Data envelopment analysis and the discriminant analysis of ratios for ranking units

The purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the Data Envelopment Analysis (DEA), in order to rank all the units on the same scale. This new method, Discriminant Data Envelopment Analysis of Ratios (DR/DEA), presents a further post-optimality analysis of DEA for organizational units when their multiple inputs and outputs are given. We construct the ratio between the composite output and the composite input, where their common weights are computed by a new non-linear optimization of goodness of separation between the two pregiven groups. A practical use of DR/DEA is that the common weights may be utilized for ranking the units on a unified scale. DR/DEA is a new use of two-group discriminant criterion that has been presented here for ratios, rather than the traditional discriminant analysis which applies to a linear function. Moreover, non-parametric statistical tests are employed to verify the consistency between the classification from DEA (efficient and inefficient units) and the post-classification as generated by DR/DEA.