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Statistical
By;Suresh T S
I PG M.Com , 314
DecisionTheory
Monday, April 17, 2023 Operations Research 2
The Decision-Making Process
Problem Decision
Quantitative Analysis
LogicHistorical DataMarketing ResearchScientific AnalysisModeling
Qualitative Analysis
EmotionsIntuitionPersonal Experience and MotivationRumors
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Steps to Good Decision Making
1. Define problem and influencing factors.
2. Establish decision criteria.
3. Select decision-making tool (model).
4. Identify and evaluate alternatives using decision-making tool (model).
5. Select best alternative.
6. Implement decision.
7. Evaluate the outcome.
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Decision Theory
Associated Terms:
Alternative (Acts)Course of action or choice. Decision-maker chooses among alternatives.
State of nature (Events) An occurrence over which
the decision maker has no control.
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1) Decision making under certaintyThe outcome of a decision alternative is known (i.e., there is only one state of nature.)
2) Decision making under riskThe outcome of a decision alternative is not known, but its probability is known.
3) Decision making under uncertaintyThe outcome of a decision alternative is not known, and even its probability is not known.
Types of Decision Making
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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
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Decision Making Under Uncertainty
1. Maximax Criterion
2. Maximin Criterion
3. Minimax Criterion
4. Laplace Criterion (Equally likelihood)
5. Hurwiczalpha Criterion ( Rationality or Realism)
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Criterion 1: Maximax (Optimistic)
An adventurous and aggressive decision maker may choose the act that would result in the maximum payoff possible
Step 1 - Pick maximum payoff of each alternative. Step 2 - Pick maximum of those maximums in Step 1;
its corresponding alternative is the decision. This is viewed as an optimistic approach, “Best of
bests”.
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Criterion 2: Maximin (Pessimistic)
This is also called Waldian criterion. This criterion of decision making stands for choice between alternative courses of action assuming pessimistic view of nature
• 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
This is viewed as a pessimistic approach, “Best of worsts”
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Criterion 3: Hurwicz (Realism)
This method is a combination of Maximin and Maximax criterion. Also known as criterion of rationality.
neither too optimistic nor too pessimistic
• Step 1 - Calculate Hurwicz value for each alternative• Step 2 - Pick the alternative of largest Hurwicz value as the
decision.
Hurwicz value of an alternative
= (row max)() + (row min)(1-)where (01) is called coefficient of realism.
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Criterion 4: Equally Likely
The decision maker makes a simple assumption that each state of nature is equally likely to occur & compute average payoff for each. Choose decision with highest average payoff.
Also known as Laplace criterion
• Step 1 - Calculate the average payoff for each alternative.• Step 2 - The alternative with highest average if the decision.
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Criterion 5: Minimax Regret
Application of the minimax criterion requires a table of losses or table of regret instead of gains.
Regret is amount you give up due to not picking the best alternative in a given state of nature.
Regret = Opportunity cost = Opportunity loss
• 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.
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