A new dynamic range directional measure for two-stage data envelopment analysis models with negative data

In the conventional data envelopment analysis (DEA) approach, decision making units (DMUs) are regarded as black boxes that transform sets of inputs into sets of outputs without considering the internal interactions taking place within each DMU. Two-stage DEA models are designed to overcome this shortfall. However, the existing two-stage DEA models can be applied only to performance measurement systems characterized by positive input-intermediate-output data while, in real world situations, data can also take negative values. We propose a new dynamic range directional measure (RDM) for two-stage DEA models that allows for negative data as well as for both desirable and undesirable carryovers. We analyze the main properties of the newly introduced model and characterize the associated efficiency notions. Finally, we present a case study in the banking industry to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures defined within it.