Revisiting the inverse transformation of undesirable factors in data envelopment analysis: A novel iterative algorithm

In many cases, the production of desirable outputs results in the joint generation of undesirable outputs, such as waste or emissions. To abate pollution and achieve the NetZero targets, it is crucial that undesirable outputs are incorporated in the efficiency assessment of the production processes. In the Data Envelopment Analysis (DEA) literature, different methods and assumptions are used to account for undesirable outputs. A very common approach is using the inverted undesirable output as a desirable output instead of the actual undesirable output in the formulation of the constraints. In this paper, we discuss that this formulation of the production possibility set (PPS) might not reflect the true production process. An alternative formulation of the PPS is introduced, where the inverse of the convex combination of undesirable outputs is used Y instead. This results in a nonlinear programming (NLP) DEA model. An iterative procedure with a linear rate of convergence is suggested to solve this NLP, and its computational efficiency is demonstrated through Monte Carlo simulations. The suggested approach and the iterative algorithm are implemented to assess the efficiency of raw material flows in the EU-27, where emissions and waste are considered undesirable outputs. Under the VRS assumption, our approach provides a more favourable efficiency assessment for DMUs.