3. Chapter Learning Objectives
Chapter Learning Objectives
LO 6-1 Understand the linkage between WBS and the project
network.
LO 6-2 Diagram a project network using AON methods.
LO 6-3 Calculate early, late, and slack activity times.
LO 6-4 Identify and understand the importance of managing the
critical path.
LO 6-5 Distinguish free slack from total slack.
LO 6-6 Demonstrate understanding and application of lags in
compressing projects or constraining the start or finish of
an activity. ~
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3
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Developing the Project Plan
Developing the Project Plan
• The Project Network
– A flow chart that graphically depicts the sequence,
interdependencies, and start and finish times of the
project job plan of activities that is the critical path
through the network.
• Provides the basis for scheduling labor and equipment.
• Enhances communication among project participants.
• Provides an estimate of the project’s duration.
• Provides a basis for budgeting cash flow.
• Identifies activities that are critical.
• Highlights activities that are “critical” and can not be delayed.
• Help managers get and stay on plan.
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Constructing a Project Network
Constructing a Project Network
• Terminology
– Activity: an element of the
project that requires time.
– Merge Activity: an activity that
has two or more preceding
activities on which it depends.
– Parallel (Concurrent)
Activities: Activities that can
occur independently and, if
desired, not at the same time.
A
C
D
B
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Constructing a Project Network (cont’d)
Constructing a Project Network (cont’d)
• Terminology
– Path: a sequence of connected, dependent activities.
– Critical path: the longest path through the activity
network that allows for the completion of all project-
related activities; the shortest expected time in which
the entire project can be completed. Delays on the
critical path will delay completion of the entire project.
A B D
(Assumes that minimum of A + B > minimum of C in length of times to complete activities.)
C
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Constructing a Project Network (cont’d)
Constructing a Project Network (cont’d)
• Terminology
– Event: a point in time when an activity is started
or completed. It does not consume time.
– Burst Activity: an activity that has more than one
activity immediately following it (more than one
dependency arrow flowing from it).
• Two Approaches
– Activity-on-Node (AON)
• Uses a node to depict an activity.
– Activity-on-Arrow (AOA)
• Uses an arrow to depict an activity.
B
D
A C
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Basic Rules to Follow in Developing
Basic Rules to Follow in Developing
Project Networks
Project Networks
1. Networks typically flow from left to right.
2. An activity cannot begin until all preceding
connected activities are complete.
3. Arrows indicate precedence and flow
and can cross over each other.
4. Each activity must have a unique identify number
that is greater than any of its predecessor activities.
5. Looping is not allowed.
6. Conditional statements are not allowed.
7. Use common start and stop nodes.
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Network Computation Process
Network Computation Process
• Forward Pass—Earliest Times
– How soon can the activity start? (early start—ES)
– How soon can the activity finish? (early finish—EF)
– How soon can the project finish? (expected time—ET)
• Backward Pass—Latest Times
– How late can the activity start? (late start—LS)
– How late can the activity finish? (late finish—LF)
– Which activities represent the critical path?
– How long can activity be delayed? (slack or float—SL)
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Forward Pass Computation
Forward Pass Computation
• Add activity times along each path in the
network (ES + Duration = EF).
• Carry the early finish (EF) to the next activity
where it becomes its early start (ES) unless…
• The next succeeding activity is a merge activity,
in which case the largest EF of all preceding
activities is selected.
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Backward Pass Computation
Backward Pass Computation
• Subtract activity times along each path in the
network (LF - Duration = LS).
• Carry the late start (LS) to the next activity
where it becomes its late finish (LF) unless
• The next succeeding activity is a burst activity,
in which case the smallest LF of all preceding
activities is selected.
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Determining Free Slack (or Float)
Determining Free Slack (or Float)
• Free Slack (or Float)
– Is the amount of time an activity can be delayed after
the start of a longer parallel activity or activities.
– Is how long an activity can exceed its early finish date
without affecting early start dates of any successor(s).
– Allows flexibility in scheduling scarce resources.
• Sensitivity
– The likelihood the original critical path(s) will change
once the project is initiated.
– The critical path is the network path(s) that has (have)
the least slack in common.
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Forward and Backward Passes Completed with Slack Times
Forward and Backward Passes Completed with Slack Times
FIGURE 6.8
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Extended Network Techniques
Extended Network Techniques
to Come Close to Reality
to Come Close to Reality
• Laddering
– Activities are broken into segments so the following
activity can begin sooner and not delay the work.
• Lags
– The minimum amount of time a dependent activity
must be delayed to begin or end.
• Lengthy activities are broken down to reduce the delay
in the start of successor activities.
• Lags can be used to constrain finish-to-start, start-to-
start, finish-to-finish, start-to-finish, or combination
relationships.
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Example of Laddering Using
Example of Laddering Using
Finish-to-Start Relationship
Finish-to-Start Relationship
FIGURE 6.12
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Use of Lags
Use of Lags
FIGURE 6.13
FIGURE 6.14
Finish-to-Start Relationship
Start-to-Start Relationship
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Use of Lags Cont’d
Use of Lags Cont’d
FIGURE 6.15
Use of Lags to Reduce
Project Duration