Transcript Scheduling the Project

Project Management in Practice
Fifth Edition
Chapter 5
Scheduling the Project
Copyright © 2014 John Wiley & Sons, Inc.
Introduction
• Project schedule is the project plan in an
altered format
• It is a convenient form for monitoring and
controlling project activities
• Can be prepared in several formats
– Gantt charts
– PERT network
– CPM network
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PERT and CPM Networks
• PERT and CPM developed independently in
1950’s
• Program Evaluation and Review Technique
(PERT)
– U.S. Navy, Booz-Allen Hamilton, and Lockheed
Aircraft
– Probabilistic activity durations
• Critical Path Method (CPM)
– Dupont De Nemours Inc.
– Deterministic activity durations
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The Language of PERT/CPM
• Activity
– A task or set of tasks
– Uses resources and time
• Event
– An identifiable state resulting from completion of one
or more activities
– Consumes no resources or time
– Predecessor activities must be completed
• Milestones
– Identifiable and noteworthy events that mark significant
progress
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The Language of PERT/CPM
Continued
• Network
– A diagram of nodes (activities or events) and arrows (directional
arcs) that illustrate the technological relationships of activities
• Path
– A series of connected activities between two events
• Critical path
– The set of activities on a path that, if delayed, will delay the
completion date of the project
• Critical Time
– The time required to complete all activities on the critical path
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Building the Network
•
There are two ways of displaying a project
network
1. Activities on arrows (AOA) network
•
•
The activities are shown as arrows and events as nodes
Generally more difficult to draw but depicts the technical
relationships of the activities well
2. Activities on nodes (AON) network
•
•
•
Each task is shown as a node and the technological
relationship is shown by the arrows
AON network usually associated with CPM
AOA network usually associated with PERT
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Sample AON Network
Table 5-1
Figure 5-3
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Sample AOA Network
Table 5-1
Figure 5-6 (a)
5-8
Which to Use?
• Mostly AON used throughout this textbook
• AON used by most of the popular software
• AON networks are easier to draw by hand
– Large (20+ activities) AOA networks are
difficult to draw
• Software to draw AOA networks is
expensive
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Finding the Critical Path and Critical
Time
•
•
•
•
•
•
•
ES: Earliest start time
EF: Earliest finish time
LS: Latest start time
LF: Latest finish time
Displayed on node as shown
ES + completion = EF
LS + completion = LF
Figure 5-9
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A Sample Problem for Finding the
Critical Path and Critical Time
Table 5-2
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The Complete Network
Table 5-2 and Figure 5-8
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The Critical Path and Completion
Time for Sample Project
Figure 5-10
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Notes on Sample Project
• All activities, and thus all paths, must be
completed to finish the project
• The shortest time for completion of the network is
equal to the longest path through the network
– In this case a-e-h-j
• If any activity on this path
is even slightly delayed,
the project will be delayed
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Calculating Activity Slack
•
•
•
•
•
•
•
ES: Earliest start time
EF: Earliest finish time
LS: Latest start time
LF: Latest finish time
Slack = LS – ES
Slack = LF – EF
Either method of calculating slack gives the same
results
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Managerial Implications
• The primary attention of the project
manager must be to activities on the critical
path
• If anything delays one of these activities,
the project will be late
• Projects are easier to manage when there is
project slack
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Doing It the Easy Way—Microsoft
Project (MSP)
• Data is entered using a tab entry table
– Shown on next slide
• MSP automatically numbers each activity
• MSP has numerous options for viewing the
data
• MSP automatically draws an AON network
– Shown on later slide
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A Microsoft Project Version of Data
in Table 5-2
Table 5-3
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A Microsoft Project Version of the
PERT/CPM Network from Table 5-3
Figure 5-11
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Calculating Probabilistic Activity
Times
• Figure below shows distribution of all possible
durations for some task
• Estimate a is such that the actual duration of the
task will be a or lower less than 1 percent of the
time
• Estimate b is such that the actual finish time will
be b or greater less than 1 percent of the time
• Estimate m is the most likely time
Figure 5-13
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Activity Expected Time and
Variance
( a  4m  b)
TE 
6
 (b  a ) 
Var    

