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Chapter 3 Decision Analysis

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Page 1: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Chapter 3

Decision Analysis

Page 2: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision Theory

• Decision theory is the analytic and systematic approach for making the best decision.

Page 3: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Features of Decision Making

• Decision making is for __________.a. past b. future c. both past and future

• A decision is about a (an) _________.a. status b. action c. condition

• The process of making decision is a process of __________.a.producing b. manufacturing c. creating

d. cooking e. selecting f. fabricating

Page 4: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Components in Decision Making (1 of 2)

• Alternatives of a decision– A list of choices, one of which will be selected

as the decision by the decision maker.

• States of Nature– Possible conditions that may actually occur

in the future, which will affect the outcome of your decision but are beyond your control.

Page 5: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Components in Decision Making (2 of 2)

• Payoffs– a payoff is the outcome of a decision

alternative under a state of nature. The larger the payoff the better.

• The decision alternatives, states of nature and payoffs are organized in a decision table.

Page 6: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision Table for the Thompson Lumber Example

Decision Alternatives

States of Nature

Favorable Market

Unfavorable Market

Build a large plant $200,000 -$180,000

Build a small plant $100,000 -$20,000

Doing nothing $0 $0

Page 7: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Types of Decision Making• Decision making under certainty

– The outcome of a decision alternative is known (i.e., there is only one state of nature.)

• Decision making under risk– The outcome of a decision alternative is not

known, but its probability is known.

• Decision making under uncertainty– The outcome of a decision alternative is not

known, and even its probability is not known.

Page 8: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision Making under Uncertainty

• The outcome of a decision alternative is not known, and even its probability is not known.

• A few criteria (approaches) are available for the decision makers to select according to their preferences and personalities.

Page 9: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Criterion 1: Maximax (Optimistic)

• Step 1. Pick maximum payoff of each alternative.

• Step 2. Pick maximum of those maximums in Step 1; its corresponding alternative is the decision.

• “Best of bests”.

Page 10: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Maximax Decision for Thompson Lumber

States of Nature Row

Decision Favorable Unfavorable Maximum

Alternatives market market

Large plant 200,000 –180,000 200,000

Small plant 100,000 –20,000 100,000

Do nothing 0 0 0

Max(Row max’s) = Max(200,000, 100,000, 0) = 200,000.

So, the decision is ‘Large plant’.

Page 11: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

For Whom?

• MaxiMax is an approach for:– Risk taker who tends not to give up

attractive opportunities regardless of possible failures, or

– Optimistic decision maker in whose eyes future is bright.

Page 12: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Criterion 2: Maximin (Pessimistic)

• Step 1. Pick minimum payoff of each alternative

• Step 2. Pick the maximum of those minimums in Step 1, its corresponding alternative is the decision

• “Best of worsts”

Page 13: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Maximin Decision for Thompson Lumber

States of Nature Row

Decision Favorable Unfavorable Minimum

Alternatives market market payoffs

Large plant 200,000 –180,000 –180,000

Small plant 100,000 –20,000 –20,000

Do nothing 0 0 0

Max(Row Min’s) = Max(–180,000, –20,000, 0) = 0.

So, the decision is ‘do nothing’.

Page 14: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

For Whom?

• MaxiMin is an approach for:– Risk averter who tends to avoid bad

outcomes despite of some possible attractive outcomes; or

– Pessimistic decision maker in whose eyes future is obscure.

Page 15: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Criterion 3: Hurwicz (Realism)

• Step 1. Calculate Hurwicz value for each alternative

• Step 2. Pick the alternative of largest Hurwicz value as the decision.

Page 16: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Hurwicz Value

• Hurwicz value of an alternative

= (row max)() + (row min)(1-)

where (01) is called coefficient of realism.

Page 17: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision by Hurwicz Valuefor Thompson Lumber

=0.8States of Nature

Decision Favorable Unfavorable Hurwicz Alternatives market market values

Large plant 200,000 –180,000 124,000Small plant 100,000 –20,000 76,000Do nothing 0 0 0

Max(Hurwicz values) = Max(124,000,76,000,0) = 124,000.So, the decision is ‘large plant’.

