数据包络分析（DEA）的交叉效率理论方法与应用研究
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摘要
现实生活中经常需要对若干个相似的决策单元进行评价和筛选。为此,一些专家学者设计了若干种评价方法,其中数据包络分析方法(Data Envelopment Analysis, DEA)已经普遍被相关学者和研究人员所接受。DEA是用来评价一组具有多输入和多输出决策单元之间相对效率的数学方法,该方法显著特点是不需要预先估计任何参数,亦不需要假定投入与产出之间的函数关系,因此一定程度上避免了主观性的干扰。正是由于具有这种独特的客观性优势,DEA在理论研究中取得了大量的成果,并且被广泛应用于实践中。然而,经典的DEA方法也存在一些缺陷,如只能将被评价决策单元区分为有效单元与非有效单元,不能进一步对有效决策单元进行优劣排序；自评体系下得到的权重容易夸大被评价决策单元某些投入或产出指标的长处,规避另一些投入和产出指标短处,从而产生评价效率值过高的问题。针对这些缺陷,DEA研究不断走向深入,一些新的理论和方法被提出来,交叉效率方法则是其中典型的代表。交叉效率方法有效结合了自评和他评体系,不但可以给所有的决策单元进行完全排序,而且还能有效解决部分极端权重的问题,从而避免评价效率值过高现象。但是交叉效率方法依旧存在一些不足,如交叉效率的权重经常存在很多组解的情况,交叉效率值的随意性比较大,使得该方法的稳定性和实用性已经受到了严重影响；采用平均交叉效率值的方案使最终交叉效率值和权重缺少相应的关联性,因此决策单元很难得到有价值的信息改进自身存在的不足；现有交叉效率方法很少考虑决策单元之间存在竞争、合作甚至竞争合作同时存在的情况。为了解决上述问题,本文将多属性决策理论和博弈理论引入交叉效率方法中进行研究,开展的研究工作主要有以下几个方面：
第一章为绪论,首先简要介绍DEA和交叉效率相关的基本理论,然后介绍与本文研究内容相关的研究现状与研究不足,主要包括：基于DEA评价排序方法、DEA交叉效率的研究现状以及污染排放权的主要分配方式。最后,在这些研究现状和不足的基础上提出本文的研究内容与研究结构。
第二章研究交叉效率不唯一性问题。首先指出了交叉效率方法在对决策单元进行效率评价时存在交叉效率多组权重的问题,并讨论了现有的改进方法存在的弊端,然后引出了本章提出的两种交叉效率二次目标模型。每种模型不但可以有效解决交叉效率多解性的缺陷,而且能尽量减少加权投入和加权产出之间的离差,使其在效率评价过程中尽可能发挥作用。
第三章针对采用平均交叉效率所存在的弊端,从多属性决策分析角度出发,提出两种不同的交叉效率集结模型来放松交叉效率的平均假设性。这两种模型既能够与经典DEA交叉效率模型保持理论一致性,又能够从不同的角度保证决策单元的优劣可比性。针对决策单元含有区间数据的情形,本章又提出了区间交叉效率模型和区间交叉效率集结模型。每种提出的模型的合理性与有效性都通过具体的实例得到了验证。
第四章首先分析了现有交叉效率方法的一些不足,即考虑决策单元之间仅存在竞争或仅存在合作的情况。然而现实中一些决策单元之间是同盟合作关系,而另一些决策单元之间可能表现出竞争关系。因此在对这些决策单元进行评价时,现有交叉效率方法就显得不适用,因为没有考虑到不同决策单元之间的实际关联关系。然后针对这个问题,本章提出两种竞争合作交叉效率方法分别对应于不同的实际博弈应用场景,最后的实例说明提出的两种方法的有效性。
第五章首次将交叉效率方法应用在污染物排放权分配中,分别从整体理性和协调个体理性角度提出不同的分配模型,解决污染物排放权初始分配和减排分摊问题。与传统排放权分配方法相比,本章提出的方法的特点就是将企业的投入和产出因素全部考虑在内,即依据企业的生产技术效率分配排污排放权。造纸厂的实例验证了本章节提出的方法的有效性和合理性,并且分配方法不存在极端不合理的分配结果。
第六章总结归纳全文所有研究的内容和主要结论,并在此基础之上指出未来需要进一步深入研究的方向。
In reality, the evaluation and selection of the decision making units (DMUs) are the common and important work. In order to evaluate DMUs, many evaluation methods have been proposed by experts and scholars. Among these methods, Data Envelopment Analysis (DEA) has been generally accepted by scholars and researchers, which could evaluate efficiencies of a set of homogenous DMUs with multiple inputs and multiple outputs. The significant characteristic of DEA is that it does not require any preliminary parameter estimation and functional relation assumptions between inputs and outputs, which avoids bias caused by human factors. Because of this advantage, DEA method has been rapidly developed and widely used. However, traditional DEA models only classify all DMUs into efficient and inefficient DMUs, and those efficient DMUs cannot be differentiated any further. In addition, these traditional models usually generate the case that the weights at very small values (or even zero) are assigned to some inputs or outputs and very large values to other inputs or outputs. This may lead to that the efficiency of DMU under evaluation is overestimated. In order to solve these problems, cross-efficiency evaluation based on DEA has been proposed, which evaluates efficiencies of DMUs through self-and peer-evaluations. This method has two main advantages. On one hand, cross-efficiency evaluation has a strong discrimination power and usually provides a full ranking for all evaluated DMUs. On the other hand, unrealistic weight results could be avoided without requiring any weight restrictions. However, there are still some defects in cross-efficiency evaluation. Firstly, the optimal weights calculated by the traditional DEA model are generally not unique, which lead to non-uniqueness of cross-efficiency scores. This has reduced the usefulness of cross-efficiency evaluation. Secondly, averaging the cross-efficiency will lose the association between weights and results, thus it will not provide information for decision makers to improve the performance of DMUs. Lastly, the existing cross-efficiency methods pay little attention to case that some specific DMUs may have a cooperative relationship while some form of competition may exist among other DMUs. To overcome these drawbacks, this paper introduces multiple attribute decision making theory and game theory into DEA for proposing new cross-efficiency approaches. The main researches of the paper are as follows.
