A new bi-level data envelopment analysis model to evaluate the Human Development Index

Document Type : Research Article

Authors

• Ensie Hajinezhad ¹
• Haniye Hajinezhad ²
• M.R. Alirezaee ¹

¹ School of Mathematics, Iran University of Science and Technology, Tehran, Iran.

² Department of Mathematics, Payame Noor University, Tehran, Iran

10.22067/ijnao.2024.82197.1252

Abstract

In the 1990s, the United Nations Development Programme introduced the Human Development Index (HDI) to determine the development degrees of countries. One deficiency in the HDI calculation is the use of equal weights for its sub-indicators. Many scholars have tried to solve this problem using a data envelopment analysis (DEA) method, particularly the one enhanced by weight restrictions. However, no specific method has been yet suggested to determine the parameters of the weight restrictions. In this paper, we use four DEA/benefit of the doubt (BoD) models enriched by the assurance regions type I (AR-I) constraints to assess human development; we aim to objectively determine the AR-I bounds. Therefore, we consider a basis as the accepted human development values and propose a bi-level optimization problem (BOP) to extract the AR-I bounds in such a way that the efficiency scores are almost the same as the basic values. On the other hand, the HDI is a globally accepted index that shows small changes year by year. So, if the UNDP decides to apply a BoD model for calculating the HDI instead of the traditional method, it is better than the scores obtained by the BoD model showing small changes in comparison with the HDI, at least in the first few years. Therefore, the HDI values are considered as the basis. Moreover, the objectively achieved AR-I bounds provide us with an insight into the way the sub-indicators affect the development scores. The bounds can be modified by the experts’ opinions, in the future.

Keywords

• Human development index (HDI)
• Data envelopment analysis (DEA)‎ , ‎ Benefit of the doubt (BoD)
• Assurance regions type I (AR-I)
• Bi-level optimization problem (BOP)

Main Subjects

• Operations Research

---