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.
Highlights
Data envelopment analysis (DEA), as introduced by Charnes et al [1], is a data-driven tool for performance evaluation, benchmarking, and multiple-criteria decision-making [2,3,4]
We demonstrate that the uniform efficiency decomposition and Nash bargaining game decomposition are equivalent in nature
Efficiency decomposition can help decision-makers to establish the inefficient source so that appropriate efforts can be devoted to improving performance
Summary
Data envelopment analysis (DEA), as introduced by Charnes et al [1], is a data-driven tool for performance evaluation, benchmarking, and multiple-criteria decision-making [2,3,4]. A new efficiency decomposition method is proposed based on the Nash bargaining game model, which results in unique stage efficiencies as well. Different from the assumption of the Nash bargaining game in Zhou et al.’s model [23], Kao and Hwang [20] view sub-stages from the perspective of a Stackbelberg game. They examine the potential sequences of two stages by assuming that one stage has the priority and maximizing its efficiency, and calculating the efficiency of the other stage afterwards. This article redefines the concept of fairness in efficiency decomposition, and proposes a rank-based model to obtain unique sub-stage efficiencies when non-uniqueness happens.
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