Abstract
Data envelopment analysis (DEA) is a nonparametric approach for measuring the relative efficiencies of peer decision-making units (DMUs). For systems with two-stage structures, where all the outputs from the first stage are the only inputs to the second stage, the centralized model, which is based on the concept of cooperative game theory, has been widely used to examine the efficiencies of such systems. We define the cross efficiencies of systems with two-stage structures. Since the centralized model may lead to multiple and unacceptable cross efficiencies and rankings of DMUs due to its high flexibility in choosing optimal weights on input and output factors, we develop a game model to obtain a unique cross efficiency measure, which is constructed from the perspective of noncooperative game. An iterative algorithm is then proposed to obtain the game cross efficiencies for the overall systems and subsystems. We use the proposed game model to evaluate the performance of top 30 US commercial banks. The results show that the game model can lead to a unique reasonable cross efficiency for each DMU.
Highlights
Data envelopment analysis (DEA) is a nonparametric approach for identifying the best practice of decision-making units (DMUs)
In order to solve the problems exist in the aforementioned game-theoretic centralized model for two-stage systems, that is, DMUs can choose very high weights on some factors and extremely low weights on other factors in order to obtain full efficiencies, we use peer evaluation instead of selfappraisal for the centralized model and define cross efficiency indicators for the whole system and two stages
We develop an iterative algorithm to obtain the best performance of all DMU simultaneously, in a cross efficiency sense
Summary
Data envelopment analysis (DEA) is a nonparametric approach for identifying the best practice of decision-making units (DMUs). A DMU can obtain a full efficiency by choosing very high weights on some factors and Journal of Applied Mathematics extremely low weights on other factors This drawback may lead to unreasonable rankings of DMUs. This drawback may lead to unreasonable rankings of DMUs This shortcoming exists in the aforementioned game-theoretic models for DMUs with two-stage structures. In order to solve the problems exist in the aforementioned game-theoretic centralized model for two-stage systems, that is, DMUs can choose very high weights on some factors and extremely low weights on other factors in order to obtain full efficiencies, we use peer evaluation instead of selfappraisal for the centralized model and define cross efficiency indicators for the whole system and two stages.
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