Efficiency analysis in two-stage data envelopment analysis with shared resources and undesirable outputs: an application in the banking sector

In classic and traditional data envelopment analysis (DEA) models, the production process is considered as single stage process and the internal structures have been ignored. In many real-world occasions, however, the processes have two- or multi-stage structures with or without shared resources. Two-stage DEA models deal with the calculation of the technical efficiency of a system, taking into consideration its internal structures. In this contribution, we consider a two-stage production process in which both stages are fed by shared resources, and there are undesirable products from the second stage. In the model we will propose, an optimal split on shared resources is given. To demonstrate the applicability of the proposed approach, data on 40 bank branches in seven years 2014-2020 is presented. In our real application in the banking sector, we find out that the most important sources of inefficiency of bank branches are related to interest revenue and overdue debt (undesirable output). Moreover, we saw that almost all branches were inefficient in the second stage (sale and service section) in all the seven years of evaluation.