A Simple Method to Construct a Group Composite Indicator with an Application
محورهای موضوعی : فصلنامه ریاضی
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.
کلید واژه: Data Envelopment Analysis (DEA), Composite indicator, Nonlinear programming, Human Development Index (HDI) ,
چکیده مقاله :
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.
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.
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