1. Project Management (lecture)
Drawing AOA networks
Project Management
(lecture)

2. CPA, CPM and PERT
Critical Path Analysis (CPA), Critical Path Method (CPM)
deterministic with only one estimation
Program Evaluation and Review Technique (PERT)
probabilistic with three estimated durations

3. Activity on Arrow (AoA) diagrams

4. Elements of an AoA (Activity-on-Arrow) diagram
Activity (arrow)
Work element or task
Can be real or not real
Name or identification (a label) of the task must be added
Event (node)
The start and/or finish of one or more activities (= the situation before or after the task/tasks)
Tail (preceding) and head (succeeding) nodes

5. Conventions Time flows from left to right
Arrows’ direction and
Labels’ order must follow this rule
Head nodes always have a number (or label) higher that of the tail node. This is the same with the arrow labels (alphabetic order).
Activity labels are placed below the arrow (despite the pictures in the textbook), duration of activity is based above the arrow (this is not a general rule, it is only for our classes)
A network has only one starting and only one ending event.
These conventions are not universal. There are many other to choose from.

6. Graphical representation
Arrows, nodes, bending of arrows
Identification of activities
Representation of time
Representation of deadlines (external constraints)

7. Dependency rule b depends on a (b is a successor of a):1 2 3 12 13 a b
b and c are independent from each other: 3 4 2 1 b c a 13 12 8

8. Consequences of the dependency rule
An event cannot be realised until all activities leading to it are complete.
No activity can start until its tail event is (or tail events are) realised.

9. Merge and burst nodes Merge nodes: Burst nodes:
Events into which a number of activities enter and one (or several) leave.
Burst nodes:
Events that have one (or more) entering activities generating a number of emerging activities.

10. Two typical errors in logic
Looping: underlying logic must be at fault
Dangling: an activity is undertaken with no result 5 6 7 e f g 2 4
5 end a c d
1 start 3 b

11. Interfacing
When an event is common to two or more subnetworks it is said to be an ‘interface’ event between those subnetworks and is represented by a pair of concentric circles. 11 13 aa ac ab 21 ba 24 bc bb bd
12 22

12. Milestones
Events which have been identified as being of particular importance in the progress of the project.
Identified by an inverted triangle over the event node (occasionally with an imposed time for the event)
1/1/2014 1 2 3 a b

13. Multiple starts and finishes
Only used in computer programs
All starting activities can occur at the start and all finish activities will occur at the end of the project.

14. Hammock activities
Artificial activities created for the representation of the overhead cost with the aim of cost control.
Embrace activities belong to the same cost centre
Zero duration time (not taking part in the time analysis), because it is artificial
Overhead cost rate is assumed to be constant over the life of the hammock.

15. Hammock activity 1 2 1 3 4 12 2 a b c
h (hammock)

16. Dummy activities
Activities that do not require resources but may in some cases take time.
They are drawn as broken (dashed) arrows.
They are always subject to the basic dependency rule.
Three occasions to use dummies:
Identity dummies
Logic dummies
Transit time dummies

17. Identity dummies
When two or more parallel activities have the same tail and head nodes. 1 3 2 a b 4 3

18. Logic dummies
When two chains of activities have a common node yet they are at least partly independent of each other. Hint: examine ANY crossroads.
Example:
Activitiy c depends on activity a
Activity d depends on activities a and b
Solution:
separate c from b with a dummy activity

19. Logic dummy example: What is the difference?2 5 4 a b 3 6 7 1 g f e d c h 2 6 4 a b 3 7 8 1 g f e d c h 5

20. Transit time dummies
If a delay must occur after the competition of an activity before the successor activity can start. 2 4 a b 3 1 d c 5 2

21. Overlapping activities
If the activities are not fully discrete
The second activity can start before the first is completed but not before it is at least partly completed. 1 2 3 10 15 a b b 1 2 3 a1 a2 4 7 15
Is the dummy activity realy needed here?

22. 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

23. 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

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

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

26. 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

27. 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’

28. Readings
Lockyer – Gordon (2005) Chapter 11

29. Thanks for the attention!