1. Critical Path Method (CPM)

2. Background & History Developed in the 1950s by the US Navy & Du Pont. Originally, the critical path method considered only logical dependencies between terminal elements Similar technique Program Evaluation Review Technique- PERT. Mostly concern with Time Constraint- not Cost or Quality. ◦ Missile program of 3000 contractor

3. What is CPM? The Critical Path Method is a sequence of individual activities of a project that must be finished on schedule so that the whole project is completed on time. It is an important tool for effective project management Commonly used with all forms of projects, including construction, software development, research projects, product development, engineering Any project with interdependent activities can apply this method of scheduling

4. Elements of CPM To construct CPM: ◦ A list of all activities required to complete the project (also known as Work Breakdown Structure) ◦ The time (duration) that each activity will take to completion ◦ The dependencies between the activities. To construct CPM: ◦ A list of all activities required to complete the project (also known as Work Breakdown Structure) ◦ The time (duration) that each activity will take to completion ◦ The dependencies between the activities. Activity Predecessor (Activity) Duration Longest Path Critical Activities Slack Time Earliest/Latest Start Earliest/Latest Finish Activity Predecessor (Activity) Duration Longest Path Critical Activities Slack Time Earliest/Latest Start Earliest/Latest Finish

5. Definitions: Float (slack) - amount of time that a task can be delayed without causing a delay to: subsequent tasks (free float) project completion date (total float) Critical path: is the sequence of activities which add up to the longest overall duration. The earliest and latest that each activity can start and finish without making the project longer Any delay of an activity on the critical path directly impacts the planned project completion date (there is no float on the critical path). A project can have several, parallel, near critical paths. An additional parallel path through the network with the total durations shorter than the critical path is called a sub- critical or non-critical path. Critical activity – activity with zero float Resource leveling – iterative process of assigning crews to activities in order to calculate their duration

6. CPM Approach List the activities & Relationship Create a start node Draw arrow(s) from start node to first activity node(s) Sequentially arrange all activities from Start Repeat process from successors for all activities Double check for missed relationship

7. CPM with Single Time Estimate Consider the following consulting project: Develop a critical path diagram and determine the duration of the critical path and slack times for all activities Activity Designation Immed. Pred.Time (Weeks) Assess customer's needsANone2 Write and submit proposalBA1 Obtain approvalCB1 Develop service vision and goalsDC2 Train employeesEC5 Quality improvement pilot groupsFD, E 5 Write assessment reportGF1

8. First draw the network A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1

9. Gannt Chart

10. Determine early start and early finish times ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 ES=4 EF=9 ES=4 EF=6 ? A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1

11. When I can start depends on when predecessors finish ES=9 EF=14 ES=14 EF=15 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 ES=4 EF=9 ES=4 EF=6 A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1

12. Determine late starts and late finish times ES=9 EF=14 ES=14 EF=15 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 ES=4 EF=9 ES=4 EF=6 A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1 LS=14 LF=15 LS=9 LF=14 LS=4 LF=9 LS=7 LF=9 ?

13. Don’t delay the project ES=9 EF=14 ES=14 EF=15 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 ES=4 EF=9 ES=4 EF=6 A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1 LS=14 LF=15 LS=9 LF=14 LS=4 LF=9 LS=7 LF=9 LS=3 LF=4 LS=2 LF=3 LS=0 LF=2

14. Critical Path & Slack ES=9 EF=14 ES=14 EF=15 ES=0 EF=2 ES=2 EF=3 ES=3 EF=4 ES=4 EF=9 ES=4 EF=6 A, 2B, 1 C, 1 D, 2 E, 5 F, 5 G, 1 LS=14 LF=15 LS=9 LF=14 LS=4 LF=9 LS=7 LF=9 LS=3 LF=4 LS=2 LF=3 LS=0 LF=2 Duration = 15 weeks Slack=(7-4)=(9-6)= 3 Wks

15. CPM with Three Activity Time Estimates

16. Expected Times

17. A, 7 B 5.333 C, 14 D, 5 E, 11 F, 7 H, 4 G, 11 I, 18 Duration = 54 Days 54 Days 41 Days 34.3 Days

18. Activity Identity Box

19. Exercise

22. Especially useful when scheduling and controlling large projects Straightforward concept and not mathematically complex Graphical networks help to perceive relationships among project activities Critical path and slack time analyses help pinpoint activities that need to be closely watched Project documentation and graphics point out who is responsible for various activities Applicable to a wide variety of projects Useful in monitoring not only schedules but costs as well Advantages

23. Project activities have to be clearly defined, independent, and stable in their relationships Precedence relationships must be specified and networked together Time estimates tend to be subjective and are subject to fudging by managers There is an inherent danger of too much emphasis being placed on the longest or critical path CPM's can be complicated, and complexity increases for larger projects Does not handle the scheduling of personnel or the allocation of resources The critical path is not always clear and needs to be calculated carefully Estimating activity completion times can be difficult Limitation

25. Practice Activity Preceding Activity(ies) Duration (days) A - 15 B - 20 C A 25 D A 10 E B 15 F B 20 G D,E 20 H D,E 30 I D,E 15 J G,C 10 K I,F 20

26. University of South Asia is considering building a new multipurpose athletic complex on campus. The complex would provide a new gymnasium for interdepartmental basketball games, expanded office space, classroom, and intramural facilities. The following activities would have to be undertaken before construction can begin. ActivityDescription Immediate Predecessors Time (weeks) ASurvey building site-6 BDevelop initial design-8 CObtain board approvalA, B12 DSelect architectC4 EEstablish budgetC6 FFinalize designD, E15 GObtain financingE12 HHire contractorF, G8 Draw a project network. Determine ES, EF, LS, LF, and slack time for each activity. Identify the critical path.