Transcript Document

Mantel, Meredith, Shafer, and Sutton
Prepared by
Scott M. Shafer,
Updated by
William E. Matthews and
Thomas G. Roberts,
William Patterson University
5 – Scheduling the Project
Copyright 2007 John Wiley & Sons, Inc.
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
Late 1950s
•
Program Evaluation and Review Technique (PERT)
• U.S. Navy, Booz-Allen Hamilton, and Lockeheed Aircraft
• Probabilistic activity durations
•
Critical Path Method (CPM)
• Dupont De Nemours Inc. developed the method
• Deterministic activity durations
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
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Activity
•
•
task or set of tasks
uses resources
•
•
•
state resulting from completion of one or more activities
consumes no resources or time
predecessor activities must be completed
Event
Milestones
•

Network
•
•
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series of connected activities between two events
Critical Path
•

diagram of nodes and arrows
used to illustrate technological relationships
Path
•
•
events that mark significant progress
set of activities on a path that if delayed will delay completion of project
Critical Time
•
time required to complete all activities on the critical path
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

Activities on Arrows (AOA) Network
Activities on Nodes (AON) Network
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

Latest Start Time (LST) – Earliest Start Time (EST) = Slack
Latest Finish time (LFT) – Earliest Finish time (EFT) = Slack
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 Three Time Estimates
• pessimistic (a)
• most likely (m)
• optimistic (b)
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( a  4m  b)
TE 
6
(b  a )

6
 (b  a ) 
Var    

 6 
2
2
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

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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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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Z
(D   )

2
=NORMDIST(D,,,TRUE)
Note: NORMDIST is a function within Excel
when using the spreadsheet method
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D    Z 
2
NORMINV(probability,,,TRUE)
Note: NORMMINV is a function within Excel
when using the spreadsheet method
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
Similarity
•

Both must enumerate the alternative path
Difference
•
Traditional statistics assume path interdependence
while simulation does not
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Finish of Activity A to start of Activity B linkage (F to S)
Start of Activity B to start of Activity C linkage (S to S)
Finish of Activity A to finish of Activity B linkage (F to F)
Start of Activity A to finish of Activity A linkage (S to F)
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Combines flowgraphs, probabilistic
networks, and decision trees
 Allows loops back to earlier events and
probabilistic branching

Any ?s
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