1. LECTURE 3

2. CRITICAL PATH METHOD - CALCULATIONS

3. An Example Network
Finish 5
Start 1 A F 2 B E 3 D C 4

4. Representation for CPM Calculation
B 6
D 2
Finish
Start
E 3
C 2
F 4

5. The “Simple” Forward Pass
Start with the first activity on the network
Traverse the network through the relationship arrows until you reach the end
For each activity, the early start is the maximum of the early finishes of the previous activities
The early finish is the early start + activity duration
Finish one level and then go to the next
This of course assumes only F-S relationships. We also have not really considered lags

6. Forward Pass Results 3 A 3 3 9 B 6 6 8 D 2 9 Finish Start 3 6 E 3 6 83
A 3 3 9
B 6 6 8
D 2 9
Finish
Start 3 6
E 3 6 8
C 2 4
F 4

7. The “simple” Backward Pass
Start with the last activity on the network
Traverse the network backwards through the relationship arrows until you reach the start
For each activity, the late finish is the minimum of the late starts of the previous activities
The late start is the late finish - activity duration
Finish one level and then go to the next

8. Backward Pass Results 3 A 3 3 9 B 6 6 8 D 2 7 9 9 Finish Start 3 6 E 33
A 3 3 9
B 6 6 8
D 2 7 9 9
Finish
Start 3 6
E 3 4 7 6 8
C 2 7 9 4
F 4 3 7

9. Introduce Floats 3 A 3 3 9 B 6 6 8 D 2 7 1 9 9 Finish Start 3 6 E 3 43
A 3 3 9
B 6 6 8
D 2 7 1 9 9
Finish
Start 3 6
E 3 4 1 7
Just talk about float as being LS-ES. WE will discuss more about this later. Float is basically the leeway that an activity has before it needs to be done. Example is that if an assignment takes 1 week and if you have 2 weeks to submit it, then you have a float of one week to goof off. You can use this float during, before or after the activity. If you delay more than a week, then you are in a problem. 6 8
C 2 7 1 9 4
F 4 3 7

10. The critical path 3 A 3 3 9 B 6 6 8 D 2 7 1 9 9 Finish Start 3 6 E 3 43
A 3 3 9
B 6 6 8
D 2 7 1 9 9
Finish
Start 3 6
E 3 4 1 7
The critical path is the path where the float is zero. We will talk more about this in the future.
The critical path is then the path where each activity has to proceed without delay. A delay in any one activity will delay the entire project.
Why is this useful? Because you can see which activities are critical and have to be carefully controlled. You can decide exactly when to start each activity and plan the sequence a little differently. If crews interfere and one activity has some float, then you can use that float to re-sequence the non-critical activity. Gantt chart etc does not give you this.
Can there be more than one critical path? Of course. E.g. if F took 9 days, that would be another critical path also.
Must there be one critical path? Yes there must
Will all activities with float = 0 be on the critical path? Most likely – we will investigate this more later 6 8
C 2 7 1 9 4
F 4 3 7

11. The final Algorithm Draw a clear and logical PD or AoN diagram
Enter Activity Durations
Perform a forward pass
Perform a backward pass
Determine floats
Check the path for which floats are zero
Mark this as the critical path.
This algorithm assumes that all relationships are F-S only.
What happens if we have relationships other than F-S? We will modify the forward pass and backward pass algorithms in a later class.

12. Another Example NetworkB
Start B E D F H G K
Finish
Do this as an in-class example

13. Representation for CPM Calculation
Start
D 2
H 6
K 2
Finish
B 4
E 4
F 6
G 3

14. Forward Pass Results 3 A 3 3 5 C 2 Start 4 6 D 2 8 H 6 K 2 Finish 43
A 3 3 5
C 2
Start 4 6
D 2 8 14
H 6 14 16
K 2 16
Finish 4
B 4 4 8
E 4 4 10
F 6 10 13
G 3

15. Backward Pass Results 3 A 3 6 3 5 C 2 6 8 Start 4 6 D 2 8 8 H 6 K 23
A 3 6 3 5
C 2 6 8
Start 4 6
D 2 8 8 14
H 6 14 16
K 2 16
Finish 4
B 4 4 8
E 4 4 10
F 6 7 13 10 13
G 3 16

16. Introduce Floats 3 A 3 6 3 5 C 2 6 8 Start 4 6 D 2 2 8 8 H 6 K 23
A 3 6 3 5
C 2 6 8
Start 4 6
D 2 2 8 8 14
H 6 14 16
K 2 16
Finish 4
B 4 4 8
E 4
Just talk about float as being LS-ES. WE will discuss more about this later. Float is basically the leeway that an activity has before it needs to be done. Example is that if an assignment takes 1 week and if you have 2 weeks to submit it, then you have a float of one week to goof off. You can use this float during, before or after the activity. If you delay more than a week, then you are in a problem. 4 10
F 6 7 3 13 10 13
G 3 3 16