Deck 13: Decision Analysis

Question 1

​The decision alternative with the best expected monetary value will always be the most desirable decision.

Answer 1

False

Question 2

Circular nodes in a decision tree indicate that it would be incorrect to choose a path from the node.

Answer 2

True

Question 3

​A high efficiency rating indicates that the sample information is almost as good as perfect information.

Answer 3

True

Question 4

A decision strategy is a sequence of decisions and chance outcomes, where the decisions chosen depend on the yet to be determined outcomes of chance events.

Question 5

Maximizing the expected payoff and minimizing the expected opportunity loss result in the same recommended decision.

Question 6

The expected value approach is more appropriate for a one-time decision than a repetitive decision.

Question 7

EVPI is always greater than or equal to EVSI.

Question 8

After all probabilities and payoffs are placed on a decision tree, the decision maker calculates expected values at state of nature nodes and makes selections at decision nodes.

Question 9

The expected value of sample information can never be less than the expected value of perfect information.

Question 10

Square nodes in a decision tree indicate that a decision must be made.

Question 11

Risk analysis helps the decision maker recognize the difference between the expected value of a decision alternative and the payoff that may actually occur.

Question 12

States of nature should be defined so that one and only one will actually occur.

Question 13

The expected value of an alternative can never be negative.

Question 14

​When the expected value approach is used to select a decision alternative, the payoff that actually occurs will usually have a value different from the expected value.

Question 15

Sample information with an efficiency rating of 100% is perfect information.

Question 16

Expected value is the sum of the weighted payoff possibilities at a circular node in a decision tree.

Question 17

Decision alternatives are structured so that several could occur simultaneously.

Question 18

​The primary value of decision trees is as a useful way of organizing how operations managers think about complex multiphase decisions.

Question 19

The minimum expected opportunity loss provides the best decision, regardless of whether the decision analysis involves minimization or maximization.

Question 20

EVPI equals the expected regret associated with the minimax decision.

Question 21

​Expected utility is a particularly useful tool when payoffs stay in a range considered reasonable by the decision maker.

Question 22

Making a good decision

A) requires probabilities for all states of nature.
B) requires a clear understanding of decision alternatives, states of nature, and payoffs.
C) implies that a desirable outcome will occur.
D) All of the alternatives are true.

Question 23

Sensitivity analysis considers

A) how sensitive the decision maker is to risk.
B) changes in the number of states of nature.
C) changes in the values of the payoffs.
D) changes in the available alternatives.

Question 24

A payoff

A) is always measured in profit.
B) is always measured in cost.
C) exists for each pair of decision alternative and state of nature.
D) exists for each state of nature.

Question 25

A decision tree

A) presents all decision alternatives first and follows them with all states of nature.
B) presents all states of nature first and follows them with all decision alternatives.
C) alternates the decision alternatives and states of nature.
D) arranges decision alternatives and states of nature in their natural chronological order.

Question 26

​The expected monetary value approach and the expected utility approach to decision making usually result in the same decision choice unless extreme payoffs are involved.

Question 27

​A risk avoider will have a concave utility function.

Question 28

​The risk neutral decision maker will have the same indications from the expected value and expected utility approaches.

Question 29

The options from which a decision maker chooses a course of action are

A) called the decision alternatives.
B) under the control of the decision maker.
C) not the same as the states of nature.
D) All of the alternatives are true.

Question 30

​The risk premium is never negative for a conservative decision maker.

Question 31

​Given two decision makers, one risk neutral and the other a risk avoider, the risk avoider will always give a lower utility value for a given outcome.

Question 32

​When monetary value is not the sole measure of the true worth of the outcome to the decision maker, monetary value should be replaced by utility.

Question 33

​The expected utility is the utility of the expected monetary value.

Question 34

States of nature

A) can describe uncontrollable natural events such as floods or freezing temperatures.
B) can be selected by the decision maker.
C) cannot be enumerated by the decision maker.
D) All of the alternatives are true.

Question 35

​The utility function for a risk avoider typically shows a diminishing marginal return for money.

