New models for data envelopment analysis: Measuring efficiency outwith the VRS frontier

Some models are presented in this paper which extend the concept of measuring superefficiency to the useful case of variable returns-to-scales (VRS), thus enabling the ranking of efficient as well as inefficient units. Two models, namely the Universal Radial Model and the Universal Additive Model, are presented that also have strong invariance properties (units and translation invariance). For both of these models a method for normalising the efficiency scores on a (0-1+) scale is presented. These models have been implemented in a software package and applied to the ranking of units in an industrial context.