IE546_Spring2024_Exam2_Solution.pdf

TEST 2, Spring 202 4 Suppose that Mr. William Bell owns a manufacturing facility in Kentucky, which happens to be in a seismic zone (i.e., an area where earthquakes tend to happen). It is known that the probability of an earthquake in the area is 15%. If there is an earthquake, the estimated total cost of damage to the facility (and to Mr. Bell’s business) is uniformly distributed between $30 million and $90 million. There are at least two options for you to mitigate such a risk. The first option is to retrofit your facility to make it more resistant to seismic activities. The retrofit will cost $40 million. After the retrofit, you estimate that the total cost of damage after an earthquake would be uniformly distributed between 10 and $30 million. The second option is to relocate your facility to an earthquake-free area, which would completely eliminate any potential damage due to earthquakes. But the cost will be $50 million. (Note: You can ignore the time value of the money when answering the following questions.) a. (20 pts) Draw a decision tree for this decision. For the continuous distributions, please use either the extended Pearson-Tukey method or the bracket median method to discretize them. (Make sure to write out the appropriate numbers at appropriate places of the tree.) b. (20 pts) Please identify all the strategies in the decision tree in Part a. Plot the risk profiles of the strategies, and analyze if there are any deterministic dominance or (first-order) stochastic dominance between the strategies. c. (20 pts) What is the expected value of perfect information in this case? d. With more in-depth research, Mr. Bell learned that in 60% of the places where an earthquake occurred, a fault line was one mile or less away. However, 40% of the places where an earthquake has not occurred are also within 1 mile of a fault line. A seismic test can be conducted to PRECISELY locate the nearest fault line to the facility. Suppose that earthquakes are predicted based on the seismic test information; i.e., an earthquake is predicted if a fault line is one mile or less away, and no earthquake is predicted otherwise. ( In geology, a fault or fault line is a planar fracture in rock in which the rock on one side of the fracture has moved with respect to the rock on the other side.) (d.1) (10 pts) What is the probability that a fault line is one mile or less away from Mr. Bell’s manufacturing facility in Kentucky? (Hint: you still have the information that the probability of an earthquake in the area is 15%.) (d.2) (10 pts) What is the probability that an earthquake can happen at the location of Mr. Bell’s manufacturing facility, given that a fault line is less than one mile away from the facility? (d.3) (20 pts) Calculate the expected value of the seismic test information. (It is recommended for you to draw a decision tree to answer this question.)

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