Chapter 5PERT AND CPM NETWORKSPowerPoint PresentationHistoryThe 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 DTHE 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 Conventions5-1Chapter 5Scheduling the Project5-2PERT AND CPM NETWORKS5-35-4History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 durations5-5The 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 completed5-6The 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 events5-7The 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 path5-8Building the NetworkAOA NetworkAON Network5-9Table 5-1 A Sample Set of Project Activities and PrecedencesTask Predecessora --b --c ad be bf c, dg e5-10Figure 5-1 Stage 1 of a Sample AON Network5-11Figure 5-2 Stage 2 of a Sample AON Network5-12Figure 5-3 A Completed Sample AON Network5-13Figure 5-4 Stage 1 of a Sample AOA Network5-14Figure 5-5 Stage 2 of a Sample AOA Network5-15Figure 5-6a A Completed Sample AOA NetworkE5-16Figure 5-6b A Completed Sample AOA Network Showing the Use of a Dummy Task5-17Table 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 45-18Figure 5-7 Stage 1 of a Sample Network5-19Figure 5-8 A Complete Network5-20Figure 5-9 Information Contents in an AON Node5-21Figure 5-10 The Critical Path and Time for Sample Project5-22Calculating Activity SlackSlack or FloatLST - EST = LFT - EFT = Slack5-23Figure 5-11 An MSP Version of PERT/CPM Network5-24Figure 5-12 A Modified Version of MSP Network5-25PROJECT UNCERTAINTY AND RISK MANAGEMENT5-26Calculating Probabilistic Activity TimesThree Time Estimates–pessimistic (a)–most likely (m)–optimistic (b)5-27Figure 5-13 The Statistical Distribution of all Possible Times for an Activity5-28Activity Expected Time and Variance22E6)(Var6)(6)4(Tababbma5-2995 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 5-3090 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 5-3195 Percent Level (Alternative Interpretation)Task will be between a and b 95 percent of the time92.3)( ab 5-3290 Percent Level (Alternative Interpretation)Task will be between a and b 90 percent of the time29.3)( ab 5-33Figure 5-14 An AON Network5-34Figure 5-15 An MSP Version of a Sample Problem Network5-35Figure 5-16 A Pert/CPM Network for the Day Care Project5-36Figure 5-17 An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/005-37The Probability of Completing the Project on Time2)(DZ=NORMDIST(D,,,TRUE)5-38Figure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-h5-39Selecting Risk and Finding D2ZD NORMINV(probability,,,TRUE)5-40THE GANNT CHART5-41Figure 5-23 A Gantt Chart of a Sample Project5-42Figure 5-24 A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST, LST, EFT, and LFT5-43Figure 5-25 A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource Requirements5-44Figure 5-26 A Progress Report on a Day Care Project Showing Actual Progress Versus Baseline5-45EXTENSIONS TO PERT/CPM5-46Precedence DiagrammingFinish-to-start linkageStart-to-start linkageFinish-to-finish linkageStart-to-finish linkage5-47Figure 5-27 Precedence Diagramming