Deck 4: Decision Analysis

Question 1

Decision alternatives are structured so that several could occur simultaneously.

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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 5

EVPI is always greater than or equal to EVSI.

Question 6

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

Question 7

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 8

The expected value of an alternative can never be negative.

Question 9

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

Question 10

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

Question 11

EVPI equals the expected regret associated with the minimax decision.

Question 12

​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 13

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

Question 14

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

Question 15

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 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

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

In an influence diagram,decision nodes are represented by

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

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

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 25

​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 26

​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 27

​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 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

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 30

​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 31

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 32

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 33

The efficiency of sample information is

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

Question 34

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 35

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 36

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 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

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 39

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 40

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 41

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 42

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.
​​
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a.if an optimistic strategy is used.
b.if a conservative strategy is used.
c.if minimax regret is the strategy.

Question 43

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 44

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 45

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.
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​

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 46

When working backward through a decision tree,the analyst should​

A)​compute the expected value at each chance node
B)​select the best chance branch at each chance node
C)​select the best chance branch at each decision node
D)​compute the expected value at each decision node

Question 47

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

Question 48

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 49

​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 50

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 51

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 52

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 53

If sample information is obtained,the result of the sample information will be either positive or negative.No matter which result occurs,the choice to select option A or option B exists.And no matter which option is chosen,the eventual outcome will be good or poor.Complete the table.

Question 54

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 55

Application of Bayes' theorem enables us to compute​

A)​the prior probability of each state of nature
B)​the posterior probability of each sample outcome
C)​the conditional probability of the sample outcomes given each state of nature
D)​the conditional probability of the states of nature given each sample outcome

Question 56

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

Question 57

A sequence of decisions and chance outcomes that provide the optimal solution to a decision problem is called​

A)​a payoff table
B)​the expected value approach
C)​a decision strategy
D)​a contingency plan

Question 58

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 59

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 60

A posterior probability associated with sample information is of the form​

A)​P(a state of nature | a sample outcome)
B)​P(a sample outcome | a state of nature)
C)​P(a decision alternative | a sample outcome)
D)​P(a sample outcome | a decision alternative)

Question 61

How can a good decision maker "improve" luck?

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

​Explain why the decision maker might feel uncomfortable with the expected value approach,and decide to use a non-probabilistic approach even when probabilities are available.

Question 64

An investor has a choice between four investments.The profitability of the investments depends upon the market.The payoff table is given below for different market conditions.
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a.A market economist has stated that there is a 25% chance that the market will stay the same,a 35% chance that the market will decrease,and a 40% chance that the market will increase.Compute the expected value for each investment.Which investment is the best?
b.Compute the expected value of perfect information.​

Question 65

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 they build a pilot plant now,they could expand it later to a full plant or license the plant to another company.It would cost them $2 million to build the pilot plant and another $2 million later to expand it.If they build the full plant now it would cost $3.5 million to construct.
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The returns they expect to get from the full production plant depend upon the market.They estimate 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.
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Before they expand the pilot plant,they plan to conduct a comprehensive study.Based on past experience,they expect the study to report a 60% chance of favorable outcome for expansion and a 40% unfavorable chance.In either case they will have to decide whether to expand to a full plant or license the pilot plant.If the report is favorable and they license it,they expect to get $3 million.However,if the report is unfavorable and they license it,they will only get $1 million.
​
Develop a decision tree for this problem and determine the optimal decision strategy.

Question 66

A fashion designer wants to produce a new line of clothes.In the production of the clothes,expensive,medium-priced,or inexpensive materials can be used.The profit associated with each type of material depends upon economic conditions next year.Below you are given the payoff table.
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An economist believes that the probability that the economy will improve is 20%,the probability that the economy will stay the same is 70%,and the probability that the economy will get worse is 10%.
​
a.Compute the expected value for each investment.Which investment is the best?
b.Compute the expected value of perfect information.​

Question 67

Show how you would design a spreadsheet to calculate revised probabilities for two states of nature and two indicators.

Question 68

Why perform sensitivity analysis? Of what use is sensitivity analysis where good probability estimates are difficult to obtain?

Question 69

Use a diagram to compare EVwPI,EVwoPI,EVPI,EVwSI,EVwoSI,and EVSI.