Chapter1firstly summarizes the fundamental theory of DEA, and then comprehensively reviews the existing research results related to this thesis. These research results include the evaluation methods based on DEA, cross-efficiency evaluation methods and the main allocation methods of emission permits. Finally, the research contents and structure of this paper are provided.
Chapter2studies on the non-uniqueness of cross-efficiency evaluation. This chapter firstly discusses the problem of non-uniqueness when cross-efficiency evaluation is used to evaluate the DMUs, and points out the disadvantages of the existing improved approaches. Then two different secondary models are proposed. Each model could not only effectively deal with the problem of non-uniqueness, but also reduce the differences between the weighted inputs or weighted outputs during the evaluation process. Thus all inputs and outputs in these newly proposed models can be fully used as much as possible.
Chapter3proposes two different cross-efficiency aggregation methods from the perspective of multiple attribute decision making to eliminate the assumption of average. The new methods not only keep theories consist with classical cross-efficiency method, but also evaluate and rank DMUs from different angles. In addition, this chapter also proposes interval cross-efficiency evaluation and aggregation methods to evaluate the efficiencies of DMUs with interval data. The validity of each proposed method is examined by the empirical example.
Chapter4firstly points out that traditional cross-efficiency methods consider the DMUs only have competitive or cooperative relationships. In reality, some specific DMUs may have a cooperative relationship, and some form of direct or indirect competition may exist among other DMUs. However, the existing DEA models cannot deal with this case. To address the need to simultaneously consider competition and cooperation, two cross-efficiency methods are proposed through comprehensively consider the defects of existing game cross-efficiency methods. Two empirical examples are illustrated to examine the validity of the proposed method.
Chapter5studies the allocation of emission permits using DEA. This chapter proposed several models from the perspectives of centralization and coordination of individual rationality to research initial allocation and reallocation of emission permits. Compared with the traditional allocation methods, the proposed DEA models consider the input and output levels simultaneously, and could provide the reasonable allocation results. A paper mill example is illustrated to examine the validity of the proposed methods.
Chapter6summarized the main research work of the thesis, and points out possible extensions for future study and improvement.
第一章为绪论,首先简要介绍DEA和交叉效率相关的基本理论,然后介绍与本文研究内容相关的研究现状与研究不足,主要包括：基于DEA评价排序方法、DEA交叉效率的研究现状以及污染排放权的主要分配方式。最后,在这些研究现状和不足的基础上提出本文的研究内容与研究结构。
第二章研究交叉效率不唯一性问题。首先指出了交叉效率方法在对决策单元进行效率评价时存在交叉效率多组权重的问题,并讨论了现有的改进方法存在的弊端,然后引出了本章提出的两种交叉效率二次目标模型。每种模型不但可以有效解决交叉效率多解性的缺陷,而且能尽量减少加权投入和加权产出之间的离差,使其在效率评价过程中尽可能发挥作用。
第三章针对采用平均交叉效率所存在的弊端,从多属性决策分析角度出发,提出两种不同的交叉效率集结模型来放松交叉效率的平均假设性。这两种模型既能够与经典DEA交叉效率模型保持理论一致性,又能够从不同的角度保证决策单元的优劣可比性。针对决策单元含有区间数据的情形,本章又提出了区间交叉效率模型和区间交叉效率集结模型。每种提出的模型的合理性与有效性都通过具体的实例得到了验证。
第四章首先分析了现有交叉效率方法的一些不足,即考虑决策单元之间仅存在竞争或仅存在合作的情况。然而现实中一些决策单元之间是同盟合作关系,而另一些决策单元之间可能表现出竞争关系。因此在对这些决策单元进行评价时,现有交叉效率方法就显得不适用,因为没有考虑到不同决策单元之间的实际关联关系。然后针对这个问题,本章提出两种竞争合作交叉效率方法分别对应于不同的实际博弈应用场景,最后的实例说明提出的两种方法的有效性。
第五章首次将交叉效率方法应用在污染物排放权分配中,分别从整体理性和协调个体理性角度提出不同的分配模型,解决污染物排放权初始分配和减排分摊问题。与传统排放权分配方法相比,本章提出的方法的特点就是将企业的投入和产出因素全部考虑在内,即依据企业的生产技术效率分配排污排放权。造纸厂的实例验证了本章节提出的方法的有效性和合理性,并且分配方法不存在极端不合理的分配结果。
第六章总结归纳全文所有研究的内容和主要结论,并在此基础之上指出未来需要进一步深入研究的方向。
In reality, the evaluation and selection of the decision making units (DMUs) are the common and important work. In order to evaluate DMUs, many evaluation methods have been proposed by experts and scholars. Among these methods, Data Envelopment Analysis (DEA) has been generally accepted by scholars and researchers, which could evaluate efficiencies of a set of homogenous DMUs with multiple inputs and multiple outputs. The significant characteristic of DEA is that it does not require any preliminary parameter estimation and functional relation assumptions between inputs and outputs, which avoids bias caused by human factors. Because of this advantage, DEA method has been rapidly developed and widely used. However, traditional DEA models only classify all DMUs into efficient and inefficient DMUs, and those