DEA cross efficiency under variable returns to scale

While cross-efficiency evaluation has been used in a wide variety of DEA applications due to its attractive mechanism, so has it been for DEA models mostly with constant returns to scale (CRS) assumption. This is due to the fact that negative VRS cross-efficiency arises for some DMUs. Since there exist many instances that require the use of the VRS DEA model, it is imperative to develop cross-efficiency measures under VRS. This chapter introduces a recent development of DEA crossefficiency evaluation approach under VRS, which is motivated by the observation that cross-efficiency evaluation is closely related to the issue of incorporation of weight restrictions and that negative VRS cross-efficiency is related to free production of outputs. The new approach is based upon a geometric interpretation of the relationship between the CRS and VRS DEA models that the VRS model can be cast as a series of CRS models under translated Cartesian coordinate systems. We illustrate this approach using a simple example and show how the VRS negative cross-efficiency problem is addressed under the new framework.