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
- on the basis of their consequences

- 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:

- 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

- $c(a)$ is not known with certainty, but we know the probability distribution on the set of $X$

- http://answers.mheducation.com/business/economics/business-economics/decisions-under-risk-and-uncertainty
- http://ids355.wikispaces.com/Ch.+5s+Decision+Making - Questions and Answers