A three-stage Data Envelopment Analysis model with application to banking industry

•Traditional Data Envelopment Analysis (DEA) treats bank branches as black boxes.•Black box DEA models primarily consider the initial inputs and the final outputs.•Intermediate measures are often lost in the traditional black box DEA models.•We propose a DEA model for banking with three stages.•Two independent parallel stages are linked to a third final stage in the model. The changing economic conditions have challenged many financial institutions to search for more efficient and effective ways to assess their operations. Data Envelopment Analysis (DEA) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogenous Decision Making Units (DMUs) by evaluating their relative efficiency. The traditional DEA treats DMUs as black boxes and calculates their efficiencies by considering their initial inputs and their final outputs. As a result, some intermediate measures are lost in the process of changing the inputs to outputs. In this study we propose a three-stage DEA model with two independent parallel stages linking to a third final stage. We calculate the efficiency of this model by considering a series of intermediate measures and constraints. We present a case study in the banking industry to exhibit the efficacy of the procedures and demonstrate the applicability of the proposed model.