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.