1. Analysing the AoA network
Project Management

2. Total Project Time
The minimum time in which the project can be completed.
Calculation: forward pass
Forward pass: calculating the earliest event times (EETs) and the earliest start times (ESTs) of all activities.
Earliest Finishing Time = EST + Duration

3. Critical path
Path: continuous series of project activities connected by logical relationships as designated in the project schedule network diagram.
Critical path: sequence of activities that has no float time, and that determines the duration of the project. It is the longest path. Activities on the critical path (or paths) are the critical activities.
The critical path can be identified by a backward pass, calculating the Latest Event Times (LETs) and the Latest Finishing Times (LFTs).
Latest Starting Time = Latest Finishing Time - Duration

4. Activity times & event times
EET = EST of all emerging activities
LET = LFT of all entering activities
Deadline
Activity identifier
Duration 1 2
EET
LET

5. TPT
EST 0
EFT 14 14 14 1 2 a 14
LST 0
LFT 14
TPT = 14

6. Float 1 2 Float on activity ‘a’: Float: 6 a 20 EST 0 EFT 14 14 14 6 2014 14 1 2 a 6 20
LST 6
LFT 20
Float: 6

7. 4 6 5 Calculate the… EET of event 6 LETs of events 4 and 522 ? 5 24 6 34 d e 8 10
Calculate the…
EET of event 6
LETs of events 4 and 5
ESTs and EFTs of activities ‘d’ and ‘e’
LSTs and LFTs of activities ‘d’ and ‘e’

8. 4 6 5 EST and EFT of ‘d’: 22 and 30 EST and EFT of ‘e’: 24 and 348 4 30 d 26 26 34 34 6 34 34 24 24 5 10 34 e 24 24
EST and EFT of ‘d’: 22 and 30
EST and EFT of ‘e’: 24 and 34
LST and LFT of ‘d’: 26 and 34
LST and LFT of ‘e’: 24 and 34

9. 15 ? 30 10 a 10 ? 20 ? 35 12 b 25 ? 8 c

10. 15 20 30 10 a 10 17 20 22 35 12 b 25 18 8 c

11. Calculate all event and activity times and the float-times, find the critical path

12. Calculate all event and activity times and the float-times, find the critical path16 16 16 31 8 24 24 24 39 20 30 29 39 20 20 20 35 35 35 38 38 38 50 51 20 20 20 35 35 36 39 39 39 51 51 35 51 35 51 30 21 51

13. Activity times and float for the previous diagram
EST
LST
EFT
LFT
Float A B C D E G H J K

14. Activity times and float for the previous diagram
EST
LST
EFT
LFT
Float A 8 16 24 B 20 C 21 30 51 D 35 E 29 39 9 G 36 38 1 H J 31 K 50

15. Four characteristics of the critical path
It starts at the first node
It is continuous
It ends at the last node
It has no float

16. Floats in the AoA network

17. Activity and event times
Activity times:
EST
LST
EFT
LFT
Event times:
EET
LET

18. Float
Time available for an activity or path in addition to its duration.
It can be positive or negative
It is a property of activities (and available only at given activities)
In case of more succeeding activities, the minimum have to be taken.
Types of float:
Total float
Free float

19. Total float 2 1 4 3 The total float possessed by an activity.
Calculation for activity j:
Total floatj = LFTj – EFTj
Identify the activity/activities possessing float below, and calculate the total float(s). 2 ?
Total float =
= 35 – 22 = 13
Total float =
= 25 – 12 = 13 12 12 35 12 10 12 25 25 1 ? 25 4 ? 22 c a 13 23 35 23 12 15 3 ? 8 35 35 15 15 b 15 d 27 27
Total float =
= 27 – 15 = 12 27
Total float =
= 35 – 23 = 12
Critical path = ?
TFT = ?

20. Total float 2 1 4 3 The total float possessed by an activity.
Calculation for activity j:
Total floatj = LFTj – EFTj = LFTj – (ESTj + Dj)
Identify the activities possessing float below, and calculate the total float for each.
Total float =
= 11 – (0+5) = 6 2 5
Total float = 23 – (5+12) = 6 12 5 11 c a 1 4 23 15 8 23 b 3 15 d 15

21. Calculating free float
The FREE FLOAT is the float possessed by an activity which, if used, will not change the float in later activities.
Free floatj = ESTj+1 – EFTj = EEThead – EETtail - D
Free float =
= 5 – 0 – 5 = 0 2 5
Free float = 23 – 5 – 12 = 6 12 5 11 c a 1 4 23 15 8 23 b 3 15 d 15

22. Positive float on the critical path
If the target time (deadline) for the project (or for a part of the project) is grater than TPT, than a float will appear on the critical path(s), too (and also on other paths).
The float will be the minimal on the critical path(s).

23. Negative float
Negative float = the time by which activities on the path or paths concerned must be reduced if the TPT is to be met. Negative float is a type of the Total Float.
If it appears on both critical and non-critial paths, than the critical path has the greatest negative float (in absolute value).
Negative float apperas when the TPT is longer than the project’s target time. 1 ? 2 a 10 3 c 15

24. Negative float
Negative float = the time by which activities on the path or paths concerned must be reduced if the TPT is to be met. Negative float is a type of the Total Float.
If it appears on both critical and non-critial paths, than the critical path has the greatest negative float (in absolute value).
Negative float apperas when the TPT is longer than the project’s target time. 1 -5 2 10 5 a 3 20 15 c
Total float: -5

25. Total float = 11 – 0 – 5 = 6 Free float = 5 – 0 – 5 = 0
Slack
It is the ’float’ measured at events, and not at activities.
Slack = LET - EET
Slack: 6
Total float = 23 – 5 – 12 = 6 Free float = 23 – 5 – 12 = 6
Total float = 11 – 0 – 5 = 6 Free float = 5 – 0 – 5 = 0 2 5 12 5 11 c a 1 4 23
TF = 0; FF = 0
TF = 0; FF = 0 15 8 23 b 3 15 d
Slack: 0
Slack: 0 15
Slack: 0

26. Readings
Lockyer – Gordon (2005) Chapter 13

27. Thanks for the attention!