Deck 15: Decision Analysis

Question 1

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

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

Answer 1

node.

Question 2

Using the Table below, which is the recommended decision alternative using the conservative approach? $$\begin{array}{l}\text { Payo ff Table }\\\begin{array} { | c | c | c | } \hline \text { Decision Alternative } & \text { State of Nature 1 } & \text { State of Nature 2 } \\\hline \text { D1 } & 5 & 7 \\\hline \text { D2 } & - 4 & 1 \\\hline \text { D3 } & 1 & - 3 \\\hline \text { D4 } & 10 & 2 \\\hline \text { D5 } & 6 & 4 \\\hline\end{array}\end{array}$$

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

Answer 2

D3

Question 3

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

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

Answer 3

minimax

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

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

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

Question 6

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 7

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 8

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

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

Question 9

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 10

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 11

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.

Question 12

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 13

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 14

Using the Table below, which is the recommended decision alternative using the optimistic approach? ? $$\begin{array}{l}\text { Payoff Table }\\\begin{array} { | c | c | c | } \hline \text { Decision Alternative } & \text { State of Nature 1 } & \text { State of Nature 2 } \\\hline \text { D1 } & 5 & 7 \\\hline \text { D2 } & - 4 & 1 \\\hline \text { D3 } & 1 & - 3 \\\hline \text { D4 } & 10 & 2 \\\hline \text { D5 } & 6 & 4 \\\hline\end{array}\end{array}$$

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

Question 15

_____________ 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 16

___________ 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 17

Brit wants to sell throw blankets for the holiday season at a local flea market. Brit purchases the throws for $15, and sells them to his customers for $35. The rental space is fixed fee of $1500 for the season. Assume there is no leftover value for unsold units. The payoff, if he orders 200 and Demand is 150, is

A)800.
B)50.
C)1050.
D)2800.

Question 18

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

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

Question 19

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 20

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

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

Question 21

___________ 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 22

__________ 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 23

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 24

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 25

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 26

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 27

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 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 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 30

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 31

Using the data below, which of the following would be the posterior probabilities, P(S_j|U)? ?
? $$\begin{array} { c c c } & \begin{array} { c } \text { Prior } \\\text { Probabilities }\end{array} & \begin{array} { c } \text { Conditional } \\\text { Probabilities }\end{array} \\\text { States of Nature } ( S j ) & P ( S j ) & P ( U \mid S j ) \\\hline S 1 & 0.65 & 0.75 \\S 2 & 0.20 & 0.35 \\S 3 & 0.15 & 0.20 \\\hline \text { Total } & 1.00 & \\\hline\end{array}$$ ?

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 32

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

A)WhatIf
B)Analytic Solver Platform
C)GoalSeek
D)Data Analysis

Question 33

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 34

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 35

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 36

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 37

_____ 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 38

Using the data below, what would be the joint probabilities, P(UÇS_j)? ? $$\begin{array} { c c c } & \begin{array} { c } \text { Prior } \\\text { Probabilities }\end{array} & \begin{array} { c } \text { Conditional } \\\text { Probabilities }\end{array} \\\text { States of Nature } ( S j ) & P ( S j ) & P ( U \mid S j ) \\\hline S 1 & 0.65 & 0.75 \\S 2 & 0.20 & 0.35 \\S 3 & 0.15 & 0.20 \\\hline \text { Total } & 1.00 & \\\hline\end{array}$$

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 39

__________ 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 40

Exponential utility functions indicate that the decision maker is

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

Question 41

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 42

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

Question 43

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.
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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 44

Jasen Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Jasen 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. Jasen decided to choose the lease option that will minimize his total 24-month cost. He is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Jasen 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 45

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 46

The following table provides information about the profit payoff of an investment strategy.
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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 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:
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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

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 49

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 50

Jasen Hansen is interested in leasing a sports-utility vehicle and has contacted three automobile dealers for pricing information. Each dealer offered Jasen 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. Jasen decided to choose the lease option that will minimize his total 24-month cost. He is not sure how many miles he will drive in the next two years. Hence, for the purpose of decision, assume that Jasen 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 Jasen's problem.

Question 51

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).
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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 52

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 53

Three decision makers have assessed payoffs for the following decision problem (payoff in dollars).
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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 54

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.
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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 55

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. These alternatives 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.
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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 56

A Manufacturing company introduces two product alternatives. The table below provides profit payoffs in thousands of dollars.
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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 57

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

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).
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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.