Page 18: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

For Whom?

• Hurwicz method can be used by decision makers with different preferences on risks. – For a person who tends to take risk, a larger

is used;– For a person who tends to be conservative, a

smaller is used.

• What if = 1?

• What if = 0?

Page 19: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Criterion 4: Equally Likely

• Step 1. Calculate the average payoff for each alternative.

• Step 2. The alternative with highest average if the decision.

Page 20: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision by Equally Likelyfor Thompson Lumber

States of Nature Row Decision Favorable Unfavorable Average Alternatives market market

Large plant 200,000 –180,000 10,000Small plant 100,000 –20,000 40,000Do nothing 0 0 0

Max(Row avg’s) = Max(10,000, 40,000, 0) = 40,000.So, the decision is ‘small plant’.

Page 21: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

For Whom?

• Equally Likely method is for the decision maker who does not have particular preference on taking or avoiding risks.

Page 22: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Criterion 5: Minimax Regret

• Step 1. Construct a ‘regret table’,

• Step 2. Pick maximum regret of each row in regret table,

• Step 3. Pick minimum of those maximums in Step 2, its corresponding alternative is the decision.

Page 23: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Regret

• Regret is amount you give up due to not picking the best alternative in a given state of nature.

• Regret = Opportunity cost = Opportunity loss

Page 24: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Payoff Table for Thompson Lumber and Column Maximums States of Nature

Decision Favorable Unfavorable

Alternatives market market

Large plant $200,000 -$180,000

Small plant $100,000 -$20,000

Doing nothing $0 $0

Column Max$200,000 $0

Page 25: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Regret Table for Thompson Lumber

States of Nature

Decision Favorable Unfavorable

Alternatives market market

Large plant $0 $180,000

Small plant $100,000 $20,000

Doing nothing $200,000 $0

Page 26: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Minimax Regret Decision for Thompson Lumber

Regret TableStates of Nature

Decision Favorable Unfavorable Row Alternatives market market Maximum

Large plant 0 180,000 180,000Small plant 100,000 20,000 100,000Do nothing 200,000 0 200,000

Min(Row max’s) = Min{180,000, 100,000, 200,000} = 100,000.

So, the minimax regret decision is ‘small plant’.

Page 27: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

For Whom?

• MiniMax Regret is an approach for the decision maker who hates the feeling of having regrets.

Page 28: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Decision Making under Risk

• The outcome of a decision alternative is not known, but its probability is known.

Page 29: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Max EMV Approach

• Step 1. Calculate EMV for each alternative.

• Step 2. Pick the alternative with highest EMV as the decision.

Page 30: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EMV – expected monetary value

• EMV of an alternative is the expected value of possible payoffs of that alternative.

• EMV

n=number of states of nature

P(Xi)=probability of the i-th state of nature

Xi=payoff of the alternative under the i-th state of nature

n

iii XPX

1

* )(

Page 31: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Example of Thompson Lumber

States of Nature

Decision Favorable Unfavorable

Alternatives market market EMV

0.5 0.5

Large plant $200,000 -$180,000 10,000

Small plant $100,000 -$20,000 40,000

Doing nothing $0 $0 0

Page 32: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Minimum EOL Approach

Step 1. Generate the opportunity loss table.

Step 2. Calculate the expected value (EOL) for each alternative in the opportunity loss table.

Step 3. Pick up the alternative with the minimum EOL.

Page 33: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Opportunity Loss Table

• Opportunity loss = Regret = Opp. cost

• Opportunity loss table = Regret Table

Page 34: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Payoff Table for the Thompson Lumber Example

Decision Alternatives

States of Nature

Favorable Market

Unfavorable Market

Build a large plant $200,000 -$180,000

Build a small plant $100,000 -$20,000

Doing nothing $0 $0

Page 35: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Opportunity Loss table and EOLfor Thompson Lumber

States of Nature

Decision Favorable Unfavorable

Alternatives market market EOL

0.5 0.5

Large plant $0 $180,000

Small plant $100,000 $20,000

Doing nothing $200,000 $0

Page 36: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Expected Value of Perfect Information (EVPI)

• It is value of additional information for better decision making.

