A Look Ahead
We will now turn our attention to several
tools and techniques associated with
Project Time Management
First, we will consider:
PERT & CPM Historical Perspective
Overview of Sequencing Techniques
ADM: Arrow Diagramming Method
Determining the Critical Path
• download ADM_Class_Example.doc
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A Look Ahead
(continued)
After that, we will continue our
exploration of tools and techniques by
considering:
The Concept of Float
download ADM_Float_Calcs.xls
Probabilistic Activity Duration Estimates
download ADM_Mean_Variance.xls
Probabilistic Project Completion
download ADM_Standard_Normal_Table.xls
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PERT/CPM
Some History
PERT was first used in the late 1950’s by
the Navy for the Polaris Missile Program
PERT => Project Evaluation & Review Technique
Development was in conjunction with the
consulting firm of Booz, Allen, and Hamilton
Development was designed to meet the
needs of the “age of massive engineering”
The Navy was concerned with performance
trends on large military projects.
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PERT/CPM
Some History (continued)
Virtually simultaneously CPM was
developed by the duPont Company and
Remington-Rand-Univac.
CPM => Critical Path Method
For use on large construction projects
Specifically targeted for process industries
The two groups were unaware of each
other's existence until about 1960.
By then, each stood on its own merits
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PERT/CPM
Some History (continued)
PERT’s strengths are in its use of
probabilistic estimates of activity durations
CPM’s strengths are in its ability to do
“time-cost trade-offs”
Today, PERT/CPM are widely recognized
as comprising one set of techniques
the differences are primarily viewed as only
of historical importance
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Activity Sequencing
Display Techniques
There are many suitable techniques for
displaying the sequence of activities
involved in a project
Gantt Charts
Precedence Diagramming
Arrow Diagramming
Conditional Diagrams
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Gantt Charts
Gantt charts use horizontal bars (or lines)
to represent activities
Gantt charts are more commonly used for
schedule display than activity sequencing
see BOK Figure 6-6 (1996 & 2000) for an
example
length of the bars show expected duration
activity inter-relationships are not explicitly shown
we will see Gantt Charts again when we
consider Resource Loading & Leveling
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The Precedence
Diagramming Method
The Precedence Diagramming Method
(PDM) uses boxes to represent activities
and arrows to represent dependencies
see BOK Figure 6-2 (1996 & 2000 for an
example
This technique is also known as the
Activity-on-Node (AON) Diagramming
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More on PDM
Dependencies can include:
Finish-to-Start
Finish-to-Finish
Start-to-Start
Start-to-Finish
Dependencies are usually indicated by the placement of the
arrow heads and tails relative to the nodes but no consistent
approach has been universally adopted.
Looping and Conditional Branching is not
allowed
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The Arrow Diagramming
Method (ADM)
The Arrow Diagramming Method (ADM)
uses the following conventions:
Arrows represent activities
"Regular" activities require time and resources
"Dummy" activities show precedence relationships
Nodes represent events
A point in time
Some nodes may represent milestone events
see BOK Figure 6-3 (1996 & 2000) for an
example
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More on ADM
Also known as Activity-on-Arrow (AOA)
Each activity is represented by one and
only one arrow in the network.
Nodes (events) are numbered uniquely.
Duplicate node numbers are not allowed
No two activities can be identified by the
same beginning and ending nodes.
Dummy activities may be required
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More on ADM
(continued)
Before an activity can begin, all activities
terminating at the activities beginning
node must be completed.
Neither the length of an activity arrow nor
its “compass” direction have any
significance.
Networks should (must) have only one
initial event and one terminal event.
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An Example to Try:
Draw an Arrow Diagram
A project consists of Activities A, B, C, D, E,
F, G, H, I, J, K, and L
A, B, and C, the 1st activities of the project, can
start simultaneously
A and B precede D
B precedes E, F, and H
F and C precede G
E and H precede I and J
C, D, F, and J precede K
K precedes L
I, G, and L are terminal activities for the project
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Let’s Examine the Example
Solution
Solution to be shown in class.
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Conclusion of Sequencing
Techniques
We’ll return to ADM in just a few minutes
but first let’s complete the set of
sequencing techniques by considering
Conditional Diagramming
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Conditional Diagramming
Conditional Diagramming methods allow
for probabilistic activities and looping
neither of these are allowed in traditional
PDM or ADM
Conditional diagramming techniques
include Graphical Evaluation and Review
Technique (GERT) and System Dynamics
these are beyond the scope of this course
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Activity Durations
The next logical step in Project Time
Management is to determine activity
durations.
We are going to defer a detailed
discussion of estimating activity durations
until later in the course.
At this point we need to introduce the
concept of the Critical Path of a project.
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The Concept of the
Critical Path
The determination of the start and
completion time of each activity on the
network diagram requires a special
calculation procedure.
This approach classifies each activity as
either critical or non-critical.
The approach is commonly known as the
Critical Path Method
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The Concept of the
Critical Path (continued)
A delay in the start or completion of a
critical path activity will cause a delay in
the completion of the entire project.
Non-critical path activities can absorb
some delay in start or completion without
impacting project completion.
The amount of delay which can be absorbed
is known as slack or float.
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The Concept of the
Critical Path (continued)
There will always be at least one
sequence of activities from the initial node
to the terminal node that is made up
entirely of critical activities.
This is known as the Critical Path of the
Project.
Any delay of a critical path activity will
delay the completion of the project.
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The Concept of the
Critical Path (continued)
The critical path defines the minimal
completion time for the project.
Multiple critical paths are possible.
Complete multiple critical paths
two or more critical paths exist from the initial
node to the terminal node of the project.
• rare in uncrashed networks, common in fully crashed
Partial multiple critical paths
two or more sets of parallel activities are critical
over some segment of the project.
• relatively common
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Determining the Critical
Path
The critical path is found by a two phase
methodology after activity durations have
been determined.
A “forward pass” is made through the
network diagram to determine the earliest
start time for each node.
A “backward pass” is made through the
network to determine the latest completion
time for each node.
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Determining the Critical
Path (continued)
This is best illustrated through an example.
Mathematical details in SPM_PERT&CPM_Math
An ADM diagram for a project is shown on
the following page
the activities themselves are not labeled, we
will use the (start node, end node) pair to
uniquely identify activities (e.g., (0,1))
duration estimates are indicated
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Class Example
Critical Path Calculations
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Forward Pass and
Backward Pass
Solution to be shown in class.
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The Critical Path
An activity lies on the critical path if it
meets the three following conditions:
The earliest start and latest completion for
the activity’s terminal node are equal;
The earliest start and latest completion for
the activity’s initial node are equal;
The difference between the earliest start of
the terminal node and the earliest start of the
initial node is the activity duration.
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The Critical Path
(continued)
Let’s re-examine the example for the
critical path.
Solution to be shown in class.
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