Basics Of PERT/CPM

PERT=Project Evaluation Review Technique

CPM = Critical Path Method

Why PERT/CPM?

• 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

• “Dummy Tasks” are Dashed Arrows

• “Critical Tasks” are Thick Arrows

Starting Point: Task Primary Properties

• Crash Limit

• Prerequisite task set (may be empty)

• Optimal Staffing

• Duration at Optimal Staffing Level

• 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:• 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:

• 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

• 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

• 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.