Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 13.5, Problem 3P
Explanation of Solution
Maximizing the expected profits:
Consider W is the event that represents the weather is warm and C is the event that represent the weather is cold.
Also, assume that Cp is the event that represents the expert predicts the weather is cold and Wp is the event that represents the expert predicts the weather is warm.
| States of nature | ||
| Strategies | Warm (W) | Cold (C) |
| Wheat | 7000 | 6500 |
| Corn | 8000 | 5000 |
| Probability | 0.6 | 0.4 |
There is 90% of chance that the expert predicts year is cold and it is actually cold, i.e., conditional probability which is given as follows:
P(Cp|C) = 0.90
Therefore, the probability that the weather is predicted as warm when it was cold is given as follows:
P(Wp|C) = 1 - P(Cp|C)
= 1 – 0.9
= 0.10
Similarly, it is given that 80% of times the weather is actually warm and the expert also predicted the same, i.e.,
P(Wp|W) = 0.80
Also, P(Cp|W) = 0.20
Calculate the probability that an expert predicts correctly or incorrectly. Let, CP and ICP denote the events correct prediction and incorrect prediction by expert. Therefore, the probabilities are as follows:
P(CP) = P(Wp|W) x P(W) + P(Cp|C) x P(C)
= (0.80 x 0.60) + (0.9 x 0.40)
= 0.48 + 0.36
= 0.84
P(CP) = P(Cp|W) x P(W) + P(Wp|C) x P(C)
= (0...
Explanation of Solution
Calculating EVSI:
Expected Value of Sample Information (EVSI) is referred to as the value of information that would be obtained from sample information. For this, first determine the expected value with the sample information (EVWSI). This is the sum of the expected value when weather forecast is performed plus the cost of weather forecast.
EVWSI = (Expected value) + (Cost of hiring expert)
= 6259.4 + 600
= 6859.4
The EVWOI value is 6800. Therefore,
EVSI = EVWSI – EVWOI
= 6859.4 – 6800
= $59...
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Chapter 13 Solutions
Operations Research : Applications and Algorithms
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