SMAA Method

3. SMAA Method

SMAA a multi-criteria decision support method that is based on the analysis of weight space for a number of decision-makers. Under this method, decision-makers do not need to express their preferences explicitly or precisely. The method describes the valuations that would make each alternative the preferred one (Lahdelma et al., 1998). In the analysis, both criteria values and weights are constrained by their distributions (Lahdelma and Salminen, 2009).

Tervonen and Lahdelma (2007) explained why SMAA method was appropriate for real-life problems as follows: The inverse weight space approach used in SMAA method is feasible for the problems for which the criteria values could not be obtained from the alternatives by decision-makers.

Rahman et al. (2016) used SMAA to assess energy policy elements in Bangladesh. Tervonen et al. (2008) used SMAA for elevator planning, Lahdelma and Salminen (2001) used SMAA-2 for the decision problem of constructing a new cargo harbor in Helsinki. Lahdelma et al. (2002) and Lahdelma et al. (2003) used SMAA-O for the problem of selecting a municipal solid waste management system. The two studies differ in using partial information and ordinal criteria. In Lahdelma and Salminen (2009), authors introduced SMAA-P method integrating piecewise linear difference functions of prospect theory into SMAA. They used the method to analyze a forest ecosystem management application.

Other applications of SMAA variants are, Hokkanen et al. (2000) for technology selection for polluted soil, strategical forest planning in Kangas et al. (2006), distribution center selection for disasters in Ağdaş et al. (2014), natural resource decision analysis in Kangas and Kangas (2003), logistics facility selection in Ağdaş (2014), government facility location selection in Karabay et al. (2014) and evaluation of maintenance alternatives in Eroğlu (2014).

3.1. SMAA-2

It has values in (0, 1) interval. The best or most acceptable alternative has the highest acceptability index. Alternatives with large acceptability values for the worst ranks should be avoided while comparing compromise solutions. If b_i^ris 0 then alternative i will never obtain the given rank r and 1 means alternative will always obtain the given rank r independent of weight choices. The rank acceptability index is computed by integral calculations over the criteria distributions and the favorable rank weights as: b_i^r= ∫_X▒〖f(ξ)∫_(W_i^r (ξ))▒〖f(w) dw dξ〗〗 (3)

The first rank acceptability index, b_i^1, is a very special index showing the alternative i is being at the first rank. For efficient alternatives the index has non-zero values and zero for the inefficient alternatives. It’s also known as acceptability index which also measures the efficiency by considering the uncertainty in criteria and decision makers’