Pert Problem
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Bowling Green State University *
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Course
MSA5160
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
docx
Pages
2
Uploaded by GabrielNaimy1992
A firm is planning a project for the development of a new product. Assume the network of
activities and data presented the excel document posted below.
1.
Using the PERT method (critical path method with three activity time estimates),
calculate the expected time and standard deviation of the time for each activity. (If you
don’t know the critical path method or the PERT method, you may search online or read a
regular textbook in project management or operations management.)
2.
Based on the expected time for each activity, using the critical path method, determine
the project duration and critical path.
3.
Using the PERT method, estimate the probability of the project to be completed within 36
weeks.
4.
Using Monte Carlo Simulation, estimate the probability of the project to be completed
within 36 weeks. Note that
the time for each activity
can be assumed to follow a normal
distribution with the mean and standard deviation calculated in 1). You can use Excel or
any other software package to develop a Monte Carlo simulation model. You may
generate 1,000 simulation replications.
For each replication, the simulation model
should determine the project completion time based on the network of activities.
5.
Are the results derived from the PERT method in 3) and from the Monte Carlo
Simulation in 4) the same? Discuss why or why not.
Activity
Immediate
Predecessor
Minimum Time
(Weeks)
Most Likely Time
(Weeks)
Maximum Time
(Weeks)
A
—
12.3
14.2
19.7
B
A
5.5
7.7
11.2
C
A
3.7
6
11.5
D
B
1.8
3.9
6.8
E
C
1.4
4.1
6.6
F
B, C
1
2.4
5.5
G
D, E, F
5
5
5
For each activity, calculate the expected time (TE) using the formula:
TE = (a + 4m + b) / 6, where a is the minimum time, m is the most likely time, and b is the
maximum time.
Calculate the standard deviation (SD) using the formula: SD = (b - a) / 6.
Apply these formulas for each activity A to G
•Identify the critical path, which is the longest path through the network.
•Calculate the project duration by summing the expected times along the critical path.
Estimate the probability of the project completion within a given time using the normal
distribution. Calculate Z-scores for the desired time (e.g., 36 weeks) using the formula: Z = (X -
TE) / SD, where X is the desired time, TE is the expected time, and SD is the standard deviation.
Use a standard normal distribution table to find the probability.
Use a software tool like Excel to simulate the project completion time. Generate random
numbers for each activity based on the normal distribution with the calculated mean and standard
deviation. Sum the times along the paths to get the project completion time. Repeat this process
for a large number of replications (e.g., 1,000 times) to estimate the probability of completing the
project within 36 weeks.
Results from the PERT method and Monte Carlo Simulation may not be exactly the same due to
the inherent assumptions and simplifications in each method. PERT assumes a beta distribution
for activity times, while Monte Carlo Simulation uses a more flexible approach based on random
sampling. Differences could also arise from how uncertainties are modeled and the underlying
assumptions about the distribution of activity times.
Any disparities could be due to the stochastic nature of the simulation and the way uncertainties
are represented. It's essential to interpret the results with an understanding of the assumptions
and limitations of each method.
The expected project duration is 35.1 weeks. The probability of the project being completed within 36
weeks is 60.2%.
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