A step by step introduction to Critical Path

1. Step by Step Critical Path
START dur=5 dur= 3 dur=6 FINISH
Activity A Activity B Activity C
A Simple Example of a Path
The CRITICAL PATH is the string of activities that will
delay the whole project if any one of them is delayed.
http://www.headfirstlabs.com/PMP/criticalpath/HeadFirstPMP_CriticalPathDrill.pdf
Great explanation, examples, and questions at:
1

2. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
A Simple Example of a Path
The Path is A -> B -> C
2

3. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
A Simple Example of a Path
The Path is A -> B -> C
The Duration of the Path equals the sum of all the durations of the
tasks in the path.
3

4. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
A Simple Example of a Path
The Path is A -> B -> C
The Duration of the Path equals the sum of all the durations of the
tasks in the path.
Path Duration = Duration of A + Duration of B + Duration of C
4

5. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
A Simple Example of a Path
The Path is A -> B -> C
The Duration of the Path equals the sum of all the durations of the
tasks in the path.
Path Duration = Duration of A + Duration of B + Duration of C
Path Duration = 5 + 3 + 6 The answer is 14
5

6. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Critical Path
dur =6 dur =9
Activity D Activity E
Note that the letters A,B,C,D,E
are just labels. They have
nothing to do with order
The Critical Path is the longest path in duration.
6

7. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Critical Path
dur =6 dur =9
Activity D Activity E
The Critical Path is the longest path in duration.
How many paths are there? What are they? What are their Durations?
7

8. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Critical Path
dur =6 dur =9
Activity D
Activity E
The Critical Path is the longest path in duration.
How many paths are there? What are they? What are their Durations?
2 A,B,C and D,E A,B,C = 14 D,E = 15
8

9. Step by Step Critical Path
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Critical Path
dur =6 dur =9
Activity D Activity E
The Critical Path is the longest path in duration.
How many paths are there? What are they? What are their Durations?
2 A,B,C and D,E A,B,C = 14 D,E = 15
D,E is longer so it is the Critical Path
9

10. Step by Step Float
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Float or Slack
dur =6 dur =9
Activity D Activity E
The Critical Path is the longest path in duration.
D,E is longer
so it is the
Critical Path
A,B,C = 14
D,E = 15
To determine the FLOAT of a path,
subtract the duration of a Path from the duration of the Critical Path
FLOAT is the
amount of time
an activity can
slip (or delay)
without causing
your project
delays.
Activities on the
CRITICAL PATH
have NO FLOAT.
Slack or Float = 0
10

11. Step by Step Float
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
How to Determine the Float or Slack
dur =6 dur =9
Activity D Activity E
The Critical Path is the longest path in duration.
D,E is longer
so it is the
Critical Path
A,B,C = 14
D,E = 15
FLOAT of A,B,C = D,E duration – A,B,C duration
15 – 14 = 1
EACH activity in A,B,C of this example has a float of 1
FLOAT is the
amount of time
an activity can
slip (or delay)
without causing
your project
delays.
Activities on the
CRITICAL PATH
have NO FLOAT.
Slack or Float = 0
11

12. Forward & Backward Pass
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
Critical Path (CP) – the longest path of activities to complete a project
Early Start (ES) – the earliest you can start an activity
Early Finish (EF) – the earliest you can finish and activity
Late Start (LS) - the latest you can start an activity (without affecting CP)
Late Finish (LF) - the latest you can finish an activity (without affecting CP)
Knowing Early Start and Early
Finish lets you know how
much freedom you have to
move the start dates of
activities without causing
problems
Knowing Late Start and Late
Finish lets you know how
much play you have in
scheduling activities
12

13. Calculating Forward Pass
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1 EF = ES + duration - 1
ES EF
Duration
LS LF
A Simple Example
13

14. Calculating Forward Pass
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1
EF = ES + duration - 1
1 5
5
LS LF
Example:
Activity A
Start = 0
ES = 0+ 1 = 1
EF = 1 + 5 – 1 = 5
A Simple Example
14

