Multicriteria Methods for Decision Aiding

Multicriteria methods serve to select, rank, classify or make detailed descriptions of alternatives on which decisions will be made [Pomerol & Barba-Romero (2000); Belton & Stewart (2002)]. These methods can be used in combination or not. Thus, for example, a specific method may be used to classify a set of viable alternatives into four categories: very good, good, mediocre and out of the question; following this, one may, by means of another method – which must however have the same axiomatic base as the method previously used – simply rank only those considered very good, in this way obtaining the best alternative of the set.
The genesis of multicriteria methods is to be found in the history of the allied forces during the Second World War. Basically, up to the first half of the twentieth century, when solving complex decision making problems, expected value was used for making decisions in random conditions; however, in many situations it was observed that the risk associated with this procedure was unacceptable. With the end of the Second World War, though, as a result of the experience gained by the Allied Forces with military logistics problems, a large number of research organisations and university departments began to dedicate their time to a systematic study of the analysis and planning of decisions, using the then recently created Operational Research. From that point there arose within the business environment, the immediate need to optimise costs and maximise profits by means of Operational Research methods. With these objectives in mind, various strictly mathematical methods were developed to find the optimum solution for transport and production problems among many others. These methods, in the main, are currently to be found in classical optimization under restrictions or mathematical programming with a single objective function, and many of them are still used today in a series of applications, such as assignment of flows to networks, establishing a minimum path and inventory optimization etc.
In classical optimization under restrictions or in mathematical programming with a single objective function one seeks the maximum or minimum value of a single objective function, submitted to a set of restrictions to be respected. This means that all the consequences derived from the choice of each one of the alternatives must be able to be reduced or expressed in terms of a single evaluating function. However, in practice, the decision maker generally uses various criteria simultaneously to evaluate the different alternatives, some of them difficult to measure in relation to non-monetary consequences (such as, for example, socio-environmental impact, product image, quality, security, comfort etc.). Although they can be incorporated to the model by means of restrictions, the difficulty of dealing with multiple dimensions at the same time as dealing with monetary ones can be observed.
Nevertheless, in the 1950s and 1960s, statistics were used – by means of the expected value concept already mentioned – to find the best solution for single criterion decision problems, through the decision tree concept. As a result of this, a more traditional view of Decision Theory would indiscriminately use this expression and the expression Decision Analysis to designate the construction and application of decision trees for decision problems with a single criterion [Raiffa (1977); (2002)]. Among the excellent works on the classical focus of decision analysis are the books by Fishburn (1970) and de Souza (2002). Examples of works which present both the classical focus as well as the basics of the multicriteria focus are Kaufman & Thomas (1977), Keeney (1982) and Carrasco & Sánchez (1990). Brown’s book (2005) presents the most modern and realistic view – therefore multicriteria based – of decision analysis.
Although attempts had been made to solve decision making problems in the presence of multiple criteria through the assignment of weights – both for alternatives and criteria –, especially in academic environments, scientifically formulated multicriteria methods oriented to real applications basically arose at the end of the 1960s, initially in Paris [Roy (1968)], and during the following decade in the United States of America [Keeney & Raiffa (1976); Saaty (1977)]. These pioneering works notably reflected dissatisfaction with the project evaluation methodologies available at that time, which were either only ordered in consequences expressed in monetary units – such as cost/benefit analyses [Weimer et al. (2005)] – or were presented as incapable of dealing simultaneously with multiple categories of consequences – monetary and non-monetary –, such as cost-effectiveness analyses [Levin & McEwan (2000)].
This being so, the multicriteria methods which arose around the 1970s were designed to solve decision making problems with the following principal characteristics:
· There were at least two criteria involved in solving the problem, these in conflict with each other.
· Both the criteria and the alternatives were not clearly defined, and the consequences of choosing a specific alternative, in relation to at least one criterion, were not duly understood.
· The criteria and the alternatives could be interlinked in such a way that a given criterion seemed to partially reflect another criterion, while the efficacy of opting for a specific alternative depended on whether another was or was not chosen, in the case of the alternatives not being mutually exclusive.
· The solution of the problem depended on a group of people, each with their own point of view, often conflicting with those of the other people.
