# Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 1 Activity Duration 1.“Guess” the activity duration, especially smaller activities. 2.Use.

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Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 1 Activity Duration 1.“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/day

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 2 Activity Duration 3.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, King Saud University PERT Dr. Khalid Al-Gahtani 3 Example of using labor cost A masonry facade consisting of 3,800 ft 2, 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, King Saud University PERT Dr. Khalid Al-Gahtani 4 Example of using labor cost How many days should be allowed to complete this task?

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 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?

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 6 Example of using Historical Data,

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 7 Example of using Historical Data,

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 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= 6

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 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, King Saud University PERT Dr. Khalid Al-Gahtani 10 If this activity is performed a large number of times and record of the actual durations is maintained, a plot of frequencies of such durations will give the beta-curve (an unsymmetrical curve).

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 11 Example I Since m > te ( 6 > 5.8 )  The person making activity estimates was pessimistic

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 12 Example II Here, since te > m, the person making this estimate was optimistic.

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 13 Even thought ‘t’ has a Beta distribution, T  N ( ,  2 )

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 14 Variance

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 15 Variance  2 (t e ) = [(b-a) /3.2] 2 –(5%-95% Assumption)  2 (t e ) = 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, King Saud University PERT Dr. Khalid Al-Gahtani 16 Project Duration (Te) Determine t e for each activity Determine Slacks and Project Duration (T e ) by forward and backward passes as in a CPM network. P (the project will be finished as time T e ) –or p(T e ) = 0.5, Since p(t e ) = 0.5i = 1, 2, 3, …, n

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 17 Te’s follow a normal distributions, and not beta- distributions as activity durations te’s do.

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 18 Example 1

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 19

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 20 Central Limit Theorem if number of CA > 4, the distribution of T is approximately normal with mean T and variance V t given by: –T = t e1 + t e2 + ……, t em (sum of the means) –V t = v t1 + v t2 + ……+ v tm (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, King Saud University PERT Dr. Khalid Al-Gahtani 21 PERT Computations

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 22 PERT Computations

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 23 PERT Computations

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 24 Probability of Meeting a schedule Date

Spring 2008, King Saud University PERT Dr. Khalid Al-Gahtani 25 Example 2: Compute 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.

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