15. Calculating Forward Pass
START
1 5
dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1
EF = ES + duration - 1
ES EF
3
LS LF
Example:
Activity B
ES =
EF =
A Simple Example
15

16. Calculating Forward Pass
START
1 5
dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1
EF = ES + duration - 1
6 8
3
LS LF
Example:
Activity B
ES = 5 + 1 = 6
EF = 6 + 3 -1 = 8
A Simple Example
16

17. Calculating Forward Pass
START
1 5
dur=5
6 8
dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1
EF = ES + duration - 1
ES EF
6
LS LF
Example:
Activity C
ES =
EF =
A Simple Example
17

18. Calculating Forward Pass
START
1 5
dur=5
6 8
dur=3 dur=6 FINISH
Activity A Activity B Activity C
ES = previous EF + 1
EF = ES + duration - 1
9 14
6
LS LF
Example:
Activity C
ES = 8 + 1 = 9
EF = 9 + 6 – 1 = 14
A Simple Example
18

19. Calculating Backward Pass
START
1 5
dur=5
6 8
dur=3
9 14
dur=6 FINISH
Activity A Activity B Activity C
LF = previous LS -1
LS = LF - duration + 1
ES EF
6
9 14
Example:
Activity C Since we are beginning
our calculations at the
end, DO NOT subtract 1
LF = 14
LS = 14 – 6 + 1 = 9
A Simple Example
19

20. Calculating Backward Pass
START
1 5
dur=5
6 8
dur=3
9 14
dur=6
9 14
FINISH
Activity A Activity B Activity C
LF = previous LS -1
LS = LF - duration + 1
ES EF
3
6 8
Example:
Activity B
LF = 9 – 1 = 8
LS = 8 – 3 + 1 = 6
A Simple Example
20

21. Calculating Backward Pass
START
1 5
dur=5
6 8
dur=3
6 8
9 14
dur=6
9 14
FINISH
Activity A Activity B Activity C
LF = previous LS -1
LS = LF - duration + 1
ES EF
3
1 5
Example:
Activity A
LF = 6 – 1 = 5
LS = 5 -5 + 1= 1
A Simple Example
21

22. Calculating Backward Pass
START
1 5
dur=5
1 5
6 8
dur=3
6 8
9 14
dur=6
9 14
FINISH
Activity A Activity B Activity C
A Simple Example
Notice that on the “Critical Path” ES = LS and EF = LF
22

23. Forward & Backward with 2 Paths
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6
dur =9
Activity D Activity E
Since I have not changed the numbers,
we have already determined that
Duration of D,E = 15 and A,B,C = 14
Path D,E is the Critical Path,
Do CRITICAL PATH calculations first
23

24. Forward & Backward with 2 Paths
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
7 15
dur =9
7 15
Activity D Activity E
Since I have not changed the numbers,
we have already determined that
Duration of D,E = 15 and A,B,C = 14
Path D,E is the Critical Path,
Activity D
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 0 + 1 = 1
EF = 1 + 6 – 1 = 6
Activity E
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 6 + 1 = 7
EF = 7 + 9 – 1 = 15
REMEMBER
In the Critical Path
ES = LS
EF = LF
24

25. Forward & Backward with 2 Paths
START
1 5
dur=5
6 8
dur=3
9 14
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
7 15
dur =9
7 15
Activity D Activity E
Since I have not changed the numbers,
we have already determined that
Duration of D,E = 15 and A,B,C = 14
Path D,E is the Critical Path,
Activity A
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 0 + 1 = 1
EF = 1 + 5 – 1 = 5
Activity C
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 8 + 1 = 9
EF = 9 + 6– 1 = 14
Activity B
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 5 + 1 = 6
EF = 6 + 3 – 1 = 8
25

26. Forward & Backward with 2 Paths
START
1 5
dur=5
6 8
dur=3
9 14
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
7 15
dur =9
7 15
Activity D Activity E
Since I have not changed the numbers,
we have already determined that
Duration of D,E = 15 and A,B,C = 14
Path D,E is the Critical Path,
Backward Pass of A,B,C
Is where it gets interesting
26

