Deck 25: Decision Analysis

Question 1

Salaries for employees would be considered a state of nature for a business firm.

Answer 1

False

Question 2

A payoff table lists the monetary values for each possible combination of:

A) mean and median.
B) mean and standard deviation.
C) event (state of nature) and act (alternative).
D) None of these choices are correct

Answer 2

C

Question 3

We calculate the expected payoff with perfect information (EPPI) by multiplying the probability of each state of nature by the largest payoff associated with that state of nature, and then summing the products.

Answer 3

True

Question 4

In decision analysis, the alternatives are referred to as events and the states of nature are referred to as acts.

Question 5

Which of the following would be considered a state of nature for a business firm?

A) Inventory levels.
B) Salaries for employees.
C) Site for new plant.
D) Worker safety laws.

Question 6

The expected value of perfect information (EVPI) is always the same as the expected opportunity loss for the best alternative. That is, EVPI = EOL*.

Question 7

The expected value of perfect information (EVPI) is the difference between the expected payoff with perfect information (EPPI) and the expected monetary value (EMV*). That is,
EVPI = EPPI - EMV*.

Question 8

Which of the following statements is correct?

A) The EMV criterion selects the act with the smallest expected monetary value.
B) The EOL criterion selects the act with the smallest expected opportunity loss.
C) The expected value of perfect information (EVPI) equals the largest expected opportunity loss.
D) All these choices are correct.

Question 9

Which of the following best describes the expected value of sample information (EVSI)?

A) EVSI is the expected payoff with perfect information (EPPI) and the expected monetary value for the best decision (EMV*).
B) EVSI is the expected monetary value with additional information (EMV´) and the expected monetary value for the best decision (EMV*).
C) EVSI is the posterior probabilities and the prior probabilities of the states of nature.
D) EVSI is the expected value of perfect information (EVPI) and the smallest expected opportunity loss (EOL*).

Question 10

In most business situations, the choice of the best alternative will be made under conditions of risk and ignorance.

Question 11

Which of the following statements is correct?

A) The expected value of perfect information (EVPI) equals the largest expected monetary value (EMV*).
B) The expected value of perfect information (EVPI) equals the smallest expected opportunity loss (EOL*).
C) The expected value of perfect information (EVPI) equals the expected payoff with perfect information (EPPI).
D) All of these choices are correct.

Question 12

The expected monetary value (EMV) of a decision alternative is the sum of the products of the payoffs and the state-of-nature probabilities.

Question 13

Which of the following would not be considered a state of nature for a business firm?

A) ASIC regulations.
B) OH&S regulations.
C) The number of employees to hire
D) Minimum wage regulations.

Question 14

The expected value of perfect information (EVPI) equals the largest expected opportunity loss (EOL*).

Question 15

In most business situations, the choice of the best alternative will be made under conditions of:

A) ignorance.
B) uncertainty.
C) risk.
D) business cycles.

Question 16

The payoff table is a table in which the rows are states of nature, the columns are decision alternatives, and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.

Question 17

The number of administration staff to employ would be considered a state of nature for a business firm.

Question 18

Which of the following best describes a decision tree?

A) A decision tree is a useful device for calculating probabilities.
B) A decision tree uses branches to represent both acts and states of nature.
C) The payoffs are shown at the end of branches of a decision tree.
D) All of these choices are correct.

Question 19

Which of the following statements is the same as the expected opportunity loss for the best alternative?

A) The expected monetary value for the best alternative.
B) The expected monetary value for the worst alternative.
C) The expected opportunity loss for the worst alternative.
D) The expected value of perfect information.

Question 20

The expected monetary value (EMV) decision is always the same as the expected opportunity loss (EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.

Question 21

We can use the payoff table to calculate the expected monetary value (EMV) and the expected opportunity loss (EOL) of each act (alternative).

Question 22

If EMV( $a _ { 1 }$ ) = $50 000, EMV( $a _ { 2 }$ ) = $65 000, and EMV( $a _ { 3 }$ ) = $45 000, then EMV* = $160 000.

Question 23

The objective of a preposterior analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

Question 24

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV*). That is, EVSI = EMV´ - EMV*.

Question 25

Define the term payoff table.

Question 26

An opportunity loss is the difference between what the decision maker's profit for an act (alternative) is and what the profit could have been had the best decision been made.

Question 27

Define the expected monetary value (EMV) of a decision alternative.

Question 28

Incentive programs for sales staff would be considered a state of nature for a business firm.

Question 29

The expected payoff with perfect information (EPPI) represents the maximum amount a decision maker would be willing to pay for perfect information.

Question 30

Define the expected payoff with perfect information (EPPI).

Question 31

Define expected opportunity loss, EOL.

Question 32

Since the expected monetary value decision is always the same as the expected opportunity loss decision, then EMV*( $a _ { i }$ ) = EOL*( $a _ { i }$ ), for any alternative $a _ { i }$ .

Question 33

If EOL( $a _ { 1 }$ ) = $13 000, EOL( $a _ { 2 }$ ) = $25 000 and EOL( $a _ { 3 }$ ) = $20 000, then EOL* = $25 000.

Question 34

In making decisions, we choose the decision with the smallest expected monetary value, or the largest expected opportunity loss.

