Comprobación de la hipótesis

Buchholz et al. (2009: 485) distinguish between two general types of MCDA, namely, multi- objective decision-making (MODM) approaches working with an indefinite set of possible scenarios, and multi-attribute decision-making (MADM), suggesting a finite set of scenarios. For instance, linear programming follows the MODM approaches, starting with a set of principles (e.g. maximising efficiency, reducing costs) and resulting in an optimised scenario. On the other hand, MADM approaches, which are the concern in this study, start with a set of scenarios/alternatives, which are further scrutinised to determine how well they fit a set of principles. MADM approaches can be further differentiated into (Belton and Stewart, 2002: 9):

 Value measurement models, which assign a numerical score to each alternative, thus ranking scenarios depending on how they score according to a weighted list of criteria;

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 Goal, aspiration and reverence level models, which are goal programming methods where ‘a mathematical programming algorithm is used to approach these goals as closely as possible’ (Belton and Stewart, 2002: 105);

 Outranking models, where the alternatives are compared pairwise to check which of them are preferred regarding each criterion (Løken, 2007). After aggregation of the results for each criterion, this approach suggests to what extent the alternatives outrank one another (Buchholz et al., 2009: 485).

 Utility and value function approaches, among which multi-attribute utility theory (MAUT) and analytic hierarchy process (AHP) theory are best known in South Africa (De Lange, 2006: 66).

These approaches synthesise assessments of the performance of alternatives against individual criteria (scores), together with inter-criteria information reflecting the relative importance of the different criteria (weights) to give an overall evaluation of each alternative, indicative of the decision makers’ preferences (Belton and Stewart, 2002: 119). MAUT and AHP differ primarily in terms of the underlying assumptions about preference measurement, the methods used to elicit preference judgements from decision makers, and the manner of transforming these into quantitative scores (Belton and Stewart, 2002: 10). MAUT is the only technique that addresses uncertainty in its axiomatic framework by analysing the expected values. AHP assesses marginal utilities by asking for the relative strengths of preferences between each pair of possible scenarios. AHP is useful, simple and consequently, a widely used tool (De Lange, 2006: 67).

In many ways, goal programming and reference point techniques represent the earliest attempts at providing formal quantitative decision aids for complex problems involving multi-criteria decisions. Goal programming (GP) was introduced by Charnes et al. (1955). This MCDM technique is regarded as the method that operationalises the Simonian ‘satisficing’ approach for the achievement of a DM’s objectives (Simon, 1955). A comprehensive review may be found in Lee and Olson (1999). The essential idea in goal programming is that, instead of optimising a set of objectives, the DM first sets targets for their achievement, and then an acceptable solution is found by minimising the deviations from the set of targets. The minimisation of deviations from predetermined targets can be accomplished using several alternative methods, and of these, the two most widely used ones are weighted goal programming (WGP) and lexicographic goal programming (LGP) (Rehman and Romero, 1993: 241). Reference point approaches start by having the decision maker specify

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achievement levels for each criterion in terms of relevant performance measures. These levels are typically of three types (De Lange, 2006: 67):

 Goal levels (performance level that will fully satisfy the goals of the decision maker);

 Exclusion levels (performance level at which, if violated, the entire scenario becomes unacceptable);

 Reference levels (expectation of the decision maker of an acceptable compromise between the conflicting demands of different criteria).

The outranking approaches differ from the value function approaches in that there is no underlying aggregative value function. The output of an analysis is not a value for each alternative, but an outranking relation among the sets of alternatives (Belton and Stewart, 2002: 233). Outranking approaches represent evidence for and against the statement that one alternative is better than another. Evidence takes the form of voting between criteria. The elimination and choice translating reality (ELECTRE) family of methods and the preference ranking organisation method of enrichment evaluations (PROMETHEE) are the two most prominent outranking approaches. Outranking approaches focus pairwise on comparisons of alternatives, and are thus generally applied to discrete choice problems (Belton and Stewart, 2002: 234).

Game theory approaches represent another type of multi-criteria decision-making where each criterion can be associated with a single player. Game theory synthesises the utility functions of individual players into a social utility function. It assumes that each criterion is associated with a particular ‘player’ and that marginal utilities can be associated with each policy scenario (Romero & Rehman, 2003: 110-113). Game theory aims at identifying solutions to the decision problem that represent the most acceptable compromise between players. Nash equilibriums – seeking the policy scenario that maximises the product of the marginal utilities – are the simplest forms of this type of approach (De Lange, 2006: 67).

The interactive multiple-criteria decision-making approach implies the progressive evolution and definition of decision makers’ preferences through interactions between them and the results generated from various runs of the model. These interactions become a dialogue in which the model responds to an initial set of the decision maker’s preferences or trade-offs, and then when this response has been examined, another set is offered, and thus the procedure progresses in an interactive and iterative way until the decision maker has found a satisfactorily outcome (Romero & Rehman, 2003: 79-102).

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Further details on the concepts, approaches and other related information on MCDA can be found, inter alia, in Belton and Stewart (2002), Romero and Rehman (2003), Hobbs et al. (1992), Buchholz et al. (2009) and (Mendoza and Martins, 2006). Due to its simplicity, the natural appeal of expressing relative importance by means of pairwise comparisons in ratio terms, and the resulting acceptance and common application – the analytic hierarchy process (AHP) was selected for the multi-criteria decision-making assessment applied in Chapter 7.