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Report
Project Scheduling: Networks,
Duration Estimation, and
Critical Path
09-01
Chapter 9 Learning Objectives
After completing this chapter, students will be able
to:
 Understand and apply key scheduling
terminology.
 Apply the logic used to create activity networks,
including predecessor and successor tasks.
 Develop an activity network using Activity-onNode (AON) techniques.
 Perform activity duration estimation based on the
use of probabilistic estimating techniques.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-02
Chapter 9 Learning Objectives
After completing this chapter, students will be able
to:
 Construct the critical path for a project schedule
network using forward and backward passes.
 Identify activity float and the manner in which it is
determined.
 Calculate the probability of a project finishing on
time under PERT estimates.
 Understand the steps that can be employed to
reduce the critical path.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-03
Project Scheduling
 Project scheduling requires us to follow some
carefully laid-out steps, in order, for the schedule to
take shape.
 Project planning, as it relates to the scheduling
process, has been defined by the PMBoK as:
The identification of the project objectives and the ordered
activity necessary to complete the project including the
identification of resource types and quantities required to
carry out each activity or task.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-04
Project Scheduling Terms
 Successors
 Predecessors
 Network diagram
 Serial activities
 Concurrent activities
B
D
A
E
F
C
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09-05
Project Scheduling Terms
• Merge activities
• Burst activities
• Node
• Path
• Critical Path
B
D
A
E
F
C
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09-06
Network Diagrams
FIGURE 9.2 Alternative Activity Networks for Term Paper Assignment
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09-07
AOA Versus 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
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09-08
Node Labels
Early Start
Activity Float
Late Start
ID Number
Early Finish
Activity Descriptor
Activity Duration
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Late Finish
09-9
Activity Node Labels Using MS Project 2010
FIGURE 9.4
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09-10
Serial Activities
Serial activities are those that flow from one to
the next, in sequence.
FIGURE 9.5
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09-11
Activities Linked in Parallel (Concurrent)
When the nature of the work allows for more than one activity
to be accomplished at the same time, these activities are called
concurrent and parallel project paths are constructed through the
network.
FIGURE 9.6
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09-12
Merge Activity
FIGURE 9.7
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09-13
Burst Activity
FIGURE 9.8
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09-14
Complete Activity Network
FIGURE 9.10
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09-15
Developing the Activity Network Using MS
Project 2010
FIGURE 9.11
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09-16
Duration Estimation Methods
 Past experience
 Expert opinion
 Mathematical derivation – Beta distribution
 Most likely (m)
 Most pessimistic (b)
2
Activity
Variance
=
s
 Most optimistic (a)
ba


 6 
2
a  4m  b
Activity Duration = TE 
6
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09-17
FIGURE 9.14 Symmetrical (Normal) Distribution for
Activity Duration Estimation
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09-18
FIGURE 9.15 Asymmetrical (Beta) Distribution for Activity Duration Estimation
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09-19
Activity Duration and Variance
Name: Project Delta
Table 9.2
Durations are listed in weeks
Activity
Description
Optimistic
Likely
Pessimistic
A
Contract signing
3
4
11
B
Questionnaire design
2
5
8
C
Target market ID
3
6
9
D
Survey sample
8
12
20
E
Develop presentation
3
5
12
F
Analyze results
2
4
7
G
Demographic analysis
6
9
14
H
Presentation to client
1
2
4
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09-20
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
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09-21
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
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09-22
Project Delta Information
Project Delta
Activity
Table 9.4
Description
Predecessors
Estimated Duration
None
5
A
Contract signing
B
Questionnaire design
A
5
C
Target market ID
A
6
D
Survey sample
B, C
13
E
Develop presentation
B
6
F
Analyze results
D
4
G
Demographic analysis
C
9
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09-23
FIGURE 9.16 Partial Project Activity Network with Task Durations
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09-24
FIGURE 9.18 Activity Network with Forward Pass
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09-25
FIGURE 9.19 Activity Network with Backward Pass
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09-26
FIGURE 9.20 Project Network with Activity Slack and Critical Path
Note: Critical path is indicated with bold arrows.
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09-27
AON Network with Laddering Effect
FIGURE 9.24
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09-28
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)
09-29
Example of a Hammock Activity
FIGURE 9.25
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09-30
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 © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-31
Summary
1. Understand and apply key scheduling
terminology.
2. Apply the logic used to create activity networks,
including predecessor and successor tasks.
3. Develop an activity network using Activity-onNode (AON) techniques.
4. Perform activity duration estimation based on
the use of probabilistic estimating techniques.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-32
Summary
5. Construct the critical path for a project schedule
network using forward and backward passes.
6. Identify activity float and the manner in which it
is determined.
7. Calculate the probability of a project finishing on
time under PERT estimates.
8. Understand the steps that can be employed to
reduce the critical path.
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-33
Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall
09-34

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