A slack analysis framework for improving composite indicators with applications to human development and sustainable energy indices

Data envelopment analysis models are used for measuring composite indicators in various areas. Although there are many models for measuring composite indicators in the literature, surprisingly, there is no methodology that clearly shows how composite indicators improvement could be performed. This article proposes a slack analysis framework for improving the composite indicator of inefficient entities. For doing so, two dual problems originated from two data envelopment analysis models in the literature are proposed, which can guide decision makers on how to adjust the subindicators of inefficient entities to improve their composite indicators through identifying which subindicators must be improved and how much they should be augmented. The proposed methodology for improving composite indicators is inspired from data envelopment analysis and slack analysis approaches. Applicability of the proposed methodology is investigated for improving two well-known composite indicators, i.e., Sustainable Energy Index and Human Development Index. The results show that 12 out of 18 economies are inefficient in the context of sustainable energy index, for which the proposed slack analysis models provide the suggested adjustments in terms of their respected subindicators. Furthermore, the proposed methodology suggests how to adjust the life expectancy, the education, and the gross domestic product (GDP) as the three socioeconomic indicators to improve the human development index of 24 countries which are identified as inefficient entities among 27 countries.