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Pert

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Pert

1. 1. Activity Duration1. “Guess” the activity duration, • especially smaller activities.2. Use Published materials: – Crew A= 1 Foreman, 2 Masons, 1 Labor – Crew A can install 200 12 Blocks/daySpring 2008, PERT 1King Saud University Dr. Khalid Al-Gahtani
2. 2. Activity Duration3. Use companies historical data: – similar to method#2. – the jobs must be similar. – Field input helps to modify historical data.4. Use the estimated labor costs to determine the activity duration. Ex) – Labor cost = \$2000. – Worker = \$100/day – task will take 20 worker days. – If a 4 workers crew is used, t= 5 days. – Estimate must be accurate.Spring 2008, PERT 2King Saud University Dr. Khalid Al-Gahtani
3. 3. Example of using labor cost• A masonry facade consisting of 3,800 ft2,• total cost per worker hour = \$31.5,• total estimated cost of labor = \$10,500,• assuming 8-hour work/days and a crew of 6 workers;Spring 2008, PERT 3King Saud University Dr. Khalid Al-Gahtani
4. 4. Example of using labor cost How many days should be allowed to complete this task?(i) da ys sho uld be a llo w ed to co m p lete this task is: 2 V = 3,800 ft R ate = \$31.5/hr T otal la bo r co st = \$10,500 \$ 10,500 N u m ber o f ho urs requ ired = = 333.33 hrs \$31.5/hr 3 3 3 .3 3 h rs D uratio n = = 6.94 7 days 8 h rs/d ay.w orkers 6 w o rkers Spring 2008, PERT 4 King Saud University Dr. Khalid Al-Gahtani
5. 5. Example of using labor cost What is the production rate that the crew must attain to keep the project on schedule and within the budget?(ii) T he pro ductio n rate that the crew m ust attain to keep the pro ject o n sc hedu le a nd w ithin the budget is: 2 3,800 ft 2 T heo retica l P ro ductio n R ate = = 547.2 ft /day 6.94 days 2 3,800 ft 2 A ctua l P ro ductio n R ate = = 542.8 ft /day 7 days Spring 2008, PERT 5 King Saud University Dr. Khalid Al-Gahtani
6. 6. Example of using Historical Data # o f 12 B lo ck s B lo cks o n this t (days) B lo cks/da y o n P ro ject pro ject 8,000 16 500 22 12,000 22 546 20.2 9,000 19 474 23.2 7,000 15 467 23.6 13,000 20 , 650 16.6 14,0000 31 452 24.4 n 21.7 n 2.76 xi ( xi X) 2 i 1 i 1 n n 1Spring 2008, PERT 6King Saud University Dr. Khalid Al-Gahtani
7. 7. Example of using Historical Data = 21.7 days, = 2.76 days - H o w ma ny da ys in o rder to be 85% ? t 85 % : at 85%  x= 1.04 days (T able A ppendix 9-1b) t-μ x=  t 85 % = + (x× ) σ = 21.7 + (1.04 × 2.76) = 24.6 25 days , - W hat % o f tim es < 28 da ys (% o f (t < 28 days)): t-μ 28 - 21.7 x= = = 2.28 σ 2.76 % o f (t < 28 days) = 0.9887 = 98.87%  at x= 2.28 from T able Appendix 9 -1bSpring 2008, PERT 7King Saud University Dr. Khalid Al-Gahtani
8. 8. Program Evaluation and Review Technique [PERT]• Activity time is very much probabilities.• three activity durations should be estimated for each activity: – Optimistic duration =a =4 – Pessimistic duration =b =7 – Most Likely duration =m =6Spring 2008, PERT 8King Saud University Dr. Khalid Al-Gahtani
9. 9. • Optimistic Duration (a): Very favorable conditions. Very low probability of being completed within this duration. (say p = 5%, shortest time)• Pessimistic Duration (b): Activity performed under very unfavorable conditions. Again, very low probabilities (say p= 5%)• Most Likely Duration (m): Usually closet to the actual durations. Very high probability.Spring 2008, PERT 9King Saud University Dr. Khalid Al-Gahtani
10. 10. If this activity is performed a large number of times andrecord of the actual durations is maintained, a plot offrequencies of such durations will give the beta-curve (anunsymmetrical curve).Spring 2008, PERT 10King Saud University Dr. Khalid Al-Gahtani
11. 11. Example I 0.5 t e (5.8) m (6) Since m > te ( 6 > 5.8 ) The person making activity estimates was pessimisticSpring 2008, PERT 11King Saud University Dr. Khalid Al-Gahtani
12. 12. Example II 0.5 a (4) m (6) t e (7) b (18) Here, since te > m, the person making this estimate was optimistic.Spring 2008, PERT 12King Saud University Dr. Khalid Al-Gahtani
