2. PERT / CPM PERTProgram Evaluation & Review Technique CPMCritical Path Method

3. Planning Projects l Tasks: Develop internal and external resource require-ments and time- phase them to the project activities l Means of Task Accomplishment: Activity descriptions, milestone charts, cash flow charts, CPM/PERT, engineering designs, time and cost estimates, material delivery plans, and so on. l Timing of Tasks: Before project is begun and modified as required during project

4. Scheduling Projects l Tasks: Develop/revise detailed guides for each resource indicating quantity, quality, and timing l Means of Task Accomplishment: Milestone charts for departments, subcontractors, and suppliers; cash flow schedule; CPM/PERT: begin-activity and complete- activity dates, and updated activity slack l Timing of Tasks: Slightly before project is begun and continued throughout project

5. Controlling Projects l Tasks: Sense noncompliance of resources with schedules, standards, and budgets; take corrective actions, shift resources, develop alternatives l Means of Task Accomplishment: Department budget reports, activity cost reports, quality compliance reports, time performance reports l Timing of Tasks: During project

6. Critical Path Method (CPM) l Designed to provide intense micro-control l The system is dynamic; it continues to provide periodic reports as the project progresses

7. Manager’s View of CPM INPUTS List of project activities List of project activities Precedence relationship among activities Precedence relationship among activities Estimate of each activity’s duration Estimate of each activity’s duration OUTPUTS Estimated duration of project Estimated duration of project Identification of critical activities Identification of critical activities Amount of slack for each activity Amount of slack for each activity CPM processing procedures

8. CPM Terminology l Activity A task or a certain amount of work required in the project Requires time to complete Represented by an arrow l Dummy Activity Indicates only precedence relationships Does not require any time of effort

9. CPM Terminology l Event Signals the beginning or ending of an activity Designates a point in time Represented by a circle (node) l Network Shows the sequential relationships among activities using nodes and arrows

10. CPM Terminology l Path A connected sequence of activities leading from the starting event to the ending event l Critical Path The longest path (time); determines the project duration l Critical Activities All of the activities that make up the critical path

11. CPM Terminology l Earliest Start (ES) The earliest that an activity can begin; assumes all preceding activities have been completed l Earliest Finish (EF) ES + activity time l Latest Finish (LF) The latest that an activity can finish and not change the project completion time l Latest Start (LS) LF - activity time

12. CPM Network Conventions 11 ab I 11 abc II 11 a b c III ca 11 db IV c d a b 33 22 11 V 22ac11 bd VI

13. Steps in CPM Analysis l Draw the CPM network A graphic view of the relationships among the required activities l Analyze the paths through the network Determine the length of each path (the time required to complete each path) Starting at the beginning of the network and working toward the end (from left to right), determine the ES and the EF for each activity... more

14. Steps in CPM Analysis l Path analysis (continued) Identify the critical path(s) (the longest path[s] through the network) The critical path(s) determines how long the project will take l... more

15. Steps in CPM Analysis l Determine the slack for each activity Working from the end of the project network (from right to left), find the LF and the LS for each activity Compute the activity’s slack slack = LS - ES = LF - EF Slack is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project

16. A Simple Project

17. Project Network

19. ESEarliest Starting (time) EFEarliest Finishing LSLatest Starting LFLatest Finishing SlackExtra Time

20. Earliest Starting/Finishing Times EF = ES + t

22. LS = LF - t

25. aoptimistic time mmost likely time bpessimistic time t = E(T)expected time = (a + 4m + b)/6 V(T)variance = (b - a) 2 /36 What if activity times are variable?

26. Activity Time Expected Value and Variance

27. Possible Paths and Statistics

28. What is the probability that the project takes at least 10 days? What is the probability that the project takes less than 7 days?