1. ME 380 Project Planning

2. Critical Path Method (CPM) Elements: Activities & Events Feature: Precedence relations ActivityDurationPrecedence A4- B5- C3A D3A E2B, C Activities Table

3. Critical Path Method (CPM) Graphical representation : Activities : (edges) Events : (vertices) C  T (Time reqd. for activity)

4. Critical Path Method (CPM) Precedence: Activities B & C precede Activity E C B E This “Event” cannot occur before both activities B & C have been completed

5. Critical Path Method Example ActivityDurationPrecedence A4- B5- C3A D3A E2B, C

6. Critical Path Method (CPM) The project sequence graph is constructed: C B E A D Now what ??? Project Start Project End

7. Critical Path Method (CPM) Events are consolidated to provide the specified precedence. “Dummy” activities are added if necessary. C B E A D Project Start Project End

8. Dummy Activity Example To be able to bolt a bracket to a panel, the operations required are : Design bracketA- Build bracketBA Build panelC- Drill holes in panelDA,C C B A D A A C C D D B

9. Critical Path Method (CPM) Activity times (duration) are added next : C B E A D Project Start Project End 5 3 3 2 4

10. Critical Path Method (CPM) The CRITICAL PATH is the path through the project on which any delay will cause the completion of the entire project to be delayed: C B E A D Project Start Project End 5 3 3 2 4

11. Critical Path Method (CPM) For fairly simple projects, the critical path is usually the longest path through the project. For projects with several parallel and interlinked activities, this may not always be the case. For more complicated projects, the critical path can be determined with an ‘earliest time’ forward sweep through the diagram followed by a ‘latest time’ reverse sweep.

12. Critical Path Method (CPM) The EARLIEST starting time of each activity is associated with the events. It corresponds to the longest time of any path from any previous event. C B E A D Project Start Project End 3 3 2 4 0 4 97 5

13. Critical Path Method (CPM) The LATEST starting time of each activity is also associated with the events. It corresponds to the longest time of any path from any subsequent event. C B E A D Project Start Project End 3 3 2 4 0 4 97 5 0 4 79

14. Critical Path Method (CPM) The CRITICAL PATH is the path along which the earliest time and latest time are the same for all events, and the early start time plus activity time for any activity equals the early start time of the next activity. C B E A D Project Start Project End 3 3 2 4 0 4 97 5 0 4 79

15. Critical Path Method (CPM) This project cannot be completed in less than 9 weeks given the expected duration of the activities. However, activities B & D could be delayed or extended by up to 2 weeks each without affecting the minimum project completion time. This is termed ‘float’ or ‘slack’ time. C B E A D Project Start Project End 3 3 2 4 0 4 97 5 0 4 79

16. Example Activity Duration Precedence A3- B3A C4- D1C E3B, D F2A, B, D G2C, F H4G I1C J3E, G K5F, H, I

17. Example C BE A D Project Start Project End H K J F I G

18. Example ActivityDurationEarliest Start Latest Start Float A3000 B3330 C4011 D1451 E36137 F2660 G2880 H410 0 I14139 J310166 K514 0

19. Summary: CPM Steps List all activities and expected durations. Construct CPM diagram for activities list. Determine EARLIEST start time for each event (working forward from project start). Determine LATEST start time for each event (working backwards from project end). Identify the CRITICAL PATH (and the ‘float’ time for any non-critical activities).

20. Using Estimates of Activity times The estimated duration of any activity is just that – an estimate. There is usually an optimistic time (shortest time, T S ) associated with any activity – 1 in 100 chance of taking less time than this. There is also usually a pessimistic time (longest time, T L ) associated with any activity – 1 in 100 chance of taking longer than this. If T M is the most likely time for a specific activity, then a mean and variance for the activity can be calculated, assuming that T S, T L and T M are the parameters describing a Beta distribution.

21. Using Estimates of Activity times The estimated time T EST is calculated as: T EST = (T S + 4.T M + T L )/6 and the variance of this is:  2 = (T L – T S ) 2 /36

22. from the previous Example ActivityDuration T M TSTS TLTL T EST Earliest Start Latest Start Float A3153.000.5 B3243.033.50.5 C43104.83000 D1151.674.83 0 E3263.336.5014.848.34 F2172.676.506.50 G2142.179.17 0 H4364.1711.34 0 I1031.174.8314.349.51 J3163.1711.3418.176.83 K53125.8315.51 0

23. PERT/CPM The critical path has now become C-D-F-G-H-K with a total estimated time of 21.3 days (i.e. 15.51 + 5.83) The std. deviation along the critical path is the square root of the sum of the individual variances:  CP =   C 2 +  D 2 +  F 2 +  G 2 +  H 2 +  K 2 which for this data is 2.36 days