27. Forward & Backward with 2 Paths
START
1 5
dur=5
2 6
6 8
dur=3
7 9
9 14
dur=6
10 15
FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
7 15
dur =9
7 15
Activity D Activity E
Since I have not changed the numbers,
we have already determined that
Duration of D,E = 15 and A,B,C = 14
Path D,E is the Critical Path,
Activity C
LF = LF of Critical Path
LS = LF - Duration +1
LF = 15
LS = 15– 6 + 1= 10
Activity A
LF = Previous LS - 1
LS = LF - Duration + 1
LF = 7 - 1= 6
LS = 6 - 5 + 1 = 2
Activity B
LF = Previous LS - 1
LS = LF - Duration + 1
LF = 10 - 1= 9
LS = 9 - 3 + 1 = 7
27

28. Forward & Backward with 2 Paths
START
1 5
dur=5
2 6
6 8
dur=3
7 9
9 14
dur=6
10 15
FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
7 15
dur =9
7 15
Activity D Activity E
What does it mean ?
It means
Activities on the Critical Path MUST start on time – on day 1
Activity A can start on day 2 and we can still meet our schedule
28

29. Forward & Backward with Many Paths
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
How many paths are there? What are they? What are their Durations?
29

30. Forward & Backward with Many Paths
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
How many paths? What are they? What are their Durations?
3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17
30

31. Forward & Backward with Many Paths
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
How many paths? What are they? What are their Durations?
3 A,B,C, D,E A,B,E A,B,C = 14 D,E = 15 A,B,E = 17
A,B,E is the longest, so A,B,E is the CRITICAL PATH
31

32. Forward & Backward with Many Paths
START
1 5
dur=5
6 8
dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6
9 17
dur =9
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
First Step: ES & EF of CRITICAL PATH
Activity A
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 0 + 1 = 1
EF = 1 + 5 – 1 = 5
Activity B
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 5 + 1 = 6
EF = 6 + 3 – 1 = 8
Activity E
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 8 + 1 = 9
EF = 9 + 9 – 1 = 17
32

33. Forward & Backward with Many Paths
START
1 5
dur=5
1 5
6 8
dur=3
6 8
dur=6 FINISH
Activity A Activity B Activity C
dur =6
9 17
dur =9
9 17
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
Second Step: LS & LF of CRITICAL PATH
This is easy for the Critical Path LS = ES LF = EF
33

34. Forward & Backward with Many Paths
START
1 5
dur=5
1 5
6 8
dur=3
6 8
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
3 8
9 17
dur =9
9 17
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
First Step: ES & EF of 2nd Longest Path D,E is 2nd longest
CAUTION
Do NOT change
values you already
calculated
Activity D ES & EF
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 0 + 1 = 1
EF = 1 + 6 – 1 = 6
Activity D LS & LF
LF = Previous LS - 1
LS = LF - Duration + 1
LF = 9 – 1 = 8
LS = 8 – 6 + 1 = 3
34

35. Forward & Backward with Many Paths
START
1 5
dur=5
1 5
6 8
dur=3
6 8
9 14
dur=6
12 17
FINISH
Activity A Activity B Activity C
1 6
dur =6
3 8
9 17
dur =9
9 17
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
Next Step: ES & EF of 3rd Longest Path A,B,C
CAUTION
Do NOT change
values you already
calculated
Activity C ES & EF
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 8 + 1 = 9
EF = 9 + 6 – 1 = 14
Activity C LS & LF
LF = LF of Critical Path
LS = LF - Duration + 1
LF = 17
LS = 17 – 6 + 1 = 12
35

