Page 171 - Contributed Paper Session (CPS) - Volume 6

CPS1866 Milica Maricic et al.

Weight
Weight
Weight
Dimension Category Indicator indicators categories dimension (a b c   )
Effective
within
within
within
weight
( )
( )
( )
c
a
b
Energy
Savings 25.00% 50.00% 33.33% 4.17%
Climate & Greenhouse 25.00% 50.00% 33.33% 4.17%
energy Gases
Renewable 25.00% 50.00% 33.33% 4.17%
Energy 50.00% 50.00% 33.33% 8.33%
Organic
Economic wellbeing Transition Employment 50.00% 50.00% 33.33% 8.33%
Farming
Genuine
Savings
33.33%
33.33%
50.00%
GDP
5.56%
33.33%
5.56%
33.33%
Economy
50.00%
33.33%
5.56%
33.33%
50.00%
Public Debt
3.2 Enhanced Scatter Search – Composite I-distance indicator (eSS-CIDI)
approach
To scrutinize the weighting scheme of the SSI and potentially to reduce
the number of indicators which are used in its computation we propose the
recently devised enhanced Scatter Search – Composite I-distance Indicator
(eSS-CIDI) approach (Maricic, 2018). The idea of the approach is to obtain a
data-driven weighting scheme which will produce the most stable rankings of
entities if the sensitivity analysis is conducted for the weighting scheme. The
stability of the ranks is measured using standard deviations of relative
contributions (Dobrota et al., 2016; Murias et al., 2008). Relative contribution

v of an indicator , i i 1,2,...,k to the overall composite index of entity
ie

, e e 1,2,...,n is the percentual share of the weighted indicator in the
overall composite index. Therefore, if the contribution of indicator i of all
observed entities varies that indicates that the stability of the results and ranks
is low (Dobrota et al., 2016; Savic et al., 2016). Accordingly, the goal is to
propose a weighting scheme which will minimize the sum of standard
deviations of relative contributions of all indicators which are used in the
framework.
The eSS-CIDI approach is conducted in three steps. The first step is to
conduct the bootstrap CIDI to devise bounds within which the novel weighting
scheme will be chosen from. The bootstrap CIDI has already been used to
restrain GAR DEA model (Data Envelopment Analysis) (Radojicic et al., 2018).
The bootstrap CIDI consists of performing the Composite I-distance Method
(CIDI) on m out of n samples without replacement where m is the subsample
size and n is the sample size. Namely, after each iteration, a novel CIDI
weighting scheme will be obtained. As the subsample size we chose 0.632 n

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