Measuring the productivity changes with double frontiers data envelopment analysis for two-stage processes

The purpose of this paper is to develop an output oriented methodology with constant return to scale (CRS) assumption for calculating productivity changes by using double frontier (optimistic and pessimistic) data envelopment analysis (DEA) simultaneously for two-stage processes. Measuring the productivity changes with Malmquist productivity index (MPI) via double frontiers DEA with single process has been defined by Wang and Lan (2011) as a geometrically average of optimistic and pessimistic point of views to generate an aggregate MPI. In order to develop and modify the previous studies, in this paper we have proposed a method to modify Wang and Lan (2011) aggregate MPI and also extend it to two-stage process which we refer to the double frontiers two-stage DEA (DFTDEA). It should be mentioned that the proposed model of this paper measures the MPI's distance functions for two individual stages and whole process for both DEA different points of view by the traditional DEA models and supposed relational models in output oriented CCR models, respectively. Therefore, the identified double frontiers two-stage DEA (DFTDEA-based MPI) is more realistic and comprehensive than the conventional optimistic or pessimistic DEA-based MPI individually. Subsequently, the proposed approach is examined to five Iranian commercial banks over the five-year period, 2009-2013.