RED ECONÓMICA Redacción: Ángel Aparicio Mourelo.

Once the type of decision process is selected, it is time to choose which methodology under this type to employ.

For DMUSU, Laplace’s principle of insufficient reason, Wald’s Maximin, Savage’s Minimax regret, Hurwicz’s method and Starr’s Domain are introduced and compared. Furthermore, a DMUSU problem is considered a two-player game, and NE is considered a method as well. The theoretical comparison of each method is summarized as follows: Laplace’s principle of insufficient reason transforms a difficult problem into a simple one by assuming that all states of nature are equally alike. The need to construct the state space to be amenable to a uniform probability distribution is a major drawback of this method. Wald’s Maximin is extremely conservative and does not provide a faithful representation of how people operate in reality. It could lead to exceedingly costly results from over- protection against uncertainty. Savage’s Minimax regret method suggests the consequences of one action should be compared with the consequences of other actions under the same state of nature. Accordingly, it only reflects the difference between each payoff and the best possible payoff in a column. Hurwicz’ method takes into account both the best and the worst possible results, weighted according to the decision maker’s attitude (optimistic or pessimistic) towards the decision. This method only considers the highest and the lowest payoff for each alternative. It does not take other non-extreme payoffs into account. Therefore, two decisions with the same minimal and maximal profits always obtain an identical Hurwicz’s measurement, even if one of them results in many small payoffs and the other one has many high payoffs. Starr’s Domain has the disadvantage of complexity of computation when there are more than three states. Since a DMUSU problem can be considered a two-player non-cooperative and non-zero-sum game, NE becomes one of the solution options for solving a DMUSU problem. Pure-strategy NE is where all players are playing pure strategies, and mixed-strategy NE is where at least one player is playing a mixed strategy. All that said, if the DM’s attitude is more conservative, Wald’s and Savage’s methods are correct. Wald’s method uses the payoff matrix. If DMs would like to have a picture of their level of regret after making such a choice, they can use Savage’s Minimax. If DMs would like to use a numerical value to represent their attitude, they can choose Hurwicz’s method. Starr’s Domain method is suitable where there are few states of nature. Laplace’s method is quite intuitive and simple to use. NE is an algorithm from game theory.

For DMUR, the principle of the EMV rule is nearly identical to the EOL rule, except that one is using a payoff matrix, the other is using an opportunity-loss matrix. The most probable state of nature rule takes only one uncertain state of nature into account; it may lead to bad decisions. The expected utility rule is a better choice when dealing with a risky decision problem (e.g., the decision can only be made once or significant amounts of money are involved in the problem), as the expected monetary value criterion cannot encompass the full range of reasoning behind a decision as a human would. Thus, the decision chosen by EMV can be different from the one the decision maker himself would choose. In short, the computation of four decision rules for DMUR is similar. The difference is that each decision rule maximizes or minimizes different objects, i.e., the expected monetary value, the expected opportunity loss, the expected utility. The decision maker needs to choose which object s/he wants to consider based on the property of each individual DMUR problem.

For MCDM, AHP requires many inputs for pairwise comparisons, which is a time- consuming process. Therefore, this method should be chosen only for a small number of criteria and alternatives. Furthermore, the potential compensation between good scores on some criteria and bad scores on others causes the loss of information. The advantage of TOPSIS is that it requires only a few inputs from the decision maker and its output is easy to understand. The drawback is that vector normalization is needed for solving multi- dimensional problems. The main advantage of ELECTRE is that it avoids compensation between criteria and any normalization process, which distorts the original data. The drawback is that it requires various technical parameters such that it is not always easy to fully understand it. The PROMETHEE method allows direct operation on the variables included in the decision matrix without requiring any normalization and is applicable even when there is insufficient information. However, its main drawback is that it is time consuming and difficult for decision makers to have a clear view of the problem, especially when there are many criteria involved.