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Chapter 9
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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-on-Node
(AON) techniques.
4. Perform activity duration estimation based on the
use of probabilistic estimating techniques.
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. Understand the steps that can be employed to
reduce the critical path.
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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.”
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Represents the conversion of project goals
into an achievable methodology.
Creates a timetable and reveals the network
logic that relates project activities to each
other.
A graphical set of sequential relationships
between project task which, when performed,
result in the completion of the project goals.
Vitally important to obtaining project goals,
being on time and on budget.
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

Allows project teams to use a method for
planning and scheduling
There are several advantages when project
networks and scheduling are done well
Show interdependence
Help schedule
resources
Facilitate communication
Determine project
completion
Identify
critical
activities
Show start &
finish dates
for task
See slide 26 for an example
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 Successors
 Predecessors
 Network diagram
 Serial activities
 Concurrent
activities
 Merge activities
 Burst activities
 Node
 Path
 Critical Path
B
D
A
E
F
C
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AOA vs. AON
The same mini-project is shown with
activities on arrow…
E
D
B
F
C
…and activities on node.
E
D
B
F
C
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1. Some determination of activity precedence ordering
must be done prior to creating the network.
2. Network diagrams usually flow from left to right.
3. An activity cannot begin until all preceding connected
activities have been completed.
4. Arrows on networks indicate precedence and logical
flow. Arrows can cross over each other, although it is
helpful for clarity’s sake to limit this effect when
possible.
5. Each activity should have a unique identifier associated
with it (number, letter, code, etc.).
6. Looping, or recycling through activities, is not permitted.
7. Although not required, it is common to start a project on
a single node. A single node point also is typically used
as a project end indicator.
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Information for Network Construction Name: Project Delta
Activity
A
Description
Contract signing
Predecessors
None
B
Questionnaire design
A
C
Target market ID
A
D
Survey sample
B, C
E
Develop presentation
B
F
Analyze results
D
G
Demographic analysis
C
H
Presentation to client
E, F, G
Construct a Network Diagram
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E
Dev. Present.
B
Design
A
Contract
D
Survey
C
Market ID
F
Analysis
H
Present
G
Demog.
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
College research paper example
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Activity A
Activity B
Activity C
Activity B
Activity D
Activity A
Activity C
Activity D
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Early
Start
ID
Number
Activity
Float
Activity Descriptor
Late
Start
Activity Late
Duration Finish
ES
ID
EF
Slack Task Name
LS Duration
LF
Early
Finish
11
0
D 24
Survey
11
13
24
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
Assumptions
◦ Based on normal working methods during normal
hours
◦ Durations are always somewhat uncertain
◦ Timeframes can be from minutes to weeks
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Methods
◦ Past experience
◦ Expert opinion
◦ Mathematical derivation based on Beta Distribution
 Most optimistic (a) time – better then planned
 Most likely (m) time – realistic expectation
 Most pessimistic (b) time – Murphy’s Law kicks in
There are only two types of estimates…lucky and wrong.
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Critical Path Method (CPM) assumes we know
a fixed time estimate for each activity and
there is no variability in activity times
Program Evaluation and Review Technique
(PERT) uses a probability distribution for
activity times to allow for variability
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Where:
a = Most optimistic time
m = Most likely time
b = Most pessimistic time
Activity D uration = T E 
a  4m  b
6
ba
Activity Variance =   

