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CHAPTER 8Decision Analysis

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LEARNING OBJECTIVES

1. List the steps of the decision-making process and describe the different types of decision-making environments.

2. Make decisions under uncertainty and under risk.

3. Use Excel to set up and solve problems involving decision tables.

4. Develop accurate and useful decision trees.

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LEARNING OBJECTIVES

5. Use TreePlan to set up and analyze decision tree problems with Excel.

6. Understand the importance and use of utility theory in decision making.

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Decision Analysis

• An analytic and systematic approach to the study of decision making• Based on logic

• Considers all possible alternatives

• Examines all available information about the future

• Applies the decision modeling approach

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Five Steps

1. Clearly define the problem2. List all possible alternatives3. Identify all possible outcomes for

each alternative4. Identify the payoff for each alternative

and outcome combination5. Use a decision modeling technique to

choose an alternative

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Thompson Lumber1. Decision: Should he make and sell

storage sheds2. Alternatives:

1. Build a large plant2. Build a small plant3. Do nothing

3. Outcomes: Demand for sheds will be 1. High2. Moderate3. Low

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Thompson Lumber

4. Payoff table

OUTCOMES

HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND

Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0

Table 8.1

5. Select and apply decision analysis model

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Decision-Making Environments

Type 1: Decision making under certainty

Type 2: Decision making under uncertainty

Type 3: Decision making under risk

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Certainty

• Consequence of every alternative is known

• Usually only one outcome for each alternative

• Seldom occurs in reality

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Uncertainty

• Probabilities of possible outcomes not known

• Decision making methods:1. Maximax

2. Maximin

3. Criterion of realism

4. Equally likely

5. Minimax regret

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Thompson Lumber

• Maximax Criterion• Maximizes the maximum payoff

OUTCOMES

HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND

Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0

Table 8.2Maximax

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Thompson Lumber

• Maximin Criterion• Maximizes the minimum payoff

OUTCOMES

HIGH MODERATE LOWALTERNATIVES DEMAND DEMAND DEMAND

Build large plant $200,000 $100,000 –$120,000Build small plant $ 90,000 $ 50,000 –$ 20,000No plant $ 0 $ 0 $ 0

Table 8.3

Maximin

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Thompson Lumber

• Criterion of Realism (Hurwicz)

Table 8.4

Thompson’s coefficient of realism a = 0.45

Realism payoff for alternative

= a x (Maximum payoff for alternative)+ (1 – a) x (Minimum payoff for alternative)

OUTCOMES

HIGH MODERATE LOW WT. AVG. FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE

Build large plant $200,000 $100,000 –$120,000 $24,000Build small plant $ 90,000 $ 50,000 –$ 20,000 $29,500No plant $ 0 $ 0 $ 0 $ 0

Realism

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Thompson Lumber

• Equally Likely (Laplace) Criterion• Highest average payoff

Table 8.5

OUTCOMES

HIGH MODERATE LOW AVERAGE FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE

Build large plant $200,000 $100,000 –$120,000 $60,000Build small plant $ 90,000 $ 50,000 –$ 20,000 $40,000No plant $ 0 $ 0 $ 0 $ 0

Equallylikely

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Thompson Lumber• Minimax Regret Criterion

Table 8.6

OUTCOMES

ALTERNATIVES HIGH DEMAND

Build large plant $200,000 – $200,000 = $ 0Build small plant $200,000 – $ 90,000 = $110,000No plant $200,000 – $ 0 = $200,000

MODERATE DEMAND

Build large plant $100,000 – $100,000 = $ 0Build small plant $100,000 – $ 50,000 = $ 50,000No plant $100,000 – $ 0 = $100,000

LOW DEMAND

Build large plant $0 – (–$120,000) = $120,000Build small plant $0 – (–$ 20,000) = $ 20,000No plant $0 – $ 0 = $ 0

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• Minimax Regret Criterion

Thompson Lumber

Table 8.7

Minimax

OUTCOMES

HIGH MODERATE LOW MAXIMUM FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE

Build large plant $ 0 $ 0 $120,000 $120,000Build small plant $110,000 $ 50,000 $ 20,000 $110,000No plant $200,000 $100,000 $ 0 $200,000

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Using Excel

Screenshot 8-1A

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Using ExcelScreenshot 8-1B

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Under Risk

• Expected Monetary Value (EMV)

EMV (Alternative i) = (Payoff of first outcome)x (Probability of first outcome)+ (Payoff of second outcome)x (Probability of second outcome)+ … + (Payoff of last outcome)x (Probability of last outcome)

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Thompson LumberOUTCOMES

HIGH MODERATE LOW EMV FORALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE

Build large plant $200,000 $100,000 –$120,000 $200,000 x 0.3+ $100,000 x 0.5

+ (–$120,000) x 0.2= $86,000

Build small plant $ 90,000 $ 50,000 –$ 20,000 $90,000 x 0.3+ $50,000 x 0.5

+ (–$20,000) x 0.2= $48,000

No plant $ 0 $ 0 $ 0 $0 x 0.3 + $0 x 0.5+ $0 x 0.2 = $ 0

Probabilities 0.3 0.5 0.2

Table 8.8

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Under Risk

• Expected Opportunity Loss (EOL)

EOL (Alternative i) = (Regret of first outcome)x (Probability of first outcome)+ (Regret of second outcome)x (Probability of second outcome)+ … + (Regret of last outcome)x (Probability of last outcome)

