Classical DEA models (such as CCR and BCC models) compute efficiencies of decisionmaking units (DMUs) based on a common efficient frontier but with no capability of differentiating efficient units. The super efficiency model was developed to rank efficient DMUs based a new efficient frontier comprised by all other DMUs. This may lead to a multi-platform problem that different efficient DMUs are evaluated based on different efficient frontiers and the resulted super efficiencies of efficient DMUs are not comparable. This paper addresses the multi-platform problem from the perspective of a cooperative game. Efficient DMUs are regarded as players and subsets of these efficient DMUs as coalitions. The effect of a coalition on a specific efficient DMU is defined as the DMU's efficiency change proportion (ECP) based on the traditional DEA models when the coalition is removed from the reference set. Basing on the ECP, we define a characteristic function as the sum of all efficient DMUs' ECPs, and prove that this function is super-additive. Then, the Shapley value is introduced as a solution of this cooperative game and applied to rank efficient DMUs. The proposed approach is demonstrated by two numerical examples. Finally, we extend the proposed approach in this paper to the VRS assumption.

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In recent decades, the high-speed development in China has caused serious air pollution in China. The present paper proposes a stochastic data envelopment analysis (DEA) model based on a general two-stage structure with comprehensively considering the randomness in both desirable and undesirable outputs to calculate the environmental efficiency of the industry system. The new proposed model is more applicable to practical system, and is applied to evaluate the performance of production and waste gas treatment in the industrial sector for China's regions along the "One Belt and One Road" in 2015. The results show that about half of the regions along "One Belt and One Road" in China are inefficient, where the performance on waste gas treatment is significantly worse than that of industrial production. Further, the managers should take different strategies for efficiency improvement in different areas because of the obvious differences in efficiency scores, in which the regions in the southeast area should pay more attention to improving waste gas treatment efficiency while that in the northwest area need to focus on industrial production efficiency.