• It is an upper bound on how much to pay for the additional information.

Page 37: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Calculating EVPI

• EVPI = (Exp. payoff with perfect information) –

(Exp. payoff without perfect information)

= EVwPI – EVw/oPI

Page 38: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVw/oPI

• EVw/oPI is the average payoff you expect to get based only on the information given in the decision table without the help of additional information.

• EVw/oPI = Max (EMV)

Page 39: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVw/oPI = Maximum EMV

States of Nature

Decision Favorable Unfavorable

Alternatives market market EMV

0.5 0.5

Large plant $200,000 -$180,000 10,000

Small plant $100,000 -$20,000 40,000

Doing nothing $0 $0 0

Since Max EMV = 40,000,

EVw/oPI = 40,000.

Page 40: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVwPI

• EVwPI is the average payoff you can get if following the perfect information about the state of nature in the future.

• EVwPI

where n=number of states of nature

bi=best payoff of i-th state of nature

Pi=probability of i-th state of nature

n

i

ii Pb1

Page 41: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVwPI for the Example of Thompson

States of Nature

Decision Favorable Unfavorable

Alternatives market market EMV

0.5 0.5

Large plant $200,000 -$180,000 10,000

Small plant $100,000 -$20,000 40,000

Doing nothing $0 $0 0

bi $200,000 $0

EVwPI = 200,000*0.5+0*0.5 = 100,000

Page 42: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVPI for Thompson Lumber

• EVwPI = 200,000*0.5 + 0*0.50 = $100,000

• EVw/oPI = Maximum EMV = $40,000

• EVPI = EVwPI – EVw/oPI

= $100,000 – $40,000

= $60,000

Page 43: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

EVPI is a Benchmark in Purchasing Additional Information

• EVPI is the maximum $ amount the decision maker would pay to purchase the additional information about the states of nature (from a consulting firm, for example).

Page 44: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

What if Information Is Not Perfect?

• In most cases, information about future is not “perfect”. We need to discount EVwPI properly in those cases.

• If you have 80% of confidence on the information, then

Expected Value of Additional Information = EVAI

= EVwPI * 80% - EVw/oPI

Page 45: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Maximum EMV, Minimum EOL, and EVPI

• The decision selected by the Maximum EMV approach is always the same as the decision selected by the Minimum EOL approach. (why?)

• The value of EVPI is equal to the value of minimum EOL. (why?)

Page 46: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

An Example

• You can play the game for many times.• Someone offers you perfect information about “landing” at the price of $65 per time. Do you

take it? If not, how much would you pay?• (See the handout of class work)

Land on ‘Head’ Land on ‘Tail’

Guess ‘Head’ $100 - $60

Guess ‘Tail’ - $80 $150

Page 47: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

In the Tossing Coin Example

• EMV for “guess Head” = $20.

• EMV for “guess Tail” = $35* (Max EMV).

• EOL for “guess Head” = $105

• EOL for “guess Tail” = $90* (Min EOL)

• EVwPI = $125, EVw/oPI=$35

• EVPI = $90

Page 48: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

Maximum average payoff per game

Alt. 1, Guess “Head”

Alt. 2, Guess “Tail”

EMV

EMV

regr

et regr

et

average payoff

average payoff

EO

L EO

LAlternatives

$

125

20

35

Page 49: Chapter 3 Decision Analysis. Decision Theory Decision theory is the analytic and systematic approach for making the best decision

How to Set Up a Decision Table

• A decision table is set up by the decision maker.

• Determine decision alternatives and states of nature.

• Determine the payoffs of each alternative under the states of nature.

• See case “Garden Salad” in class work.