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an introduction to management science

Questions and Answers of An Introduction to Management Science

=3. Formulate a payoff table from a description of the problem.
=4. Describe and evaluate several alternative criteria for making a decision based on a payoff table.
=5. Apply Bayes’ decision rule to solve a decision analysis problem.
=6. Formulate and solve a decision tree for dealing with a sequence of decisions.
=7. Use TreePlan to construct and solve a decision tree.
=8. Perform sensitivity analysis with Bayes’ decision rule.
=9. Determine whether it is worthwhile to obtain more information before making a decision.
=10. Use new information to update the probabilities of the states of nature.
=11. Use SensIt to perform sensitivity analysis when dealing with a sequence of decisions.
=12. Use utilities to better reflect the values of payoffs.
=13. Describe some common features in the practical application of decision analysis.
=1. A manufacturer introducing a new product into the marketplace. What will be the reaction of potential customers? How much should be produced? Should the product be test marketed in a small
=2. A financial firm investing in securities. Which are the market sectors and individual securities with the best prospects? Where is the economy headed? How about interest rates?How should these
=3. A government contractor bidding on a new contract. What will be the actual costs of the project? Which other companies might be bidding? What are their likely bids?
=4. An agricultural firm selecting the mix of crops and livestock for the upcoming season.What will be the weather conditions? Where are prices headed? What will costs be?
=5. An oil company deciding whether to drill for oil in a particular location. How likely is there to be oil in that location? How much? How deep will they need to drill? Should geologists
=5. What is meant by the possible states of nature?
=6. What is meant by prior probabilities?
=7. What do the payoffs represent in a payoff table?
=1. Identify the maximum payoff from any state of nature for each decision alternative.
=2. Find the maximum of these maximum payoffs and choose the corresponding decision alternative.
=1. Identify the state of nature with the largest prior probability.
=2. Choose the decision alternative that has the largest payoff for this state of nature.
=2. What are some criticisms of the maximax criterion?
=4. What are some criticisms of the maximin criterion?
=9. What are some criticisms of Bayes’ decision rule?
=1. What is a decision tree?
=2. What is a decision node in a decision tree? An event node?
=1. What are posterior probabilities of the states of nature?
=5. What is the formula for calculating P(state and finding)?
=6. What is the formula for calculating P(finding)?
=1. What does a decision tree display?
=2. What is happening at a decision node?
=3. What is happening at an event node?
=6. What calculation needs to be performed at each event node?
=7. What comparison needs to be made at each decision node?
=3. What is a major limitation of using a data table to perform sensitivity analysis on a large problem?
=4. How many data cells can be varied at a time when using the Plot option of SensIt?
=5. Can the Spider option of SensIt consider more data cells at a time than the Plot option?
=6. What is a limitation of a spider graph that is overcome by a tornado diagram?
=1. What are utilities intended to reflect?
=3. What is the fundamental property of utility functions?
=2. What is the purpose of an influence diagram?
=9.1. You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem without probabilities.
=a. Which alternative should be chosen under the maximax criterion?
=b. Which alternative should be chosen under the maximin criterion?
=9.2. Follow the instructions of Problem 9.1 with the following payoff table.
=9.3. Jean Clark is the manager of the Midtown Saveway Grocery Store. She now needs to replenish her supply of strawberries. Her regular supplier can provide as many cases as she wants. However,
=a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.
=b. If Jean is dubious about the accuracy of these prior probabilities and so chooses to ignore them and use the maximax criterion, how many cases of strawberries should she purchase?
=c. How many cases should be purchased if she uses the maximin criterion?
=d. How many cases should be purchased if she uses the maximum likelihood criterion?
=e. How many cases should be purchased according to Bayes’ decision rule?
=f. Jean thinks she has the prior probabilities just about right for selling 10 cases and selling 13 cases, but is uncertain about how to split the prior probabilities for 11 cases and 12 cases.
=9.4.* Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen.He currently has been offered three major investments and he would like to
=a. Reapply Bayes’ decision rule when the prior probability of a stable economy is 0.3 and the prior probability of a worsening economy is 0.6.
=b. Reapply Bayes’ decision rule when the prior probability of a stable economy is 0.7 and the prior probability of a worsening economy is 0.2.
=c. Construct a decision tree by hand for this problem with the original prior probabilities.
=Ad. Use TreePlan to construct and solve a decision tree for this problem with the original prior probabilities.
