Analysing the AoN network

Project Management

(seminar)

Activity label & description

Data on the activity node

EST EFT

DurationLST LFT

Total Float

Total Project Time• The shortest time in which the project can

be completed. Determined by the critical path.

• Calculation: forward pass

Forward pass: The earliest start times (EST) of all activities are calculated.

Trom these the earliest finishing times (EFT) are also calculated

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 are the critical activities.

• The critical path can be identified by a backward pass, calculating the Latest Finishing Times (LFT), and from these the Latest Starting Times (LST).

Floats in AoN

• Total float: the time by which an activity can be delayed or extended without affecting the TPT.It can be used to delay the start of an activity or to increase its duration. TF = LST - EST

• Free float: the time by which an activity can be delayed or extended without affecting the start of any succeding activity. FF = ESTj+1 - EFTj

Example: organising a conference• Objectives:

to organise a 3 days long open scientific conference with 100-200 participants, 30-50 lectures, buffet reception, a conference book of the best studies and TV and radio interviews with some of the most known lecturers.

• Create the WBS chart and create the task list with estimated durations and precedence relations (in a table form)

• Plot both the AoA and AoN diagram• Calculate the TPT, identify the critical path the total

and the free float times.

Example: WBS

Project

Book MarketingEvent

management

Organising interviewsEditing

Collecting articles

Publishing

Peer reviewing

Arranging event

Infra-structure

Organising participants

StaffFacilities Materials

Invitation and

marketing

Activity label

Task description Duration Immediate predecessors

a Invitation

b Organising participants

c Facilities

d Staffing

e Materials

h Collecting articles

j Peer reviewing

k Publishing

l Organising interviews

m Arranging event

Activity label

Task description Duration(weeks)

Immediate predecessors

a Invitation 2

b Organising participants 4

c Facilities 3

d Staffing 4

e Materials 3

h Collecting articles 6

j Peer reviewing 3

k Publishing 5

l Organising interviews 1

m Arranging event 1

Activity label

Task description Duration(weeks)

Immediate predecessors

a Invitation 2 –

b Organising participants 4 a

c Facilities 3 b

d Staffing 4 b

e Materials 3 b

f Collecting articles 6 b

g Peer reviewing 3 f

h Organising interviews 1 c, d, e

i Publishing 5 g

j Arranging event 1 h, i

Task list with precedence relations

AoA

1 0

0 3 6

62 2

2

4 9

19

5 10

19

6 10

19

7 12

12 8 15

15

9 20

2010 21

21

2a

3e

4 d

3 4

b

c

f

6

3g

i

1h

5

1j

TPT = 21

CP: a-b-f-g-i-j

AoN

a

0 20

0 22

b

2 60

2 64

f

6 120

6 126

e

6 910

16 193

d

6 106

15 194

c

6 910

16 193

g

12 150

12 153

i

15 200

15 205

j

20 210

20 211

h

10 119

19 201

1

0

0 0

0

000

1

9

TPT: 21CP: a-b-f-g-i-jTPT: 21CP: a-b-f-g-i-j

Activity times for the previous diagram(continue individually)

Activity Duration EST LST EFT LFT Total float

Free float

a 2 0 2 0 2 0 0

b 4 2 6 2 6 0 0

C 3 6 9 16 19 10 1

d

e

f

g

h

i

j

Example 2 (for individual practice)a) Draw the AoA and AoN diagram with the data below:

Activity label

Duration(weeks)

Immediate predecessors

a 1 –

b 2 a

c 5 a

d 3 a

e 2 b

f 2 e

g 4 f, c, d

b) Determine the TPT and the critical path and activity floats.

c) Compute the EETs, LETs and slack for every node in the AoA & ESTs, LSTs, EFTs, LFTs in the AoN diagram.

Solution: AoA

1 0

0

4 4

7

5 5

53 3

3

2 1

1 6 7

7

1a1a

2e2e

2b2b

5c5c

3d3d

4g4g

2f2f

7 11

11

TPT: 11CP: a-b-e-f-gTPT: 11CP: a-b-e-f-g

Float: 0Float: 0

Float: 0Float: 0

Float: 0Float: 0

Float: 0Float: 0

T. float: 3F. float: 3T. float: 3F. float: 3

Float: 0Float: 0Slack: 0Slack: 0 Slack: 0Slack: 0Slack: 0Slack: 0

Slack: 3Slack: 3

Slack: 0Slack: 0Slack: 0Slack: 0

Slack: 0Slack: 0

T. float: 1F. float: 1T. float: 1F. float: 1

00

Solution: AoN

a

0 10

0 11

0

b

1 30

1 32

c

1 61

2 75

0

d

1 43

4 73

3

f

5 70

5 72

e

3 50

3 22

1

g

7 110

7 114

0

00

TPT: 11CP: a-b-e-f-gTPT: 11CP: a-b-e-f-g

Example 3

1 0

0

4 2

5

3 5

5

2 2

2 5 8

8

2a2a

3e3e

2b2b

5c5c

3d3d

4g4g

7 14

14

6 12

14

1f1f

2h2h

a) Calculate the EETs and LETs.b) Create a precedence table (with task, duration, immediate predecessor, total and free

floats).

00

SolutionActivity Duration Total

floatFree float

a 2 0 0

b 2 0 0

C 5 1 1

d 3 3 3

e 3 0 0

f 1 5 5

g 4 0 0

h 2 0 0

Readings

• Lockyer – Gordon (2005) Chapter 14.

Thanks for the attention!