The desirable input of undesirable factors in data envelopment analysis

Recent papers have provided a number of overviews in connection with the fast growing literature on bad outputs in Data Envelopment Analysis (DEA), such as defective products, emissions and waste. However, there does not seem to exist any comprehensive overview of the opposite phenomenon, particularly not regarding DEA, namely of bads as undesirable objects or factors which are desirable input (flow) into transformation processes, e.g. into waste incineration. Moreover, the terms ‘bad input’ and ‘(un-)desirable input/factor’ are not clearly defined. We use a purely preference-based notion for the desirability of inputs and outputs. A systematic literature search reveals only 22 DEA articles which explicitly address the (desirable) input of bads as original undesirable factors, i.e. as input into the first stage of a single- or multi-stage process. Their detailed analysis shows that current approaches are based on two core ideas involving various efficiency measures. Only four papers deal with real applications of original undesirable factors, namely waste water treatment. Moreover, those disposability assumptions for DEA models often critically discussed in relation to bad outputs (e.g. weak disposability) are not used in these papers, presumably because the processes modelled are themselves disposal processes. Finally, we exemplarily demonstrate how DEA models with bads as inputs (and outputs) can be systematically derived from a decision-theoretic generalization of DEA methodology proposed in the literature.