· The restrictions of the problem were not well defined, meaning that doubts could exist in respect of what was a criterion and what was a restriction.
· Some of the criteria were quantifiable – for example, in terms of monetary units – while others were only so by means of judgement values made against a scale.
· The scale for a specific criterion could be cardinal (that is, numerical), verbal (or possible to be expressed in ordinary language) or ordinal (by establishing relations of ranking), depending on the data available and the nature of the criteria.
Other complications could arise in a real context of decision making, but these seven aspects mentioned characterised the essence of this complexity. In general, decision making problems with these characteristics were considered – and are still considered today – badly formulated problems.
At the same time, a consciousness developed that one should not intend the use of these new methods to lead necessarily to an optimum solution – in the sense of a solution which would ideally be the best possible according to all the points of view relevant to the problem –, but instead, at least to a solution which represented a satisfactory compromise between these points of view. In this way, something was perceived which has become a consensus today: multicriteria methods are heuristic, conceived to deal with decision making problems which have a finite (or countable) number of possible alternative solutions.
As has already been mentioned here, multicriteria methods are used in the analysis which precedes the decision making. Nevertheless, one cannot ignore the fact that the field of application of these methods also includes evaluating at which point a decision already taken has met or not the objectives of the problem. Therefore, it is said that multicriteria methods can be used before or after an implementation. In the first case, one talks of an analysis (of the decision) ex ante, that is, before the decision is made, serving to generate recommendations for the decision making itself. In the second case, it is said that the analysis (of the decision) is ex post, in other words, after the decision has been made, seeking through this analysis to learn from the decisions already made.
Although there are, in the decision analyst’s tool-box, a much greater number of multicriteria methods than the number of problems the analyst is called upon to solve, normally the choice of one particular method, as opposed to the others, is guided by a solid knowledge of a reasonably large number of methods on the part of this professional. This knowledge includes the adequacy of applying each method to the problem, considering here the following principal aspects: (i) the nature of the problem to be solved (that is, selection, ranking, classification and description); (ii) the possible means of collecting and compiling the data; (iii) the structure of the relationships among the objectives of the problem; and (iv) the type of communication to be expected between the analyst and the decision maker, chiefly during the decision analysis stages.
The main characteristics of the most commonly used methods shall now be examined. For a panoramic view of the relatively large number of multicriteria methods available today to practitioners of Decision Theory, see, for example, Schärlig (1990), Vinke (1992), Bana and Costa (1990), Clímaco (1997) and Triantaphyllou (2000).
A very common error committed by novice decision analysts is to try to resolve a specific decision problem by means of commercially available software. However, the software must never be used without the decision analyst having an understanding, principally from a technical point of view, of the analytical method which is embedded in it. On the other hand, the application of any decision aiding method must start from the premise that the problem to be solved has already been adequately structured. Consequently, the stage called problem structuring is crucial and must never be omitted [Montibeller Neto et al. (2008); Bana and Costa et al. (1999); Rosenhead and Mingers (2008); Belton, Ackermann & Sheperd (1997)]. Thus, although the emphasis underlying the use of a multicriteria method is essentially in the modelling and the analysis of the problem, as well the subsequent calculations, the significant need to give due attention to the structuring process is recognised. Even simple techniques, such as Pros and Cons Analysis [Baker et al. (2001)] and the Kepner-Tregoe Decision Analysis [Kepner & Tregoe (1981)] are useful as a first exercise in organising ideas around a decision making problem in the presence of multiple criteria.
Having said this, a listing is made here of some among the main multicriteria decision aiding methods, with important sources of information on them. The following methods are listed in alphabetical order.
· AHP & ANP [Saaty (1988; 1990; 1994; 2001)]
· Dutch Methods of Multicriteria Decision Aiding [Lootsma (1993; 1994a; 1994b); Ancot (1988); Delft & Nijkamp (1977); Jansen (1994); Nijkamp (1977); Nijkamp, Rietveld & Voogd (1990); Paelink & Nijkamp (1976); Rietveld (1980); Voogd (1989)]
· ELECTRE [Roy & Bouyssou (1993)]
· MACBETH [Bana and Costa & Vansnick (1999; 2000)]
· MAUT [Clemen & Reilly (2001); Keeney & Raiffa (1976)]
· PROMÉTHÉE [Brans & Mareschal (2002)]
· Rough Sets Theory [Pawlak (1982); Slowinski (1992)]
· TODIM [Gomes & Lima (1992a; 1992b); Trotta, Nobre & Gomes (1999); Gomes & Rangel (2007)]
· Verbal Decision Analysis [Larichev & Moshkovich (1997); Larichev & Olson (2001)]
In the following section we shall explain one of these methods and show how it can be applied to the practice of decision making aiding.

Bibliographical references

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