Deck 12: Decision Analysis

Question 1

The Hurwicz criterion multiplies the best payoff by the coefficient of optimism.

Answer 1

True

Question 2

Regret is the difference between the payoff from the best decision and all other decision payoffs.

Answer 2

True

Question 3

Regret and opportunity loss mean the same thing.

Answer 3

True

Question 4

The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.

Question 5

The minimax criterion minimizes the maximum payoff.

Question 6

The maximax criterion is optimistic.

Question 7

The Hurwicz criterion is a compromise between the maximax and maximin criteria.

Question 8

The maximax criterion results in the maximum of the maximum payoffs.

Question 9

A payoff table is a means of organizing a decision situation, including the payoffs from different decisions given the various states of nature.

Question 10

The coefficient of optimism is a measure of the decision maker's optimism.

Question 11

Expected opportunity loss is the expected value of the regret for each decision.

Question 12

The Hurwicz criterion is a compromise between the minimax and minimin criteria.

Question 13

The maximin criterion maximizes the minimum regret.

Question 14

The minimax regret criterion maximizes the minimum regret.

Question 15

A dominant decision is one that has a better payoff than another decision under each state of nature.

Question 16

The maximin approach involves choosing the alternative with the highest payoff.

Question 17

The equal likelihood criterion assigns a probability of 0.5 to each state of nature.

Question 18

The appropriate criterion is dependent on the risk personality and philosophy of the decision maker.

Question 19

The minimax regret criterion minimizes the maximum regret.

Question 20

A state of nature is an actual event that may occur in the future.

Question 21

________ is the difference between the payoff from the best decision and all other decision payoffs.

Question 22

A decision tree is a diagram consisting of circular decision nodes, square probability nodes, and branches.

Question 23

The ________ is a compromise between the maximax and the maximin criterion.

Question 24

When using decision trees, branches with the greatest expected value are selected.

Question 25

A(n) ________ decision is one that has a better payoff than another decision under each state of nature.

Question 26

When the ________ criterion is used, the maximum of the maximum payoffs is selected.

Question 27

A posterior probability is the likelihood that an event has occurred after the decision maker has reached a decision.

Question 28

A ________ decision tree illustrates a situation requiring a series of decisions.

Question 29

A conditional probability is the probability that two events will occur simultaneously.

Question 30

When the ________ criterion is used, the maximum of the minimum payoffs is selected

Question 31

When the ________ criterion is used, the decision maker selects the decision alternative that minimizes the maximum regret.

Question 32

________ is a measure of personal satisfaciton derived from money.

Question 33

Additional information is used to alter the marginal probability of occurrence of an event in Bayesian analysis.

Question 34

The expected value of perfect information divided by the expected value of sample information is the efficiency of perfect information.

Question 35

Events are mutually exclusive if one, and only one, can occur at a time.

Question 36

People who forgo a high expected value to avoid a disaster with a low probability are ________.

Question 37

The ________ is a measure of the decision makers optimism.

Question 38

The efficiency of sample information is the ratio of the expected value of sample information to ________.

Question 39

A ________ structures decisions with a series of nodes.

Question 40

The ________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information.

Question 41

Compute the expected value of perfect information assuming that the probability of S2
is equal to 0.4.

Question 42

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

What decision would be made under maximax?

Question 43

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what investment would be made using the expected value criterion?

Question 44

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

If he uses the minimax regret criterion, how many new workers will he hire?

Question 45

If only one of three events can occur at any given time, the events are ________.

Question 46

The difference in the expected value with additional information and without additional information is ________.

Question 47

A manager has developed a payoff table that indicates the profits associated with a set of alternatives under two possible states of nature.

If the manager uses minimax regret as the decision criterion, which of the alternatives would she choose?

Question 48

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the group is optimistic, what decision should they make?

Question 49

If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05, respectively, what is the expected value of perfect information?

Question 50

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

If he uses the maximin criterion, how many new workers will he hire?

Question 51

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the group chooses to minimize their maximum regret, what activity will they choose?

Question 52

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the group is conservative, what decision will they make?

Question 53

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion?

Question 54

A manager has developed a payoff table that indicates the profits associated with a set of alternatives under two possible states of nature.

If the manager uses maximin as the decision criterion, which of the alternatives should she choose?

Question 55

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

What decision would be made under maximin?

Question 56

An investor is consider four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.

What decision would be made under minimax regret?

Question 57

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively, then what is the EVPI for this situation?

Question 58

Use the expected value criterion to select the best alternative. Assume that the probability of S2 is equal to 0.4.

Question 59

If the decision maker receives additional information such that the marginal probabilities of certain events should be modified, these revised probabilites are called ________.

Question 60

The efficiency of sample information multiplied by the expected value of perfect information is ________.

Question 61

A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000.
Draw a decision tree.

Question 62

What action would you choose according to minimax regret criterion?

Question 63

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what is the expected value of perfect information?

Question 64

Consider the following decision tree.
What is the expected value at node 4?

Question 65

Construct the regret table.

