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Critical Path Analysis

Critical Path Analysis. Precedence Diagram Method CPM PERT. Critical Path Analysis. why do it? what are the inputs? the process using the outputs PERT and uncertainty. The Context. identify tasks sequence estimate resources analysis scheduling optimisation.

jonah-hill
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Critical Path Analysis

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  1. Critical Path Analysis Precedence Diagram Method CPM PERT

  2. Critical Path Analysis • why do it? • what are the inputs? • the process • using the outputs • PERT and uncertainty

  3. The Context • identify tasks • sequence • estimate • resources • analysis • scheduling • optimisation

  4. What are the Benefits? • critical path • non-critical activities

  5. What are the Inputs? • tasks • sequence/dependencies • durations

  6. Sequence The most common dependencies Task B depends upon Task A; B cannot start until A is finished Task A Task B Task B Tasks B and C depend on Task A; neither can start until A is finished, but B and C are independent of each other Task A Task C Task A Task C depends upon Task A and B; C cannot start until both A and B are finished Task C Task B

  7. early finish time early start time duration task number and/or name late finish time late start time float Rules & Conventions • Just one start • Just one finish • No danglers Sometimes called ‘slack’

  8. Task 02 Task 03 Task 07 Task 01 Task 04 Task 05 Task 09 Task 06 Task 08 The Process Stage 1 - Draw

  9. Task 02 Task 03 Task 04 early start time early finish time Task 01 duration task number and/or name late finish time late start time float The Process And so on So the EFT of task 02 is ‘the end of Day 10’ Stage 2 – The Principle – Forward Pass EST of the first task is ‘the start of Day 1’ So the EFT of the first task is ‘the end of Day 4’ Which means that the EST of task 02 is ‘the start of Day 5’ 11 5 10 6 4 1 4 11 Duration 1 2 3 4 5 6 7 8 9 10

  10. 3 4 8 10 7 4 Task 02 Task 03 5 17 13 Task 07 12 1 3 6 9 3 18 1 3 4 18 10 Task 01 Task 04 Task 05 Task 09 2 7 6 Task 06 Task 08 The Process Stage 2 – the ‘Forward Pass’ Duration = 18 5 2 4

  11. 3 8 10 Task 03 5 17 13 Task 07 12 1 3 18 18 10 Task 05 Task 09 2 7 6 Task 08 The Process Stage 2 – The Principle – Backward Pass Transfer the EFT to the LFT 12 17 13 18 18 12 Late Start date is (LFT-Duration +1) 17 16 And Tasks 03 and 05 MUST finish by the end of day 12 If Task 09 LST is 18 then Task 07 and Task 08 MUST finish by the end of day 17 Late Start date is (LFT-Duration +1)

  12. 3 4 8 10 7 4 Task 02 Task 03 12 10 2 2 9 6 5 17 13 Task 07 12 1 3 6 9 3 18 1 3 4 18 10 0 13 17 Task 01 Task 04 Task 05 Task 09 4 12 18 1 18 3 9 0 0 0 10 0 2 7 6 Task 06 Task 08 16 10 17 The Process Stage 3 – the ‘Backward Pass’ 5 2 4 10 14 15

  13. Some Unusual Links & Relationships Some variations from the finish to start link... 3 days Task B depends upon Task A, but with a 3 day delay; B cannot start until 3 days after A is finished Task A Task B Task A The start of Task C depends on the start of Task A; this is a start-to-start link; it may also incorporate a delay Task C Task A The finish of Task C depends upon the finish of Task A Task C

  14. Using the Outputs • Gantt Charts • resource histograms • resource smoothing • optimising the schedule

  15. Scheduling task res. Duration Calendar task 1 task 2 task 3 task 4 task 5 task 6 task 7 2 days 3 days 1 day 2 days 7 days 4 days 1 day Jane Bill Jane Jim Bill Jane Bill

  16. Task 02 Task 01 Task 04 Task 03 PERT & Uncertainty 5 The critical path looks like tasks 01-02-04 2 4 4 But what if you are not sure about the duration for Task 03?

  17. Task 02 Task 01 Task 04 Task 03 PERT & Uncertainty The better estimate for Task 03 might be its PERT estimate, or Expected Value, EV) 5 2 4 EV = O + 4L + P ___________ 6 O = Optimistic estimate (say 2) L = Most Likely (say 4) P = Pessimistic (say 12) 4 In this example the EV = 5, which does, in fact change the critical path

  18. PERT & Uncertainty But how confident can we be in these results? An duration’s spread is the degree to which estimates of the duration differ from each other. If every estimate of duration were about equal, the estimate would have very little spread. There are many measures of spread. The distributions on this page have the same mean but differ in spread: the distribution on the bottom is more spread out.

  19. PERT & Uncertainty Standard deviation is used as a measure of spread. In a normal distribution, about 68% of estimates are within one standard deviation of the mean and about 95% of the estimates are within two standards deviations of the mean. EV = O + 4L + P ___________ 6 O = Optimistic estimate (say 2) L = Most Likely (say 4) P = Pessimistic (say 12) SD = (P – O)/6 In our example SD = (12-2)/6 = 1.666 So, we could say that, for task 03: With 68% certainty, the duration will be between 2.34 and 5.66 (4 ± SD) With 95% certainty the duration will be between 0.68 and 7.32 (4 ± 2SD)

  20. Task 06 Classroom Practice - 1 4 2 Task 02 Task 03 3 Task 07 9 4 5 2 Task 04 Task 05 Task 09 Task 01 4 1 Task 08

  21. Classroom Practice - 2 4 2 Task 02 Task 03 5 Task 05 6 2 5 Task 01 Task 04 Task 07 4 Task 06

  22. Task 06 Classroom Practice - 3 2 2 Task 02 Task 03 3 Task 07 7 5 2 Task 01 Task 05 Task 09 4 + 4 days

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