 6 
2
2
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95 Percent Level
• Task will be a or lower 5 percent of the
time
• Task will be b or greater 5 percent of the
time
(b  a )

3 .3
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90 Percent Level
• Task will be a or lower 10 percent of the
time
• Task will be b or greater 10 percent of the
time
(b  a )

2 .6
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The Probabilistic Network
• Expected time (TE) for each activity is calculated
• Variance (σ2) for each activity is calculated
• TE for each activity is used to find the critical path
and critical time for the network
– Slack is calculated in the usual fashion
• The variance (σ2) of a path is the sum of the
activity variances for that path
– Standard deviation (σ) is the square of the variance
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The Probabilistic Network, an
Example
Table 5-4
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Is it Really the Critical path
• Given uncertainty, cannot be sure that any specific
path is the critical path
• “Critical” path may take less than expected while
another path takes longer
• Only after the fact do we know which path was
actually critical
• Managerial implication is the project manager
must carefully manage all paths that have a
reasonable probability of becoming critical
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Once More the Easy Way
• Microsoft Project can easily handle the
probabilistic network
– However, it does not perform some of the calculations
– These can be done in Excel
• Microsoft Project calculates using a calendar
rather than days
• Uses a real-world calendar including weekends
and holidays
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The Probability of Completing the
Project on Time
• Can the project be completed in X days?
• Can be answered with the information
available concerning the level of uncertainty
for the various project activities
– Assumes activities are statistically independent
• To complete a project by a specified time
requires that all the paths in the network be
completed by the specified time
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The Probability of Completing the
Project on Time Continued
• Determining the probability that a project is
completed by a specified time requires calculating
the probability that all paths are finished by the
specified time
• We then calculate the probability that the entire
project is completed within the specified time by
multiplying these probabilities together
– This requires the assumption that the paths are
statistically independent
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Calculating Path Probability
• D = desired project completion Z  D   
 2
time
– 50 in this example
• μ = the sum of the TE activities
on the path being investigated

50  47 
1.78  0.25  0.00  4.00
 1.10
– 47 in this example
• σ2u = the variance of the path
being considered
• A Z of 1.10 yields a probability
of 0.8643 or 86 percent
Table 5-4
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The Statistical Distribution of the
Completion Times for Example
Figure 5-18
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Selecting Risk and Finding D
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Simulation
• Simulation is a different approach to
managing risk
• Builds on the probabilistic functions already
discussed
• Helps to understand the consequences of
uncertainty
• Provides insight into the range and
distribution of project completion times
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Crystal Ball Chart for Project
Completion Time
Figure 5-19
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Traditional Statistics vs. Simulation
• Both approaches assume that task times are
statistically independent
• Both approaches assume the paths are independent
– A simulation can circumvent the assumption of
statistical independence by including the activity or
path dependencies as part of the model
• Simulation requires less computational effort
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The Gantt Chart
• Henry Gantt developed the Gantt chart
around 1917
• It displays project activities as bars
measured against a horizontal time scale
• Most popular way of exhibiting sets of
related activities in the form of schedules
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The Chart
• Gantt charts are easy to draw
• Problems arise when several tasks begin at the
same time and have the same duration
– Can make it hard to find critical path
– Only a problem on hand-drawn charts
• Software shows critical path using some visual
method
• Even with software, technical dependencies are
harder to see on a Gantt chart
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A Gantt Chart of a Sample Project
Figure 5-21
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A Gantt Chart Showing Critical
Path, Path Connections, Other Data
Figure 5-22
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Extensions to PET/CPM
• Application of fuzzy set theory to aid in
estimating activity durations
• Extensions to precedence diagramming
• Goldratt’s Critical Chain
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Precedence Diagramming
• Finish to start (F to S)
– Finish of Activity A to start of Activity B
• Start to start (S to S)
– Start of Activity A to start of Activity B
• Finish to finish (F to F)
– Finish of Activity A to finish of Activity B
• Start to finish (S to F)
– Start of Activity A to finish of Activity B
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Precedence Diagramming
Conventions
Figure 5-25
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Copyright
Copyright © 2014 John Wiley & Sons, Inc.
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