 6 
2
2
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Project variance is computed by summing the
variances of activities on the critical path
Project variance = (variances of activities on
critical path)
Project standard deviation =
Project Variance
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Task Predecessor a m b mean variance
Z
-7 8 15 9.00
1.78
Y
Z
13 16 19 16.00
1.00
X
Z
14 18 22 18.00
1.78
W
Y, X
12 14 16 14.00
0.44
V
W
1 4 13 5.00
4.00
T
W
6 10 14 10.00
1.78
S
T, V
11 14 19 14.33
1.78
1.
Determine the expected duration and variance of each activity.
2.
Sketch the network described in the table.
3.
Determine the expected project time and standard deviation.
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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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Activity
Description
Predecessors
Estimated Duration
A
Contract signing
None
5
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
H
Presentation to client
E, F, G
2
Construct the critical path.
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B
Design
5
A
Contract
5
E
Dev. Present
6
D
Survey
13
C
Market ID
6
F
Analysis
4
H
Present
2
G
Demog.
9
Critical Path is indicated in bold
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Forward Pass Rules (ES & EF)
◦ ES + Duration = EF
◦ EF of predecessor = ES of successor
◦ Largest preceding EF at a merge point becomes
ES for successor
Backward Pass Rules (LS & LF)
ES
ID
EF
Slack
Task Name
LS Duration
LF
◦ LF – Duration = LS
◦ LS of successor = LF of predecessor
◦ Smallest succeeding LS at a burst point becomes
LF for predecessor
Calculate the forward/backwards pass.
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5
0
B 10
Design
5
A
5
Contract
5
5
10
16
6
11
C
11
Market ID
6
E
Dev. Present
D 24
Survey
13
24
11
G
F
28
28
H
30
Analysis
Presentation
4
2
20
Demograph.
9
ES
ID
EF
Slack
Task Name
LS Duration
LF
23
5
6
B 10
Design
5
11
0
A
5
Contract
0
5
5
5
C
11
Market ID
5
6
11
10
E
16
Dev. Present
22
6
11
D 24
Survey
11 13 24
28
24
F
28
Analysis
24
11
G
4
28
H
30
Presentation
28
28
2
30
20
Demograph.
19
9
28
ES
ID
EF
Slack
Task Name
LS Duration
LF
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Informs us of the amount an activity can be
delayed without delaying the overall project.
It is determined as a result of performing the
forward and backward pass through the network.
Calculated either by
◦ LF-EF = Slack
◦ LS-ES = Slack

The critical path is the network path with “0”
slack.*
◦ *This assumes a deadline has not been set for LF that is
within our calculated project time.
◦ *Negative float is a result of the project time being
longer than a set project end time.
Calculate the slack time and determine critical path.
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5
1
6
0
0
0
B 10
Design
5
11
A
5
Contract
5
5
11
0
11
5
C
11
0 Market ID
5
6
11
10
12
E
16
Dev. Present
22
D 24
Survey
13 24
6
24
11
28
F
28
28
H
30
0
Analysis
0 Presentation
24
4
28
G
28
2
30
20
8 Demograph.
19
Critical Path is indicated in bold
9
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ES
ID
EF
Slack
Task Name
LS Duration
LF
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Task
Predecessor
Time
A
--
4
B
A
9
C
A
11
D
B
5
E
B
3
F
C
7
G
D, F
3
H
E, G
2
K
H
1
1. Sketch the
network described
in the table.
2. Determine the ES,
LS, EF, LF, and
slack of each
activity.
3. Determine the
critical path.
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
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Project ABC can be completed more efficiently if subtasks are
used.
Example: A does not need to be completely finished before work
on B starts.
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)
B3(2)
C2(3)
C3(3)
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Used as a summary 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
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Eliminate tasks on the critical path
◦ remove task with no value
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Convert serial paths to parallel when possible
Overlap sequential tasks
◦ use laddering when possible
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Shorten the duration on critical path tasks
Shorten
◦
◦
◦
◦
early tasks (have you read “The Goal”)
longest tasks
easiest tasks
tasks that cost the least to speed up – “crashing”
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1. Define the following terms: Path, Activity, Early
start, Early finish, Late start, Late finish,
Forward pass, Backward pass, Node, AON,
Float, Critical Path, PERT
2. Distinguish between serial activities and
concurrent activities. Why do we seek to use
concurrent activities as a way to shorten a
project’s length?
3. List three methods for deriving duration
estimates for project activities. What are the
strengths and weaknesses associated with each
method?
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4. In your opinion, what are the chief benefits and
drawbacks of using beta distribution
calculations (based on PERT techniques) to
derive activity duration estimates?
5. “The shortest total length of a project is
determined by the longest path through the
network.” Explain the concept behind this
statement. Why does the longest path
determine the shortest project length?
6. The float associated with each project task can
only be derived following the completion of the
forward and backward passes. Explain why this
is true.
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Now that Joe has agreed to your WBS, he wants to
review a schedule and present it to the president.
She is a “big picture” thinker and does not usually
get involved with the details, so Joe wants to limit
the content of the diagram you show her to the
basics that concern her.
You have also worked with your team on
estimating the durations of each of the work
packages in the WBS. Note that in this case, the
work packages are the scheduled activities. Here
is your current plan for the briefing to the
president:
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1. Build a network diagram
2. Calculate forward pass, backward pass,
float, and critical path
3. Be ready to address—
◦ How long will the project take?
◦ When should you begin installing new furniture,
communications equipment, and computers if you
want to be in the new office by July 31?
◦ What items are on the critical path?
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