Basics Of PERT/CPM

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

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