a new bi-level data envelopment analysis model to evaluate the human development index

In the 1990s, the united nations development programme (undp) in-troduced 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, particu-larly the one enhanced by weight restrictions. indeed no specific methodhas been yet suggested to determine the parameters of the weight restric-tions. 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 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 calculat-ing the hdi instead of the traditional method, then 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.