estimating the mpi in vrs technologies by cross evaluation method

In this study, the cross evaluation technique is applied for estimating the malmquist productivity index (mpi) of decision making units (dmus) over two time periods in the variable return to scale technologies. the cross evaluation models of data envelopment analysis (dea) increases the rationality of results by averaging all self and peer assessment scores of each dmu. to deal with the probable multiple optimal solution, the benevolent secondary goal is used. maintaining the optimal score of dmu under evaluation, the benevolent model optimize the efficiency average of other dmus. finally, the mpi and its decomposition values of 14 iranian airplanes companies over five time periods (2016-2020) are estimated by the proposed method.