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Project Scheduling 2 -Calculating variance and probabilities -PERT/CPM - YouTube
Channel: Joshua Emmanuel
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Hello there!
In this video on project scheduling, I will
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be calculating expected times and variances
for uncertain activity times. I鈥檒l also
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be calculating probabilities of completing
a project at specified times. And lastly,
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I鈥檒l be calculating the completion time
of a project at a stated probability.
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Here we have a table showing activity predecessors
and their uncertain time estimates. Optimistic,
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Most Likely, and Pessimistic times are represented
by a, m, and b respectively.
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To calculate the expected time t we apply
this formula: t = a plus 4m plus b over 6.
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So the expected time for A is calculated as
4 + 4 times 6 + 14, divided by 6. And that
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gives 7.
We do the same for Activity B, C, D, E, F,
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and G.
And using these expected activity times and
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predecessors, I completed the project network
from scratch in an earlier video. You will
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find the link provided in description.
The critical path is BDEF and the project
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completion time is 32 weeks.
Note that the project completion time can
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also be found by adding up the expected activity
times for the critical activities.
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Now, the formula for calculating the variance
for each activity is b minus a divided by
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6 squared.
Just like the project completion time can
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be found by adding up the expected activity
times for critical activities, the project
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variance is also found by adding up the variances
for critical activities. So we only need to
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calculate the variances for the critical activities.
Thus, for B, the variance is 2.78, for D,
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1.78, for E, 2.78 and for F, the variance
is 1.
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And adding these, we have the project variance
of 8.33. Then taking the square root we have
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the project standard deviation of 2.8867.
Although the uncertain time estimates are
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beta distributed, we can approximate the project
completion time by a normal distribution.
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In this case, with mean equals 32 and standard
deviation 2.8867.
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So we can apply the z formula to answer these
questions.
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First, we find the probability that the project
will be completed within 35 weeks. That is,
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x equals 35 and that gives z = 1.04. And looking
it up in tables we have a less-than area of
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.8508.
For x greater than 31, we have z greater than
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-0.35. The area less than -0.35 is 0.3632.
And subtracting it from 1 we obtain the more-than
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area of 0.6368.
Between 31 and 35, we find the area between
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their z values of -0.35 and 1.04 by subtracting
the smaller area from the larger one. And
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that gives 0.4876.
For d), less than 31 or more than 35 is the
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complement of our result in c). So we just
subtract the result from 1 to obtain 0.5124.
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Next, if we want a 90% probability of completing
the project on time, we do a reverse lookup
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for a less-than area of 0.90. That will correspond
to a z-score of 1.28.
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And substituting that into the z formula we
obtain a completion time of about 35.7. That
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is, the project should begin about 36 weeks
earlier in order to be completed on time with
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a 90% probability.
And that鈥檚 it for this video.
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Thanks for watching.
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