CD-ROM Chapter 17CD-ROM Chapter 17

Introduction to Introduction to Decision AnalysisDecision Analysis

Chapter 17 - Chapter 17 - Chapter Chapter OutcomesOutcomesAfter studying the material in this chapter, you should be able to:Describe the decision-making environments of certainty and uncertainty.Construct both a payoff table and an opportunity loss table.Define the expected value criterion.Apply the expected value criterion in decision situations.Compute the value of perfect information.

Chapter 17 - Chapter 17 - Chapter Chapter OutcomesOutcomes (continued)(continued)

After studying the material in this chapter, you should be able to:Develop a decision tree and explain how it can aid decision making in an uncertain environment.Discuss the difference between risk seeking and risk avoiding behavior.Construct an individual risk preference function.

Decision-Making Decision-Making EnvironmentsEnvironments

CertaintyCertainty refers to a decision environment in which the results of selecting each alternative are known before the decision is made.

Decision-Making Decision-Making EnvironmentsEnvironments

UncertaintyUncertainty refers to a decision environment in which the decision maker does not know what outcome will occur when an alternative is selected.

Decision-Making Decision-Making EnvironmentsEnvironments

The goal of decision analysis is The goal of decision analysis is to focus on making good to focus on making good decisions, which in the long run decisions, which in the long run should result in an increased should result in an increased number of good outcomes.number of good outcomes.

Decision CriteriaDecision Criteria

The states of naturestates of nature are the possible outcomes in a decision situation over which the decision maker has no control.

Decision CriteriaDecision Criteria

A payoffpayoff is the outcome (profit or loss) for any combination of alternative states of nature. The outcomes of all possible combinations of alternatives and states of nature constitute a payoff tablepayoff table.

Decision CriteriaDecision Criteria(Table 17-2)(Table 17-2)

Fisher Fabrication Payoff Table

DEMAND (STATES OF NATURE)

Alternative S11 Large Increase S22 Moderate Increase S33 Small Increase

A11 Large Investment $6,000,000 $4,000,000 $-2,600,000

A22 Medium Investment 2,500,000 5,000,000 -1,000,000

A33 Small Investment 2,000,000 1,500,000 1,200,000

Decision CriteriaDecision Criteria

The maximax criterionmaximax criterion is an optimistic decision criterion for dealing with uncertainty without using probability. For each option, the decision maker finds the maximum possible payoff and then selects the option with the greatest maximum payoff.

Decision CriteriaDecision Criteria

The maximin criterionmaximin criterion is a pessimistic (conservative) decision criterion for dealing with uncertainty without using probability. For each option, the decision maker finds the minimum possible payoff and then selects the option with the greatest minimum payoff.

Decision CriteriaDecision Criteria

The opportunity lossopportunity loss is the difference between the actual payoff that occurs for a decision and the optimal payoff for the same decision.

Decision CriteriaDecision Criteria

The minimax regret criterionminimax regret criterion is a decision criterion that considers the costs of selecting the “wrong” alternative. For each sate of nature, the decision maker finds the difference between the best payoff and each other alternative and uses these values to construct an opportunity-loss table. The decision maker then selects the alternative with the minimum opportunity loss (or regret).

Decision CriteriaDecision Criteria(Table 17-3)(Table 17-3)

DEMAND (STATES OF NATURE)

Alternative S11 Large Increase S22 Moderate Increase S33 Small Increase

A11 Large Investment $0 $1,000,000 $3,800,000

A22 Medium Investment 3,500,000 0 2,200,000

A33 Small Investment 4,000,000 3,500,000 0

Fisher Fabrication Opportunity-Loss Table

Decision CriteriaDecision Criteria(Table 17-4)(Table 17-4)

Fisher Fabrication Maximum Regret Table

Alternative MAXIMUM OPPORTUNITY LOSS, OR REGRET

A11 Large Investment $3,800,000

A22 Medium Investment 3,500,000 (smallest regret)

A33 Small Investment 4,000,000

Decision CriteriaDecision Criteria

The expected-value criterionexpected-value criterion is a decision criterion that employs probability to select the alternative that will produce the greatest average payoff or minimum average loss.

Decision CriteriaDecision Criteria

EXPECTED VALUEEXPECTED VALUE

where:xi = The ith outcome of the specified

alternative measured in some units, such as dollars P(xi) = The probability of outcome xi occurring k = number of potential outcomes

and:

)()(1

i

k

ii xPxxE

0.1)( ixP

0.1)(0.0 ixP

Decision CriteriaDecision Criteria

CLASSICAL PROBABILITY CLASSICAL PROBABILITY ASSESSMENTASSESSMENT

occurcan outcomeany waysofnumber Total

occurcan x waysofNumber )( xP

Decision CriteriaDecision Criteria

RELATIVE FREQUENCY OF RELATIVE FREQUENCY OF OCCURRENCE PROBABILITYOCCURRENCE PROBABILITY

where:n

xxP

occurs timesof Number)(

sobservanceof Numbern

Decision CriteriaDecision Criteria(Table 17-5)(Table 17-5)

MACHINE A MACHINE B

Repair Cost Probability Repair Cost Probability

$0 0.1 $0 0.2

1,000 0.5 1,000 0.3

5,000 0.3 5,000 0.4

10,000 0.1 10,000 0.1

Decision CriteriaDecision Criteria(Table 17-6)(Table 17-6)

MACHINE A MACHINE B

Repair Cost Probability xP(x) Repair Cost Probability xP(x)

$0 0.1 $0 $0 0.2 $0

1,000 0.5 500 1,000 0.3 300

5,000 0.3 1,500 5,000 0.4 2,000

10,000 0.1 1,000 10,000 0.1 1,000

Expected Repair Cost $3,000 Expected Repair Cost $3,300

Decision-Tree AnalysisDecision-Tree Analysis

A decision treedecision tree is a diagram that illustrates the correct ordering of actions and events in a decision-analysis problem. Each act or event is represented by a node on the decision tree.

Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-1)(Figure 17-1)

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Decision

Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-2)(Figure 17-2)

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DecisionEvent

Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-3)(Figure 17-3)Don’t sign

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PaperbackDecisionEvent

Decision

Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-4)(Figure 17-4)Don’t sign

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Paperback

100,000 copies

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DecisionEvent

Risk Preference AttitudesRisk Preference Attitudes

A risk-neutral attituderisk-neutral attitude refers to the preference for risk under which the alternative with the highest expected payoff or lowest expected cost will be selected.

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-11)(Figure 17-11)

Buy

Don’t Buy

Merger

No Merger

$0

$10

Xircom Stock Purchase Example

(0.5)

(0.5)

-$5

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-12)(Figure 17-12)

Buy

Don’t Buy

Merger

No Merger

$0

$100

Xircom Stock Purchase Example

(0.5)

(0.5)

-$50

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-13)(Figure 17-13)

Buy

Don’t Buy

Merger

No Merger

$0

$10,000

Xircom Stock Purchase Example

(0.5)

(0.5)

-$5,000

Risk Preference AttitudesRisk Preference Attitudes

A risk-averse attituderisk-averse attitude refers to the preference for risk such that the decision maker could select an alternative with a lower expected payoff in order to avoid the possibility of an undesirable outcome.

Risk Preference AttitudesRisk Preference Attitudes

Certainty equivalentCertainty equivalent is the value that would make a decision maker indifferent between taking an uncertain gamble versus receiving that value instead of taking the gamble.

Risk Preference AttitudesRisk Preference Attitudes

A risk-seeking attituderisk-seeking attitude refers to the preference for risk such that the decision maker could select an alternative with a lower expected payoff in hopes of achieving an outcome with a more desirable result.

Risk Preference AttitudesRisk Preference Attitudes

The risk preference functionrisk preference function is the graph that describes a decision maker’s preference for risk over the range of possible payoffs.

Risk Preference AttitudesRisk Preference Attitudes

A standard gamble approachstandard gamble approach is the approach for assessing risk-preference functions that involves setting up a series of 50-50 gambles between two payoffs and determining the certainty equivalent for each gamble.

Risk Preference AttitudesRisk Preference Attitudes

A preference quotientpreference quotient refers to the measure of the relative utility for the outcomes of a decision on a scale between 0.0 and 1.0.

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-16)(Figure 17-16)

Play

Don’t Play

End ValuesEnd Values

CE = ?

$10,000

Assessing the Risk-Preference Function: Standard Gamble 1

0.5

0.5

-$2,000

q Valuesq Values

1.0

0.0

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-17)(Figure 17-17)

Play

Don’t Play

End ValuesEnd Values

CE = ?

$10,000

Assessing the Risk-Preference Function: Standard Gamble 2

0.5

0.5

$4,000

q Valuesq Values

1.0

0.5

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-18)(Figure 17-18)

Play

Don’t Play

End ValuesEnd Values

CE = ?

$4,000

Assessing the Risk-Preference Function: Standard Gamble 3

0.5

0.5

-$2,000

q Valuesq Values

0.5

0.0

Risk Preference AttitudesRisk Preference Attitudes

Risk premiumRisk premium is the difference between the expected value of an event and the certainty equivalent. The risk premium will be zero for a risk-neutral decision maker, positive for a risk-averse decision maker, and negative for a risk-seeking decision maker.

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-19)(Figure 17-19)

$0 $2,000 $4,000$6,000$8,000$10,0000

0.25

0.50

0.75

1

-$2,000

Risk-Neutral Preference Function

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-23)(Figure 17-23)

$0 $2,000 $4,000$6,000$8,000$10,0000

0.25

0.50

0.75

1

-$2,000

Risk-Averse Preference Function

Risk Preference AttitudesRisk Preference Attitudes(Figure 17-26)(Figure 17-26)

$0 $2,000 $4,000$6,000$8,000$10,0000

0.25

0.50

0.75

1

-$2,000

Risk-Seeking Preference Function

Key TermsKey Terms• Certainty• Certainty Equivalent• Decision Tree• Expected Value• Expected-Value

Criterion• Maximax Criterion• Maximin Criterion• Minimax Regret

Criterion

• Opportunity Loss• Payoff• Preference Quotient• Risk-Averse Attitude• Risk-Neutral Attitude• Risk-Preference

Function• Risk Premium• Risk-Seeking

Attitude

Key TermsKey Terms(continued)(continued)

• Standard Gamble Approach

• State of Nature

• Uncertainty