基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。     

考虑决策单元竞争合作动态变化的DEA博弈交叉效率方法

利用DEA方法进行相对效率评估时,决策单元通常需要考虑多重目标,且随着目标的变化,决策单元间竞争合作状态也会发生动态变化。传统竞合模型虽然考虑了决策单元间竞争与合作同时存在的现象,但忽视了竞争合作关系动态变化的过程。本文以竞争合作对策为切入点,将多目标规划中的优先因子引入传统DEA博弈交叉效率模型中,提出了带有优先等级的多目标DEA博弈交叉效率模型,即动态竞合博弈交叉效率模型。该模型充分体现了不同目标下决策单元间竞争合作关系的动态变化,其焦点由传统竞合模型对多重最优权重现象的改善,转向对最优效率得分的直接寻找。利用DEA动态竞合博弈交叉效率模型,本文对环境污染约束下2014年长三角地区制造业投入产出绩效进行了客观的评估。分析结果表明:DEA动态竞合博弈交叉效率模型收敛速度优于传统DEA博弈交叉效率模型,其交叉效率得分收敛于唯一的纳什均衡点;不同目标重要性的差异程度,对最终排名结果不产生明显影响,不需要确切指出。     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

基于动态网络DEA模型的机场绩效研究

在已有网络DEA的基础上加入时间维度,构建了多时段下具有串联决策单元内部结构的复杂系统动态网络DEA效率评价模型.模型与传统DEA模型相比,既克服了传统DEA无视系统内部结构的缺陷,又在传统DEA的决策空间和目标空间基础上加入了时间维度,可以考察决策单元在不同时段的效率变化,从而对解决多时段内的复杂系统效率评估问题具有更为现实的应用价值.运用模型对区域多机场系统中的机场运营效率进行了计算,结果表明:1)动态网络DEA模型综合机场多年的投入产出,引入联系变量将相邻两时段连接起来,系统全面地评价多年来机场的整体运营水平,避免了传统模型将各年度独立评价的不足.2)江苏7家机场在2006-2010年仅南京禄口机场动态效率值为1,其余机场效率值都比较低,说明这些机场5年整体运营不佳,需要进一步加强管理和改进.     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

基于交叉效率DEA和熵IAHP对物流企业绩效评价

本文在研究了现有文献对物流企业绩效评价的基础上,基于超效率DEA用以计算效率值的权值只在对被评价单元最有利的特定范围内取值、忽视绩效评价的公平性和IAHP方法主观判断性较大的缺陷,提出了交叉效率DEA和熵IAHP方法。交叉效率DEA的中心思想是采用互评体系,弥补了超效率DEA方法只是选择对被评价决策单元最有效的权重忽视公平性的缺陷。熵IAHP方法是客观确定权重的熵权法和体现决策者偏好的IAHP方法的结合,这有效地解决了IAHP方法确定指标权重时主观性过大的缺陷。笔者给出了交叉效率DEA和熵IAHP模型评价物流企业绩效的基本步骤,最后通过一个实例验证了此方法的有效性和优越性。     

基于随机前沿分析的三阶段DEA改进模型分析

针对传统三阶段DEA模型第二阶段存在部分投入值调整幅度过大的问题,提出了一种改进的三阶段DEA模型.该方法引入环境影响因子的概念,采用一个合适的统计方法来识别环境影响的重要性,进而提出一个新的调整公式,最后通过算例证明了传统三阶段DEA模型存在的不足以及所提出的模型的可行性与有效性.     

投入变量缺失系统DEA效率评价

针对投入变量缺失生产服务系统,提出一种基于DEA的相对效率评价方法.由于该系统的投入无法确知,首先需要依据产出对各决策单元(DMU)进行分组,并将其相对效率分解为组内效率与组间效率.对于组内效率,引人虚拟投入变量利用传统超效率DEA模型进行评价.而对于组间效率,则建立扩展的超效率DEA模型.最终以两类效率之积评价所有决策单元之间的相对效率.理论分析表明:投入缺失系统内决策单元有效的充要条件是其组内效率及其所在组的组间效率均有效.文章最后以基金项目评审为例进行实证分析,说明了本方法的合理性与可行性.     

改进的公共权重的区间DEA效率评价

提出了一种改进的公共权重的考虑非期望产出的区间数据包络模型(DEA)评价模型.通过Pearson相关性检验,VIF检验法和容忍度检验法对投入,期望产出和非期望产出指标进行约简,并计算出指标的客观权重,引入调和参数使客观权重满足DEA模型限制条件且存在最优解.该模型有效解决了传统DEA模型中可能发生的公共权重分配为零的情况发生,同时考虑了指标负面评价的情况,增加评价结果的区分度.对中国北方十个省份的矿业环境治理效率进行了实证分析,构建了矿山生态环境治理效率评价体系,与相关文献进行比较,表明该模型的有效性且可以有效降低计算复杂度,提高计算效率.     

模糊非径向DEA模型的可信度求解

传统的DEA模型(CCR、BCC)的径向效率度量是不完全的.它们只是分别地度量输入效率与输出效率,且效率度量没有考虑非零的输入松弛与输出松弛.修正的Russell方法消除了这些缺陷.基于修正的Russell方法,利用可信度方法,模糊DEA模型得以建立并求解.一个算例佐证了这一方法.     

