Deck 4: Decision Analysis

Question 1

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

Answer 1

True

Question 2

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

Answer 2

C

Question 3

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

Answer 3

True

Question 4

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 5

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

Question 6

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 7

Decision alternatives are structured so that several could occur simultaneously.

Question 8

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

Question 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

Which of the methods for decision making without probabilities best protects the decision maker from undesirable results?

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

Question 18

The efficiency of sample information is

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

Question 19

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 20

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 21

The expected value of an alternative can never be negative.

Question 22

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

Question 23

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 24

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

Question 25

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 26

EVPI equals the expected regret associated with the minimax decision.

Question 27

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

Question 28

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 29

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 30

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?
Home Sales Number of Months
0 1
1 2
2 1
3 2
4 1
5 3
6 2

Question 31

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(I_{1SYMBOL 189 \f "Symbol"}80,000)= .1;P(I_{1SYMBOL 189 \f "Symbol"}100,000)= .2;P(I_{1SYMBOL 189 \f "Symbol"}120,000)= .6;P(I_{1SYMBOL 189 \f "Symbol"}140,000)= .3.Should Dollar purchase the forecast?

Question 32

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 33

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?

Question 34

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 35

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 36

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 37

EVPI is always greater than or equal to EVSI.

Question 38

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(I_{1SYMBOL 189 \f "Symbol"}s₁)= .7 and P(I_{1SYMBOL 189 \f "Symbol"}s₂)= .4.New World Marketing has indicators J₁ and J₂ for which P(J_{1SYMBOL 189 \f "Symbol"}s₁)= .6 and P(J_{1SYMBOL 189 \f "Symbol"}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 39

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 40

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

Question 41

Dollar Department Stores has received an offer from Harris Diamonds to purchase Dollar's 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(I_{1SYMBOL 189 \f "Symbol"}80,000)= .1;P(I_{1SYMBOL 189 \f "Symbol"}100,000)= .2;P(I_{1SYMBOL 189 \f "Symbol"}120,000)= .6;P(I_{1SYMBOL 189 \f "Symbol"}140,000)= .3.Should Dollar purchase the forecast?

Question 42

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

Question 43

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

Question 44

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 45

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 46

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?
Topic: Sensitivity analysis

Question 47

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 48

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.