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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!