Deck 18: Statistical Tools for Managers

Question 1

Analytic decision making is based on logic and considers all available data and possible alternatives.

Answer 1

True

Question 2

A state of nature is an occurrence of a situation over which the decision maker has little or no control.

Answer 2

True

Question 3

The expected value with perfect information assumes that all states of nature are equally likely.

Answer 3

False

Question 4

The last step of the decision-making process is to

A) develop a model
B) evaluate each alternative
C) pick the best alternative
D) implement the decision
E) check the decision with senior management

Question 5

The expected monetary value of a decision alternative is the sum of all possible payoffs from the alternative, each weighted by the probability of that payoff occurring.

Question 6

The expected value of perfect information is the same as the expected value with perfect information.

Question 7

In a decision tree, the expected monetary values are computed by working from right to left.

Question 8

An example of a conditional value would be the payoff from selecting a particular alternative when a particular state of nature occurs.

Question 9

Which of the following is not considered a step in the decision-making process?

A) Clearly identify the problem.
B) Select the best alternative.
C) Develop objectives.
D) Evaluate alternatives.
E) Minimize costs whenever possible.

Question 10

If a decision maker knows for sure which state of nature will occur, he/she is making a decision under certainty.

Question 11

In a decision tree, a square symbol represents a state of nature node.

Question 12

The last step in the analytic decision process clearly defines the problem and the factors that influence it.

Question 13

The maximax criterion of decision making requires that all decision alternatives have an equal probability of occurrence.

Question 14

If a decision maker has to make a certain decision only once, expected monetary value is a good indication of the payoff associated with the decision.

Question 15

If a decision maker can assign probabilities of occurrences to the states of nature, then the decision-making environment is Decision Making under Uncertainty.

Question 16

An example of expected monetary value would be the payoff from selecting a particular alternative when a particular state of nature occurs.

Question 17

The first step, and a key element, in the decision-making process is to

A) consult a specialist
B) clearly define the problem
C) develop objectives
D) monitor the results
E) select the best alternative

Question 18

A square node on a decision tree infers that

A) the node splits into various states of nature, of which only one will occur
B) there are several alternatives available
C) the manager must choose an alternative
D) both B and C
E) A, B, and C

Question 19

The maximin criterion is pessimistic, while the maximax criterion is optimistic.

Question 20

Decision trees and decision tables can both solve problems requiring a single decision, but decision tables are the preferred method when a sequence of decisions is involved.

Question 21

The likelihood that a decision maker will ever receive a payoff precisely equal to the EMV when making any one decision is

A) low (near 0%)
B) high (near 100%)
C) dependent upon the number of alternatives
D) dependent upon the number of states of nature
E) none of the above

Question 22

The expected value with perfect information

A) equals EVPI - EMV
B) requires that each decision alternative have a known probability of occurrence
C) is an input into the calculation of the expected value of perfect information
D) is the average of the maximax and the maximin
E) none of the above

Question 23

What is the EMV for Option 1 in the following decision table?

A) 15,000
B) 17,000
C) 17,500
D) 18,500
E) 20,000

Question 24

The difference between the expected payoff under perfect information and the maximum expected payoff under risk is

A) expected monetary value
B) economic order quantity
C) expected value of perfect information
D) PERT
E) expected monetary payoff

Question 25

When solving decision trees, what phrase represents the act of dropping an alternative from consideration because it is less favorable than another available option?

A) cut the leaf
B) open the hatch
C) shake the tree
D) punt the ball
E) prune the branch

Question 26

A decision maker who uses the maximin criterion when solving a problem under conditions of uncertainty is

A) an optimist
B) a pessimist
C) an economist
D) an optometrist
E) making a serious mistake; maximin is not appropriate for conditions of uncertainty

Question 27

The outcome of an alternative/state of nature combination is a(n)

A) price
B) conditional value
C) expected value
D) conditional probability
E) All of the above are correct.

Question 28

Expected monetary value is most appropriate for problem solving that takes place

A) when conditions are average
B) when all states of nature are equally likely
C) when all alternatives are equally likely
D) under conditions of uncertainty
E) under conditions of risk

Question 29

The decision criterion that would be used by an optimistic decision maker solving a problem under conditions of uncertainty would be the

A) expected monetary value criterion
B) equally likely criterion
C) maximax criterion
D) maximin criterion
E) minimin criterion

Question 30

A decision-maker using the maximax criterion on the problem below would choose Alternative __________ because the maximum of the row maximums is __________.

