Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale

Increasing attention has been given to the development of specific techniques to deal with interconnections between outputs, inputs, and undesirable outputs for data envelopment analysis (DEA) models. These techniques offer the advantages of improving the realism and the flexibility of DEA models; two aspects of crucial importance to convince practitioners about the attractiveness and the reliability of DEA models. In this paper, we propose a unifying methodology coherent with previous works to model these interconnections. We suggest treating the outputs as the fundamental component of the production process by modelling every output individually. This gives us the option of considering the interconnections with the inputs and the undesirable outputs. In particular, we make a distinction between undesirable outputs/inputs that are due to/used by all the outputs, and those that are due/allocated to specific outputs. Attractively, our methodology also offers the option of setting a different returns-to-scale assumption for each output-specific production process, and to choose between different types of convexity. We demonstrate the usefulness of our methodology with the case of the US electricity plants producing fossil and non-fossil electricity generation.