1. Project Management CPM Method Tutorial-p1
Objectives and Information Step 1. Developing the Network Step 2. Determining the Duration Step 3. Determining the Critical Path (s) part 2
Developed by:
Alex J. Ruiz-Torres, Ph.D.

2. Objectives and Information

3. Objectives and Information
There are two goals when analyzing a project plan using the CPM method.
1. Determine the duration of the project
2. Determine the critical path activities. In other words, the activities that determine the duration.
From a management perspective, the activities that need to be managed with more attention as any delay will delay the project.
Delay in activities that are not in a critical path will (up to a point) not have an effect on the duration of the project.

4. Objectives and Information
The project information that must be already defined:
Set of Activities
Activity duration
Precedence relationships
Example
Activity Code
Time
(Weeks)
Predecessors Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y

5. Step 1. Developing the Network

6. Step 1. Developing the Network
We use a Network representation of the project.
Nodes to represent the activities
Arcs to represent the relationships
We draw left to right.
Activity D
Activity M
this means activity D must be complete before activity M can be started

7. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Left to right Z
Z has no predecessors, so to the “extreme” left

8. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Left to right R Z
R goes after Z, so to its right

9. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Left to right R Z
U goes after Z, so to its right U

10. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Left to right U Z
Given no relationship between R and U, their
position is not relevant. R

11. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Left to right U Z
Arcs are added to indicate the U and R can only
start after Z is completed. R

12. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y U X Z
X and Y starts after U and R are finished,
so to their right R Y

13. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y U X Z
X can start after both R and U are finished R Y

14. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y U X Z
Y can start after both R and U are finished R Y

15. Step 1. Developing the Network
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y U X Z A
A can start after both
X and Y are finished R Y

16. Step 2. Determining the Duration

17. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
We draw a box next to each node
ES EF
LS LF
ES EF
LS LF U X
ES EF
LS LF
ES EF
LS LF Z A R Y
ES EF
LS LF
ES EF
LS LF

18. Step 2. Determining the Duration
ES = Early Start: earliest time by which an activity can start for the estimated Duration
EF = Early Finish: earliest time by which an activity can end for the estimated Duration
LS = Late Start: latest time by which an activity can start for the estimated Duration
LF = Late Finish: latest time by which an activity can end for the estimated Duration
ES EF
LS LF Z

19. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
We always start at time 0.
ES =0 for all activities with no predecessors.
WE ‘MOVE’ from LEFT to RIGHT
ES EF
LS LF
ES EF
LS LF U X
0 EF
LS LF
ES EF
LS LF Z A R Y
ES EF
LS LF
ES EF
LS LF

20. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
EF = ES + Activity Time
ES =0 + 3 for Activity Z
ES EF
LS LF
ES EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
ES EF
LS LF
ES EF
LS LF

21. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
The Earliest Activity U can start depends on the time activity Z is finished. Same for R
3S EF
LS LF
ES EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S EF
LS LF
ES EF
LS LF

22. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
At this time we do not know when X starts as we have yet to determine when U and R are completed.
3S EF
LS LF
?S EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S EF
LS LF
ES EF
LS LF

23. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
The EF for Activity U is ES + Time, thus 3 + 7
The EF for Activity R is its ES + Time, thus 3 + 5
3S10
LS LF
ES EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S 8
LS LF
ES EF
LS LF

24. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
The Earliest Activity X can start is when both U and R are finished. In other words the maximum of the EF’s. The max (8, 10) = 10.
3S10
LS LF
10 EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S 8
LS LF
ES EF
LS LF

25. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
Same for Y.
3S10
LS LF
10 EF
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S 8
LS LF
10 EF
LS LF

26. Step 2. Determining the Duration
Code
Time
Pred. Z 3 - R 5 U 7 X 6
R, U Y 9 A 4
X, Y
EF = ES + Activity Time
For X,
For Y,
3S10
LS LF
10 16
LS LF U X
0 3
LS LF
ES EF
LS LF Z A R Y
3S 8
LS LF
10 19
LS LF

27. Step 2. Determining the Duration
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 EF
LS LF Z A
ES of Activity A depends on EF of X and Y.
Max of 16 and 19 = 19 R Y
3S 8
LS LF
10 19
LS LF

28. Step 2. Determining the Duration
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 LF
EF = ES + Activity Time
= 23
Largest EF of the
Network
= Project
Duration
= 23 Weeks Z A R Y
3S 8
LS LF
10 19
LS LF

29. End of part 1
Part 2 will demonstrate how the determine the critical path.