On performance evaluation with a dual-role factor

This paper provides rigorous analytical discussions of the dual-role factor classification problem in Data Envelopment Analysis (DEA). We study two approaches taking opposite directions: one (the conventional and popular approach) clarifies the input/output roles prior to analysis, while the other incorporates the dual roles into the analysis. We show that both approaches are necessary and related. The former requires modification and the latter is a special empirical implication of the former after modifying. Two pitfalls are discussed, i.e., providing underestimated efficiency and a benchmark contradicting the role classification. Finding pitfalls in the form of observing slacks in the empirical implementation applying the standard DEA models with pre-classified roles, we suggest that a Pareto–Koopmans efficiency measure can help avoid unmeaningful outcomes even without considering the interaction among the dual-role factor and other inputs and outputs.