Abstract

ACOSTA-FLORES, José Jesús. Algorithm to analyze decisions with multiple objectives under uncertainty. Ing. invest. y tecnol. [online]. 2019, vol.20, n.1. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2019.20n1.010.

The objective of this article is to present a simple algorithm for the analysis of decisions with multiple objectives and uncertainty where one decision maker and one analyst interact themselves. This algorithm is based on the methodology of Decision Analysis and consists of a set of steps that guide the analyst. In some steps he will have to make calculations and in others to interact with the decision maker. Initially he collects information that permits him to detect the behavior of the decision maker. This type of behavior may be risk aversion, risk prone or risk neutrality. With this information and using uniform probability functions the problem with uncertainty is transformed into one with certainty, but it continues with the same objectives of the original problem. Then the analyst performs a dominance analysis to eliminate the dominated alternatives. If after performing such analysis there were only one alternative, it would be the solution. If there are more than one alternative he interacts with the decision maker to perform even swaps in order to remove a measure of effectiveness. After he has removed it the analyst returns to the dominance analysis. They continue to alternate both analysis, the dominance and the even swaps, until we had only one alternative. One of the limitations of this algorithm is the use of only the uniform probability density function instead of others because they are unknown. Another of its limitations is the existence of a unique decision maker. We can say although the algorithm uses concepts of Decision Theory, its formal development is original. Finally, a hypothetical example was used to determine the best location of an airport to illustrate the use of the algorithm. We can observe in this example that in addition to the technical aspects it is possible to consider also other relevant aspects.

Keywords : Decisions; multiple objectives; uncertainty; utility functions; certainty equivalents; criteria of dominance; compensatory permutes.

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