Deck 13: Decision Analysis

Question 1

The primary value of decision trees is that they provide a useful way to organize how operations managers think about complex multiphase decisions.

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

Under the minimax regret approach to decision making,EVPI equals the expected regret that is associated with the minimax decision.

Question 5

The expected value of an alternative can never be negative.

Question 6

EVPI is always greater than or equal to EVSI.

Question 7

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 8

Circular nodes in a decision tree are considered chance nodes.

Question 9

For a chance node,the expected value is the weighted average of the payoffs,where the weights are the state-of-nature probabilities.​

Question 10

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

Question 11

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

Question 12

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

Question 13

Regret is the difference between the payoff associated with a particular decision alternative and the payoff associated with the decision that would yield the most desirable payoff for a given state of nature.

Question 14

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 15

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

Question 16

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

Question 17

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

Question 18

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 19

Decision alternatives are structured so that several could occur simultaneously.

Question 20

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 21

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 22

The efficiency of sample information is

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

Question 23

When the expected utility approach and the expected value approach applied to monetary payoffs result in the same action,these are characteristics generally associated with a risk-neutral decision maker.

Question 24

States of nature

A)are the possible outcomes for a chance event.
B)can be selected by the decision maker.
C)cannot be enumerated by the decision maker.
D)None of these are correct.

Question 25

A risk avoider is a decision maker who would choose a guaranteed payoff over a lottery with a superior expected payoff.

Question 26

Decision tree probabilities refer to the probability of

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

Question 27

Utility is the term for a measure of the total worth or relative desirability of a particular outcome.

Question 28

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 29

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 these are correct.

Question 30

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

Question 31

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 32

Sensitivity analysis

A)considers how sensitive the decision maker is to risk.
B)considers how changes in the number of states of nature can impact the recommended decision.
C)considers how changes in various aspects of the problem affect the recommended decision alternative.
D)None of these are correct.

Question 33

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

Question 34

As long as the monetary value of payoffs stays within a range that the decision maker considers reasonable,selecting the decision alternative with the best expected value usually leads to selection of the most preferred decision.

Question 35

Given two decision makers,one a risk taker and the other a risk avoider,the risk avoider will show a diminishing marginal return for money.

Question 36

To find the expected value of sample information (EVSI),

A)use prior and sample information probabilities to calculate revised probabilities.
B)use indicator probabilities to calculate prior probabilities.
C)use sample information to revise the sample information probabilities.
D)None of these are correct.

Question 37

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

A)called the decision alternatives.
B)not under the control of the decision maker.
C)the same as the states of nature.
D)None of these are correct.

Question 38

If P(high)= 0.3,P(low)= 0.7,P(favorable | high)= 0.9,and P(unfavorable | low)= 0.6,then P(favorable)=

A)0.10.
B)0.27.
C)0.30.
D)0.55.

Question 39

A payoff

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

Question 40

Which of the following 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 41

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(n)

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

Question 42

A decision tree provides

A)the only 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 43

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 44

In an influence diagram,decision nodes are represented by

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

Question 45

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 46

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 47

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

A)risk avoider.
B)risk taker.
C)optimist.
D)optimizer.

Question 48

Super Cola is also considering the introduction of a root beer drink.The company thinks the probability that the product will be a success is 0.6.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)= 0.7 and P(I₁ | s₂)= 0.4.New World Marketing has indicators J₁ and J₂ for which P(J₁ | s₁)= 0.6 and P(J₁ | s₂)= 0.3.
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 $4000,which firm should Super Cola hire?

Question 49

East West Distributing is in the process of trying to determine where it should schedule next year's production of a popular line of kitchen utensils that it distributes.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 $1000s)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 it choose for manufacturing?
b.Over what range of values for the "bill passing" will the solution in part (a)remain optimal?
​

Question 50

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 51

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 52

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

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

Question 53

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 54

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 55

Decision tree probabilities are primarily used to

A)analyze more complex problems and to identify an optimal sequence of decisions.
B)analyze less complex problems while identifying the optimal sequence of decisions.
C)find overlooked choices to the problem.
D)None of these are correct.

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

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)= 0.2,P($100,000)= 0.3,P($120,000)= 0.1,and P($140,000)= 0.4.
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)= 0.1; P(I₁ | 100,000)= 0.2; P(I₁ | 120,000)= 0.6; P(I₁ | 140,000)= 0.3.Should Dollar purchase the forecast?
​

Question 58

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 59

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 60

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 0.3,0.4,0.2,and 0.1,respectively.The dealer is considering conducting a telephone survey on 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 61

Metropolitan Cablevision has the choice of using one of three DVR systems.Profits are believed to be a function of customer acceptance.The payoff to Metropolitan for the three systems is as follows:
​ ​
The probabilities of customer acceptance for each system are as follows:
​ ​
The first vice president believes that the indifference probabilities for Metropolitan should be as follows:
​ ​
The second vice president believes Metropolitan should assign the following utility values:
​ ​
a.Which vice president is a risk taker? Which one is risk averse?
b.Which system will each vice president recommend?
c.Which system would a risk-neutral vice president recommend?

Question 62

Use graphical sensitivity analysis to determine the range of values of the probability of state of nature s₁ over which each of the decision alternatives has its largest expected value.

