project networks

Project Networks

Two Approaches• Activity-on-Arrow (AOA): Uses an arrow to depict an

activity • Activity-on-Node (AON): Uses a node to depict an

activity

Activity on Arrow (AOR)Activities are

shown by ArrowLength of Arrow may show relative time to

complete tasks

Nodes show where activities end and begin in

sequence.The starting node for an

activity is the activity’s “i-node,” the

ending node is the “j-node.

Task A Task B Task C

Task DTask

E

Each project has a starting “i-node” and

ending “j-node”

Activity on Arrow (AOR)

Task A Task B Task C

Task DTask

E

Activity on Node (AON)

Start

Task A

Task B

Task E

Task C

Task D

End

Activity on Node (AON)Activities are show in nodes or

boxes

Start

Task A

Task B

Task E

Task C

Task D

End

Project Has a Start and an

End

Task C is a predecessor to Task E and a

successor to Task A

Arrow show dependencies. Task D can’t start until both

Task A and B have completed

Project Networks

BTask

CTask

DTask

ETask

FTask

ATask

• Networks typically flow from left to right.• An activity cannot begin until all of its

preceding activities are complete.• Arrows indicate precedence and can cross

over each other.• Identify each activity with a unique

identifier; this identifier must increment (1.2.3, A,B,C, etc.) as the network proceeds.

• Looping is not allowed.• Conditional statements are not allowed.• Use start and stop nodes.

Project Networks Rules

• Terminology:

A

C

B D

Constructing a Project Network

• Parallel (concurrent) activities: Activities that can occur independently and, if desired, at the same time.• Merge activity: an activity that has two or more preceding activities on which it depends.

• Activity: an element of theproject that requires time.

Time

• Terminology B

D

A C

Constructing a Project Network (cont’d)

• Burst activity: an activity that has more than one activity immediately following it (more than one dependency arrow flowing from it).

• Milestone: a point in time when an activity is started or completed. It does not consume time.

Q

Project Networks

BTask

CTask

DTask

ETask

FTask

ATask

Project Networks

BTask

CTask

DTask

ETask FTask

ATask

= Early StartES

Time-Related Task Properties

= Early FinishEF = Late StartLS = Late FinishLF = Slack or FloatSL

= Duration

DRATask

Tasks

ES EF

LS LF

SLA

DR

A

4

Project Networks

C

3

B

8

D

2

E

3

F

10

Critical PathES ID EFSLLS DR LF

Longest Path through the project network (not the path with the most number of tasks, but the one that takes the longest).

=Any delay of a task on the critical path will delay the entire project. PM needs to watch=Tasks with zero slack=

Critical Path

A

4

Project Networks

C

3

B

8

D

2

E

3

F

10

A-B-D-F 4+8+2+10 = 24A-C-E-F 4+3+3+10 = 20

ES ID EFSLLS DR LF

A

4

Project Networks

C

3

B

8

D

2

E

3

F

10

A-B-D-F 4+8+2+10 = 24A-C-E-F 4+3+3+10 = 20

ES ID EFSLLS DR LF