36. Forward & Backward with Many Paths
START
1 5
dur=5
1 5
6 8
dur=3
6 8
9 14
dur=6
12 17
FINISH
Activity A Activity B Activity C
1 6
dur =6
3 8
9 17
dur =9
9 17
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
Next Step: ES & EF of 3rd Longest Path A,B,C
CAUTION
Do NOT change
values you already
calculated
Activity C ES & EF
ES = Previous EF + 1
EF = ES + Duration - 1
ES = 8 + 1 = 9
EF = 9 + 6 – 1 = 14
Activity C LS & LF
LF = LF of Critical Path
LS = LF - Duration + 1
LF = 17
LS = 17 – 6 + 1 = 12
36

37. Forward & Backward with Many Paths
START
1 5
dur=5
1 5
6 8
dur=3
6 8
9 14
dur=6
12 17
FINISH
Activity A Activity B Activity C
1 6
dur =6
3 8
9 17
dur =9
9 17
Activity D Activity E
Now to make it interesting A question on the test may be like this
We have added a dependency between B & E
What does it mean?
Activity A
Can start on day 1 or as
late as Day 3 without
affecting schedule
Activity C
Can start no earlier than
day 9, but it can start as
late as day 12 without
affecting schedule
The Critical Path is
A,B,E
37

38. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
38
How many paths are there? What are they? What are their Durations?

39. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
39
How many paths are there? What are they? What are their Durations?
It is easier to track the paths and then count them
Do the easy ones first

40. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
40
How many paths are there? What are they? What are their Durations?
A, B,C D,E
Are there others?

41. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
41
How many paths are there? What are they? What are their Durations?
A, B,C D,E
D,B,C
Any More?

42. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
42
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
Next step: compute duration

43. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
43
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
A,B,C = D,E =
D,B,C = D,B,C =
Next step: compute duration

44. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
44
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
A,B,C = D,E =
D,B,C = D,B,C =
Next step: compute duration

45. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
45
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
A,B,C=5+3+6 D,E=6+9
D,B,C=6+3+6 D,B,E=6+3+9
Next step: compute duration

46. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
46
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
A,B,C=14 D,E=15
D,B,C=15 D,B,E=18

47. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
47
How many paths are there? What are they? What are their Durations?
4 A, B,C D,E
D,B,C D,B,E
A,B,C=14 D,E=15
D,B,C=15 D,B,E=18
I forgot a path

48. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
We have added a dependency between D & B
48
How many paths are there? What are they? What are their Durations?
4 5 A, B,C D,E
D,B,C D,B,E
A,B,E
A,B,C=14 D,E=15
D,B,C=15 D,B,E=18
A,B,E = 5+3+9 = 17
I forgot a path

49. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
49
How many paths are there? What are they? What are their Durations?
5 A, B,C D,E
D,B,C D,B,E
A,B,E
A,B,C=14 D,E=15
D,B,C=15 D,B,E=18
A,B,E = 17
Time to do Forward & Backward Pass on the Critical Path
D,B,E is the longest. So D,B,E is the Critical Path

50. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
50
D,B,E is the longest. So D,B,E is the Critical Path
Activity D
ES = Previous EF + 1
EF = ES + Duration - 1
Activity B
ES = Previous EF + 1
EF = ES + Duration - 1
Activity E
ES = Previous EF + 1
EF = ES + Duration - 1

51. Working together to Solve
START dur=5 dur=3 dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
51
D,B,E is the longest. So D,B,E is the Critical Path
Activity D
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 0 + 1 = 1
EF = 1 + 6 -1 = 6
Activity B
ES = Previous EF + 1
EF = ES + Duration - 1
Activity E
ES = Previous EF + 1
EF = ES + Duration - 1

52. Working together to Solve
START dur=5
7 9
dur=3 dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6 dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
52
D,B,E is the longest. So D,B,E is the Critical Path
Activity D
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 0 + 1 = 1
EF = 1 + 6 -1 = 6
Activity B
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 6 + 1 = 7
EF = 7 + 3 – 1 = 9
Activity E
ES = Previous EF + 1
EF = ES + Duration - 1

