Deck 20: Decision Analysis

Question 1

Future events which cannot be controlled by the decision maker are called

A)indicators
B)states of nature
C)prior probabilities
D)posterior probabilities

Answer 1

B

Question 2

A decision criterion which weights the payoff for each decision by its probability of occurrence is known as the

A)payoff criterion
B)expected value criterion
C)probability
D)expected value of perfect information

Answer 2

B

Question 3

Exhibit 20-1
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 20-1. The expected value of the best alternative is

A)8.8
B)9.6
C)22.0
D)None of the answers are correct.

Answer 3

D

Question 4

The uncontrollable future events that can affect the outcome of a decision are known as

A)alternatives
B)decision outcome
C)payoff
D)states of nature

Question 5

A line or arc connecting the nodes of a decision tree is called a(n)

A)junction
B)intersection
C)branch
D)node

Question 6

The expected value of information that would tell the decision maker exactly which state of nature is going to occur is

A)the expected value of sample information
B)the expected value of perfect information
C)the maximum information
D)the expected value

Question 7

In computing an expected value (EV), the weights are

A)decision alternative probabilities
B)in pounds or some unit of weight
C)in dollars or some units of currency
D)the state-of-nature probabilities

Question 8

Information about a state of nature is known as

A)natural information
B)states information
C)a sampling method
D)an indicator

Question 9

Prior probabilities are the probabilities of the states of nature

A)after obtaining sample information
B)prior to obtaining of perfect information
C)prior to obtaining sample information
D)after obtaining perfect information

Question 10

Experts in problem solving agree that the first step in solving a complex problem is to

A)decompose it into a series of smaller subproblems
B)acquire the best software available for solving it
C)assign several teams to work on it simultaneously
D)recognize your staff's limitations and hire expert consultants

Question 11

The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based upon given indicator information, is called

A)marginal probability
B)conditional probability
C)posterior probability
D)None of the answers are correct.

Question 12

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)optimal information
B)expected value of sample information
C)expected value of perfect information
D)efficiency of information

Question 13

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

A)junction
B)intersection
C)intersection point
D)node

Question 14

A graphic presentation of the expected gain from the various options open to the decision maker is called

A)a payoff table
B)a decision tree
C)the expected opportunity loss
D)the expected value of perfect information

Question 15

The expected opportunity loss of the best decision alternative is the

A)expected value
B)payoff
C)expected value of perfect information
D)None of the answers are correct.

Question 16

The process of revising prior probabilities to create posterior probabilities based on sample information is a

A)revision process
B)sampling revision
C)Bayesian revision
D)posterior revision

Question 17

A tabular representation of the payoffs for a decision problem is a

A)decision tree
B)payoff table
C)matrix
D)sequential matrix

Question 18

The probabilities of states of nature after revising the prior probabilities based on given indicator information are

A)the expected probabilities
B)the posterior probabilities
C)the prior probabilities
D)None of the answers are correct.

Question 19

For a decision alternative, the weighted average of the payoffs is known as

A)the expected value of perfect information
B)the expected value
C)the expected probability
D)perfect information

Question 20

A tabular presentation of the expected gain from the various options open to a decision maker is called

A)a payoff table
B)a decision tree
C)the expected opportunity loss
D)the expected value of perfect information

Question 21

Exhibit 20-1
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 20-1. The expected value of alternative A is

A)7.4
B)11.6
C)8.8
D)13

Question 22

Exhibit 20-1
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 20-1. The recommended decision alternative based on the expected value is

A)A
B)B
C)C
D)All alternatives are the same.

Question 23

Exhibit 20-5
Below you are given a payoff table involving three states of nature and three decision alternatives. The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 20-5. The recommended decision alternative based on the expected value is

A)A
B)B
C)C
D)All of the answers are correct.

Question 24

Exhibit 20-4
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.3.
Refer to Exhibit 20-4. The recommended decision alternative based on the expected value is

A)A
B)B
C)C
D)All alternatives are the same.

Question 25

The probability of one event given the known outcome of a (possibly) related event is known as

A)unconditional probability
B)joint probability
C)marginal probability
D)conditional probability

Question 26

Exhibit 20-3
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 20-3. The recommended decision based on the expected value criterion is

A)A
B)B
C)C
D)All alternatives are the same.

