# The right decision: for Example, with the rule of the smallest regret

The Savage-Niehans-rule is also referred to as the rule of the smallest regret. First of all, a “Matrix of regret must be installed”. To do this, one first determines for each possible environmental state, the maximum values that would be in the choice of the correct Alternative in the best case possible. This is the maximum result per column (if the state of the Environment 1 entry, then I would have chosen the best Alternative 1, if the environment condition 2 occurs, then I would have chosen the best Alternative 3, etc.). The column maxima are marked in the Matrix in bold.

As a result, the regret matrix by the maximum Column of the result of e_{ij }is removed. For the first column of the calculation way is shown in the other columns, the corresponding results are.

As a “regret matrix” can be described, because the decision-makers to measure what escapes him, if he is not elected upon the occurrence of an environmental condition, the Alternative, which would have been in this case, the best. He has, for example. a_{1 }is selected and then occurs the state of the Environment 4 a, then it achieves only a value of 50. In the choice of a_{2 }he would have but 120 can get. He lamented a “loss” of 70 due to his wrong decision. This could also be called opportunity costs or benefit losses.

Then the line maximum, so the maximum Regret at a Alternative and selects the Alternative in which the Maximum is minimal.

In this case, the decision makers would take Alternative 1, because he missed in the choice of this Alternative, in the most unfavourable case, a lower Benefit due to a wrong decision, as in the case of Alternatives 2 and 3.

Also in this case, not all of the information for the assessment, but again only the maximum values. In addition, the decision-makers, in turn, is very pessimistic, because he makes the worst possible case for the scale of his decision. A decision according to this criterion can be, nevertheless, from the point of view of a Manager’s rational, if it is made for bad decisions responsible. This is a “defensive suggests” Decide.

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The Text comes from the teaching and textbook of Professor Göbel: decisions in companies.