Critical path Method

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