chapter 3
DESCRIPTION
Chapter 3. Fundamentals of Decision Theory Models. Decision Theory. Decision theory is the analytic and systematic methodology for making the best decision. Features of Decision Making. Decision making is for __________. a. past b. futurec. both past and future - PowerPoint PPT PresentationTRANSCRIPT
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
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.
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.
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
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.
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.
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”.
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’.
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.
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”
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’.
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.
Criterion 3: Hurwicz (Realism)
• Step 1. Calculate Hurwicz value for each alternative
• Step 2. Pick the alternative of largest Hurwicz value as the decision.
Hurwicz Value
• Hurwicz value of an alternative
= (row max)() + (row min)(1-)
where (01) is called coefficient of realism.
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’.
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?
Criterion 4: Equally Likely
• Step 1. Calculate the average payoff for each alternative.
• Step 2. The alternative with highest average if the 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’.
For Whom?
• Equally Likely method is for the decision maker who does not have particular preference on taking or avoiding risks.
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.
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
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
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
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’.
For Whom?
• MiniMax Regret is an approach for the decision maker who hates the feeling of having regrets.
Decision Making under Risk
• The outcome of a decision alternative is not known, but its probability is known.
Max EMV Approach
• Step 1. Calculate EMV for each alternative.
• Step 2. Pick the alternative with highest EMV as the 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
* )(
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
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.
Opportunity Loss Table
• Opportunity loss = Regret = Opp. cost
• Opportunity loss table = Regret Table
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
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
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.
Calculating EVPI
• EVPI = (Exp. payoff with perfect information) –
(Exp. payoff without perfect information)
= EVwPI – EVw/oPI
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)
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.
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
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
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
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).
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
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?)
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
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
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
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.