Deck 13: Decision Analysis

Question 1

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.

Answer 1

D

Question 2

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

Answer 2

B

Question 3

Decision alternatives are structured so that several could occur simultaneously.

Answer 3

False

Question 4

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

Question 5

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 6

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 7

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 8

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

Question 9

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 10

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 11

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

Question 12

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 13

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 14

The efficiency of sample information is

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

Question 15

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

Question 16

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 17

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

Question 18

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 19

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 20

The expected value of an alternative can never be negative.

Question 21

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 22

EVPI $\ge$ EVSI

Question 23

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(I₁ $\mid$ 80,000) = .1; P(I₁ $\mid$ 100,000) = .2; P(I₁ $\mid$ 120,000) = .6; P(I₁ $\mid$ 140,000) = .3.Should Dollar purchase the forecast?

Question 24

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. $$\begin{array} { c c c } \text { Choice/Event } & \text { Event 1 } & \text { Event 2 } \\\hline \text { A } & 0 & 20 \\\text { B } & 4 & 16 \\\text { C } & 8 & 0\end{array}$$

Question 25

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 26

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 27

A payoff table is given as $$\begin{array} { c | r r r } & & { \text { State of Nature } } \\\text { Decision } & \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\\hline d_{1} & 250 & 750 & 500 \\d_{2} & 300 & -250 & 1200 \\d_{3} & 500 & 500 & 600\end{array}$$
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 28

EVPI equals the expected regret associated with the minimax decision.

Question 29

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. $$\begin{array} { c | r r } && { \text { State of Nature } } \\\text { Decision } & s _ { 1 } & s _ { 2 } \\\hline d _ { 1 } & 8 & 10 \\d _ { 2 } & 4 & 16 \\d _ { 3 } & 10 & 0\end{array}$$

Question 30

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

Question 31

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

Question 32

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 33

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

Question 34

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 35

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

Question 36

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 37

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 38

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

Question 39

How can a good decision maker "improve" luck?

Question 40

A payoff table is given as $$\begin{array} { c | r r r } & & { \text { State of Nature } } \\\text { Decision } & \mathrm { s } _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } \\\hline d_{1} & 10 & 8 & 6 \\d_{2} & 14 & 15 & 2 \\d_{3} & 7 & 8 & 9\end{array}$$
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 41

A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs Rank the decision alternatives on the basis of expected value.

Question 42

For the payoff table below, the decision maker will use P(s₁) = .15, P(s₂) = .5, and P(s₃) = .35. What alternative would be chosen according to expected value?