Question 63

Consider the following problem with four states of nature,three decision alternatives,and the following payoff table (in $s):
​
​
The indifference probabilities for three individuals are as follows:
​ ​
a.Classify each person as a risk avoider,risk taker,or risk neutral.
b.For the payoff of $400,what premium will the risk avoider pay to avoid risk? What premium will the risk taker pay to have the opportunity of the high payoff?
c.Suppose each state is equally likely.What are the optimal decisions for each of these three people?
​

Question 64

Determine decision strategies based on expected value and on expected utility for this decision tree.Use the following utility function:
​ ​

Question 65

Three decision makers have assessed utilities for the problem whose payoff table appears below.​ ​ ​
a.Plot the utility function for each decision maker.
b.Characterize each decision maker's attitude toward risk.
c.Which decision will each person prefer?
​
​

Question 66

Super Cola is considering the introduction of a new eight-oz.root beer.The probability that the root beer will be a success is believed to equal 0.6.The payoff table is as follows:
​ ​
Company management has determined the following utility values:
​ ​
a.Is the company a risk taker,risk averse,or risk neutral?
b.What is Super Cola's optimal decision?
​

Question 67

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.Show your work (regret table).​ ​
a.If an optimistic strategy is used.
b.If a conservative strategy is used.
c.If minimax regret is the strategy.

Question 68

The Dollar Department Store chain has the opportunity of acquiring 3,5,or 10 leases from the bankrupt Granite Variety Store chain.Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years.There are four possible states of the economy as modeled by Dollar Department Stores,and its president estimates P(s₁)= 0.4,P(s₂)= 0.3,P(s₃)= 0.1,and P(s₄)= 0.2.The utility has also been estimated.Given the payoffs (in $1,000,000s)and utility values below,which decision should Dollar make?
​ ​ ​

Question 69

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 70

Burger Prince Restaurant is considering the purchase of a $100,000 fire insurance policy.The fire statistics indicate that in a given year the probability of property damage in a fire is as follows:
​ ​
a.If Burger Prince was risk neutral,how much would it be willing to pay for fire insurance?
b.If Burger Prince has the utility values given below,approximately how much would it be willing to pay for fire insurance?
​
​

Question 71

For the payoff table below,the decision maker will use P(s₁)= 0.15,P(s₂)= 0.5,and P(s₃)= 0.35.​ ​
a.What alternative would be chosen according to expected value?
b.For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1 -p),the decision maker expressed the following indifference probabilities.
c.What alternative would be chosen according to expected utility?
​

Question 72

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.Show a regret table.​ ​
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?

Question 73

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,and which would you choose?
​

Question 74

A decision maker has the following utility function:
​ ​
What is the risk premium for the payoff of 50?

Question 75

Chez Paul is contemplating either opening another restaurant or expanding its existing location.The payoff table for these two decisions is as follows:
​ ​
Paul has calculated the indifference probability for the lottery having a payoff of $160,000 with probability p and -$80,000 with probability (1 -p)as follows:
​ ​
a.Is Paul a risk avoider,a risk taker,or risk neutral?
b.Suppose Paul has defined the utility of -$80,000 to be 0 and the utility of $160,000 to be 80.What would be the utility values for -$40,000,$20,000,and $100,000 based on the indifference probabilities?
c.Suppose P(s₁)= 0.4,P(s₂)= 0.3,and P(s₃)= 0.3.Which decision should Paul make? Compare with the decision using the expected value approach.
​
​

Question 76

A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs.​ ​
For the lottery p(80)+ (1 -p)(-50),this decision maker has assessed the following indifference probabilities:
​ ​
Rank the decision alternatives on the basis of expected value and on the basis of expected utility.

Question 77

A Pacific Northwest lumber company is considering the expansion of one of its mills.The question is whether to do it now or wait one year and reconsider.If it expands now,the major factors are the state of the economy and the level of interest rates.The combination of these two factors results in five possible situations.If it does not expand now,only the state of the economy is important and three conditions characterize the possibilities.The following table summarizes the situation:
​ ​
a.Draw the decision tree for this problem.
b.What is the expected value for expanding?
c.What is the expected value for not expanding?
d.Based on expected value,what should the company's decision(s)be?
​

Question 78

Sunshine Manufacturing Company has developed a unique new product and must now decide between two facility plans.The first alternative is to build a large new facility immediately.The second alternative is to build a small plant initially and to consider expanding it to a larger facility three years later if the market has proven favorable.​
Marketing has provided the following probability estimates for a 10-year plan:
​ If the small plant is expanded,the probability of demands over the remaining seven years is 7/8 for favorable and 1/8 for unfavorable.The accounting department has provided the payoff for each outcome.​ Use these estimates to analyze Sunshine's facility decision.​
a.Perform a complete decision tree analysis.
b.Recommend a strategy to Sunshine.
c.Determine what payoffs will result from your recommendation.
​

Question 79

A chemical company is trying to decide whether to build a pilot plant now for a new chemical process or to build the full plant now.If it builds a pilot plant now,it could expand later to a full plant or license the plant to another company.It would cost $2 million to build the pilot plant and another $2 million later to expand it.If the company builds the full plant now,it would cost $3.5 million to construct.​
The returns the company expects to get from the full production plant depend on the market.There is a 60% chance the market will be robust,a 30% chance it will remain stable,and a 10% chance it will become stagnate.The returns are estimated to be $5 million if it is robust,$3 million if it is stable,and $1 million if it is stagnate.​
Before the company expands the pilot plant,it plans to conduct a comprehensive study.Based on past experience,it expects the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance.In either case,it will have to decide whether to expand to a full plant or license the pilot plant.If the report is favorable and the company licenses it,the company expects to get $3 million.However,if the report is unfavorable and the company licenses it,the company will only get $1 million.​
Develop a decision tree for this problem and determine the optimal decision strategy.

Question 80

Fold back this decision tree.Clearly state the decision strategy you determine.​