This paper suggests that the efficiency of a system (decision-making unit) and its subsystem cannot be properly measured using a two-stage data envelopment analysis (DEA) model either in cooperative or non-cooperative evaluation. Indeed, the existing methods subjectively determine the status of the subsystems in the whole system. The two-stage DEA models, either cooperative game or non-cooperative game, are used to analyze the environmental efficiency. However, when the actual relationship between the two subsystems is inconsistent with the subjective relationship assumptions, the overall efficiency of the system and the efficiency of each subsystem will be biased. The conventional two-stage DEA models require predetermining the relationship between the subsystems within the system based on the subjective judgment of the decision-maker. Based on this, this paper proposes a three-step method to solve the two-stage DEA. First, the position relation among subsystems is determined according to the optimal weights through the model. According to the status relationship among subsystems, the decision units are grouped, and the two-stage DEA model of cooperative game or non-cooperative game is used to analyze the efficiency in each group. This method reduces the subjectivity of decision making and analyzes the efficiency of each decision unit applying the most appropriate two-stage DEA model to find the source of inefficiency. Finally, this paper verifies the rationality and validity of the method by analyzing the water use efficiency of industrial systems in China. It is found that most regions in China value economic development more than environmental protection (as evidenced by the DEA weights). What is more, the method proposed by the paper can be generalized for any two-stage DEA problem.
Environmental Efficiency Evaluation of Chinese Industry Systems by Using Non-Cooperative Two-Stage DEA Model