Deck 12: Decision Analysis

Question 1

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

A) maximin
B) maximax
C) minimax
D) minimin

Answer 1

maximin

Question 2

For a minimization problem, the conservative approach often is referred to as the _____ approach.

A) maximin
B) minimax
C) minimin
D) maximax

Answer 2

minimax

Question 3

Which of the following is true of decision trees when used to solve a complex problem?

A) They provide a useful way to decompose the problem.
B) They are used to compute a decision maker's risk tolerance.
C) They can be converted into truth tables.
D) They can be used only when the decision maker is risk neutral.

Answer 3

They provide a useful way to decompose the problem.

Question 4

A measure of the outcome of a decision such as profit, cost, or time is known as a _____.

A) branch
B) payoff
C) regret
D) forecasting index

Question 5

An intersection or junction point of a decision tree is called a(n) _____.

A) node
B) stem
C) intercept
D) branch

Question 6

Choosing a decision alternative that maximizes the minimum profit is a feature of the _____ approach.

A) expected value
B) optimistic
C) conservative
D) maximin regret

Question 7

The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature is known as _____.

A) best payoff
B) opportunity loss
C) risk profile
D) utility

Question 8

For a minimization problem, the optimistic approach often is referred to as the _____ approach.

A) maximin
B) minimax
C) minimin
D) maximax

Question 9

Lines showing the alternatives from decision nodes and the outcomes from chance nodes are called _____.

A) weights
B) payoffs
C) diagonals
D) branches

Question 10

Chance nodes are

A) nodes provided at the end of the states-of-nature branches.
B) nodes indicating points where an uncertain event will occur.
C) nodes provided at the end of the decision alternative branches where a payoff is shown.
D) nodes indicating points where a decision is made.

Question 11

_____ refer to graphical representations of the decision problems that show the sequential nature of the decision-making process.

A) Influence diagrams
B) Utility functions
C) Decision trees
D) Payoff tables

Question 12

Reference - 12.1: Use the payoff table given below for a maximization problem to answer questions 18-19.

Reference - 12.1: Which is the recommended decision alternative using the conservative approach?

A) D1
B) D5
C) D2
D) D3

Question 13

The states of nature are defined so that they are _____. This means that at least one state of nature must occur at a given time for a chance event.

A) collectively exhaustive
B) mutually exclusive
C) certain events
D) optimistic outcomes

Question 14

A(n) _____ refers to the result obtained when a decision alternative is chosen and a chance event occurs.

A) payoff table
B) outcome
C) state of nature
D) node

Question 15

No more than one state of nature can occur at a given time for a chance event. This indicates that the states of nature are defined such that they are _____.

A) collectively exhaustive
B) mutually exclusive
C) independent outcomes
D) conservative events

Question 16

For a maximization problem, the optimistic approach often is referred to as the _____ approach.

A) minimin
B) maximin
C) minimax
D) maximax

Question 17

The _____ approach evaluates each decision alternative in terms of the best payoff that can occur.

A) conservative
B) optimistic
C) maximin regret
D) expected value

Question 18

Reference - 12.1: Use the payoff table given below for a maximization problem to answer questions 18-19.

Reference - 12.1: Which is the recommended decision alternative using the optimistic approach?

A) D1
B) D4
C) D2
D) D5

Question 19

_____ are possible outcomes for chance events that affect the consequences associated with a decision alternative.

A) Payoffs
B) Forecasts
C) Decision trees
D) States of nature

Question 20

An uncertain future event affecting the consequence associated with a decision is known as a _____.

A) chance event
B) decision alternative
C) decision node
D) payoff

Question 21

For a particular maximization problem, the payoff for best decision alternative is $15.7 million while the payoff for one of the other alternatives is $12.9 million. The regret associated with the alternate decision would be

A) $28.6 million.
B) $15.7 million.
C) $0.129 million.
D) $2.8 million.

Question 22

_____ is the study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.

A) Risk analysis
B) Cost analysis
C) Certainty analysis
D) Optimization

Question 23

Which of the following tools is used to create decision trees in Excel?