Question 27

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

A)population information
B)sampling without replacement
C)sample information
D)conditional information

Question 28

Exhibit 20-3
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 20-3. The expected value of the best alternative equals

A)13,000
B)14,000
C)15,000
D)16,000

Question 29

The probability of both sample information and a particular state of nature occurring simultaneously is

A)joint probability
B)unconditional probability
C)marginal probability
D)conditional probability

Question 30

Exhibit 20-4
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.3.
Refer to Exhibit 20-4. The expected value of the best alternative is

A)10.2
B)13.2
C)28.0
D)51.0

Question 31

Exhibit 20-3
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of the occurrence of state of nature S₁ is 0.4.
Refer to Exhibit 20-3. The expected value of perfect information equals

A)13,000
B)14,000
C)15,000
D)16,000

Question 32

Exhibit 20-5
Below you are given a payoff table involving three states of nature and three decision alternatives. The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 20-5. The expected value of perfect information is

A)18.2
B)11.7
C)51
D)37

Question 33

Exhibit 20-5
Below you are given a payoff table involving three states of nature and three decision alternatives. The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 20-5. The expected value of the best alternative is

A)5.0
B)6.5
C)7.5
D)9.0

Question 34

Exhibit 20-2
Below you are given a payoff table involving three states of nature and two decision alternatives. The probability that S₁ will occur is 0.1; the probability that S₂ will occur is 0.6; and the probability that S₃ will occur is 0.3.
Refer to Exhibit 20-2. The expected value of perfect information equals

A)12
B)4
C)37
D)29

Question 35

Exhibit 20-1
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.2.
Refer to Exhibit 20-1. The expected value of perfect information is

A)6.2
B)2.0
C)13.6
D)4.8

Question 36

Exhibit 20-4
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.3.
Refer to Exhibit 20-4. The expected value of alternative C is

A)10.2
B)13.2
C)12.9
D)26

Question 37

Exhibit 20-4
Below you are given a payoff table involving two states of nature and three decision alternatives. The probability of occurrence of S₁ = 0.3.
Refer to Exhibit 20-4. The expected value of perfect information is

A)1.5
B)1.2
C)1.0
D)4.8

Question 38

Exhibit 20-2
Below you are given a payoff table involving three states of nature and two decision alternatives. The probability that S₁ will occur is 0.1; the probability that S₂ will occur is 0.6; and the probability that S₃ will occur is 0.3.
Refer to Exhibit 20-2. The recommended decision based on the expected value criterion is

A)A
B)B
C)Both alternatives are the same.
D)None of the answers are correct.

Question 39

Exhibit 20-5
Below you are given a payoff table involving three states of nature and three decision alternatives. The probability of occurrence of S₁ is 0.2 and the probability of occurrence of S₂ is 0.3.
Refer to Exhibit 20-5. The expected value of alternative C is

A)30
B)6.5
C)5.7
D)5.5

Question 40

Exhibit 20-2
Below you are given a payoff table involving three states of nature and two decision alternatives. The probability that S₁ will occur is 0.1; the probability that S₂ will occur is 0.6; and the probability that S₃ will occur is 0.3.
Refer to Exhibit 20-2. The expected value of the best alternative equals

A)29
B)105
C)12
D)38.5

Question 41

Assume you are faced with the following decision alternatives and two states of nature. The payoff table is shown below. Assume the states of nature have the following probabilities: P(S₁) = 0.4, P(S₂) = 0.6
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value of perfect information.

Question 42

Nodes indicating points where an uncertain event will occur are known as

A)decision nodes
B)chance nodes
C)marginal nodes
D)conditional nodes

Question 43

The result obtained when a decision alternative is chosen and a chance event occurs is known as

A)happenstance
B)consequence
C)alternative probability
D)conditional probability

Question 44

Assume you are faced with the following decision alternatives and two states of nature. The probability of the occurrence of state of nature 1 is 0.35. The payoff table is shown below:
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 45

The owner of a new gourmet kitchenware shop wishes to determine how many days and evenings to keep the shop open. The various payoffs (in $ 1,000s) are indicated in the table below. Assume the probabilities of the three states of nature are P(S₁) = 0.60, P(S₂) = 0.30, and P(S₃) = 0.1.
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 46

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 47

You are given the following payoff table: Assume the following probability information is given:
a.Find the values of P(I₁) and P(I₂).
b.What are the values of P(S₁ | I₁), P(S₂ | I₁), P(S₁ | I₂), and P(S₂ | I₂)?
c.Use the decision tree approach and determine the optimal decision strategy. What is the expected value of the solution?
d.Determine the expected value of sample information.

