Network AnalysisTerminology

• Activity– A specific task or set of tasks that are required by

the project;– use up resources; and– take time to complete.

• Event– The result of completing one or more activities.– An identifiable end state occurring at a particular

point of time.

Network• The combination of all activities (usually drawn in arcs) and events (usually

drawn in nodes at the beginning and end of each arc) define the project and activity precedence relationships.

• Usually is drawn from left to right.

• Arrows placed on the arcs indicate the direction of flow.

• Before an event can be realised that is achieved immediately proceeding events must be completed. These are called predecessors.

• Thus, an event represents a moment in time when each and every predecessor activity has been competed.

• Events have use no resources and have no time duration. They are merely points on the network -- conditions on the system that can be recognised --.

• Path– The series of connected activities (or intermediate

events) between any two events in the network.

• Critical– Activities, events or paths which if delayed will delay

completion of the project.• - A projects critical path is understood to mean that

sequence of critical activities (and critical events) that connect the projects start to it’s finish event.

1 2

3

4

5 6A

B

C

D

E

F

G

Two ways of drawing networks (AOA)Sample: Activity On Arc

Sample Activity On Node (AON)

A

B

C

D

E

F

G

Action Plan

OBJECTIVE: To complete:……………………………….

MEASURES OF PERFORMANCE………………………. ……………….………………………………………………..

CONSTRAINTS……………………………………………..

Tasks Precedence Time Cost Who Doesa - 5 days - -b - 4 days - -c a 6 days - -d b 2 days - -e b 5 days - -f c,d 8 days - -

Activity On Arc• If we make the assumption that node 1 denotes the

event called “START” • Activities a and b have no predecessors, so we can

assume their source is at START (node 1) and their destination nodes will be numbers 1 & 2 respectively.

1

2

3

a

b

1

2

3

a

b5

4

6

c

d

e

Tasks Precedence Time Cost Who Does

a - 5 days - -b - 4 days - -c a 6 days - -d b 2 days - -e b 5 days - -f c,d 8 days - -1

2

3

a

b

5

4 6c

d

e

f

START

If we add c, d and e to the network we can see that c follows a, d follows b and e also follows a.We can see from the action plan that activity f must follow both c and d. However, any activity must only have its source in 1 node it can be seen then that there is a need to collapse nodes 4 and 5 (and renumber them)

• The action plan indicates no further activity is required to complete the task, so we have reached the end of this particular plan. Once again we can redraw the network to show the final activities (those with no successors ends in a single node).

1

2

3

a

b

5

4c

d

e

f

END

START

Tasks Precedence Time Cost Who Does

a - 3 days - -b - 4 days - -c a 6 days - -d b 2 days - -e b 5 days - -f c,d 2 days - -g e 2 days - -h f,g, 8 days - -

Draw a network diagram for the above action plan

Action Plan

1

2

3

a

b

5

4c

d

e

f

ENDSTART

6

7g

h

Tasks Precedence Time Cost Who Does

a - 3 days - -b - 4 days - -c a 6 days - -d b 2 days - -e b 5 days - -f c,d 2 days - -g e 2 days - -h f,g, 8 days - -

2

a

b

1

Wrong

1

2

3

a

b

Dummy

Right !!!

If two activities occur between the same two events there is a need to use a dummy activity indicated by a dashed line. for example if both activity a and b start from node 1 and end at node 2.

Networking current activitiesNetworking current activities