Chapter 5PERT AND CPM NETWORKSHistoryThe Language of PERT/CPMThe Language of PERT/CPM continuedThe Language of PERT/CPM concludedBuilding the NetworkTable 5-1 A Sample Set of Project Activities and PrecedencesFigure 5-1 Stage 1 of a Sample AON NetworkFigure 5-2 Stage 2 of a Sample AON NetworkFigure 5-3 A Completed Sample AON NetworkFigure 5-4 Stage 1 of a Sample AOA NetworkFigure 5-5 Stage 2 of a Sample AOA NetworkFigure 5-6a A Completed Sample AOA NetworkFigure 5-6b A Completed Sample AOA Network Showing the Use of a Dummy TaskTable 5-2 A Sample Problem for Finding the Critical Path and Critical TimeFigure 5-7 Stage 1 of a Sample NetworkFigure 5-8 A Complete NetworkFigure 5-9 Information Contents in an AON NodeFigure 5-10 The Critical Path and Time for Sample ProjectCalculating Activity SlackFigure 5-11 An MSP Version of PERT/CPM NetworkFigure 5-12 A Modified Version of MSP NetworkPROJECT UNCERTAINTY AND RISK MANAGEMENTCalculating Probabilistic Activity TimesFigure 5-13 The Statistical Distribution of all Possible Times for an ActivityActivity Expected Time and Variance95 Percent Level90 Percent Level95 Percent Level (Alternative Interpretation)90 Percent Level (Alternative Interpretation)Figure 5-14 An AON NetworkFigure 5-15 An MSP Version of a Sample Problem NetworkFigure 5-16 A Pert/CPM Network for the Day Care ProjectFigure 5-17 An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00The Probability of Completing the Project on TimeFigure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-hSelecting Risk and Finding DSIMULATIONTraditional Statistics Versus SimulationTHE GANNT CHARTFigure 5-23 A Gantt Chart of a Sample ProjectFigure 5-24 A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST, LST, EFT, and LFTFigure 5-25 A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource RequirementsFigure 5-26 A Progress Report on a Day Care Project Showing Actual Progress Versus BaselineEXTENSIONS TO PERT/CPMPrecedence DiagrammingFigure 5-27 Precedence Diagramming ConventionsOther MethodsCopyrightMEM 612 Project ManagementChapter 5Scheduling the ProjectMEM 612 Project ManagementPERT AND CPM NETWORKSMEM 612 Project ManagementHistory•Late 1950s–Program Evaluation and Review Technique (PERT)•U.S. Navy, Booz-Allen Hamilton, and Lockeheed Aircraft•Probabilistic activity durations–Critical Path Method (CPM)•Dupont De Nemours Inc.•Deterministic activity durationsMEM 612 Project ManagementThe Language of PERT/CPM•Activity–task or set of tasks–use resources•Event–state resulting from completion of one or more activities–consume no resources or time–predecessor activities must be completedMEM 612 Project ManagementThe Language of PERT/CPM continued•Milestones–events that mark significant progress•Network–diagram of nodes and arcs–used to illustrate technological relationships•Path–series of connected activities between two eventsMEM 612 Project ManagementThe Language of PERT/CPM concluded•Critical Path–set of activities on a path that if delayed will delay completion of project•Critical Time–time required to complete all activities on the critical pathMEM 612 Project ManagementBuilding the Network•AOA Network•AON NetworkMEM 612 Project ManagementTable 5-1 A Sample Set of Project Activities and PrecedencesTask Predecessora --b --c ad be bf c, dg eMEM 612 Project ManagementFigure 5-1 Stage 1 of a Sample AON NetworkMEM 612 Project ManagementFigure 5-2 Stage 2 of a Sample AON NetworkMEM 612 Project ManagementFigure 5-3 A Completed Sample AON NetworkMEM 612 Project ManagementFigure 5-4 Stage 1 of a Sample AOA NetworkMEM 612 Project ManagementFigure 5-5 Stage 2 of a Sample AOA NetworkMEM 612 Project ManagementFigure 5-6a A Completed Sample AOA NetworkMEM 612 Project ManagementFigure 5-6b A Completed Sample AOA Network Showing the Use of a Dummy TaskMEM 612 Project ManagementTable 5-2 A Sample Problem for Finding the Critical Path and Critical TimeActivity Predecessor Durationa -- 5 daysb -- 4c a 3d a 4e a 6f b, c 4g d 5h d, e 6i f 6j g, h 4MEM 612 Project ManagementFigure 5-7 Stage 1 of a Sample NetworkMEM 612 Project ManagementFigure 5-8 A Complete NetworkMEM 612 Project ManagementFigure 5-9 Information Contents in an AON NodeMEM 612 Project ManagementFigure 5-10 The Critical Path and Time for Sample ProjectMEM 612 Project ManagementCalculating Activity Slack•Slack or FloatLST - EST = LFT - EFT = SlackMEM 612 Project ManagementFigure 5-11 An MSP Version of PERT/CPM NetworkMEM 612 Project ManagementFigure 5-12 A Modified Version of MSP NetworkMEM 612 Project ManagementPROJECT UNCERTAINTY AND RISK MANAGEMENTMEM 612 Project ManagementCalculating Probabilistic Activity Times•Three Time Estimates–pessimistic (a )–most likely (m)–optimistic (b)MEM 612 Project ManagementFigure 5-13 The Statistical Distribution of all Possible Times for an ActivityMEM 612 Project ManagementActivity Expected Time and Variance22E6)(Var6)(6)4(TababbmaMEM 612 Project Management95 Percent Level•Task will be a or lower 5 percent of the time•Task will be b or greater 5 percent of the time3.3)( ab MEM 612 Project Management90 Percent Level•Task will be a or lower 10 percent of the time•Task will be b or greater 10 percent of the time6.2)( ab MEM 612 Project Management95 Percent Level (Alternative Interpretation)•Task will be between a and b 95 percent of the time92.3)( ab MEM 612 Project Management90 Percent Level (Alternative Interpretation)•Task will be between a and b 90 percent of the time29.3)( ab MEM 612 Project ManagementFigure 5-14 An AON NetworkMEM 612 Project ManagementFigure 5-15 An MSP Version of a Sample Problem NetworkMEM 612 Project ManagementFigure 5-16 A Pert/CPM Network for the Day Care ProjectMEM 612 Project ManagementFigure 5-17 An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00MEM 612 Project ManagementThe Probability of Completing the Project on Time2)(DZ=NORMDIST(D ,,,TRUE)MEM 612 Project ManagementFigure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-hMEM 612 Project ManagementSelecting Risk and Finding D2ZD NORMINV(probability,,,TRUE)MEM 612 Project ManagementSIMULATIONMEM 612 Project ManagementTraditional Statistics Versus Simulation•Similarities–must