Question 36

​The outcome with the highest payoff will also have the highest utility.

Question 37

Which of the methods for decision making best protects the decision maker from undesirable results?

A) the optimistic approach
B) the conservative approach
C) minimum regret
D) minimax regret

Question 38

​A risk neutral decision maker will have a linear utility function.

Question 39

​To assign utilities, consider the best and worst payoffs in the entire decision situation.

Question 40

​When the payoffs become extreme, most decision makers are satisfied with the decision that provides the best expected monetary value.

Question 41

For a maximization problem, the conservative approach is often referred to as the

A) minimax approach.
B) maximin approach.
C) maximax approach.
D) minimin approach.

Question 42

​The approach to determining the optimal decision strategy involves

A) ​a forward (left to right) pass through the decision tree.
B) ​a backward (right to left) pass through the decision tree.
C) ​choosing the outcome of a chance event with the greatest probability.
D) ​choosing the outcome of a chance event with the greatest payoff.

Question 43

The efficiency of sample information is

A) EVSI*(100%)
B) EVSI/EVPI*(100%)
C) EVwoSI/EVwoPI*(100%)
D) EVwSI/EVwoSI*(100%)

Question 44

For a minimization problem, the optimistic approach is often referred to as the

A) minimax approach
B) maximin approach
C) maximax approach
D) minimin approach

Question 45

Decision tree probabilities refer to

A) the probability of finding the optimal strategy
B) the probability of the decision being made
C) the probability of overlooked choices
D) the probability of an uncertain event occurring

Question 46

To find the EVSI,

A) use the EVPI to calculate sample information probabilities.
B) use indicator probabilities to calculate prior probabilities.
C) use prior and sample information probabilities to calculate revised probabilities.
D) use sample information to revise the sample information probabilities.

Question 47

If P(high) = .3, P(low) = .7, P(favorable | high) = .9, and P(unfavorable | low) = .6, then P(favorable) =

A) .10
B) .27
C) .30
D) .55

Question 48

​A decision tree provides

A) ​a heuristic method for analyzing decisions.
B) ​a deterministic approach to decision analysis.
C) ​the absolute value of the decision.
D) ​an objective way of determining the relative value of each decision alternative.

Question 49

​The purchase of insurance and lottery tickets shows that people make decisions based on

A) ​expected value.
B) ​sample information.
C) ​utility.
D) ​maximum likelihood.

Question 50

​When consequences are measured on a scale that reflects a decision maker's attitude toward profit, loss, and risk, payoffs are replaced by

A) ​utility values.
B) ​multicriteria measures.
C) ​sample information.
D) ​opportunity loss.

Question 51

​Which of the following is not an advantage of using decision tree analysis?

A) ​the ability to see clearly what decisions must be made
B) ​the ability to see clearly in what sequence the decisions must occur
C) ​the ability to see clearly the interdependence of decisions
D) ​the ability to see clearly the future outcome of a decision

Question 52

For a minimization problem, the conservative approach is often referred to as the

A) minimax approach
B) maximin approach
C) maximax approach
D) minimin approach

Question 53

​The expected utility approach

A) ​does not require probabilities.
B) ​leads to the same decision as the expected value approach.
C) ​is most useful when excessively large or small payoffs are possible.
D) ​requires a decision tree.

Question 54

For a maximization problem, the optimistic approach is often referred to as the

A) minimax approach
B) maximin approach
C) maximax approach
D) minimin approach

Question 55

​Decision tree probabilities refer to the probability of

A) ​an uncertain event occurring.
B) ​the decision being made.
C) ​finding an optimal value.
D) ​overlooked choices.

Question 56

Which of the following approaches to decision making requires knowledge of the probabilities of the states of nature?

A) minimax regret
B) maximin
C) expected value
D) conservative

Question 57

​The difference between the expected value of an optimal strategy based on sample information and the "best" expected value without any sample information is called the

A) ​information sensitivity.
B) ​expected value of sample information.
C) ​expected value of perfect information.
D) ​efficiency of sample information.

