# Decision Support Tool

## Ranking between alternatives is a common difficult task.

Since all the available designs cannot be ordered completely, all the Pareto optimal solutions can be regarded as equally desirable in the mathematical sense. Hence, we need decision makers (DMs) to identify the most preferred one among the solutions. The decision maker is a person who can express preference information related to the conflicting objectives.

Ranking between alternatives is a common and difficult task especially when several solutions are available or when many objective or decision makers are involved. The decision makers choose one reasonable alternative from among a limited set of available ones; design decisions usually reflect the competencies of each decision maker. When more than one decision attribute exists, making coherent choices can be a very difficult task.

Multi-Criteria Decision Making (MCDM) refers to the solving of decision problems involving multiple and conflicting goals, coming out with a final solution that represents a good compromise that can be accepted by all the team. modeFRONTIER MCDM allows the user to classify all the available alternatives through pair-wise comparisons on attributes and designs. Moreover, modeFRONTIER helps DMs verifying the coherence of all the relationships. To be coherent, a set of relationships should be both rational and transitive. To be rational means that if the decision maker thinks that the solution A is better than the solution B, then the solution B is worse than the solution A. To be transitive means that if the decision maker says that A is better than B and B is better than C, then the solution A should be always considered better than the solution C.

So, we can say that the Multi Criteria Decision Making tool provided in modeFRONTIER assists the Decision Maker in finding the best solution from among a set of reasonable alternatives. It allows the correct grouping of outputs into single utility function that is coherent with the preferences expressed by the user and it does not have the same drawbacks of a weighted function.

The following algorithms are actually available in modeFRONTIER:

• Linear MCDM that can be used when the number of decision variables is small;
• GA MCDM that does not perform an exact search but is more efficient than the previous method.
• Hurwicz used for the uncertain decision problems. This criterion represents a compromise between the maximax and maximin criteria. The decision maker is neither optimistic nor pessimistic. With this criterion, the decision attributes are weighted by a coefficient that is a measure of the decision maker's optimism. For example, when the Hurwitz weight is equal to zero, the maximax criterion is used. With this criterion, the decision maker selects the design that represents the maximum of the best attribute. On the contrary, when the Hurwitz weight is equal to one, the reverse approach to the maximax criterion is used. The maximin criterion is based on the assumption that the decision maker is pessimistic about the future. With this criterion, the minimum value of the attributes for each designs are compared, and the design that produces the maximum of the minimum value must be chosen;
• Savage MADM used for the uncertain decision problems where both the decision states and their likelihoods are unknown. This algorithm examines the regret (i.e. losses) resulting when the value of the selected alternative is smaller than the optimized value. Then, the minimax criterion suggests that the decision maker should look at the maximum regret of each strategy selecting the one with the smallest value.