Generalizing cross redundancy in data envelopment analysis

Lee and Choi (2010) proved that a cross redundant output in a CCR or BCC DEA study is unnecessary and can be eliminated from the model without affecting the results of the study. A cross redundant output, as characterized by Lee and Choi, can be expressed as a specially constrained linear combination of both some outputs and some inputs. This article extends the contributions of Lee and Choi (2010) in at least three ways: (i) by adding precision and clarity to some of their definitions; (ii) by introducing specific definitions that complement the ones in their paper; and (iii) by conducting some additional analysis on the impact of the presence of other types of linear dependencies among the inputs and outputs of a DEA model. One reason that it is important to identify and remove cross redundant inputs or outputs from DEA models is that the computational burden of the DEA study is decreased, especially in large applications.

► A cross redundancy is a linear dependent relationship between DEA inputs and outputs.
► A cross redundant input or output can be removed from a DEA model without changing the DEA efficiency scores.
► Cross redundant attributes unnecessarily increase the amount of data to be processed.