53. Working together to Solve
START dur=5
7 9
dur=3 dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
10 18
dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
53
D,B,E is the longest. So D,B,E is the Critical Path
Activity D
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 0 + 1 = 1
EF = 1 + 6 -1 = 6
Activity B
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 6 + 1 = 7
EF = 7 + 3 – 1 = 9
Activity E
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 9 + 1 = 10
EF = 10 + 9 -1 = 18

54. Working together to Solve
START dur=5
7 9
dur=3 dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
10 18
dur =9
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
54
D,B,E is the longest. So D,B,E is the Critical Path
Time to compute LS & LF for the Critical Path

55. Working together to Solve
START dur=5
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
55
D,B,E is the longest. So D,B,E is the Critical Path
On the Critical Path LS = ES and LF = EF
Because there is NO FLOAT on the Critical Path
Next Step: Compute for next longest path

56. Working together to Solve
START dur=5
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
56
D,B,E is the longest. So D,B,E is the Critical Path
A,B,E is 2nd Longest

57. Working together to Solve
START dur=5
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
57
D,B,E is the longest. So D,B,E is the Critical Path
In A,B,E B & E are already done, so only compute A
CAUTION
Do NOT change
values you already
calculated
Activity A
ES = Previous EF + 1
EF = ES + Duration – 1
Activity A
LF = LF of Critical Path
LS = LF - Duration + 1

58. Working together to Solve
START
1 5
dur=5
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
58
D,B,E is the longest. So D,B,E is the Critical Path
CAUTION
Do NOT change
values you already
calculated
Activity A
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 0 + 1 = 1
EF = 1 + 5- 1 = 5
Activity A
LF = Previous LS - 1
LS = LF - Duration + 1

59. Working together to Solve
START
1 5
dur=5
2 6
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
59
D,B,E is the longest. So D,B,E is the Critical Path
CAUTION
Do NOT change
values you already
calculated
Activity A
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 0 + 1 = 1
EF = 1 + 5- 1 = 5
Activity A
LF = Previous LS - 1
LS = LF - Duration + 1
LF = 7 - 1= 6
LS = 6 - 5 + 1 = 2

60. Working together to Solve
START dur=5
7 9
dur=3
7 9
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
60
D,B,E is the longest. So D,B,E is the Critical Path
CAUTION
Do NOT change
values you already
calculated
Activity C
ES = Previous EF + 1
EF = ES + Duration – 1
Activity C
LF = LF of Critical Path
LS = LF - Duration + 1

61. Working together to Solve
START dur=5
7 9
dur=3
7 9
10 15
dur=6 FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
61
D,B,E is the longest. So D,B,E is the Critical Path
CAUTION
Do NOT change
values you already
calculated
Activity C
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 9 + 1 = 10
EF = 10 + 6 -1 = 15
Activity C
LF = LF of Critical Path
LS = LF - Duration + 1

62. Working together to Solve
START
1 5
dur=5
2 6
7 9
dur=3
7 9
10 15
dur=6
13 18
FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
Now to make it even MORE interesting! A question on the test may be like this
62
D,B,E is the longest. So D,B,E is the Critical Path
CAUTION
Do NOT change
values you already
calculated
Activity C
ES = Previous EF + 1
EF = ES + Duration – 1
ES = 9 + 1 = 10
EF = 10 + 6 -1 = 15
Activity C
LF = LF of Critical Path
LS = LF - Duration + 1
LF = 18
LS = 18 – 6 + 1 = 13

63. What do we know from this?
START
1 5
dur=5
2 6
7 9
dur=3
7 9
10 15
dur=6
13 18
FINISH
Activity A Activity B Activity C
1 6
dur =6
1 6
10 18
dur =9
10 18
Activity D Activity E
63
• Project Length is 18 days
• Critical Path is D,B,E
• There is no float on D,B,E
• Tasks D, B, & E must start on time
• Task D must start on Day 1
• There are 5 Paths
• Task A could start on Day 2
And NOT affect Schedule
• Task C could start on Day 13
And NOT affect Schedule
• ES, EF, LS & LF of each task
A link to more on Critical Path and Forward & Backward Pass The Link