Decision Analysis
Decision Under Certainty
Let
- $A$ be a finite set of alternatives (possible decisions)
- $X$ be a set of consequences (usually some financial metrics)
- $c: A \mapsto X$ a consequence function
- $c(a) \in X$ is a consequence of implementing action $a \in A$
Problem:
- to compare alternatives and find the optimal one
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on the basis of their consequences
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When $ A $ is very large - need Optimization techniques - When $x \in X$ is multi-dimensional, i.e. $x = (x_1, …, x_m)$ need to apply Multi-Objective Optimization and/or MCDA
For these models we make a strong assumption:
- we can quantify the consequences of taking different actions with certainty
However this assumption is not always true
- we often can face situations when consequences $c(a)$ of taking a decision $a$ are not known with certainty
There are two categories of decision analysis tools that help model this:
Decision Under Uncertainty
- we are not able to asses the distribution, but we can list all possible scenarios
Methods
- Max Min Strategy - extreme pessimism
- Max Max Strategy - extreme optimism
- Hurwitz’s Index - between the extreme pessimism and the extreme optimism
- Min Max Regret Strategy - when we want to minimize the regret of a missed opportunity
- Laplace Rule - the principle of insufficient reasoning
Decision Under Risk
- $c(a)$ is not known with certainty, but we know the probability distribution on the set of $X$
Links
- http://answers.mheducation.com/business/economics/business-economics/decisions-under-risk-and-uncertainty
- http://ids355.wikispaces.com/Ch.+5s+Decision+Making - Questions and Answers