Management Science
231 MIS
Exercises Answers
Exercise1
According to the diagram above, answer to the following questions:
1. Determine the different paths for this project
2. Then determine the critical path
3. Calculate the earliest times , the latest times and the slack
Solution:
1. Critical Path:
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Management Science
231 MIS
The critical path is path B-C-D-G-H 20
2. ES/EF and LS/LF:

Earliest start /earliest finish

Latest start/latest finish:
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Management Science
231 MIS
3. Slack time:
Exercise2:
1. Complete the following table (the expected time and the variance for
each activity)
2. Using the network on node (NON) shown below determine the project
paths and then the critical path
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Management Science
231 MIS
The critical path is:
A-C-E-G-H = 2+2+4+5+2 = 15
3. Determine the variance and the standard deviation of the project

Project variance (σp2 ) = )∑variances of all critical path activities)
σp2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11
= 3.11

Project standard deviation (σp)
=SQRT (Project variance)
σp = SQRT ( 3.11) = 1.76
4.
Using forward pass and backward pass determine the earliest times,
the latest times and the slack times for this project.
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Management Science
231 MIS
Forward pass:
Backward pass:
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Management Science
231 MIS
5. What is the probability of finishing the project within 16 weeks?
Z = (Target time – expected time)
σp
Z = (16 - 15) = 0.57
1.76
This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.
6. What project duration does General Foundry have a 99% chance of
completing the project within?
i.e. Prob (proj duration < ? ) = 0.99
Z = (? - 15) = 2.33
1.76
So ? = 15 + 2.33 x 1.76 = 19.1 weeks
Instructor: sihem smida
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