Integration of directional distance formulation of DEA and canonical correlation

Data envelopment analysis (DEA) which has been widely used in recent times for measuring productive efficiency of decision making units (DMUs). The main limitation of DEA is that many numbers of DMUs comes out to be efficient when there are relatively large number of input and output variables as compared to number of DMUs under evaluation. In extreme cases may cause the majority of the units to be efficient. Tackle this limitation canonical correlation analysis (CCA) is applied in this paper. This paper develops a method that integrates the directional distance formulation of DEA and CCA to measure the efficiency and rank the DMUs. There are situations in which more than one significant canonical correlation exists with both positive and negative values. This problem is addressed in this paper by using directional distance function approach to measure the efficiency, where negative canonical correlation exists. This method can also be applied where two or more canonical correlations are significant. Keywords: data envelopment analysis; DEA; canonical correlation; directional distance function; efficiency. Reference to this paper should be made as follows: Shetty, U. and Pakkala, T.P.M. (2016) ` and canonical correlation', Int. J. Business Performance and Supply Chain Modelling, Vol. 8, No. 1, pp.66­77. Copyright © 2016 Inderscience Enterprises Ltd. Introduction Data envelopment analysis (DEA) is a non-parametric technique of frontier estimation that determines both the relative efficiency of a number of decision-making units (DMUs) and the targets for their improvement. DMUs can represent any set of organisations or departments that perform fundamentally the same task with the same set of variables. DEA measures the relative efficiency of DMUs with multiple inputs and outputs and assumes neither a specific functional form for the production function nor the inefficiency distribution, in contrast to parametric statistical approaches. Problems...