CE 3010-Decision Methods for Civil Engineering Design HW#20 Decision Tree-1 Univ

Question

CE 3010-Decision Methods for Civil Engineering Design HW#20 Decision Tree-1 University of Missouri Two alternative designs of levees are being compared. Overtopping is the major cause of levee damage during flooding. The maximum annual flood level of a river, H follows a lognormal distribution with a mean of 24 ft and standard deviation of 3ft. Specifications of the two levee designs are shown below: loanermal sctbutionhm Design B $1.5 Million/mile $45,000/mile $4 Millions/mile 28.7 ft. Design A Construction Cost $1 Million/mile Annual Maintenance $35,000/mile Damage Losses $4 Millions/mile Height 27.9 ft. A. Considering appropriate convention of symbols, draw a decision tree assuming two outcomes for each design (Damage and No damage) B. Calculate the overtopping return period, T, for each design. (Hint: T-1/p, where p is the probability that the levee will be overtopped during any given year). Note: round the T period up to the nearest integer. C. What is the probability of one or more overtopping in the next 30 years? (Poisson's) D. Ifthe design life is 30 years, it is required to apply engineering economics to calculate all outcome costs assuming an interest rate of 7%. (Hint: the levee requires yearly maintenance in addition to any damage cost). Show cash flow diagrams. E. Which design should be used according to the expected monetary value (EMV)?

Explanation / Answer

Year 0

Year 1-15

Year 15

Initial investment

-53000

Annual cost

-2850

Salvage value

4500

Net cost

-53000

-2850

4500

Present value $1 I = 15% N = 15 years

1

5.8474

0.1229

Net present value

-53000

-16665

553

Net present value total

-69112

Year 0

Year 1-15

Year 15

Initial investment

-53000

Annual cost

-2850

Salvage value

4500

Net cost

-53000

-2850

4500

Present value $1 I = 15% N = 15 years

1

5.8474

0.1229

Net present value

-53000

-16665

553

Net present value total

-69112

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