A) MegaStat
B) Analytic Solver Platform
C) Arena
D) Data Analysis

Question 24

_____ refers to the probability of one event, given the known outcome of a (possibly) related event.

A) Joint probability
B) A priori probability
C) Decisive probability
D) Conditional probability

Question 25

The utility function for money is a curve that depicts the relationship between

A) decision alternative and utility.
B) branch probabilities and utility.
C) regret and utility.
D) monetary value and utility.

Question 26

The parameter R in an exponential utility function represents

A) the decision maker's risk tolerance.
B) the utility function's error tolerance.
C) the posterior probability.
D) the likely profit/loss from the investment.

Question 27

The weighted average of the payoffs for a chance node is known as the_____.

A) median value
B) variance of the node
C) risk measure
D) expected value

Question 28

The study of how changes in the probability assessments for the states of nature or changes in the payoffs affect the recommended decision alternative is known as _____.

A) uncertainty analysis
B) cost analysis
C) sensitivity analysis
D) probability analysis

Question 29

The minimax regret approach is

A) purely optimistic.
B) purely conservative.
C) both purely optimistic and purely conservative.
D) neither purely optimistic nor purely conservative.

Question 30

_____ refer to the probabilities of the states of nature after revising the prior probabilities based on sample information.

A) Preliminary probabilities
B) Perfect probabilities
C) Joint probabilities
D) Posterior probabilities

Question 31

The probabilities of both sample information and a particular state of nature occurring simultaneously are termed as _____.

A) joint probabilities
B) probable probabilities
C) preliminary probabilities
D) posterior probabilities

Question 32

Reference - 12.2: Use the data below and Bayes' theorem to answer questions 34-35.

Reference - 12.2: What would be the joint probabilities, P(U ∩ Sj)?

A) 0.83, 0.12, and 0.05
B) 0.49, 0.07, and 0.03
C) 0.47, 0.49, and 0.04
D) 1.00, 0.59, and 1.00

Question 33

A _____ is a decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.

A) risk taker
B) risk-neutral
C) risk avoider
D) risk-creator

Question 34

Exponential utility functions indicate that the decision maker is _____.

A) risk monitor
B) risk averse
C) risk neutral
D) risk taker

Question 35

_____ is a measure of the total worth of a consequence reflecting a decision maker's attitude toward considerations such as profit, loss, and risk.

A) Cost-to-company
B) Utility
C) Decision value
D) Regret

Question 36

What would be the value added by a market analysis undertaken, if the expected value with sample information is $8.56 million and the expected value without sample information is $6.39 million?

A) $8.56 million
B) $6.39 million
C) $2.17 million
D) $14.95 million

Question 37

Reference - 12.2: Use the data below and Bayes' theorem to answer questions 34-35.

Reference - 12.2: Which of the following would be the posterior probabilities, P(Sj|U)?

A) 0.83, 0.12, and 0.05
B) 0.49, 0.07, and 0.03
C) 0.47, 0.49, and 0.04
D) 1.00, 0.59, and 1.00

Question 38

A special case of sample information where the information tells the decision maker exactly which state of nature is going to occur is known as_____ information.

A) perfect
B) mutual
C) conditional
D) prior

Question 39

Bayes' theorem

A) can be used only for cases where conditional probabilities are unknown.
B) cannot be used to calculate posterior probabilities.
C) enables the use of sample information to revise prior probabilities.
D) is useful for determining optimal decisions without requiring knowledge of probabilities of the states of nature.

Question 40

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as _____.

A) joint probability
B) sample information
C) conditional probability
D) expected utility

Question 41

Translate the following monetary payoffs into utilities for a decision maker whose utility function is described by an exponential function with R = 6450: -$3000, -$1500, $0, $1500, $3000, $4500, $6000, $7500, $9000.

Question 42

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars):

The indifference probabilities are as follows:
a. Plot the utility function for money for each decision maker.
b. Classify each decision maker as a risk avoider, a risk taker, or risk neutral.
c. For the payoff of 40, what is the premium that the risk avoider will pay to avoid risk? What is the premium that the risk taker will pay to have the opportunity of the high payoff?

