Data envelopment analysis (DEA) is a linear programming and production theory-based nonparametric approach that is generally used for efficiency analysis. Older DEA models, such CCR and BCC, can only identify decision-making units (DMUs) efficient or inefficient. The super-efficiency DEA model enables efficient DMUs to be ranked. A change in efficient DMUs can be measured using Malmquist index model, and the Malmquist productivity change index can be decomposed multiplicatively into an efficiency-change component (Effch) and a technical change component (Techch). This paper analyzes the water use efficiency in Shandong Province between 2006 and 2015 using Malmquist productivity index (TFP). The results show that: (1) the mean of super-efficiency scores of 17 cities in Shandong Province for the period 2006–2015 is between 0.965 and 2.760; (2) the water use efficiency was positive in 2006–2007, 2007–2008, and 2013–2014; however, it was negative in the other periods between 2006 and 2015; and (3) technical change is the key influencing factor on water use efficiency of 17 cities in Shandong Province. So, we suggest that Shandong Province encourage technological innovation to promote water use efficiency.

中文翻译：

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使用超高效数据包络分析法分析用水效率

数据包络分析（DEA）是一种基于线性编程和生产理论的非参数方法，通常用于效率分析。较旧的DEA模型（例如CCR和BCC）只能识别有效或无效的决策单位（DMU）。超高效DEA模型可对高效DMU进行排名。可以使用Malmquist指数模型测量有效DMU的变化，并且可以将Malmquist生产率变化指数乘以分解成效率变化成分（Effch）和技术变化成分（Techch）。本文利用马尔姆奎斯特生产率指数（TFP）分析了2006年至2015年山东省的用水效率。结果表明：（1）2006-2015年山东省17个城市的超效率得分平均值在0.965和2.760之间；（2）2006-2007年，2007-2008年和2013-2014年的用水效率为正；但是，在2006年至2015年的其他期间，这是负面的；（3）技术变化是影响山东省17个城市用水效率的关键因素。因此，我们建议山东省鼓励技术创新以提高用水效率。