A) A; 60
B) B; 80
C) C; 70
D) D; -100
E) D; 140

Question 31

A decision-maker using the maximin criterion on the problem below would choose Alternative __________ because the maximum of the row minimums is __________.

A) A; 55
B) B; 30
C) C; 70
D) D; 140
E) D; 10

Question 32

There are three equally likely states of nature (High, Medium, and Low demand). If the large factory will post profits of $50,000, $25,000, and - $10,000 under these states of nature, respectively, what is the EMV of the factory?

A) $50,000
B) $25,000
C) $28,333.33
D) $21,666.67
E) none of the above

Question 33

Doing nothing would yield how much profit if favorable market conditions prevail according to the following decision table?

A) $5,000
B) $20,000
C) -$10,000
D) $0
E) unable to determine

Question 34

A tabular presentation that shows the outcome for each decision alternative under the various possible states of nature is called a(n)

A) isoquant table
B) payback period matrix
C) payoff table
D) feasible region
E) decision tree

Question 35

The expected value of perfect information (EVPI) is the

A) payoff for a decision made under perfect information
B) payoff under minimum risk
C) average expected payoff
D) difference between the payoff under perfect information and the payoff under risk
E) none of the above

Question 36

The expected value with perfect information is

A) the maximum EMV for a set of alternatives
B) the same as the expected value of perfect information
C) valuable in situations involving risk
D) the average return obtained when the decision maker knows which state of nature is going to occur before the decision is made
E) obtained using conditional probabilities

Question 37

The following decision tree has how many state of nature nodes

A) 0
B) 1
C) 2
D) 3
E) 4

Question 38

In terms of decision theory, an occurrence or situation over which the decision maker has no control is called a(n)

A) decision under uncertainty
B) decision tree
C) state of nature
D) alternative
E) none of the above

Question 39

The highest value for the equally likely criterion is __________; this occurs with alternative __________.

A) $20,000; Option 1
B) $25,000; Option 2
C) $28,000; Option 3
D) $32,000; Option 3
E) $60,000; Option 3

Question 40

A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0. If the two states of nature are equally likely, how much should he pay for perfect information?

A) $0
B) $25,000
C) $50,000
D) $100,000
E) unable to determine

Question 41

A problem that involves a sequence of decisions

A) cannot be analyzed with expected monetary value
B) can be better analyzed with a decision tree than by a decision table
C) must be analyzed in the same order that the decisions are made
D) cannot be analyzed with decision tree software
E) can only be analyzed using decision making under certainty

Question 42

What is the EMV for Option 1 in the following decision table?

A) 10,000
B) 18,000
C) 20,000
D) 22,000
E) 30,000

Question 43

A(n) __________ is a tabular means of analyzing decision alternatives and states of nature.

Question 44

Decision trees

A) give more accurate solutions than decision tables
B) give less accurate solutions than decision tables
C) are especially powerful when a sequence of decisions must be made
D) are rarely used because one needs specialized software to graph them
E) are too complex to be used by decision makers

Question 45

__________ is the expected payout or value of a variable that has different possible states of nature, each with an associated probability.

Question 46

What is the expected value of perfect information of the following decision table?

A) 0
B) 20
C) 50
D) 150
E) 200

Question 47

What is the EMV for Option 2 in the following decision table?

A) 50
B) 100
C) 170
D) 200
E) 350

Question 48

What is the EMV for Option 2 in the following decision table?

A) 5,000
B) 21,000
C) 25,000
D) 29,000
E) 45,000

Question 49

__________ is the criterion for decision making under certainty that assigns equal probability to each state of nature.

Question 50

A retailer is deciding how many of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $8 per unit and sells for $25 per unit. The conditional value for the decision alternative "Stock 3" and state of nature "Sell 1" is

A) 1.4 units
B) $1 profit
C) $25 profit
D) $-8 profit
E) none of the above

Question 51

__________ is the difference between the payoff under perfect information and the payoff under risk.

Question 52

What is the EMV for Option 1 in the following decision table?

