Group 3 - Lucia Horta, Kaylen Malley, Mitchell Young
IE 417
1-19-11
Problem 2 - Pg 772
A nuclear power company is deciding whether or not to build a nuclear power plant at Diablo Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at Diablo and $20 Million at Roy Rogers city. If the company builds at Diablo, however, and an earthquake occurs at Diablo during the next five years, construction will be terminated and the company will lose $10 million (and will still have to build a power plant at Roy Rogers City). A priori, the company believes there is a 20% chance that an earthquake will occur at Diablo during the next five years. For $1 million, a geologist can be hired to analyze the fault structure at Diablo Canyon. He will either predict that an earthquake will occur or that an earthquake will not occur. The geologist's past record indicates that he will predict an earthquake on 95% of the occasions for which an earthquake will occur and no earthquake on 90% of the occasions for which an earthquake will not occur. Should the power company hire the geologist?
*Dollar values in millions
Explanation of given probability information:
From the problem, we are given the probabilities that an earthquake will occur and will not occur within the next 5 years. We are also given the probability of the geologist predicting correctly given that there is or isn’t an earthquake. Given that there is an earthquake, 95% of the time the geologist predicts correctly by determining that an earthquake will occur. Given that there is no earthquake, 90% of the time the geologist predicts correctly by determining that no earthquake will occur. We also determined the compliments of these probabilities. 5% of the time, the geologist will predict that there will be no earthquake when there is actually an earthquake and 10% of the time the geologist will predict that there will be an earthquake given that no earthquake actually occurs.
WinQSB:
Input:
Output:
Sensitivity Analysis: How much can we spend on the geologist?
Spend 1.05 million
Input:
Output:
Spend 1.08 million
Input:
Output:
Spend 1.09 million
Input:
Output:
Spend 1.095 million
Input:
Output:
Spend 1.096 million
Input:
Output:
Spend 1.1 million
Input:
Output:
SA Summary Table:
Amt to spend on Geologist ($ in millions) / Expected Outcome / WinQSB Output / Decision to make1 / -$13.9 / Hire à
If Predict earthquake à BuildRR
If predict no earthquake à Build Diablo / Hire geologist, if predicts earthquake build at Roy Rogers, if predicts no earthquake build at Diablo
1.05 / -$13.95 / Hire à
If Predict earthquake à BuildRR
If predict no earthquake à Build Diablo / Hire geologist, if predicts earthquake build at Roy Rogers, if predicts no earthquake build at Diablo
1.08 / -$13.98 / Hire à
If Predict earthquake à BuildRR
If predict no earthquake à Build Diablo / Hire geologist, if predicts earthquake build at Roy Rogers, if predicts no earthquake build at Diablo
1.09 / -$13.99 / Hire à
If Predict earthquake à BuildRR
If predict no earthquake à Build Diablo / Hire geologist, if predicts earthquake build at Roy Rogers, if predicts no earthquake build at Diablo
1.095 / -$14 / Hire à
If Predict earthquake à BuildRR
If predict no earthquake à Build Diablo / Hire geologist, if predicts earthquake build at Roy Rogers, if predicts no earthquake build at Diablo
1.096 / -$14 / Don’t hire à BuildRR/D1 à E/NE / Don’t hire geologist, build at Diablo
1.1 / -$14 / Don’t hire à BuildRR/D1 à E/NE / Don’t hire geologist, build at Diablo
è Turning point between 1.095 and 1.096 million (if geologist charges more than 1.095 million for services, don’t hire)
Utility Function:
Line Equation
y = mx + b
Finding Slope:
m = 1 / (difference of Smallest and Largest net return)
m = 1 / [ -10 - (-31)]
m = 1/21
Finding y-intercept:
Solve for b and use one given point.
b = y - mx
b = 0 - (1/21)(-31)
b = (31/21)
Line equation:
y = (1/21)x + (31/21)
U(-10 M) = 1
U(-31 M) = 0
U(-11 M) = .95
U(-20 M) = .5
U(-21 M) = .476
U(-30 M) = .0476
WinQSB Input with Utility Values
WinQSB Output with Utility Values
Decision Tree
Dear Manager,
After performing analysis on whether or not the company should decide to build the new nuclear plant in Diablo Canyon or Roy Rogers City, and whether or not to hire a geologist to predict future earthquakes at Diablo, we have found the following decisions to be most beneficial to the company.
The company should hire the geologist to predict if an earthquake will hit Diablo in the next five years. If the geologist predicts that an earthquake will occur, the company should decide to build the plant at Roy Rogers. However, if the geologist predicts that no earthquake will occur, then the company should build the plant at Diablo. Following this plan would cost the company an expected amount of $13.9 million dollars. It is important to realize that this expected amount is not an exact value that the company will be spending after one trial, but is instead the amount the company would expect to spend after repeating this decision many times. However, making this decision of hiring the geologist will cost the company either $31 million or $11 million if the hired geologist predicts that no earthquake will occur and we build at Diablo, or it could cost the company a total of $21 million of the geologist predicts an earthquake to occur, in which case the company would instead build at Roy Rogers City.
It is also important to know that if the geologist decides to raise his prices, we would still want to use his predictions for up to an additional $95,000 and pay him a total of $1,095,000. However, if the geologist decides to raise his prices to $1,096,000 or more, the company is better off to not use his services and instead build at Diablo Canyon.