Question 48

A group of investors wants to open up a jewelry store in a new shopping center. The investors are trying to decide whether to stock the store with inexpensive jewelry, medium-priced jewelry, or expensive jewelry. The probability of their choice depends upon the economic conditions. The payoff table below gives the anticipated profits for different states of the economy. The probability of prosperity is 0.5.
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 49

The Video Game Supply Company (VGS) is deciding whether to set production next year at 2,000, 2,500, or 3,000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed:
a.Determine the expected value of each alternative and indicate what should be the production target.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 50

An investor has a choice between four investments. The profitability of the investments depends upon the market. The payoff table is given below for different market conditions.
a.A market economist has stated that there is a 25% chance that the market will stay the same, a 35% chance that the market will decrease, and a 40% chance that the market will increase. Compute the expected value for each investment. Which investment is the best?
b.Compute the expected value of perfect information.

Question 51

A fashion designer wants to produce a new line of clothes. In the production of the clothes, expensive, medium-priced, or inexpensive materials can be used. The profit associated with each type of material depends upon economic conditions next year. Below you are given the payoff table. An economist believes that the probability that the economy will improve is 20%, the probability that the economy will stay the same is 70%, and the probability that the economy will get worse is 10%.
a.Compute the expected value for each investment. Which investment is the best?
b.Compute the expected value of perfect information.

Question 52

When working backward through a decision tree, the analyst should

A)compute the expected value at each chance node
B)select the best chance branch at each chance node
C)select the best chance branch at each decision node
D)compute the expected value at each decision node

Question 53

Below you are given a payoff table involving two states of nature and two decision alternatives. The probability of the occurrence of S₁ is 0.3.
a.Compute the expected value for each decision. Which decision is the best?
b.Compute the expected value of perfect information.

Question 54

You are given the following payoff table: Assume the following probability information is given:
a.Find the values of P(I₁) and P(I₂).
b.Determine the values of P(S₁ | I₁), P(S₂ | I₁), P(S₁ | I₂), and P(S₂ | I₂).
c.Use the decision tree approach and determine the optimal strategy. What is the expected value of your solution?

Question 55

Suppose we are interested in investing in one of three investment opportunities: d₁, d₂, or d₃. The following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible economic conditions-S₁, S₂, and S₃:
Assume the states of nature have the following probabilities of occurrence: P(S₁) = 0.2 P(S₂) = 0.3 P(S₃) = 0.5
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 56

An automobile manufacturer must make an immediate decision on the car size which should account for the majority of the firm's production two years from now. The firm perceives three possible states of nature at that time: S₁, gasoline will be rationed; S₂, gasoline will be readily available at close to current prices; and S₃, gasoline will be readily available, but at much higher prices. The firm has determined the following profit payoff table (in $l,000s).
a.An economist at the auto company has advised the firm that the probabilities of the states of nature are P(S₁) = .2, P(S₂) = .5, and P(S₃) = .3. Find the expected value for the three decisions.
b.Which decision should be chosen under the expected value criterion?
c.Determine the expected value of perfect information.

Question 57

A sequence of decisions and chance outcomes that provide the optimal solution to a decision problem is called

A)a payoff table
B)the expected value approach
C)a decision strategy
D)a contingency plan

Question 58

A posterior probability associated with sample information is of the form

A)P(a state of nature | a sample outcome)
B)P(a sample outcome | a state of nature)
C)P(a decision alternative | a sample outcome)
D)P(a sample outcome | a decision alternative)

Question 59

Suppose we are interested in investing in one of three investment opportunities: d₁, d₂, or d₃. The following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible economic conditions: S_l, S₂, and S₃. The probability of the occurrence of S₁ is 0.1, and the probability of the occurrence of S₂ is 0.3.
a.Determine the expected value of each alternative and indicate which decision alternative is the best.
b.Determine the expected value with perfect information about the states of nature.
c.Determine the expected value of perfect information.

Question 60

Application of Bayes' theorem enables us to compute

A)the prior probability of each state of nature
B)the posterior probability of each sample outcome
C)the conditional probability of the sample outcomes given each state of nature
D)the conditional probability of the states of nature given each sample outcome

Question 61

Assume you have a sum of money available which you would like to invest in one of the two available investment plans: Stocks or bonds. The conditional payoffs of each plan under two possible economic conditions are as follows:
a.If the probability of Economic Condition I occurring is 0.8, where should you invest your money? Use the expected value criterion and show your complete work.
b.Compute the expected value of perfect information (EVPI).
c.What kind of probabilities of Economic Conditions I and II should there be before you would be indifferent between investing in stocks and bonds? (i.e., compute the probabilities for which you will be indifferent between investing in stocks or bonds.)