Question 58

In an influence diagram, decision nodes are represented by

A) circles or ovals
B) squares or rectangles
C) diamonds
D) triangles

Question 59

​Values of utility

A) ​must be between 0 and 1.
B) ​must be between 0 and 10.
C) ​must be nonnegative.
D) ​must increase as the payoff improves.

Question 60

​Utility reflects the decision maker's attitude toward

A) ​probability and profit.
B) ​profit, loss, and risk.
C) ​risk and regret.
D) ​probability and regret.

Question 61

If the payoff from outcome A is twice the payoff from outcome B, then the ratio of these utilities will be

A) ​2 to 1.
B) ​less than 2 to 1.
C) ​more than 2 to 1.
D) ​unknown without further information.

Question 62

​The probability for which a decision maker cannot choose between a certain amount and a lottery based on that probability is

A) ​the indifference probability.
B) ​the lottery probability.
C) ​the uncertain probability.
D) ​the utility probability.

Question 63

Super Cola is also considering the introduction of a root beer drink. The company feels that the probability that the product will be a success is .6. The payoff table is as follows: ​
The company has a choice of two research firms to obtain information for this product. Stanton Marketing has market indicators, I₁ and I₂ for which P(I₁ | s₁) = .7 and P(I₁ | s₂) = .4. New World Marketing has indicators J₁ and J₂ for which P(J₁ | s₁) = .6 and P(J₁ | s₂) = .3.
a.​What is the optimal decision if neither firm is used? Over what probability of success range is this decision optimal?
b.What is the EVPI?
c.Find the EVSIs and efficiencies for Stanton and New World.
d.If both firms charge $5,000, which firm should be hired?
e.​If Stanton charges $10,000 and New World charges $4,000, which firm should Super Cola hire? Why?

Question 64

​A decision maker whose utility function graphs as a straight line is

A) ​conservative.
B) ​a risk taker.
C) ​risk neutral.
D) ​a risk avoider.

Question 65

A payoff table is given as
​
a.What choice should be made by the optimistic decision maker?
b.What choice should be made by the conservative decision maker?
c.What decision should be made under minimax regret?
d.If the probabilities of d₁, d₂, and d₃ are .2, .5, and .3, respectively, then what choice should be made under expected value?
e.What is the EVPI?

Question 66

Transrail is bidding on a project that it figures will cost $400,000 to perform. Using a 25% markup, it will charge $500,000, netting a profit of $100,000. However, it has been learned that another company, Rail Freight, is also considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid of about $470,000. Transrail really wants this project and is considering a bid with only a 15% markup to $460,000 to ensure winning regardless of whether or not Rail Freight submits a bid.
a.
Prepare a profit payoff table from Transrail's point of view.
b.
What decision would be made if Transrail were conservative?
c.
If Rail Freight is known to submit bids on only 25% of the projects it considers, what decision should Transrail make?
d.
Given the information in (c), how much would a corporate spy be worth to Transrail to find out if Rail Freight will bid?

Question 67

?A decision maker has chosen .4 as the probability for which he cannot choose between a certain loss of 10,000 and the lottery p(-25000) + (1 - p)(5000). If the utility of -25,000 is 0 and of 5000 is 1, then the utility of -10,000 is

A) ?.5
B) ?.6
C) ?.4
D) ?4

Question 68

An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost $220 and sell for $300. Because the oven company is coming out with a new product line in two months, any ovens not sold next month will have to be sold at the dealer's half price clearance sale. Additionally, the appliance dealer feels he suffers a loss of $25 for every oven demanded when he is out of stock. On the basis of past months' sales data, the dealer estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be .3, .4, .2, and .1, respectively.
The dealer is considering conducting a telephone survey on the customers' attitudes towards microwave ovens. The results of the survey will either be favorable (F), unfavorable (U) or no opinion (N). The dealer's probability estimates for the survey results based on the number of units demanded are: ​
a.
What is the dealer's optimal decision without conducting the survey?
b.
What is the EVPI?
c.
Based on the survey results what is the optimal decision strategy for the dealer?
d.
What is the maximum amount he should pay for this survey?

