Basics Of PERTCPM PERTProject Evaluation Review Technique CPM

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 • “Critical Tasks” are Thick Arrows • “Dummy Tasks” are Dashed Arrows

Starting Point: Task Primary Properties • • • 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: • • 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.