1. Project Management CPM Method Tutorial-p2
Objectives and Information Step 1. Developing the Network Step 2. Determining the Duration Step 3. Determining the Critical Path (s)
Developed by:
Alex J. Ruiz-Torres, Ph.D.

2. Step 3. Determining the Critical Path(s)

3. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
3S10
LS LF
10 16
LS LF U X
0 3
LS LF
19 23
LS 23 Z A
For the activity with largest EF.
Let LF = EF R Y
3S 8
LS LF
10 19
LS LF

4. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
3S10
LS LF
10 16
LS LF U X
0 3
LS LF
19 23
ES EF
LS LF Z A
Calculate Late Start
LS = LF – Activity Time
LS = 23 – 4 = 19 R Y
3S 8
LS LF
10 19
LS LF

5. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
3S10
LS LF
10 16
LS LF U X
0 3
LS LF
19 23
ES EF
LS LF Z A
We ‘MOVE’ to the LEFT R Y
3S 8
LS LF
10 19
LS LF

6. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
When only one relationship, then
LF = LS of predecessor
ES EF
LS LF
3S10
LS LF
10 16
LS L19 U X
0 3
LS LF
19 23 Z A R Y
3S 8
LS LF
10 19
LS LF

7. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
When only one relationship, then
LF = LS of predecessor
3S10
LS LF
10 16
LS L19 U X
0 3
LS LF
19 23 Z A R Y
3S 8
LS LF
10 19
LS L19

8. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
LS = LF – Activity Time
= 19 – 6 = 13
3S10
LS LF
10 16
13L19 U X
0 3
LS LF
19 23 Z A R Y
LS = LF – Activity Time
= 19 – 9 = 10
3S 8
LS LF
10 19
10 L19

9. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
When an Activity precedes two or more, the minimum LS becomes its LF
Min (13, 10)
= 10
3S10
LS 10
10 16
13L19 U X
0 3
LS LF
19 23 Z A R Y
3S 8
LS LF
10 19
10 L19

10. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
When an Activity precedes two or more, the minimum LS becomes its LF
Min (13, 10)
= 10
3S10
LS 10
10 16
13L19 U X
0 3
LS LF
19 23 Z A R Y
3S 8
LS 10
10 19
10 L19

11. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
LS = LF – Activity Time
= 10 – 7 = 3
3S10
3S 10
10 16
13L19 U X
0 3
LS LF
19 23 Z A
LS = LF – Activity Time
= 10 – 5 = 5 R Y
3S 8
5S 10
10 19
10 L19

12. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
LF of Z = Min of LS from U and R
= Min (3, 5) = 3
3S10
3 10
10 16
13L19 U X
0 3
LS 3
19 23 Z A R Y
3S 8
5S 10
10 19
10 L19

13. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
LS = LF – Activity Time
LS = 3 – 3 = 0
3S10
3 10
10 16
13L19 U X
0 3
0S 3
19 23 Z A R Y
3S 8
5S 10
10 19
10 L19

14. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
We now determine the SLACK of each Activity. SLACK = LF – EF
3S10
3 10
10 16
13L19 U X
0 3
0S 3
19 23 Z A R Y
3S 8
5S 10
10 19
10 L19

15. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
SLACK = LF – EF
S = 0
3S10
3 10
10 16
13L19
S = 3 U X
0 3
0S 3
19 23
S = 0
S = 0 Z A R Y
S = 2
3S 8
5S 10
10 19
10 L19
S = 0

16. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
All Activities with a Slack = 0 are part of a Critical Path.
A Critical Path is a sequence of activities from “start” to “end” with activities with 0 Slack.
3S10
3 10
10 16
13L19
S = 0
S = 3 U X
0 3
0S 3
19 23
S = 0
S = 0 Z A R Y
S = 2
3S 8
5S 10
10 19
10 L19
S = 0

17. Step 3. Determining the Critical Path(s)
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
CP = Z – U – Y – A
Activity X has 3 weeks of slack
Activity R has 2 weeks of slack
3S10
3 10
10 16
13L19
S = 0
S = 3 U X
0 3
0S 3
19 23
S = 0
S = 0 Z A R Y
S = 2
3S 8
5S 10
10 19
10 L19
S = 0