Question 43

Harold has visited a casino and paid an entry fee of $20,000 to play the game of cards. Below is the payoff table in terms of the decision to play or not to play the game (Note: Harold will not pay the entry fee if he does not want to play and the below payoff table includes the entry fee):
a. In his previous visits, Harold has won 1 out of every 5 games that he has played. Use the expected value approach to recommend a decision.
b. Assume that the utilities for 50,000 and -20,000 are 10 and 0, respectively. If a particular decision maker assigns an indifference probability of 0.0001 to the $0 payoff, would Harold play the game? Use expected utility to justify your answer.

Question 44

The following table provides information about the profit payoff of an investment strategy.
a. What is the optimal decision strategy if perfect information were available?
b. What is the expected value for the decision strategy developed in part a?
c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?
d. What is the expected value of perfect information?

Question 45

Emil Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Emil a 24-month lease with no down payment due at the time of signing. Each lease includes a monthly cost, mileage allowances, and the cost for additional miles and the details are given in the below table.

Emil decided to choose the lease option that will minimize his total 24-month cost. Emil is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Emil wants to evaluate options of driving 20,000 miles per year, 23,000 miles per year, and 25,000 miles per year. a. What is the decision, and what is the chance event?
b. Construct a payoff table for Emil's problem.

Question 46

Consider an advertising company which has to decide on investing with the current team that has a 50 percent chance of earning a net profit of $35,000 and a 50 percent chance of losing $17,500 invested. a. Write the equation for the exponential function that approximates the advertising company's utility function.
b. Plot the exponential utility function for this advertising company for x values between -30,000 and 45,000. Is the management for the advertising company risk seeking, risk neutral, or risk averse?
c. Suppose the management would like to invest more on marketing and actually be willing to make an investment that has a 50 percent chance of earning $50,000 and a 50 percent chance of losing $25,000. Plot the exponential function that approximates this utility function and compare it to the utility function from part b. Is the management becoming more risk seeking or more risk averse?

Question 47

The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River Basin. The mining company is considering two payment-plan options to buy the mines:
I. 100% Payment
II. Installment-Payment
The payoff received will be based on the quality of coal obtained from the mines which has been categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in million dollars resulting from the various combinations of options and quality are provided below:
a. Suppose that management believes that the probability of obtaining High Quality coal is 0.55, probability of Normal Quality Coal is 0.35, and probability of Poor Quality Coal is 0.1. Use the expected value approach to determine an optimal decision.
b. Suppose that management believes that the probability of High Quality coal is 0.25, probability of Normal Quality Coal is 0.4, and probability of Poor Quality Coal is 0.35. What is the optimal decision using the expected value approach?

Question 48

A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return of investment from the mall. The profit payoff table for management (in millions of dollars) after 5 years is provided below.

The probabilities are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25. a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether the construction company should attempt to obtain a better estimate of the response.

Question 49

Meega airlines decided to offer direct service from Akron to Clearwater beach, Florida. Management must decide between full-price service using a company's new fleet of jet aircraft and a discount-service using smaller capacity commuter planes. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service on Clearwater beach: high, moderate, and low. The following table shows the estimated quarterly profits (in thousands of dollars):

The probabilities for the demand is P(High) = 0.3, P(Medium) = 0.5, and P(Low) = 0.2, respectively. a. What is the optimal decision strategy if perfect information were available?
b. What is the expected value for the decision strategy developed in part a?
c. Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?
d. What is the expected value of perfect information?

Question 50

Visual Park is considering marketing one of its two television models for coming Christmas season: Model A or Model B. Model A is a unique featured television and appears to have no competition. Estimated profits (in thousand dollars) under high, medium, and low demand are given below:

Visual Park is optimistic about the TV Model B. However, the concern is that profitability will be affected if a competitor launches a TV model which has similar features as Model B. Estimated profits (in thousand dollars) with and without competition is as follows:

a. Develop a decision tree for the Visual Park problem.
b. For planning purposes, Visual Park believes there is a 0.7 probability that its competitor will launch a TV model similar to Model B. Given this probability of competition, the director of planning recommends marketing the Model A. Using expected value, what is your recommended decision?
c. Show a risk profile for your recommended decision.
d. Use sensitivity analysis to determine the probability of competition for Model B would have to be for you to change your recommended decision alternative.