efficient DMUs cannot be differentiated any further. In addition, these traditional models usually generate the case that the weights at very small values (or even zero) are assigned to some inputs or outputs and very large values to other inputs or outputs. This may lead to that the efficiency of DMU under evaluation is overestimated. In order to solve these problems, cross-efficiency evaluation based on DEA has been proposed, which evaluates efficiencies of DMUs through self-and peer-evaluations. This method has two main advantages. On one hand, cross-efficiency evaluation has a strong discrimination power and usually provides a full ranking for all evaluated DMUs. On the other hand, unrealistic weight results could be avoided without requiring any weight restrictions. However, there are still some defects in cross-efficiency evaluation. Firstly, the optimal weights calculated by the traditional DEA model are generally not unique, which lead to non-uniqueness of cross-efficiency scores. This has reduced the usefulness of cross-efficiency evaluation. Secondly, averaging the cross-efficiency will lose the association between weights and results, thus it will not provide information for decision makers to improve the performance of DMUs. Lastly, the existing cross-efficiency methods pay little attention to case that some specific DMUs may have a cooperative relationship while some form of competition may exist among other DMUs. To overcome these drawbacks, this paper introduces multiple attribute decision making theory and game theory into DEA for proposing new cross-efficiency approaches. The main researches of the paper are as follows.
Chapter1firstly summarizes the fundamental theory of DEA, and then comprehensively reviews the existing research results related to this thesis. These research results include the evaluation methods based on DEA, cross-efficiency evaluation methods and the main allocation methods of emission permits. Finally, the research contents and structure of this paper are provided.
Chapter2studies on the non-uniqueness of cross-efficiency evaluation. This chapter firstly discusses the problem of non-uniqueness when cross-efficiency evaluation is used to evaluate the DMUs, and points out the disadvantages of the existing improved approaches. Then two different secondary models are proposed. Each model could not only effectively deal with the problem of non-uniqueness, but also reduce the differences between the weighted inputs or weighted outputs during the evaluation process. Thus all inputs and outputs in these newly proposed models can be fully used as much as possible.
Chapter3proposes two different cross-efficiency aggregation methods from the perspective of multiple attribute decision making to eliminate the assumption of average. The new methods not only keep theories consist with classical cross-efficiency method, but also evaluate and rank DMUs from different angles. In addition, this chapter also proposes interval cross-efficiency evaluation and aggregation methods to evaluate the efficiencies of DMUs with interval data. The validity of each proposed method is examined by the empirical example.
Chapter4firstly points out that traditional cross-efficiency methods consider the DMUs only have competitive or cooperative relationships. In reality, some specific DMUs may have a cooperative relationship, and some form of direct or indirect competition may exist among other DMUs. However, the existing DEA models cannot deal with this case. To address the need to simultaneously consider competition and cooperation, two cross-efficiency methods are proposed through comprehensively consider the defects of existing game cross-efficiency methods. Two empirical examples are illustrated to examine the validity of the proposed method.
Chapter5studies the allocation of emission permits using DEA. This chapter proposed several models from the perspectives of centralization and coordination of individual rationality to research initial allocation and reallocation of emission permits. Compared with the traditional allocation methods, the proposed DEA models consider the input and output levels simultaneously, and could provide the reasonable allocation results. A paper mill example is illustrated to examine the validity of the proposed methods.
Chapter6summarized the main research work of the thesis, and points out possible extensions for future study and improvement.
引文
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