Question 66

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.

Pedro is extremely pessimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why?

Question 67

What action would you choose according to expected value criterion?

Question 68

Lucky Lucy is playing the slots in Reno, Nevada, holding her last silver dollar. There are three possible payoffs if she wins: one cherry, $1; two cherries, $5; or three cherries, $50. Anything else on the slot machine loses.
Construct the payoff table for Lucky Lucy.

Question 69

What is the maximum amount that you would be willing to pay for perfect information?

Question 70

The quality control manager for ENTA Inc. must decide whether to accept (A1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3).

What action would you choose according to maximax criterion?

Question 71

The quality control manager for ENTA Inc. must decide whether to accept (A1), further analyze (A2), or reject (A3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (S1), 50 % chance that the lot is fair quality (S2), and 20% chance that the lot is good quality (S3).

What action would you choose according to maximin criterion?

Question 72

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.
$$\begin{array} { | l | c | c | c | } \hline \text { School } & \text { Scenario 1 } & \text { Scenario 2 } & \text { Scenario 3 } \\\hline \text { Vanderbilt } & 95 & 20 & - 10 \\\hline \text { Texas Tech } & 55 & 60 & 60 \\\hline \text { Seattle } & 90 & 10 & 80 \\\hline \text { Northeastern State } & 65 & 50 & 60 \\\hline\end{array}$$

-Summer bursts into the meeting and announces that there's another way to consider the issue. Since Napoleon will have to live with his choice for the rest of his life, he might consider selecting the alternative that will cause him the least pain in hindsight when he compares his outcome with what he might have gained. Which criterion is she talking about, what is the best school for this criterion, and why?

Question 73

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.
$$\begin{array} { | l | c | c | c | } \hline \text { School } & \text { Scenario 1 } & \text { Scenario 2 } & \text { Scenario 3 } \\\hline \text { Vanderbilt } & 95 & 20 & - 10 \\\hline \text { Texas Tech } & 55 & 60 & 60 \\\hline \text { Seattle } & 90 & 10 & 80 \\\hline \text { Northeastern State } & 65 & 50 & 60 \\\hline\end{array}$$

-Napoleon's Uncle Rico believes that the scenarios are not necessarily equally likely, and suggests that the likelihood of occurrence of Scenario 2 is 0.4 and the likelihood of occurrence of Scenarios 1 and 3 are both 0.3. What two criteria are most appropriate and what is the resulting decision?

Question 74

The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what are the expected net revenues for the number of workers he will decide to hire?

Question 75

A manufacturer must decide whether to build a small or a large plant at a new location. Demand at the location can be either low or high, with probabilities estimated to be 0.4 and 0.6, respectively. If a small plant is built, and demand is high, the production manager may choose to maintain the current size or to expand. The net present value of profits is $223,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 50% chance that the net present value of the returns will be 330,000 and a 50% chance the estimated net present value of profits will be $210,000. If a small facility is built and demand is low, there is no reason to expand and the net present value of the profits is $200,000. However, if a large facility is built and the demand turns out to be low, the choice is to do nothing with a net present value of $40,000 or to stimulate demand through local advertising. The response to advertising can be either modest with a probability of .3 or favorable with a probability of .7. If the response to advertising is modest, the net present value of the profits is $20,000. However, if the response to advertising is favorable, then the net present value of the profits is $220,000. Finally, if the large plant is built and the demand happens to be high, the net present value of the profits $800,000.
Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the manufacturer choose?

Question 76

Napoleon is contemplating four institutions of higher learning as options for a Masters in Business Administration. Each university has strong and weak points and the demand for MBA graduates is uncertain. The availability of jobs, student loans, and financial support will have a significant impact on Napoleon's ultimate decision. Vanderbilt and Seattle University have comparatively high tuition, which would necessitate Napoleon take out student loans resulting in possibly substantial student loan debt. In a tight market, degrees with that cachet might spell the difference between a hefty paycheck and a piddling unemployment check. Northeastern State University and Texas Tech University hold the advantage of comparatively low tuition but a more regional appeal in a tight job market. Napoleon gathers his advisory council of Kip and Pedro to assist with the decision. Together they forecast three possible scenarios for the job market and institutional success and predict annual cash flows associated with an MBA from each institution. All cash flows in the table are in thousands of dollars.

Kip tends to be extremely optimistic. Which decision making criterion would he naturally select and what conclusion would he recommend to Napoleon? Why?

Question 77

Consider the following decision tree.
What is the value associated with node 3?

Question 78

Consider the following decision tree.
Which decision, A or B, is best? What is the expected value of this decision?

Question 79

Napoleon doesn't know what to think, since he has no idea which scenario will happen. Which criterion is he well-suited for and what is his decision?

Question 80

If a student attends every management science class, the probability of passing the course is 0.80; but if the student only attends randomly, then the probability of passing the course is 0.50. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.10 if the student has attended at random.
Passing the course is worth 5 credits. Full time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit.
Use a decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the make up exam and that the payoff for failing is equal to 0.