13. 13. Even thought „t‟ has a Beta distribution, T N( , 2) T or Spring 2008, PERT 13 King Saud University Dr. Khalid Al-Gahtani
14. 14. Variance A ct ivit y ( A ) A ct ivit y (B ) a = 4 2 m = 6 6 b = 8 10 4 24 8 2 4(6) 10 te = 6 6 6 6 8 4 10 2 te ( A ) 1 . 25 te ( B ) 2 .5 3 .2 3 .2Spring 2008, PERT 14King Saud University Dr. Khalid Al-Gahtani
15. 15. Variance• 2 (te) = [(b-a) /3.2]2 – (5%-95% Assumption)• 2 (te) = Uncertainty about the activity durations, where: – If (b-a) is a large figure, greater uncertainty. – If (b-a) is small amount, less uncertainty.Spring 2008, PERT 15King Saud University Dr. Khalid Al-Gahtani
16. 16. Project Duration (Te)• Determine te for each activity• Determine Slacks and Project Duration (Te) by forward and backward passes as in a CPM network.• P (the project will be finished as time Te) – or p(Te) = 0.5, Since • p(te) = 0.5 i = 1, 2, 3, …, nSpring 2008, PERT 16King Saud University Dr. Khalid Al-Gahtani
17. 17. • Te‟s follow a normal distributions, and not beta- distributions as activity durations te‟s do. Te = t e*Spring 2008, PERT 17King Saud University Dr. Khalid Al-Gahtani
18. 18. Example 1 A B C D a = 4 3 2 4 m = 6 8 4 5 b = 8 9 7 6 2 2 2 2 2 2 (t e ) = [(b-a)/3.2 ] (1.25 ) (1.875 ) (1.5625 ) (0.625 ) te 6 7.33 4.17 5 P ro ject D uratio ns T e = 6 + 7.33 + 4.17 + 5 o r, T e = 22.50 da ys 2 2 2 2 (T e ) = 1 .2 5 1 .8 7 5 1 .5 6 3 0 .6 2 5 = (T e ) = 2.81 3Spring 2008, PERT 18King Saud University Dr. Khalid Al-Gahtani
19. 19. TE TE TE 2 TE TE 3 TE 18.0 19.5 21.0 2 4.0 25.5 27.0 22.5 TESpring 2008, PERT 19King Saud University Dr. Khalid Al-Gahtani
20. 20. Central Limit Theorem• if number of CA > 4, the distribution of T is approximately normal with mean T and variance Vt given by: – T = te1+ te2 + ……, tem (sum of the means) – Vt = vt1 + vt2 + ……+ vtm (sum of the variances)• The distributions of the sum of activity times will BE NORMAL regardless of the shape of the distribution of actual activity performance times.Spring 2008, PERT 20King Saud University Dr. Khalid Al-Gahtani
21. 21. PERT Computations 1) (i) C o m pu te: - E xpected activity d u ratio n ( t e ) a 4m b te = w here 6 a = O ptim ist ic d uratio n m = m o st lik e ly du rat io n b = pessim ist ic du ratio n - S tand ard d ev iatio n o f an act iv ity ( te) b a (t e ) = 3 .2Spring 2008, PERT 21King Saud University Dr. Khalid Al-Gahtani
22. 22. PERT Computations ( i) 2) C o m pute: 2 - V ar ia nce o f an act ivit y ( te) 2 2 b a (t e ) = 3 .2 3) ( ii) D o C P M ana lysis, using ‘t e ’ as activit y tim e s. * 4) ( iii) Ident ify C r it ica l A na lys is. t e ( iv) P ro ject T im e (T e ) 5) * Te = teSpring 2008, PERT 22King Saud University Dr. Khalid Al-Gahtani
23. 23. PERT Computations (6 ) C o m p u te: i) 2 - P ro ject V aria nce (T e ) 2 * (T e ) = ( te ) - F o r m u lt ip le crit ica l p aths, co nsid er the h ig he st to tal o f v ar ia nces . - P ro ject Standard D ev iatio n (T e ) 2 * (T e ) = (te ) or 2 b a (T e ) = 3 .2Spring 2008, PERT 23King Saud University Dr. Khalid Al-Gahtani
24. 24. Probability of Meeting a schedule DateSTEPS i) Set the variance (Vt) of the initial event to zero, ii) Ignore other scheduled dates (if any), iii) Compute the mean duration of the longest path (critical path) to the scheduled date event, iv) Compute the total variance to the scheduled date event using the longest path. For multiple critical paths, consider the highest total of variances. v) P (T ≤ Ts ) = P (Z ≤ z) Ts - z= Table 9.1 given z  find P tSpring 2008, PERT 24King Saud University Dr. Khalid Al-Gahtani
25. 25. Example 2: D uratio n E stim ates activit y D epend o n a m b A 1 1 7 B 1 4 7 C 2 2 8 D A 1 1 1 E B 2 5 14 F C 2 5 8 G E 3 6 15Compute the followings: 1. Project mean duration and variance. 2. Probability of completing the project three days earlier than expected. 3. Probability of completing the project three days later than expected. 4. The date for the terminal event that meets a probability of being finished with the project at or less than 84% of the time. 5. Probability of completing activity E by day 9. Spring 2008, PERT 25 King Saud University Dr. Khalid Al-Gahtani