Chapter 16: Program Evaluation and Review Techniques (PERT)

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1 Chapter 16: Program Evaluation and Review Techniques (PERT) PERT PERT is a method for determining the length of a construction project and the probability of project completion by a specified date PERT is based on probabilistic activity durations 1

2 Recall that AON diagrams were based on deterministic activity durations When we assume that the duration of activity rebar columns is 10 days, what does that really mean? will rebar columns take exactly 10 days to complete? or will the actual duration vary from the estimated duration? It could mean that, on average, the duration is 10 days To accommodate the uncertainty associated with activity duration estimates, PERT is based on probabilistic activity durations 2

3 Since construction companies engage in work that they have done in the past, this results in multiple occurrences of the same activity and a historical record of durations or productivities PERT relies on activity durations that are established either by an analysis of historical data or through estimates of the range of probable activity durations Such data can be shown as a frequency histogram like the one shown below Histogram of Duration (days), with Normal Curve for a construction activity Duration (days) Source: Weber (2005, p.226) 3

4 No matter of the actual distribution, there are three measures of central tendency: mean, mode, and median Histogram of Duration (days), with Normal Curve for a construction activity Duration (days) Source: Weber (2005, p.226) Histogram of Duration (days), with Normal Curve for a construction activity Duration (days) Mean = Mode = 10 (most frequent occurrence) Median = 11 (equal number of observations above it and equal number of observations below it) Note also that the range of observations = 16 8 = 8 4

5 If all activities have been performed multiple times in the past enough times to generate a frequency histogram, a sample can be taken from each distribution that will give a duration for each activity Activity durations in PERT are based on three time estimates: Optimistic duration Most likely duration Pessimistic duration Histogram of Duration (days), with Normal Curve for a construction activity Duration (days) Optimistic duration: assumes maximum productivity How many days in this example? Pessimistic duration: assumes the worst productivity How many days in this example? 5

6 Histogram of Duration (days), with Normal Curve for a construction activity Duration (days) Most likely: most often based on historical performance How many days in this example? Calculating the mean estimate of duration The mean estimate of the activity duration is computed as follows t e = t o + 4 m p t 6 + t 6

7 t e = t o + 4 m p t 6 + t t e = mean or expected activity duration t o :optimistic activity duration t m : most likely activity duration t p : pessimistic activity duration Network calculations In PERT, project duration is called project mean duration (T e ) T e is calculated based on the regular forward pass using the activity mean durations t e for every activity 7

8 Example Calculating the Standard deviation Note that the mean value of the activity duration does not convey any information about the degree of uncertainty It would be helpful to have a measure to describe the extent to which the duration is expected to vary from the derived mean value Such a measure is known as the Standard Deviation (S) 8

9 We can use S to describe the extent to which the duration is expected to vary from the derived mean Standard deviation (S) = Range of activity durations 6 S = 6 tp to Note that 6 in the equation refers to ±3 standard deviations from the mean of a normal distribution, which contains 99.73% of all population values The variance Variance( V ) = S 2 = ( 6 tp to ) 2 S = V Note that S Pr oject = SCP = V CP 9

10 Example Slack In PERT, what we used to know as float is called slack Activity Total Slack = ATS Activity Free Slack = AFS 10

11 Calculating the probability of meeting deadline dates Based on the normal distribution, we can calculate the probability of project completion within certain duration The probabilities of occurrence of a specific duration can be determined by simply knowing the number of standard deviations that the value in question is away from the mean The standard normal curve areas table is set up to give information of the probability that a particular duration will be less than some specified value that is given in terms of the number of standard deviations that the value extends beyond the mean 11

12 Te = 24 days Ts = 27 days This is the normal distribution The probability to complete the project in 24 days (mean duration) or less = 50%, which is the area under the curve Te = 24 days Ts = 27 days Now to find the probability of completing the project in 27 days, we need to find out the number of standard deviations that T s (specified date) is away from T e Z Ts T = SCP e 12

13 Z = Ts T SCP e Z = = 1.43 Te = 24 days Ts = 27 days From the table, Z=1.43; probability = Therefore the probability of project completion in 27 days or less = 92.4% PERT 13

14 PERT The Program Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze and represent the tasks involved in completing a given project. Example For the following project determine the following! The Critical Path ( C.P) What is The probability of finishing the project before or on day number 21? What is the finish time for the project with a probability of 95 %? 14

15 Activity Pre. Duration To Tm Tp A B A C A D A B E C C F D E G F B H F D I F G N H I To Tm Tp Activity Te 15

16 4 6 7 B E H A C G N F D I 2.17 Determination of Critical Path : - Each Path Give us a specific duration, and we will take the longest : Days 17.34Days 19 Days Days Days Days 13.34Days 13.51Days C.P 16

17 Critical Path Activities Are : A, B, E, H, N Te (project) = 19 days 2) What is The probability of finishing the project before or on day number 21? Z = (Ts Te ) / Scp Standard Deviation For The Project (Scp) = S², where S : standard deviation for each Critical activity S for each activity = (Tp To ) / 6 Activity S A 0.50 B 0.50 E 0.50 H 0.50 N

So, : Scp = (.5²) + (.5²) + (.5²) + (.5²) + (.33²) = 1.

18 So, : Scp = (.5²) + (.5²) + (.5²) + (.5²) + (.33²) = And : Z = (21 19 ) / = 1.9 So, the probability of completing the project In 21 days is 97.13% 3) What is the finish time for the project with a probability of 95 %? From the Z-Table we find that the Z value that has a probability of 95% equals to = 1.65 So, Z = (Ts Te) / Scp 1.65 = ( Ts 19 ) / We Get Ts = Days 18

Project Time Planning. Ahmed Elyamany, PhD

Project Time Planning. Ahmed Elyamany, PhD Project Time Planning Ahmed Elyamany, PhD 1 What is Planning The Development of a workable program of operations to accomplish established objectives when put into action. Done before project starts Planning