A) 200
B) 240
C) 250
D) 260
E) 300

Question 53

A decision tree is a(n)

A) algebraic representation of alternatives and states of nature
B) behavioral representation of alternatives and states of nature
C) matrix representation of alternatives and states of nature
D) graphic representation of alternatives and states of nature
E) tabular representation of alternatives and states of nature

Question 54

All of the following steps are taken to analyze problems with decision trees except

A) define the problem
B) structure or draw a decision tree
C) assign probabilities to the alternatives
D) estimate payoffs for each possible alternative/state of nature combination
E) solve the problem by computing expected monetary values for each state of nature node

Question 55

What is the expected value with perfect information of the following decision table?

A) 5,000
B) 10,000
C) 40,000
D) 60,000
E) 70,000

Question 56

What is the EMV for Option 2 in the following decision table?

A) 10,000
B) 16,000
C) 20,000
D) 24,000
E) 30,000

Question 57

A retailer is deciding how many of a certain product to stock. The historical probability distribution of sales for this product is 0 units, 0.2; 1 unit, 0.3; 2 units, 0.4, and 3 units, 0.1. The product costs $8 per unit and sells for $25 per unit. The largest conditional value (profit) in the entire payoff table for this scenario is

A) $-24 profit
B) $-8 profit
C) $17 profit
D) $51 profit
E) $75 profit

Question 58

__________ is the criterion for decision making under uncertainty that finds an alternative that maximizes the minimum outcome or consequences.

Question 59

A primary advantage of decision trees compared to decision tables is that decision trees

A) are more accurate
B) are faster
C) are smaller
D) are cheaper
E) can be used for sequential problems

Question 60

What is the expected value with perfect information in the following decision table?

A) 50
B) 200
C) 260
D) 300
E) 350

Question 61

In the context of decision-making, define state of nature.

Question 62

A branch of a decision tree that is less favorable than other available options may be __________.

Question 63

What limitation(s) do decision trees overcome compared to decision tables?

Question 64

If a decision maker is a pessimist, what decision-making criterion is appropriate? Why?

Question 65

Identify and describe three methods used for decision making under conditions of uncertainty.

Question 66

The construction manager for Acme Construction, Inc. must decide whether to build single family homes, apartments, or condominiums. This is not a product-mix problem, but an all-or nothing decision. He will hire workers and rent equipment appropriate for one action only. He estimates annual profits (in thousands of dollars) will vary with population trends as follows:
a. If he uses the maximin criterion, which type of dwellings will he choose to build? Show your supporting calculations.
b. If he uses the equally likely criterion, which kind of dwellings will he choose to build? Show your supporting calculations.
c. If the construction manager were an optimist, what criterion would he choose? What would be the choice of dwelling for that criterion? Show your supporting calculations.

Question 67

What are decision tables?

Question 68

An operations manager's staff has compiled the information below for four manufacturing alternatives (E, F, G, and H) that vary by production technology and the capacity of the machinery. All choices enable the same level of total production and have the same lifetime. The four states of nature represent four levels of consumer acceptance of the firm's products. Values in the table are net present value of future profits in millions of dollars. Forecasts indicate that there is a 0.1 probability of acceptance level 1, 0.2 chance of acceptance level 2, 0.4 chance of acceptance level 3, and 0.3 change of acceptance level 4.
Using the criterion of expected monetary value, which production alternative should be chosen?

Question 69

A(n) __________ is an occurrence or situation over which the decision maker has little or no control.

Question 70

What is a conditional value?

Question 71

In the context of decision-making, define alternative.

Question 72

Which technique results in an optimistic decision? Why?

Question 73

Define expected monetary value (EMV).

Question 74

Describe the meaning of EVPI. Provide an example in which EVPI can help a manager.

Question 75

An operations manager's staff has compiled the information below for four manufacturing alternatives (A, B, C, and
D) that vary by production technology and the capacity of the machinery. All choices enable the same level of total production and have the same lifetime. The four states of nature represent four levels of consumer acceptance of the firm's products. Values in the table are net present value of future profits in millions of dollars.

a. Assuming a maximax strategy, which alternative would be chosen?
b. If maximin were used, which would be chosen?
c. If the states of nature were equally likely, which alternative should be chosen?

Question 76

Explain the graphical shapes used in decision tree analysis.

Question 77

Identify, in order, the six steps of analytical decision making.

Question 78

How is the expected value of perfect information (EVPI) found?

Question 79

A(n) __________ is a graphical means of analyzing decision alternatives and states of nature.

Question 80

The square symbol used in drawing a decision trees represents a __________ node.