PERT analysis for backyard swimming pool construction scheduling
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Decision Making and Planning in Construction
The formula to determine the most probable to complete the backyard swimming pool is as follows:
Where
a = Optimistic
m = Most probable
b =Pessimistic
The study uses Microsoft Excel software to calculate the probable time for the project. The results show that the project will be complete within 49.5 days, which is approximately 50 days as revealed in Table 1 below.
Activity
Immediate Predecessor
Duration in Days
Optimistic
Most Probable
Pessimistic
Expected Time
Project Schedule
The study uses the Microsoft Excel to develop the project schedule and output is revealed below:
The PERT distribution to complete the project is in Fig 1 as follows
Fig 1: PERT Distribution to Complete the Project
The stimulation to determine the expected time to complete the Swimming Pool project with 90% confidence is as follows:
Activity
Variance
Variance
A
(6-3)/36
0,08
B
(6-2)/36
0,11
C
(7-5)/36
0,06
D
(10-7) /36
0,08
E
(6-2)/36
0,11
F
(3-1)/36
0,06
G
(10-5)/36
0,14
H
(10-6)/36
0,11
i
(5-3)/36
0,06
Total
0,81
The next is to find the Standard Deviation (SD), which is the square root of the variance as follows:
Thus, Square root of 0.81 =0.90 days.
Thus, there is 90% confidence that the project will complete at expected time.
3. What is the estimated probability that the project can be completed in 25 or fewer days?
The critical part of the project is A-C-F and expected time is 12.83. The variance is 0.20, and the standard deviation is 0.44. Thus, P (X 25) is 65%.
Problem II
Activity
Optimistic
Most Probable
Pessimistic
Expected Times
Variance
A
4.0
5.0
6.0
B
2.5
3.0
3.5
C
6.0
7.0
8.0
D
5.0
5.5
9.0
E
5.0
7.0
9.0
F
2.0
3.0
4.0
G
8.0
10.0
12.0
H
6.0
7.0
14.0
Optimistic
Most Probable
Pessimistic
Expected Time
Variance
a m
b
A
4
5
6
5,00
0,06
B
2,5
3
3
2,92
0,01
C
6
7
8
7,00
0,06
D
5
5,5
9
6,00
0,11
E
5
7
9
7,00
0,11
F
2
3
4
3,00
0,06
G
8
10
12
10,00
0,11
H
6
7
14
8,00
0,22
Critical Path = A-C-G-H.
Thus, the critical path is 5+7+10+7 =29 days
Variance = 0.06+0.06+0.11+0.22= 0.45
• = 29 days
2 = 0.45 days
Estimated probability of completing the project:
(1) Within 21 weeks
2 = 0.45 days =0.67
In 21 weeks
13,43
Z = (x-)/ = (30-21)/0.67
In 22 weeks
11,94
Z = (x-)/ = (30-22)/0.67
In 25 weeks
Z = (x-)/ = (30-25)/0.67
7,46
Answer to Question 4
I will provide the past records of the projects which I have successfully completed. I will submit a letter of recommendations from reputable general contractors in the country.
Reference
Anderson, D. R., Sweeney, D. J., Williams, T. A., Wisniewski, M., & Pierron, X. (2017). An introduction to management science: quantitative approaches to decision making. Andover, Hampshire: Cengage Learning EMEA.
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2003). Solutions manual, An introduction to management science: quantitative approaches to decision making, 10th edition. Cincinnati, OH: Thomson/South-Western.
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