Cross Malmquist Productivity Index in Data Envelopment Analysis

In Data Envelopment Analysis (DEA), the Malmquist Productivity Index (MPI) is an important instrument used to assess dynamic performance. In this paper, to deal with overestimation, to increase rationality, and to reduce dependence on self-assessment results, we equip MPI with the cross-evaluation strategy. The MPI values measured from self and peer points of view are not the same necessarily, even significantly different or strongly inconsistent, and none of them can be ignored. Therefore, to match the results for the two common up-down and bottom-up strategies in building MPI indices, and to retain the multiplicative structure at the aggregate level, we use the geometric mean to aggregate the self and peer MPIs. Because the MPI indices of all units are calculated with several common bundle weights, the resulting values are consistent and therefore comparable. We will show the usability of the proposed method using a real example of 20 branches of an Iranian bank in 2017–2018.