Deck 4: Decision Analysis

Question 1

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

Answer 1

D

Question 2

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

Answer 2

A

Question 3

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

Answer 3

D

Question 4

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 5

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 6

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 7

The efficiency of sample information is

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

Question 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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

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

Question 19

The approach to determine 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 20

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 21

Pruning a branch of a decision tree occurs at chance events.

Question 22

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

Question 23

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

Question 24

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

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 is always greater than or equal to EVSI.

Question 27

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

Question 28

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

Question 29

Decision alternatives are structured so that several could occur simultaneously.

Question 30

Decision trees are appropriate for multiphase decisions in an environment of certainty.

Question 31

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

Question 32

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

Question 33

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 34

The expected value of an alternative can never be negative.

Question 35

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

Question 36

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 37

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

Question 38

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

Question 39

EVPI equals the expected regret associated with the minimax decision.

Question 40

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 41

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 42

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

Question 43

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 44

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 45

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 46

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 47

Characterize each of the non-probabilistic approaches to decision making (i.e.- minimin,minimax,maximin,and maximax)in terms of it relating to a minimization or maximization problem and whether it is a pessimistic or optimistic approach.

Question 48

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 49

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

Question 50

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

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

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

Question 53

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 54

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

Question 55

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 56

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 57

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:
P(F | D = 0)= .1
P(F | D = 2).3
P(U | D = 0)= .8
P(U | D = 2)= .1
P(F | D = 1)= .2
P(F | D = 3).9
P(U | D = 1)= .3
P(U | D = 3)= .1
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 58

How can a good decision maker "improve" luck?

Question 59

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 60

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 61

A Pacific Northwest lumber company is considering the expansion of one of its mills.The question is whether to do it now,or wait for one year and re-consider.If they expand now,the major factors of importance are the state of the economy and the level of interest rates.The combination of these two factors results in five possible situations.If they do 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 62

A manufacturing company is considering expanding its production capacity to meet a growing demand for its product line of air fresheners.The alternatives are to build a new plant,expand the old plant,or do nothing.The marketing department estimates a 35 percent probability of a market upturn,a 40 percent probability of a stable market,and a 25 percent probability of a market downturn.Georgia Swain,the firm's capital appropriations analyst,estimates the following annual returns for these alternatives:
a. Use a decision tree analysis to analyze these decision alternatives.
b. What should the company do?
c. What returns will accrue to the company if your recommendation is followed?

Question 63

The 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 ten-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: With these estimates,analyze Sunshine's facility decision and:
a. Perform a complete decision tree analysis.
b. Recommend a strategy to Sunshine.
c. Determine what payoffs will result from your recommendation.

Question 64

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.