Nowadays competitiveness has become a key economic feature both in policy and in academia. The Global Competitiveness Index (GCI) of the World Economic Forum is one of the best known competitiveness indices, which measures the microeconomic and macroeconomic foundations of national competitiveness. It conceives competitiveness as the set of institutions, policies and factors that determines the level of productivity of a country. This index allows total substitutability between the twelve pillars that aim to measure the different dimensions of competitiveness, albeit partially modulated by some different weights. In this paper, we implement a multi-criteria approach with new alternative normalization and aggregation formulas for such pillars of competitiveness. In particular, we propose two innovations for the computation of the GCI: (i) a double reference point scheme in the normalization; and (ii) an aggregation function which deals with the problem of substitutability between pillars. We calculate three alternative global competitiveness indices (weak, strong and mixed) with different degrees of substitutability, as well as the mixed index without normalizing. We suggest the use of a suitable mixed index alongside the GCI.