=Ae. In preparation for performing sensitivity analysis, consolidate the data and results on the same spreadsheet as the decision tree constructed in part d (as was done in Figure 9.6 for the case
=Af. Use the spreadsheet (including the decision tree) obtained in parts d and e to do parts a and b.
=A g. Expanding the spreadsheet as needed, generate a data table that shows which investment Warren should make and the resulting expected profit for the following prior probabilities of a stable
=h. For each of the three investments, find the expected profit when the prior probability of a stable economy is 0 and then when it is 0.9 (with the prior probability of an improving economy fixed
=9.7.* Consider a decision analysis problem whose payoffs (in units of thousands of dollars) are given by the following payoff table:State of Nature Alternative S1 S2 A1 80 25 A2 30 50 A3 60 40 Prior
=Ae. Use TreePlan to construct and solve a decision tree for this problem.Af. Expanding the spreadsheet containing this decision tree as needed, perform sensitivity analysis with the decision tree by
=9.8. You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem:
=a. Which alternative should be chosen under the maximax criterion?
=b. Which alternative should be chosen under the maximin criterion?
=c. Which alternative should be chosen under the maximum likelihood criterion?
=d. Which alternative should be chosen under Bayes’ decision rule?
=e. Construct a decision tree by hand for this problem.Af. Use TreePlan to construct and solve a decision tree
=for this problem.A g. Perform sensitivity analysis with this decision tree by generating a data table that shows what happens when the prior probability of S1 increases in increments of 0.05 from
=A h. Repeat part g when it is the prior probability of S2 that remains fixed at its original value.
=A i. Repeat part g when it is the prior probability of S1 that remains fixed at its original value while the prior probability of S2 increases in increments of 0.05 from 0 to 0.4.
=j. If you feel that the true probabilities of the states of nature should be within 10 percent of the given prior probabilities, which alternative would you choose?
=9.9. Dwight Moody is the manager of a large farm with 1,000 acres of arable land. For greater efficiency, Dwight always devotes the farm to growing one crop at a time. He now needs to make a
=a. Develop a decision analysis formulation of this problem by identifying the decision alternatives, the states of nature, and the payoff table.Ab. Construct a decision tree for this problem and
=Ac. Using Bayes’ decision rule, do sensitivity analysis with respect to the prior probabilities of moderate weather and damp weather (without changing the prior probability of dry weather) by
=9.10. Barbara Miller makes decisions according to Bayes’decision rule. For her current problem, Barbara has constructed the following payoff table (in units of hundreds of dollars) and she now
=9.11. You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem:
=a. According to Bayes’ decision rule, which alternative should be chosen?
=b. Find the expected value of perfect information.
=Ac. Check your answer in part b by recalculating it with the help of a decision tree.
=d. You are given the opportunity to spend $1,000 to obtain more information about which state of nature is likely to occur. Given your answer to partb, might it be worthwhile to spend this money?
=9.12.* Betsy Pitzer makes decisions according to Bayes’ decision rule. For her current problem, Betsy has constructed the following payoff table (in units of dollars):
=a. Which alternative should Betsy choose?
=b. Find the expected value of perfect information.
=Ac. Check your answer in part b by recalculating it with the help of a decision tree.
=d. What is the most that Betsy should consider paying to obtain more information about which state of nature will occur?
=9.13. Using Bayes’ decision rule, consider the decision analysis problem having the following payoff table (in units of thousands of dollars):
=a. Which alternative should be chosen? What is the resulting expected payoff?
=b. You are offered the opportunity to obtain information that will tell you with certainty whether the first state of nature S1 will occur. What is the maximum amount you should pay for the
=c. Now repeat part b if the information offered concerns S2 instead of S1.
=d. Now repeat part b if the information offered concerns S3 instead of S1.
=e. Now suppose that the opportunity is offered to provide information that will tell you with certainty which state of nature will occur (perfect information). What is the maximum amount you
=f. If you have the opportunity to do some testing that will give you partial additional information (not perfect information) about the state of nature, what is the maximum amount you should
=9.14. Reconsider the Goferbroke Co. case study, including its analysis in Sections 9.6 and 9.7. With the help of the consulting geologist, Jennifer Flyer now has obtained some historical data that
=a. Revise Figure 9.12 to find the new posterior probabilities.
=Tb. Use the corresponding Excel template to check your answers in part a.
=c. Revise Figure 9.16 to find the new decision tree.What is the resulting optimal policy?

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