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

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

Activity on Arrow (AoA) diagrams

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

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.

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

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

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.

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.

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

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

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

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.

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.

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

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

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

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

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

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

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?

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

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

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

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

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

4 6 5 Calculate the… EET of event 6 LETs of events 4 and 5 22 ? 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’

Readings Lockyer – Gordon (2005) Chapter 11

Thanks for the attention!