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.     

Multiobjective data envelopment analysis

Data envelopment analysis (DEA) is popularly used to evaluate relative efficiency among public or private firms. Most DEA models are established by individually maximizing each firm's efficiency according to its advantageous expectation by a ratio. Some scholars have pointed out the interesting relationship between the multiobjective linear programming (MOLP) problem and the DEA problem. They also introduced the common weight approach to DEA based on MOLP. This paper proposes a new linear programming problem for computing the efficiency of a decision-making unit (DMU). The proposed model differs from traditional and existing multiobjective DEA models in that its objective function is the difference between inputs and outputs instead of the outputs/inputs ratio. Then an MOLP problem, based on the introduced linear programming problem, is formulated for the computation of common weights for all DMUs. To be precise, the modified Chebychev distance and the ideal point of MOLP are used to generate common weights. The dual problem of this model is also investigated. Finally, this study presents an actual case study analysing R&D efficiency of 10 TFT-LCD companies in Taiwan to illustrate this new approach. Our model demonstrates better performance than the traditional DEA model as well as some of the most important existing multiobjective DEA models.     

Network DEA approach to airports performance assessment considering undesirable outputs

In this paper, a directional distance approach is proposed to deal with network DEA problems in which the processes may generate not only desirable final outputs but also undesirable outputs. The proposed approach is applied to the problem of modelling and benchmarking airport operations. The corresponding network DEA model considers two process (Aircraft Movement and Aircraft Loading) with two final outputs (Annual Passenger Movement and Annual Cargo handled), one intermediate product (Aircraft Traffic Movements) and two undesirable outputs (Number of Delayed Flights and Accumulated Flight Delays). The proposed approach has been applied to Spanish airports data for year 2008 comparing the computed directional distance efficiency scores with those obtained using a conventional, single-process directional distance function approach. From this comparison, it can be concluded that the proposed network DEA approach has more discriminatory power than its single-process counterpart, uncovering more inefficiencies and providing more valid results.     

A new robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

Dual models of interval DEA and its extension to interval data

The purpose of this paper is to develop a new DEA with an interval efficiency. An original DEA model is to evaluate each DMU optimistically. There is another model called “Inverted DEA” to evaluate each DMU pessimistically. But, there are no relations essentially between DEA and inverted DEA. Thus, we formulate a DEA model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints. Thus, two end points can construct an interval efficiency. With the same idea, we deal with the interval inefficiency model which is inverse to interval efficiency. Finally, we extend the proposed DEA model to interval data and fuzzy data.     

A non-radial DEA approach to measuring environmental performance

Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. Past studies about the application of DEA to environmental performance measurement often follow the concept of radial efficiency measures. In this paper, we present a non-radial DEA approach to measuring environmental performance, which consists of a non-radial DEA-based model for multilateral environmental performance comparisons and a non-radial Malmquist environmental performance index for modeling the change of environmental performance over time. A case study of OECD countries using the proposed non-radial DEA approach is also presented. It is found that the environmental performance of OECD countries as a whole has been improved from 1995 to 1997.     

Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data

The objective of the present paper is to propose a novel pair of data envelopment analysis (DEA) models for measurement of relative efficiencies of decision-making units (DMUs) in the presence of non-discretionary factors and imprecise data. Compared to traditional DEA, the proposed interval DEA approach measures the efficiency of each DMU relative to the inefficiency frontier, also called the input frontier, and is called the worst relative efficiency or pessimistic efficiency. On the other hand, in traditional DEA, the efficiency of each DMU is measured relative to the efficiency frontier and is called the best relative efficiency or optimistic efficiency. The pair of proposed interval DEA models takes into account the crisp, ordinal, and interval data, as well as non-discretionary factors, simultaneously for measurement of relative efficiencies of DMUs. Two numeric examples will be provided to illustrate the applicability of the interval DEA models.     

基于CAR-DEA方法的环境效率评价研究

现有环境效率评价的DEA方法没有考虑多维偏好约束问题,即不同决策单元对不同期望产出和不期望产出的偏好不同. 以地区为例,不同地区对GDP、废水和废气赋予的权重偏好各不相同. 在这种情况下,由于各决策单元的偏好约束不同,形成多维偏好约束集,在传统DEA模型中容易出现无可行解现象. 针对这一问题,基于CAR-DEA方法,结合保证域理论,提出一种解决多维偏好约束集问题的环境效率评价模型. 采用中国工业系统的环境效率评价实例对提出的方法进行了分析和说明.     

Performance evaluation: An integrated method using data envelopment analysis and fuzzy preference relations

In a multi-attribute decision-making (MADM) context, the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives. This paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations. This proposed approach includes three stages. First, pairwise efficiency scores are computed using two DEA models: the CCR model and the proposed cross-evaluation DEA model. Second, the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation. Third, by use of the row wise summation technique, we yield a priority vector, which is used for ranking decision-making units (DMUs). For the case of a single output and a single input, the preference relation can be directly obtained from the original sample data. The proposed approach is validated by two numerical examples.