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# Slack and Project Duration

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The following project is to be scheduled using the expected times found using the approximation to the beta distribution. All duration estimates are in weeks:

Activity a m B Predecessors
A 2 5 8 -
B 4 10 22 A
C 1 4 16 B
D 4 6 8 A
E 4 6 11 A
F 1 2 6 E
G 3 4 17 D,E
H 1 2 3 C,F,G

A- Find the early start and late start schedule for each activity as well as its total and free
slack.

B- What is the critical path duration? What is the variance for the critical path? What is the
probability that the project will be completed in 24 weeks?

C- Using evidence from this specific project, explain if the estimate found in (B) is optimistic,
and why, or why not?

#### Solution Preview

See the attached file. Thanks

The following project is to be scheduled using the expected times found using the approximation to the beta distribution. All duration estimates are in weeks:

Activity a m B Predecessors
A 2 5 8 -
B 4 10 22 A
C 1 4 16 B
D 4 6 8 A ...

#### Solution Summary

The solution examines slack and project duration. The critical path duration is determined.

\$2.19

## Finding the Critical Path and Project Duration

The construction of a cottage requires the performance of certain tasks. The following table lists the various tasks with their priority relationship.

Activity o m p Predecessors
A 8 10 12 None
B 6 7 9 None
C 3 3 4 None
D 10 20 30 A
E 6 7 8 C
F 9 10 11 B,D,E
G 6 7 10 B,D,E
H 14 15 16 F
I 10 11 13 F
J 6 7 8 G,H
K 4 7 8 I,J
L 1 2 4 G,H

a. Calculate slack for each activity.
b. What is the critical path?
c. What is the project duration?
d. Determine the probability that the project will be finished in 80 days or less.

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