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Thompson Lumber

Table 8.9

OUTCOMESHIGH MODERATE LOW EOL FOR

ALTERNATIVES DEMAND DEMAND DEMAND ALTERNATIVE

Build large plant $ 0 $ 0 $120,000 $0 x 0.3 + $0 x 0.5+ $120,000 x 0.2

= $24,000

Build small plant $110,000 $ 50,000 $ 20,000 $110,000 x 0.3+ $50,000 x 0.5+ $20,000 x 0.2

= $62,000

No plant $200,000 $100,000 $ 0 $200,000 x 0.3+ $100,000 x 0.5

+ $0 x 0.2 = $110,000

Probabilities 0.3 0.5 0.2

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Decision Trees

• Presents decision alternatives and outcomes in a sequential manner

Decision node

Outcome node

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High Demand

Moderate Demand

Low Demand

High Demand

Moderate Demand

Low Demand

All Demands

$200,000

$100,000

–$120,000

Payoffs

$90,000

$50,000

–$20,000

$0

Decision Trees

• Thompson Lumber

1

2

3

Large Plant

Small Plant

No Plant

Decision Node

Outcome Node

Figure 8.1

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Decision Trees

• Thompson Lumber

High Demand (0.30)

Moderate Demand (0.50)

Low Demand (0.20)

High Demand (0.30)

Moderate Demand (0.50)

Low Demand (0.20)

All Demands

$200,000

$100,000

–$120,000

Payoffs

$90,000

$50,000

–$20,000

$0

1

2

3

Large Plant

Small Plant

No Plant

Decision Node

Outcome Node

Figure 8.2

Probability

$86,000

$48,000

$0

1EMV = $200,000 x 0.3 + $100,000 x 0.05 + (–$120,000) x 0.2 = $86,000

2EMV = $90,000 x 0.3 + $50,000 x 0.05 + (–$20,000) x 0.2 = $48,000

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Decision Trees

• Thompson Lumber

Figure 8.3

1

2

3

Large Plant

Small Plant

No Plant

Decision Node

EMV = $86,000

EMV = $48,000

$0

EMV = $0

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Using TreePlan With Excel

Screenshot 8-3A

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Using TreePlan With Excel

Screenshot 8-3B

(a)

(b)

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Using TreePlan With Excel

Screenshot 8-3B

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Using TreePlan With Excel

Screenshot 8-3C

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Using TreePlan With Excel

Screenshot 8-3D

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Utility Theory

• An alternative to EMV

• Incorporates a person’s attitude toward risk

• A utility function converts a person’s attitude toward money and risk into a number between 0 and 1

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Utility Theory

= $100,000 x 0.5 + $0 x 0.5

Figure 8.6

$35,000

$50,000Tails (0.5)

Heads (0.5)

$35,000

Payoffs

$100,000

$0

$50,000

Accept Offer

Reject Offer

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Jane’s Utility Function

Figure 8.7

Certainty Equivalent

EMV = $25,000

$50,000

Outcome 2 (0.5)

Outcome 1 (0.5)

$50,000

?

$0

Alternative

Alternative 2

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Jane’s Utility Function

• Worst payoff utility = 0

• Best payoff utility = 1

• Certainty equivalent – the minimum guaranteed amount you are willing to accept to avoid the risk associated with a gamble

U($15,000) = U($0) x 0.5 + U($50,000) x 0.5 = 0 x 0.5 + 1 x 0.5 = 0.5

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Jane’s Utility Function

• Repeat for multiple amountsUtility Value

1.00 –

0.80 –

0.60 –

0.40 –

0.20 –

0.00 –| | | | | |

$0 $10,000 $20,000 $30,000 $40,000 $50,000 Monetary Value

U ($27,000) = 0.75

U ($50,000) = 1.00

U ($6,000) = 0.25

U ($15,000) = 0.50

U ($50) = 0.00

Figure 8.8

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Jane’s Utility Function

• Risk premium• The EMV a person is willing to give up to

avoid the risk associated with a gamble

Risk premium = (EMV of gamble) – (Certainty equivalent)

• Risk avoider/risk adverse: Risk premium > 0

• Risk indifferent/risk-neutral: Risk premium = 0

• Risk seeker/risk-prone: Risk premium < 0

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Exponential Utility Function

• Risk avoider

U(X) = 1 – e–X/R

Risk In

diffe

rent

Risk Seeker

Risk Avoider

Monetary Outcome

Util

ity

Figure 8.9

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Utility as a Criteria

• Utility replaces monetary values in decision tree

Best Choice

Figure 8.10

EMV = –$4,000

$0

| |$0

Invest

Do Not Invest$0

Big Success (0.2)$40,000

Payoffs

$10,000

–$30,000Failure (0.5)

Moderate Success (0.3)1

2

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Utility as a CriteriaFigure 8.11

U ($40,000) = 1.00

U ($0) = 0.15

U ($10,000) = 0.30

U ($30,000) = 0.00

| | | | | | | |–$30,000 $–20,000 –$10,000 $0 $10,000 $20,000 $30,000 $40,000

Utility Value

1.00 –

0.80 –

0.60 –

0.40 –

0.20 –

0.00 –Monetary Value

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Utility as a Criteria

• Utility replaces monetary values in decision tree

Best Choice

Figure 8.10

0.29

0.15

0.29

| |Invest

Do Not Invest0.15

Big Success (0.2)1.00

Utilities

0.30

0.00Failure (0.5)

Moderate Success (0.3)1

2

Expected Utility