Transcript Basics Of PERT/CPM

Basics Of PERT/CPM
PERT=Project Evaluation Review Technique
CPM = Critical Path Method
Why PERT/CPM?
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Prediction of deliverables
Planning resource requirements
Controlling resource allocation
Internal program review
External program review
Performance evaluation
Uniform wide acceptance
The CPM Diagram
• “Tasks” are Arrows
• “Events” are Circles
• “Critical Tasks” are Thick Arrows
• “Dummy Tasks” are Dashed Arrows
Starting Point:
Task Primary Properties
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Prerequisite task set (may be empty)
Optimal Staffing
Duration at Optimal Staffing Level
Crash Limit
Fixed and Variable costs
If a task seems too complex or involved to
easily determine primary properties . . .
Break the task up into simpler tasks . . .
Or create a CPM sub-project.
We will use PERT/CPM
Analysis to determine Task
Secondary properties:
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Tail Event and Head Event
Earliest Start, Earliest Complete
Latest Start, Latest Complete
Critical / Non-Critical Status
Total Float, Free Float
Scheduled Start, Scheduled Complete
Actual Staffing, Duration, and Variable Costs
We will then use Task Secondary
Properties to generate Project
Management Tools:
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Gantt Chart (Project Schedule)
Manpower Chart
Expenditure Curves
Project Completion (PC)
Generate Initial CPM Diagram
• Must strictly enforce all prerequisite
relationships.
• Number of events is initially unknown
• Critical path is initially unknown
• Iterative Process
• Try to minimize number of Dummy Tasks
CPM Hint #1
• Add or remove events at your pleasure.
• Do not number events until last.
CPM Hint #2
• The initial event is the Tail Event for all
tasks which have empty prerequisite sets
(Initial Tasks).
• The Final Event is the Head Event for all
tasks which are not members of any
prerequisite set (Final Tasks).
CPM Hint #3
• Tasks which have identical prerequisite sets
have the same Tail Event
CPM Hint #4
• Starting with the Final Tasks, work
backwards, enforcing the smallest
prerequisite sets first.
• Use Dummy Tasks to enforce any
prerequisites in large sets which have
already been enforced in a smaller set.
Finish CPM Diagram
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Remove all redundant Dummy Tasks
Remove all redundant Events
Number all remaining events
Not really finished . . haven’t identified
critical tasks yet.
Generate PERT Chart:
Enter Data for Each Task
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Task Symbol
Tail Event
Head Event
Task Duration (TD)
Forward Pass:
Determine Earliest Start (ES) and
Earliest Complete (EC)
for each Task
• For all Initial Tasks, ES = 0
• Once ES is Determined, EC equals ES plus TD.
• The ES for all tasks with tail [i] is equal to the
largest value of EC for all tasks with head [i].
• PC is the largest value of EC for all Final Tasks.
Backward Pass:
Determine Latest Start (LS) and
Latest Complete (LC)
for each Task
• For all Final Tasks, LC = PC
• Once LC is Determined, LS equals LC minus TD.
• The LC for all tasks with head [j], is equal to the
smallest value of LS for all tasks with tail [j].
• At least one Initial Task must have LS = 0; none
may be negative.
Determine Total Float (TF):
Allowable delay in start of task which
will not delay Project Completion
For task with tail [i] and head [j],
TF[i,j] = (LC[j] – ES[i]) – TD[i,j]
=LS[i,j] – ES[i]
• ES[i] is earliest start for all tasks with tail [i].
• LC[j] is latest complete for all tasks with head [j].
• LS[i,j] is latest start for task with tail [i] and head [j].
Determine Free Float (FF):
Allowable delay in start of task which
will not delay start of any other task.
For task with tail [i] and head [j],
FF[i,j] = ES[j] - ES[i] - TD[i, j]
= ES[j] - EC[i,j]
Determine Critical Path
• All Tasks with zero Total Float are Critical.
• Any delay in these Tasks will delay Project
Completion.
• Darken these Tasks to finish CPM Diagram.