Question 62

A maintenance department replaces a malfunctioning machine with a standby machine if one is available; otherwise, they repair the broken machine as soon as possible. When a standby machine is available, production down time is greatly reduced. The department has reviewed its historical maintenance records on machine breakdowns and found this pattern for the past four weeks: If a standby machine is not available when a breakdown occurs, the estimated cost is $400 due to lost production time, overtime usage on the other machines, and emergency repair procedures. On the other hand, weekly cost for machines not in use is estimated to be $200 due to storage and special handling expenses. The department manager wants to use a payoff table to determine how many standby machines they should maintain.
a. Construct a table showing the cost associated with each decision alternative (number of computers stocked) and state of nature (number of computers needed) combination.
b. Compute the probability of each state of nature.
c. How many standby computers should be stocked in order to minimize their expected costs?

Question 63

You are given a decision situation with three possible states of nature S₁, S₂, and S₃. The prior probabilities of the three states are 0.20, 0.45, and 0.35. With sample information I, you are provided with the following information.
a.Compute P(I).
b.Compute the revised probabilities of P(S₁|I), P(S₂|I), and P(S₃|I).

Question 64

Consider the following profit payoff table. What should the probabilities of S₁ and S₂ be so that the expected values of the two decision alternatives equal one another?

Question 65

An automobile manufacturer stocks an electric motor unit that is used in many of their production line robots. As this is the major item to fail in a robot, it is important that enough of them are kept in storage. Since these precision motors are very expensive (over $10,000 each) it is also very important not to keep too many on the shelf. Long costs are $200 and short costs are $325 per unit. Data on monthly breakdown experience is as follows:
a. Construct a table showing the cost associated with each decision alternative (number of motors stocked) and state of nature (number of motors needed) combination.
b. Compute the probability of each state of nature.
c. How many standby motors should be stocked in order to minimize their expected costs?

Question 66

Michael, Nancy, & Associates (MNA) produce color printers. The demand for their printers could be light, medium, or high with the following probabilities. The company has three production alternatives for the coming period. The payoffs (in millions of dollars) associated with the three alternatives are shown below.
a.Compute the expected value of the three alternatives. Which alternative would you select, based on the expected values?
b.Compute the expected value with perfect information (i.e., expected value under certainty).
c.Compute the expected value of perfect information (EVPI).

Question 67

Cashman Co. will be leasing a new copier and is considering four plans. The company has determined it will make 12,600, 14,400, 16,200, 18,000, 19,800, or 21,600 copies per month with probabilities of .05, .10, .15, .25, .25, and .20 respectively.
a. Construct a monthly payoff table for Cashman in terms of costs.
b. What is the optimal plan using the expected value approach? (Hint: This is a cost minimization problem.)

Question 68

Shannon Lipscomb & Associates (SLA) are producers of a new brand of personal computers. SLA is considering employing a market research firm to supply indicator information related to the demand for their computers. The information would consist of forecasts of light demand (I₁) or heavy demand (I₂) for SLA's computers. The following conditional probabilities reflect the accuracy of the market research firm's forecasts:
a.Compute the posterior probabilities.
b.What decision should be taken if the market research firm forecasts light demand (I₁)? Heavy demand (I₂)?
c.Calculate the expected value of sample information.
d.Compute the expected value of perfect information.

Question 69

Super Cola is considering the introduction of a root beer drink. The company feels that the probability of the new drink being successful is .6. The payoff table is as follows. Super Cola has a choice of two research firms to obtain information for this new 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. (Be sure to compute probabilities to the third decimal place.)
a.What is the optimal decision if neither research firm is used?
b.Compute the expected value of perfect information (EVPI).
c.Find the EVSIs for Stanton and New World.
d.If both research firms charge $5,000, which firm should be hired?
e.If Stanton charges $10,000 and New World charges $5,000, which firm should Super Cola hire?

Question 70

The following payoff table shows profits for two decision alternatives under three different states of nature. It is known that the probability of the occurrence of state of nature 1 is 0.1.
a.What should the probabilities of states of nature 2 and 3 be so that the expected values of the two decision alternatives equal one another?
b.Determine the expected values.

Question 71

Assume you have a sum of money available that you would like to invest in one of the three available investment plans: stocks, bonds, or money market. The conditional payoffs of each plan under two possible economic conditions are shown below. The probability of the occurrence of economic condition I is 0.28.
a.Compute the expected value of the three investment options. Which investment option would you select, based on the expected values?
b.Compute the expected value with perfect information (i.e., expected value under certainty).
c.Compute the expected value of perfect information (EVPI).