Question 35

Opportunity loss is the difference between what the decision maker's payoff for an act is and what the payoff would have been had the best decision been made.

Question 36

In general, the expected monetary values (EMV) do not represent possible payoffs.

Question 37

Define the expected value of perfect information (EVPI).

Question 38

Worker safety laws would be considered a state of nature for a business firm.

Question 39

The prior probabilities determine whether or not sample information should be purchased to revise the posterior probabilities associated with the state of nature.

Question 40

In general, the branches of a decision tree represent stages of events.

Question 41

A payoff table is shown below. The following prior probabilities are assigned to the states of nature:
P( ) = 0.2, P( ) = 0.7, P( ) = 0.1.
a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Question 42

The following table displays the payoffs (in thousands of dollars) for five different decision alternatives under three possible states of nature: The prior probabilities of the states of nature are:
P( ) = 0.2, P( ) = 0.3, P( ) = 0.5
a. Calculate the expected monetary value for each alternative with present information. What decision should be made using the EMV criterion?
b. Calculate the expected payoff with perfect information.
c. Calculate the expected value of perfect information.
d. Convert the payoff table to an opportunity loss table.
e. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?

Question 43

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline80\quad&120\quad&9\quad \\60&130&170\\200&140&100\\\hline\end{array}\end{array}$
Prior Probabilities:
P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1.
Likelihood Probabilities: $\begin{array}{ll}&\quad I_1\quad\quad I_2\quad\quad I_3\\\begin{array}{ll}s_1\\s_2\\s_3\end{array}&\begin{array}{|lll|}\hline0.5\quad&0.3\quad&0.2\quad \\0.2&0.6&0.2\\0.1&0.2&0.7\\\hline\end{array}\end{array}$
A) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ .
B) Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
C) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ .
D) Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
E) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 3 }$ .
F) Use the posterior probabilities from e. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
G) Use your answers to parts a. to f. to calculate the expected monetary value with additional information.
H) Calculate the expected value of sample information.

Question 44

Describe how to use a decision tree.

Question 45

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below.
Payoff Table: Prior Probabilities:
P( ) = 0.4, P( ) = 0.5, P( ) = 0.1.
Likelihood Probabilities: a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Question 46

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: Prior Probabilities:
P( ) = 0.4, P( ) = 0.6.
Likelihood Probabilities: a. Determine the EMV decision.
b. Set up the opportunity loss table.
c. Determine the EOL decision.
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?

Question 47

Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. Assume that the following probabilities are assigned to the three market conditions:
P( ) = 0.2, P( ) = 0.4, P( ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

Question 48

A high-school student who started doing photography as a hobby is considering going into the photography business. The anticipated payoff table is: The following prior probabilities are assigned to the states of nature:
P(poor) = 0.4, P(fair) = 0.4 , P(super) = 0.2.
a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?
d. Review the decisions made in a. and c. Is this a coincidence? Explain.
e. What is the expected payoff with perfect information?
f. What is the expected value of perfect information? What does it mean?

Question 49

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below.
Payoff Table: $\begin{array}{ll}&\text { Alternative }\\\text { State of Nature }&\quad a_1\quad\quad a_2\quad\quad a_3\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|lll|}\hline 0.95 & 0.05&33 \\0.08 & 0.92 &25\\\hline\end{array}\end{array}$
Prior Probabilities:
P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6.
Likelihood Probabilities: $\begin{array}{ll}&\quad I_1\quad\quad I_2\\\begin{array}{ll}s_1\\s_2\end{array}&\begin{array}{|ll|}\hline 0.95 & 0.05 \\0.08 & 0.92 \\\hline\end{array}\end{array}$
A) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ .
B) Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*.
C) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ .
D) Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the $\text { EMV } ^ { * }$ .
E) Use your answers to parts a. to d. to calculate the expected monetary value with additional information.
F) Calculate the expected value of sample information.

Question 50

A company must decide whether or not to change its packaging to a more environmentally safe material. The impact of the decision on profits depends on which of the following three possible scenarios develops in the future.
Scenario 1:
The media do not focus heavily on concerns about packaging, and no new laws requiring changes in packaging are passed. Under this scenario, the company will make $35 million if they change their packaging now, but will make $75 million if they do not change their packaging now.
Scenario 2:
The media focus heavily on concerns about packaging, and no new laws requiring changes in packaging are passed. Under this scenario, the company will make $50 million if they change their packaging now, but will make $55 million if they do not change their packaging now.
Scenario 3:
The media focus heavily on concerns about packaging, and new laws requiring changes in packaging are passed. Under this scenario, the company will make $60 million if they change their packaging now, but will make only $15 million if they do not change their packaging now.
The prior probabilities of the three scenarios are 0.3, 0.5 and 0.2, respectively.
a. Develop a payoff table for this decision situation.
b. What decision will be made to maximise expected payoff?
c. What is the most the company should be willing to pay for a research study designed to reduce its uncertainty about media and legal developments concerning packaging?
d. Set up the opportunity loss table.
e. Which decision has the minimum expected opportunity loss?

Question 51

A payoff table is shown below: The following prior probabilities are assigned to the states of nature:
P( ) = 0.3, P( ) = 0.7.
a. Calculate the expected monetary value for each act with present information. What decision should be made using the EMV criterion?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?
d. What is the expected payoff with perfect information?
e. What is the expected value of perfect information?