1. PERT=Project Evaluation Review Technique CPM = Critical Path Method
Basics Of PERT/CPM
PERT=Project Evaluation Review Technique
CPM = Critical Path Method

2. Why PERT/CPM? Prediction of deliverables
Planning resource requirements
Controlling resource allocation
Internal program review
External program review
Performance evaluation
Uniform wide acceptance

3. The CPM Diagram “Tasks” are Arrows “Events” are Circles
“Critical Tasks” are Thick Arrows
“Dummy Tasks” are Dashed Arrows

4. Starting Point: Task Primary Properties
Prerequisite task set (may be empty)
Optimal Staffing
Duration at Optimal Staffing Level
Crash Limit
Fixed and Variable costs

5. 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.

6. 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

7. We will then use Task Secondary Properties to generate Project Management Tools:
Gantt Chart (Project Schedule)
Manpower Chart
Expenditure Curves
Project Completion (PC)

8. 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

9. CPM Hint #1 Add or remove events at your pleasure.
Do not number events until last.

10. 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).

11. CPM Hint #3
Tasks which have identical prerequisite sets have the same Tail Event

12. 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.

13. 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.

14. Generate PERT Chart: Enter Data for Each Task
Task Symbol
Tail Event
Head Event
Task Duration (TD)

15. 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.

16. 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.

17. 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].

18. 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]

19. 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.