### Project Scheduling: Networks, Duration Estimation, and

```Project Scheduling: Networks,
Duration Estimation,
and Critical Path
Chapter 9
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-1
•
•
•
•
•
Project Scheduling Terms
Successors
Predecessors
Network diagram
Serial activities
Concurrent activities
B
D
A
E
F
C
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-2
Project Scheduling Terms
•
•
•
•
•
Merge activities
Burst activities
Node
Path
Critical Path
B
D
A
E
F
C
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-3
Network Diagrams
Show
interdependence
Help
schedule
resources
Facilitate
communication
Determine project
completion
Show
start &
finish
dates
Identify
critical
activities
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-4
AOA Vs. AON
The same mini-project is shown with activities on
arc…
B
E
D
F
C
…and activities on node.
E
D
B
F
C
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-5
Node Labels
Early
Start
Activity
Float
Late
Start
ID
Number
Early
Finish
Activity Descriptor
Activity
Duration
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
Late
Finish
9-6
Duration Estimation Methods
• Past experience
• Expert opinion
• Mathematical derivation – Beta distribution
– Most likely (m)
– Most pessimistic (b)
– Most optimistic (a)
ba
Activity Variance = s  

 6 
2
2
a  4m  b
Activity Duration = TE 
6
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-7
1. Sketch the network described in the table.
2. Determine the expected duration and variance of each
activity.
Task Predecessor
Z
-Y
Z
X
Z
a
7
13
14
b
8
16
18
c
15
19
22
W
V
T
Y, X
W
W
12
1
6
14
4
10
16
13
14
S
T, V
11
14
19
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-8
Constructing the Critical Path
• Forward pass – an additive move through the
network from start to finish
• Backward pass – a subtractive move through
the network from finish to start
• Critical path – the longest path from end to end
which determines the shortest project length
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-9
Rules for Forward/Backward Pass
Forward Pass Rules (ES & EF)
– ES + Duration = EF
– EF of predecessor = ES of successor
– Largest preceding EF at a merge point becomes EF
for successor
Backward Pass Rules (LS & LF)
– LF – Duration = LS
– LS of successor = LF of predecessor
– Smallest succeeding LS at a burst point becomes LF
for predecessor
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-10
Task Predecessor Time
A
-4
B
A
9
C
A
11
D
E
F
B
B
C
5
3
7
G
H
K
D, F
E, G
H
3
2
1
1. Sketch the network
described in the table.
2. Determine the ES,
LS, EF, LF, and slack
of each activity
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-11
Laddering Activities
Project ABC can be completed more efficiently if
subtasks are used
A(3)
A1(1)
B(6)
A2(1)
B1(2)
Laddered
ABC=12 days
C(9)
ABC=18 days
A3(1)
B2(2)
C1(3)
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B3(2)
C2(3)
C3(3)
9-12
Hammock Activities
Used as summaries for subsets of activities
0 A 5
5 B 15
15 C 18
0 5
5 10 15
15 3 18
5
0 Hammock 18
0
18
18
Useful with a complex
project or one that has
a shared budget
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-13
Reducing the Critical Path
•
•
•
•
•
Eliminate tasks on the CP
Convert serial paths to parallel when possible
Overlap sequential tasks
Shorten the duration on critical path tasks
Shorten
–
–
–
–
early tasks
longest tasks
easiest tasks
tasks that cost the least to speed up
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-14
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall
9-15
```