Variable range measure: A new range measure for super-efficiency model based on DDF in presence of nonpositive data

Abstract

In order to handle the nonpositive data and increase the discrimination power, we propose a new DDF superefficiency model called variable range measure (VRM). VRM is translation-invariant and unit-invariant. VRM is feasible when data set contains zero or negative data. The super-efficiency obtained by VRM is less than or equal to two. Range adjusted measure (RAM) makes input contraction and output expansion along the direction vector in a balanced way, but it is target-invariant. The range directional model (RDM) for super-efficiency might be infeasible, but it is target-variant. We combine the advantages of RAM and RDM into VRM so that VRM is target-variant and feasible under super-efficiency. Output vector of the direction vector proposed by Lin and Liu (2019) (LL model) might be zero for some DMUs. VRM overcomes the shortcomings of the LL model. We show that the VRM direction vector is a good proxy of the RAM direction vector by examples.