A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design

Abstract

Data envelopment analysis (DEA) is a data-driven tool for performance evaluation, benchmarking and multiple-criteria decision-making. This article investigates efficiency decomposition in a two-stage network DEA model. Three major methods for efficiency decomposition have been proposed: uniform efficiency decomposition, Nash bargaining game decomposition, and priority decomposition. These models were developed on the basis of different assumptions that led to different efficiency decompositions and thus confusion among researchers. The current paper attempts to reconcile these differences by redefining the fairness of efficiency decomposition based on efficiency rank, and develops a rank-based model with two parameters. In our new rank-based model, these three efficiency decomposition methods can be treated as special cases where these parameters take special values. By showing the continuity of the Pareto front, we simplify the uniform efficiency decomposition, and indicate that the uniform efficiency decomposition and Nash bargaining game decomposition can converge to the same efficiency decomposition. To demonstrate the merits of our model, we use data from the literature to evaluate the performance of 10 Chinese banks, and compare the different efficiency decompositions created by different methods. Last, we apply the proposed model to the performance evaluation of sustainable product design in the automobile industry.