A note on a new method based on the dispersion of weights in data envelopment analysis

In a very recent paper by Bal et al. (Bal, H., Örkcü, H. H., & Çelebioğlu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Computers & Industrial Engineering, 54(3), 502–512), a data envelopment analysis (DEA) model which incorporates the coefficients of variations (CVs) of input–output weights was proposed to improve the discrimination power of DEA and balance input–output weights. This note points out that the input and output weights in DEA are of different dimensions and units. The weights with different dimensions and units cannot be simply added together and averaged. In other words, the DEA model with the inclusion of CVs of input–output weights, which was referred to as CVDEA model for short, makes no sense if input and output data are not normalized to eliminate their dimensions and units. This note also illustrates the facts that the CVDEA model can cause significant efficiency changes when a scale transformation is performed for an input or output and may produce multiple local optimal solutions due to its nonlinearity, leading to totally different assessment conclusions. These facts reveal that the CVDEA model suffers from serious drawbacks and its applications for efficiency assessment should be very cautious.