Question 69

A decision maker has developed the following decision tree. How sensitive is the choice between N and P to the probabilities of states of nature U and V?

Question 70

East West Distributing is in the process of trying to determine where they should schedule next year's production of a popular line of kitchen utensils that they distribute. Manufacturers in four different countries have submitted bids to East West. However, a pending trade bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc.
After careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000's) based on whether or not the trade bill passes: ​
a.
If East West estimates that there is a 40% chance of the bill passing, which country should they choose for manufacturing?
b.
Over what range of values for the "bill passing" will the solution in part (a) remain optimal?

Question 71

The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do.
​​ ​
a.
if an optimistic strategy is used.
b.
if a conservative strategy is used.
c.
if minimax regret is the strategy.

Question 72

​When the utility function for a risk-neutral decision maker is graphed (with monetary value on the horizontal axis and utility on the vertical axis), the function appears as

A) ​a convex curve.
B) ​a concave curve.
C) ​an 'S' curve.
D) ​a straight line.

Question 73

A payoff table is given as
​
a.What decision should be made by the optimistic decision maker?
b.What decision should be made by the conservative decision maker?
c.What decision should be made under minimax regret?
d.​If the probabilities of s₁, s₂, and s₃ are .2, .4, and .4, respectively, then what decision should be made under expected value?
e.What is the EVPI?

Question 74

Dollar Department Stores has just acquired the chain of Wenthrope and Sons Custom Jewelers. Dollar has received an offer from Harris Diamonds to purchase the Wenthrope store on Grove Street for $120,000. Dollar has determined probability estimates of the store's future profitability, based on economic outcomes, as: P($80,000) = .2, P($100,000) = .3, P($120,000) = .1, and P($140,000) = .4.
a.Should Dollar sell the store on Grove Street?
b.What is the EVPI?
c.Dollar can have an economic forecast performed, costing $10,000, that produces indicators I₁ and I₂, for which P(I₁ | 80,000) = .1; P(I₁ | 100,000) = .2; P(I₁ | 120,000) = .6; P(I₁ | 140,000) = .3. Should Dollar purchase the forecast?

Question 75

Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of $1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month.
a. Compute the monthly salary payoff table for Jim.
b. For this payoff table find Jim's optimal decision using: (1) the conservative approach, (2) minimax regret approach.
c. Suppose that during the past year the following is Jim's distribution of home sales. If one assumes that this a typical distribution for Jim's monthly sales, which salary plan should Jim select?

Question 76

​When the decision maker prefers a guaranteed payoff value that is smaller than the expected value of the lottery, the decision maker is

A) ​a risk avoider.
B) ​a risk taker.
C) ​an optimist.
D) ​an optimizer.

Question 77

Fold back the decision tree and state what strategy should be followed.
​

Question 78

The Super Cola Company must decide whether or not to introduce a new diet soft drink. Management feels that if it does introduce the diet soda it will yield a profit of $1 million if sales are around 100 million, a profit of $200,000 if sales are around 50 million, or it will lose $2 million if sales are only around 1 million bottles. If Super Cola does not market the new diet soda, it will suffer a loss of $400,000.
a.
Construct a payoff table for this problem.
b.
Construct a regret table for this problem.
c.
Should Super Cola introduce the soda if the company: (1) is conservative; (2) is optimistic; (3) wants to minimize its maximum disappointment?
d.
An internal marketing research study has found P(100 million in sales) = 1/3; P(50 million in sales) = 1/2; P(1 million in sales) = 1/6. Should Super Cola introduce the new diet soda?
e.
A consulting firm can perform a more thorough study for $275,000. Should management have this study performed?

Question 79

If p is the probability of Event 1 and (1 − p) is the probability of Event 2, for what values of p would you choose A? B? C? Values in the table are payoffs.

Question 80

Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands.
​ ​
a.
What decision should be made by the optimist?
b.
What decision should be made by the conservative?
c.
What decision should be made using minimax regret?