In this video, I'll talk about the project evaluation and review technique or PERT.
We have seen several project network examples so far.
In those examples, we assume that the duration of each activity is known precisely.
In reality, the duration of each activity cannot be estimated with a 100% accuracy.
So, the duration of each activity (i, j) can be modeled as a random variable Tij.
Then, we can use the project evaluation and review technique or PERT to estimate the duration
of each activity and the duration of the critical path.
PERT requires that the project manager estimates each activity's duration under three different
conditions.
a is the estimate of the activity’s duration under the most favorable conditions.
For the house building project we talked about in the previous videos, the conditions can
be the weather is always sunny, it's not too hot or too cold, the construction materials
can be delivered to the site quickly, and so on.
b is the estimate of the activity’s duration under the least favorable conditions.
For example, it rains a lot, the weather is too hot for the workers to continue to work,
some needed construction materials are sold out and require a long time to be delivered.
m is the estimate of the activity's duration under the most likely conditions.
PERT requires the assumption that Tij follows a beta distribution.
The mean or expected value of Tij can be approximated by the duration under the best case scenario
plus 4 times the duration under the most likely case scenario plus the duration under the
worst case scenario divided by 6.
This is a good estimate based on experience.
The variance of Tij can be approximated by the duration under the worst case scenario
minus the duration under the best case scenario squared and then divided by 36.
Let's check PERT using this example.
We have seen this house-building example in previous videos.
We use PERT to estimate the values of a, m, and b for every activity.
For example, under the most favorable conditions, the duration of activity B, which is represented
by T12, is 7 days; under the most likely conditions, the duration is 9 days, and under the least
favorable conditions, the duration is 11 days.
Now let's use the formula to calculate the expected duration, 7 plus 4 times 9 plus 11
divided by 6.
It is 9 days.
Following the same procedure, we can find the expected durations for all other activities.
The duration of the dummy activity is always 0.
For this example, we know from previous videos that if the durations are known precisely
the critical path is B-Dummy-C-E-F.
The duration of the critical path is 38, which is the total length of the project.
Now assume the critical path will not change even if we consider the uncertainties.
Then we can calculate the duration of the critical path by adding up all the expected
durations of the activities on the critical path.
It is equal to 38.5 days.
Now let's calculate the variance of the duration for activity B. 11 minus 7 squared divided
by 36.
It is 0.44.
Following the same procedure, we can find the variance values of durations for all other
activities.
The variance for the dummy activity is always 0.
The variance of the duration of the critical path can be calculated by adding up all the
variance values of the activities on the critical path.
It is equal to 2.13.
The standard deviation is the square root of the variance.
It is equal to 1.46.
After we get the expected duration and the standard deviation for the critical path,
we can find the probability that the project will be finished within a certain number of
days.
Assume the duration of the critical path follows the normal distribution.
Its mean is 38.5 days, and the standard deviation is 1.46.
Then the probability that the project will be completed within 37 days can be calculated
by converting it to a standard normal distribution with the mean 0 and the standard deviation
1 like this.
You can look up the normal distribution table.
You can also use some online tools or a programming language to find the probability.
It is 0.15.
It means the chance of finishing the project within 37 days is 15%.
Okay, that is the project evaluation and review technique.
Thanks for watching.