ME 380 Project Planning ME 380 The Design

ME 380 Project Planning ME 380 The Design Process 1

Critical Path Method (CPM) Elements: Activities & Events Feature: Precedence relations Activity A B C Duration 4 5 3 Precedence A D E 3 2 A B, C Activities Table ME 380 The Design Process 2

Critical Path Method (CPM) Graphical representation : Activities : (edges) C T (Time reqd. for activity) Events : (vertices) ME 380 The Design Process 3

Critical Path Method (CPM) Precedence: Activities B & C precede Activity E B E C This “Event” cannot occur before both activities B & C have been completed ME 380 The Design Process 4

Critical Path Method Example Activity A B C D E ME 380 Duration 4 5 3 3 2 The Design Process Precedence A A B, C 5

Critical Path Method (CPM) The project sequence graph is constructed: D A Project Start C Now what ? ? ? B E Project End ME 380 The Design Process 6

Critical Path Method (CPM) n n Events are consolidated to provide the specified precedence. “Dummy” activities are added if necessary. A D Project Start B C Project End E ME 380 The Design Process 7

Dummy Activity Example To be able to bolt a bracket to a panel, the operations required are : n n Design bracket Build panel Drill holes in panel A C ME 380 D A A B C D A A, C B C The Design Process D A B C D 8

Critical Path Method (CPM) n Activity times (duration) are added next : A 4 Project Start ME 380 B 5 3 C D 3 E 2 The Design Process Project End 9

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: A 4 Project Start ME 380 B 5 3 C D 3 E 2 The Design Process Project End 10

Critical Path Method (CPM) n For fairly simple projects, the critical path is usually the longest path through the project. n For projects with several parallel and interlinked activities, this may not always be the case. n 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. ME 380 The Design Process 11

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. 0 Project Start ME 380 A 4 B 5 4 3 C 7 The Design Process D 3 E 2 Project End 9 12

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. 0 0 Project Start ME 380 A 4 B 5 4 4 3 C 7 7 The Design Process D 3 E 2 Project End 9 9 13

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. 0 0 Project Start ME 380 A 4 B 5 4 4 3 C 7 7 The Design Process D 3 E 2 Project End 9 9 14

Critical Path Method (CPM) n n 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. 0 0 Project Start ME 380 A 4 B 5 4 4 3 C 7 7 The Design Process D 3 Project End E 2 9 9 15

Example Activity A B C D E F G H I J K ME 380 Duration 3 3 4 1 3 2 2 4 1 3 5 The Design Process Precedence A C B, D A, B, D C, F G C E, G F, H, I 16

Example B A Project Start E J F G D C I ME 380 The Design Process H K Project End 17

Example ME 380 Activity Duration Earliest Start Latest Start Float A 3 0 0 0 B 3 3 3 0 C 4 0 1 1 D 1 4 5 1 E 3 6 13 7 F 2 6 6 0 G 2 8 8 0 H 4 10 10 0 I 1 4 13 9 J 3 10 16 6 K 5 14 14 0 The Design Process 18

Summary: CPM Steps n List all activities and expected durations. n Construct CPM diagram for activities list. n Determine EARLIEST start time for each event (working forward from project start). n Determine LATEST start time for each event (working backwards from project end). n Identify the CRITICAL PATH (and the ‘float’ time for any non-critical activities). ME 380 The Design Process 19

Using Estimates of Activity times n n The estimated duration of any activity is just that – an estimate. There is usually an optimistic time (shortest time, TS) associated with any activity – 1 in 100 chance of taking less time than this. There is also usually a pessimistic time (longest time, TL) associated with any activity – 1 in 100 chance of taking longer than this. If TM is the most likely time for a specific activity, then a mean and variance for the activity can be calculated, assuming that TS, TL and TM are the parameters describing a Beta distribution. ME 380 The Design Process 20

Using Estimates of Activity times The estimated time TEST is calculated as: TEST = (TS + 4. TM + TL)/6 and the variance of this is: 2 = (TL – TS)2/36 ME 380 The Design Process 21

from the previous Example Activity Duration TM TS TL TEST Earliest Start Latest Start Float A 3 1 5 3. 0 0 0. 5 B 3 2 4 3. 0 3 3. 5 0. 5 C 4 3 10 4. 83 0 0 0 D 1 1 5 1. 67 4. 83 0 E 3 2 6 3. 33 6. 50 14. 84 8. 34 F 2 1 7 2. 67 6. 50 6. 5 0 G 2 1 4 2. 17 9. 17 0 H 4 3 6 4. 17 11. 34 0 I 1 0 3 1. 17 4. 83 14. 34 9. 51 J 3 1 6 3. 17 11. 34 18. 17 6. 83 K 5 3 12 5. 83 15. 51 0 ME 380 The Design Process 22

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 ME 380 The Design Process 23