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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)
Don’t sign
Sign Contract
Decision
Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-2)(Figure 17-2)
Don’t sign
Sign Contract
Unfavorable Review
Favorable Review
DecisionEvent
Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-3)(Figure 17-3)Don’t sign
Sign Contract
Unfavorable Review
Favorable Review
Hardcover
PaperbackDecisionEvent
Decision
Decision-Tree AnalysisDecision-Tree Analysis(Figure 17-4)(Figure 17-4)Don’t sign
Sign Contract
Unfavorable Review
Favorable Review
Hardcover
Paperback
100,000 copies
1,000,000 copies
50,000 copies
1,500,000 copies
DecisionEvent
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