Network planning
Learning objectives
After these lectures you should be able to:
- Produce and analyse activities networks
- Calculate earliest and latest start and finishing times
for activities
- Calculate activity floats and determine the critical
path(s) through a network
- Update networks as new information becomes available
PDM
Footings/1 wk
Brickwork/3 wks
Landscape/1 wk
Roof/ 2 wks
Fence/1 wk
A
ES
EF
t
LS
LF
TF
FF
A = Activity description, i.e. ‘Brickwork’
t = Duration (usually in work days)
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
TF = Total Float
FF = Free Float
Network analysis
Forward pass
0
1
1
A/1
B/3
1
ES
EF
Name/Duration
4
1.5
C/0.5
4
6
D/2
1.5
6
8
F/2
2
D/0.5
NOTE: ES for the first activity is ‘0’, not ‘1’!
Network analysis
Backward pass
0
1
1
A/1
0
4
4
B/3
1
1
1
6
D/2
4
1.5
C/0.5
5
5.5
ES
EF
Name/Duration
LS
LF
6
8
F/2
4
6
1.5
2
6
8
D/0.5
5.5
6
NOTE: The backward pass starts with the same
LF value as the last EF for the final activity
Activity
Draw an PDM network for this project. Then do a forward and
backward pass.
Activity
A
B
C
D
E
F
G
H
Duration
5
5
12
3
6
8
14
5
Depends on
None
A
A
C
B and 2/3 of C
B and 2/3 of C
A
D, E, F and G
Solution
0 5
A/5
0 5
13 21
F/8
13 21
5 10
B/5
8 13
13 19
E/6
15 21
5 13
C1/8
5 13
13 17
C2/4
14 18
5 19
G/14
7 21
17 20
D/3
18 21
21 26
H/5
21 26
Development of a network
Level 1
Level 2
Level 3
Final
Activity Float
Critical activities: Have no float and are therefore fixed in time.
ES = LS and EF = LF
Total Float (TF): The amount of time that an activity can be delayed,
without that affecting the project completion time.
TF = LF – EF = LS – ES
Free Float (FF): The amount of time an activity can be delayed, without
that affecting the start of any following activity.
FF = ES(any following activity) – EF
13 21
F/8
13 21
0 5
A/5
0 5
5 10
B/5
8 13
13 19
E/6
15 21
5 13
C1/8
5 13
13 17
C2/4
14 18
17 20
D/3
18 21
5 19
G/14
7 21
Determine the Critical Paths(s) and all activity floats!
21 26
H/5
21 26
Activity
A
B
C1
C2
D
E
F
G
H
TF
0
3
0
1
1
2
0
2
0
FF Critical?
0
Yes
3
0
Yes
0
1
2
0
Yes
2
0
Yes
Critical Path = A - C1 - F - H
13 21
F/8
13 21
0 5
A/5
0 5
5 10
B/5
8 13
13 19
E/6
15 21
5 13
C1/8
5 13
13 17
C2/4
14 18
17 20
D/3
18 21
5 19
G/14
7 21
Critical Path (A – C1 – F – H) highlighted in network
21 26
H/5
21 26
Tutorial: Critical Path Method (CPM)
Carry out a critical path analysis for the following project in order to determine the total
completion time for the project and the critical activities. Illustrate the critical path(s) in
the CPM network. Calculate and list the Total and Free floats for all activities.
Activity
A
B
C
D
E
F
G
H
I
J
K
L
Duration
3 weeks
2
5
6
4
4
5
8
9
6
18
4
Depends on activity
A
A and B
Half of D
C
D
C and E
D
I and H
B
K