A Simple Method to Construct a Group Composite Indicator with an Application

Subject Areas : International Journal of Mathematical Modelling & Computations

Davood Nejatpour ¹ , Abdollah Hadi-Vencheh ^{2 *} , Ali Jamshidi ³

1 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
2 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
3 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.

Received: 2025-01-12 Accepted : 2025-04-24 Published : 2025-04-26

Keywords: Data Envelopment Analysis (DEA), Composite indicator, Nonlinear programming, Human Development Index (HDI) ,

Abstract :

In this paper, we propose a novel and straightforward nonlinear programming approach for aggregating individual composite indicators (CIs) into a group-level composite indicator (e.g., an aggregate CI for a group of entities). Drawing on performance measurement literature, our model is designed to be both simple and computationally efficient, requiring no specialized solvers for implementation. The proposed approach addresses the growing need for robust and interpretable methods to synthesize multidimensional data, particularly in contexts where policymakers and researchers aim to compare and benchmark the performance of groups or regions. To demonstrate the practical application of our method, we compute an aggregate Human Development Index (HDI) for the European Union (EU) region using HDI sub-indicators from individual EU member states. This case study highlights the model’s ability to integrate diverse dimensions of human development—such as health, education, and standard of living—into a single, coherent metric. By doing so, we provide a tool for evaluating the collective progress of the EU region while preserving the unique contributions of each member state. Our approach offers several advantages: (1) it is computationally accessible, making it suitable for a wide range of applications; (2) it allows for flexibility in weighting and aggregation, accommodating diverse policy priorities; and (3) it provides a transparent framework for constructing group-level CIs, enhancing their utility for decision-making and public communication.

References:

[1] D. K. Despotis,. Measuring human development via data envelopment analysis: The case of Asia and the Pacific. Omega, 33(5) (2005), 385–390, https://doi.org/10.1016/j.omega.2004.07.006.
[2] D. C.Esty, , M. A.Levy, , T. Srebotnjak, , A. de Sherbinin, C. H.Kim, and B. Anderson, Pilot environmental performance index. Yale Center for Environmental Law & Policy (2006).
[3] M. Jefferson, Sustainable energy development: Performance and prospects. Renewable Energy, 31(5) (2006), 571–582. https://doi.org/10.1016/j.renene.2005.08.011.
[4] R. Karagiannis and G. Karagiannis. Intra- and inter-group composite indicators using the BOD model. Socio-Economic Planning Sciences, 62(2017)1–8. https://doi.org/10.1016/j.seps.2017.01.003.
[5] E. Lafuente, M. Araya and J. C. Leiva, Assessment of local competitiveness: A composite indicator analysis of Costa Rican counties using the ‘Benefit of the Doubt’ model. Socio-Economic Planning Sciences, 71(2020), 100864. https://doi.org/10.1016/j.seps.2020.100864.
[6] A. Mergoni, G. DI,nverno and L. Carosi, A composite indicator for measuring the environmental performance of water, wastewater, and solid waste utilities, Utilities Policy, 70 (2021), 101285. https://doi.org/10.1016/j.jup.2021.101285.
[7] P. Morais and A. S. Camanho, Evaluation of performance of European cities with the aim to promote quality of life improvements, Omega, 39(4) (2011)398–409, https://doi.org/10.1016/j.omega.2010.09.005.
[8] M. Nardo, M. Saisana, A. Saltelli and S. Tarantola, Tools for composite indicators building. European Commission (2005).
[9] M. Nardo, M. Saisana, A. Saltelli, S. Tarantola, E. Giovannini and A. Hoffman, Handbook on constructing composite indicators: Methodology and user guide. OECD Publishing (2008).
[10] N. Rogge, On aggregating benefit of the doubt composite indicators. European Journal of Operational Research, 264(1) (2018), 364–369. https://doi.org/10.1016/j.ejor.2017.06.052.
[11] A. D. Sagar and A. Najam, The human development index: A critical review. Ecological Economics, 25(3) (1998), 249–264. https://doi.org/10.1016/S0921-8009(97)00168-7.
[12] M. Saisana and S. Tarantola, State-of-the-art report on current methodologies and practices for composite indicator development, Joint Research Centre, European Commission (2002).
[13] A. Saltelli, Composite indicators between analysis and advocacy, Social Indicators Research, 81(1) (2008) 65–77. https://doi.org/10.1007/s11205-006-0024-9.
[14] M. Sánchez, J. López and F. Rodríguez, Machine learning for composite indicator construction: A data-driven approach. Expert Systems with Applications, 176 (2021), 114789. https://doi.org/10.1016/j.eswa.2021.114789.
[15] Y. Wang, X. Chen and Z. Zhang, Renewable energy adoption in developing countries: A composite indicator approach. Renewable and Sustainable Energy Reviews, 156 (2022), 111935, https://doi.org/10.1016/j.rser.2021.111935.
[16] A. Xavier, R. Fragoso and M. D. B. C. Freitas, Building sustainability composite indicators using a multi-criteria approach. European Journal of Operational Research, In press, https://doi.org/10.1016/j.ejor.2025.04.024, (2025).
[17] P. Zhou, B. W. Ang and K. L. Poh, A mathematical programming approach to constructing composite indicators. Ecological Economics, 62(2) (2007), 291–297. https://doi.org/10.1016/j.ecolecon.2006.12.020.