Relaxing The Impact Of Extreme Units In Data Envelopment Analysis

Data envelopment analysis (DEA) is a nonparametric linear programming technique for measuring the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and outputs. DEA assessments, however, are proved to be sensitive to extreme units that deviate substantially in their input/output patterns. In this paper we introduce an approach for handling extreme observations in DEA, i.e., observations that exhibit irregularly high values in some outputs and/or low values in some inputs. Unlike the usual practice of removing such observations, we retain them in the production possibility set reducing their impact on the other units. Our modeling approach is based on the concept of diminishing returns, assuming that the contribution of an output (input) to the efficiency score diminishes as the output increases beyond a pre-specified level, i.e., the level beyond which a value is characterized as extreme. According to our approach the original data set is transformed to an augmented data set, where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. We illustrate our approach with a numerical example.