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# Program evaluation review technique (pert)

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• What is the formula for finding mean deviation in Pert?

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### Program evaluation review technique (pert)

1. 1. Engineering MangementProgram Evaluation Review Technique (PERT) Prepared by : Anas Tomeh Fira Eid Prepared for : Dr. Reema Nassar
2. 2. Objective of the presentation• To understand the formula , the use and the benefits of Program , Evaluation ,and Review Technic (PERT) analysis .
3. 3. What is the PERT ?Program (Project) Evaluation and Review Technique (PERT): isa project management tool used to schedule, organize, andcoordinate tasks within a project. It is basically a method toanalyse the tasks involved in completing a givenproject, especially the time needed to complete each task, andto identify the minimum time needed to complete the totalproject.
4. 4. When we use PERT ? • PERT is used when activity times are uncertain. – Determine the duration of the project . – Decision making under risk (“P” for probabilistic)
5. 5. Determine the duration of the project • OPTIMISTIC TIME: Best time if everything goes perfectly • REALISTIC TIME: Most likely time • PESSIMISTIC TIME: A worst-case situation B + 4M + P Expected Time = ------------------- 6
6. 6. Determine the duration of the project • Example: For excavation activity let : B = 12 days M = 18 days P = 60 What is the expected time for this activity? Sol : 12 + 4(18) + 60 Expected Time = ------------------------- 6 = 24 days
7. 7. Determine the duration of the project Activity Predecessor Optimistic Normal Pessimistic Te (B) (m) (P) (B+4m+P)/6 A --- 2 4 6 4.00 B --- 3 5 9 5.33 C A 4 5 7 5.17 D A 4 6 10 6.33 E B, C 4 5 7 5.17 F D 3 4 8 4.50 G E 3 5 8 5.17 f
8. 8. Determine the duration of the project D F A C Start Finish B E G
9. 9. Determine the duration of the project D F D:6.33 D:4.5 ES:4 ES:10.33 EF:10.33 EF:14.83 A D:4 ES:0 EF:4 C D:5.17 Finish Start ES:4 ES:0 D:0 EF:9.17 ES:19.51 EF:0 EF:19.51 B E G D:5.33 D:5.17 D:5.17 ES:0 ES:9.17 ES:14.34 EF:5.33 EF:14.34 EF:19.51
10. 10. Determine the duration of the project D F D:6.33 D:4.5 ES:4 ES:10.33 EF:10.33 EF:14.83 LS:8.68 LS:15.01 LF:15.01 LF:19.51 A D:4 ES:0 EF:4 LS:0 LF:4 C D:5.17 Start Finish ES:4 D:0 D:0 EF:9.17 ES:0 ES:19.51 LS:4 EF:0 EF:19.51 LF:9.17 LS:0 LS:19.51 LF:0 LF:19.51 B E G D:5.33 D:5.17 D:5.17 ES:0 ES:9.17 ES:14.34 EF:5.33 EF:14.34 EF:19.51 LS:3.84 LS:9.17 LS:14.34 LF:9.17 LF:14.34 LF:19.51
11. 11. Determine the duration of the project Critical Path Critical Path: A-C-E-G • Path A-D-F = 14.83 work days • Path A-C-E-G = 19.51 work days • Path B-E-G = 15.67 work days
12. 12. Determine the duration of the project Critical Path Activity LF-EF Total A 4-4 0 B 9.17 – 5.33 3.84 C 9.17 – 9.17 0 D 15.01 – 10.33 4.68 E 14.34 – 14.34 0 F 19.51 – 14.83 4.68 G 19.51 – 19.51 0
13. 13. Assessing Risks • Risk is a measure of the probability (and consequences) of not completing a project on time. • A major responsibility of the project manager at the start of a project is to develop a risk-management plan. • A Risk-Management Plan identifies the key risks to a project’s success and prescribes ways to circumvent them.
14. 14. Assessing Risks • With PERT’s three time-estimates, we get a mean (average) time and a variance for each activity and each path. – We also get a project mean time and variance. • In order to compute probabilities (assuming a normal distribution) we need the activity means and variances. – Most computer packages calculate this for you.
15. 15. Assessing RisksPath Time (wks) 12 I 27 48 1563A-I-K33 33A-F-K28 28 A KA-C-G-J-K 67 0 12 12 F 22 Latest 63 69 LatestB-D-H-J-K 69 2 1214 53 1063 start 63 6 69 finishB-E-J-K 43 time time C 12 22 22 G 57 Start Finish 14 1024 24 59 35 0 B9 9 D19 19 H 59 59 J 63 0 9 9 9 1019 19 4059 59 4 63 9 E 33 35 2459
16. 16. Assessing Risks• What is the probability that our sample project will finish in 69 weeks as scheduled? 100% (Why?) – Because we used CPM! • (This means we were certain of all of our activity times.) – If we weren’t certain, we should have used PERT • You can’t do risk analysis if you use CPM
17. 17. Assessing Risks • Calculate standard deviation – Standard deviation- average deviation from the estimated time • SD=(TP-T0)/6 – higher the SD is the greater amount of uncertainty exists • Calculate variance – reflects the spread of a value over a normal distribution • V=SD2 – a large variance indicates great uncertainty, a small variance indicates a more accurate estimate
18. 18. Assessing Risks What is the Probability of it taking 72 weeks? Critical Critical Path = B - D - H - J – K = 69 weeks Path T = 72 weeks C = 69 weeks Varianc T–C e 2 =  (variances of activities along critical path) = z 2 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z= 72 – 69 11.89 Look up Z value in normal distribution table Z = 0.870 Pz = .8078 or 80.78% (Probability of it taking 72 weeks)
19. 19. Assessing Risks Look up the Z value (0.870) in the table of normal distribution. .8078 or 80.78% is the probability of the project taking up to 72 wks. Going over 72 weeks would be 100 – 80.78 = 19.22%
20. 20. Assessing Risks Normal distribution: Length of critical Mean = 69 weeks; path is 69 weeks  = 3.45 weeks Probability of taking 72 weeks is 0.8078 Probability of or 80.78% exceeding 72 weeks is 0.1922 or 19.22% 69 72 Project duration (weeks)
21. 21. Assessing Risks • Assume a PERT project critical path takes 40 days, and that the variance of this path is 2.147 – You wish to know the probability of the project going over 42 days. • Compute the standard deviation of the critical path. (Take the square root of the variance of 2.147) Std. Dev. = 1.465 – POM/QM software gives you the variance of the critical path. • Compute the Z value: Z = (absolute time difference) / Std. Dev. In this example, Z = (42 days - 40 days) / 1.465 = 1.365 • Look up the Z value of 1.365 in a Normal Distribution table to get the probability of the project taking 42 days. • Subtract it from 100% to get the probability of going over 42.
22. 22. Assessing Risks Look up the Z value (1.365) in the table of normal distribution. (In this case you need to interpolate between the Z values of .9313 and .9147) .9139 or 91.39% is the probability of the project taking up to 42 days. Going over 42 days is thus 100 - 91.39 = 8.61%
23. 23. Thank you for attention Any Questions ????