19

20. Calculating the Critical Path
First develop a good network diagram
Add the duration estimates for all activities on
each path through the network diagram
The longest path is the critical path
If one or more of the activities on the critical path
takes longer than planned, the whole project
schedule will slip unless the project manager
takes corrective action
20