Question 51

Consider a decision situation with four possible states of nature: s1, s2, s3, and s4. The prior probabilities are P(s1) = 0.35, P(s2) = 0.15, P(s3) = 0.20, P(s4) = 0.30. The conditional probabilities are P(C|s1) = 0.2, P(C|s2) = 0.09, P(C|s3) = 0.15, and P(C|s4) = 0.20. Find the revised (posterior) probabilities P(s1|C), P(s2|C), P(s3|C), and P(s4|C).

Question 52

The following payoff table shows the profit for a decision problem with three states of nature and three decision alternatives:
a. Suppose P(s1) = 0.1, P(S2) = 0.3, and P(S3) = 0.6. What is the best decision using the expected value approach?
b. Suppose that the probability of sate of nature, s1, s2, and s3 changes to 0.4, 0.2, and 0.4, respectively. What is the best decision using the expected value approach in this case?

Question 53

A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low. The level of response and the size of the mall will decide the return of investment from the mall. The profit payoff table for management (in millions of dollars) after 5 years is provided below.

The probabilities for the state of nature are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25. a. A test market study of the potential response for the mall in that area is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|High) = 0.35; P(U|High) = 0.65
P(F|Moderate) = 0.45; P(U|Moderate) = 0.55
P(F|Low) = 0.20; P(U|Low) = 0.80
What is the probability that the market research report will be favorable?
b. Show the decision tree for this problem.

Question 54

Emil Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Emil 24-month lease with no down payment due at the time of signing. Each lease includes a monthly cost, mileage allowances, and the cost for additional miles and the details are given in the below table.

Emil decided to choose the lease option that will minimize his total 24-month cost. Emil is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Emil wants to evaluate options of driving 20,000 miles per year, 23,000 miles per year, and 25,000 miles per year. a. Construct a decision tree based on the payoff table constructed in the previous problem.
b. Recommend a decision based on the use of optimistic, conservative, and minimax regret approaches?

Question 55

A Manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars.

The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30.
A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2
P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5
Use Bayes' theorem to compute the conditional probability of the demand being up, stable, or down, given each market research outcome.

Question 56

Meega airlines decided to offer direct service from Akron to Clearwater beach, Florida. Management must decide between full-price service using a company's new fleet of jet aircraft and a discount-service using smaller capacity commuter planes. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service on Clearwater beach: high, moderate, and low. The following table shows the estimated quarterly profits (in thousands of dollars):

a. If the demand probabilities are 0.3, 0.5, and 0.2, what is the best decision using the expected value approach?
b. Construct a risk profile for the optimal decision in part a. What is the probability of the profit exceeding $700,000?

Question 57

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars):

The indifference probabilities are as follows:

If P(s₁) = 0.30, P(s₂) = 0.55, and P(s₃) = 0.15, find a recommended decision for each of the three decision makers.

Question 58

The Golden Jill Mining Company is interested in procuring 10,000 acres of coal mines in Powder River Basin. The mining company is considering two payment-plan options to buy the mines:
I. 100% Payment
II. Installment-Payment
The payoff received will be based on the quality of coal obtained from the mines which has been categorized as High, Normal, and Poor Quality as well as the payment plan. The profit payoff in million dollars resulting from the various combinations of options and quality are provided below:
a. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event?
b. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Question 59

Greentrop Pharmaceutical Products are the world leader in the area of sleep aids. Its major product is "Dozealot". The Research-and-Development Division has defined two alternatives to improve the quality of the product, which are simple reformulations of the product to minimize the side effects and to improve the product efficacy. To conduct an analysis, management has decided to consider the possible demands for the drug under each alternative. The following payoff table shows the projected profit in millions of dollars.
a. Construct a decision tree for this problem.
b. If the decision maker knows nothing about the probabilities of three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Question 60

A manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars.

The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30. a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether the manufacturing company should attempt to obtain a better estimate of the response.