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# Decision Analysis

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Use the data in the following payoff matrix and regret matrix to answer the following questions:

Payoff Matrix

Airport is Built at Location
Land Purchased at Location(s) A B
A \$75.0 \$15.0
B (\$25.0) \$125.0
A&B \$52.0 \$66.0
None \$0.0 \$0.0

Regret Matrix

Airport is Built at Location
Land Purchased at Location(s) A B
A \$0.0 \$110.0
B \$100.0 \$0.0
A&B \$23.0 \$59.0
None \$75.0 \$125.0

17. What is the optimal decision regarding at which location(s) to purchase property using the MAXIMAX decision rule?

18. What is the optimal decision regarding at which location(s) to purchase property using the MAXIMIN decision rule?

19. What is the optimal decision regarding at which location(s) to purchase property using the Criterion of Realism decision rule, assuming that the coefficient of realism is 0.55?

20. What is the optimal decision regarding at which location(s) to purchase property using the Equally Likely decision rule?

21. What is the optimal decision regarding at which location(s) to purchase property using the MINIMAX Regret decision rule?

22. What is the optimal decision regarding at which location(s) to purchase property using the Expected Monetary Value decision rule, assuming the probability of the airport being built at location A is 0.55?

23. What is the optimal decision regarding at which location(s) to purchase property using the Expected Opportunity Loss decision rule, assuming the probability of the airport being built at location A is 0.55?

A consulting firm has contacted your company claiming that their analysis conclusively indicates that the probability the airport will be built at location A is 0.55 (i.e., they have perfect information regarding the probability of the airport being built at location A). The consultant has offered to share their analysis with your company for a fee of \$25.0 million.

24. What is the Expected Value of Perfect Information in this scenario?

25. Should your company accept the consultant's offer?

Develop a sensitivity analysis matrix that summarizes the expected monetary value for each possible alternative relative to the probability of location A being selected. Vary the probability of location A being selected from 0.0 to 1.0 in increments of 0.01. Plot the expected monetary value for each possible alternative versus the probability of location A being selected.

26. For what range of probability of the airport being built at location A is purchasing property at location A the optimal decision?

27. For what range of probability of the airport being built at location A is purchasing property at location B the optimal decision?

28. For what range of probability of the airport being built at location A is purchasing property at both locations A and B the optimal decision?

29. For what range of probability of the airport being built at location A is purchasing property at neither location A nor location B the optimal decision?

https://brainmass.com/math/probability/decision-analysis-356106

#### Solution Summary

The solution is comprised of a detailed explanation of the various aspects of Decision Analysis. This step-by-step calculation and explanation of these complicated topics provides students with a clear perspective of Maximax Criterion, Maximin Criterion, Equal Likelihood Criterion, Minimax Regret Criterion, Expected Value Criterion, Expected Value, Expected Opportunity Loss, Sensitivity Analysis, etc.

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## Linear Programming, Queueing Analysis, Simulations, Decision Analysis and Forecasting

A) What are 2 possible ways to improve the service rate of a waiting line operation?

B) Briefly describe how simulation could be used to assist decision makers in regards to new product development?

C) Give an example of how Decision analysis could be used to determine an optimal strategy? Briefly describe several decision alternatives a decision maker would be faced with and possible uncertain future events to consider.

D) What is the difference between quantitative forecasting methods and qualitative forecasting methods?

E) Under what circumstances would it be more appropriate to use quantitative rather than qualitative forecasting methods?

F) Give an example of a situation when using quantitative forecasting would be appropriate?

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