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.     

基于样本评价的广义数据包络分析方法

传统DEA方法是一种依据自评体系评价的方法,而无法自主选择参照系.为了解决DEA方法可以同时依据自评体系和其它参照系进行评价问题,首先给出了广义DEA有效的概念.然后,给出了一类基于样本单元评价的广义数据包络分析模型,包括面向输入的广义DEA模型、面向输出的广义DEA模型以及加性广义DEA模型.最后,分析了上述这些模型与传统DEA模型之间的关系,探讨了广义DEA有效与相应多目标规划Pareto有效之间的关系,并给出了决策单元的投影性质以及决策单元的有效性排序方法.     

用超效率综合DEA模型来研究DEA有效性

对超效率综合DEA模型,有三个定理来判断其不可行性,其中一个定理基于加性模型来判断,并证明:当模型不可行时被评决策单元的扩展DEA有效性,由此给出了对扩展DEA有效的决策单元排序的方法,此外,对不含非阿基米德无穷小的基于输入(输出)的超效率综合DEA模型,当其最优值为1时,有一个定理来判断被评单元的DEA有效性.     

基于交叉评价策略的DEA灰色关联排序模型

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

基于交叉评价策略的DEA灰色关联排序模型北大核心

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

Interval DEA模型中决策单元的投影问题

在传统的DEA模型中,最优相对效率模型是在不大于1的范围内研究决策单元的效率的,最差相对效率模型是在不小于1的范围内研究决策单元的效率,这两种模型在研究投影问题时,是在不同的范围内进行的,有一定的片面性.将在interval DEA模型中,研究决策单元的投影问题,该模型是在相同的约束域内研究最优和最差相对效率模型,得出的结论将更加全面,通过两个定理给出了非DEA有效的决策单元在DEA有效面上的投影表达式和非DEA无效的决策单元在DEA无效面上的投影表达式.同时,通过一个实例对决策单元在interval DEA模型中的投影结果与在传统的DEA模型的投影结果进行了比较,发现投影结果比传统模型得到的投影结果对实际的生产有更强的指导意义.     

广义超效率区间DEA模型及其有效性研究

根据样本单元的区间投入、区间产出定义最大样本生产可能集,建立基于最大样本生产可能集的广义超效率区间DEA模型,然后定义了待评价决策单元基于广义超效率区间DEA模型的超效率区间,并讨论了待评价决策单元的有效性,最后通过实例表明了广义超效率区间DEA模型的实用性.     

修正的整数DEA模型及其在中西部高校社科研究中的应用

传统的DEA模型有时并不能给出含有整数值决策单元的准确投影方向,而现有的整数DEA模型还存在投影值不准确以及模型过于复杂等不足.因此,首先指出并说明已有整数DEA模型存在的问题.其次,给出了一个修正的整数DEA模型,并讨论了模型的性质以及与已有模型的关系.考虑到现实评价中投入产出指标同时含有整数与非整数的情况,进而给出了在修正模型下的混合整数DEA模型.最后,应用提出的模型分析并比较了中国中西部102所高校的社科研究效率及优化问题.     

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。     

决策单元的投影问题研究

在传统的DEA模型中,不论是最优相对效率模型或者最差相对效率模型,它们研究投影问题都是在不同的约束域内进行的,得出的结论都有一定的片面性.在bounded DEA模型中,决策单元的效率计算是在一个区间内进行的,可以同时研究非DEA有效的决策单元在有效前沿面上的投影和非DEA无效的决策单元在DEA无效面上的投影,得出的结论更加科学合理,并以定理的形式给出了投影结果的表达式.通过一个实例将投影结果与传统模型中得出的投影结果进行了比较,发现bounded DEA模型得到的投影结果对实际的生产具有更强的指导意义.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

Measuring super-efficiency in DEA in the presence of infeasibility

Super-efficiency data envelopment analysis (DEA) model is obtained when a decision making unit (DMU) under evaluation is excluded from the reference set. Because of the possible infeasibility of super-efficiency DEA model, the use of super-efficiency DEA model has been restricted to the situations where constant returns to scale (CRS) are assumed. It is shown that one of the input-oriented and output-oriented super-efficiency DEA models must be feasible for a any efficient DMU under evaluation if the variable returns to scale (VRS) frontier consists of increasing, constant, and decreasing returns to scale DMUs. We use both input- and output-oriented super-efficiency models to fully characterize the super-efficiency. When super-efficiency is used as an efficiency stability measure, infeasibility means the highest super-efficiency (stability). If super-efficiency is interpreted as input saving or output surplus achieved by a specific efficient DMU, infeasibility does not necessary mean the highest super-efficiency.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

生产可能集为凸包时的相对有效性评价模型

给出了一个评价决策单元相对有效性的新的DEA模型,它所对应的生产可能集被称为凸包形生产可能集,同时讨论了该模型解的存在性,定义了决策单元技术DEA有效和"上投影"的概念,断定一个决策单元的"上投影"相对于原来的决策单元是技术DEA有效的。最后给出一个应用新模型进行设施农业效率评价的例子。     

Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method

Data envelopment analysis methods classify the decision making units into two groups: efficient and inefficient ones. Therefore, the fully ranking all DMUs is demanded by most of the decision makers. However, data envelopment analysis and multiple criteria decision making units are developed independently and designed for different purposes. However, there are some applications in problem solving such as ranking, where these two methods are combined. Combination of multiple criteria decision making methods with data envelopment analysis is a new idea for elimination of disadvantages when applied independently. In this paper, first the new combined method is proposed named TOPSIS-DEA for ranking efficient units which not only includes the benefits of both data envelopment analysis and multiple criteria decision making methods, but also solves the issues that appear in former methods. Then properties and advantages of the suggested method are discussed and compared with super efficiency method, MAJ method, statistical-based model (CCA), statistical-based model (DR/DEA), cross-efficiency—aggressive, cross-efficiency—benevolent, Liang et al.’s model, through several illustrative examples. Finally, the proposed methods are validated.     

熵权DEA混合多目标评价方法研究

提高多目标决策问题评价结果的客观性、准确性,一直是决策科学研究的重要课题.结合熵权、DEA等数学方法对多目标决策问题进行研究,构造混合评价方法.首先通过构造熵权模型,获取主观权重;其次DEA的方法对多目标决策问题进行综合评价,得到问题的综合评价值,最后根据评价结果进行问题分析和判断.算例结果表明,方法能够应用于多目标决策问题,评价结果客观、准确.     

A distance friction minimization approach in data envelopment analysis: A comparative study on airport efficiency

This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving projection model, for both input reduction and output increase. In this approach, a generalized distance function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional projection function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner.     

基于C~2R模型的广义链式网络DEA模型

传统网络DEA方法是将传统DEA方法评价过程中的"黑箱"打开,考虑输入到输出的中间环节,对生产过程中的各个环节分别评价。传统网络DEA方法获得的是相对于有效决策单元评价的结果,但有时可能要相对于非有效决策单元或者非决策单元进行评价,传统网络DEA方法无法解决该类问题。为此给出相对于非有效决策单元或者非决策单元进行评价的基于C~2R模型的广义链式网络DEA模型,并探讨相关性质.     

具有包容关系的结构异质DEA效率评价方法

指标结构同质是数据包络分析（DEA）方法的基本假设之一;然而,现实问题的复杂性使得该假设常常难以完全被满足.针对具有包容关系的产出结构异质问题,通过解析决策单元（DMU）之间生产结构的内在关系来构建一种分阶段的DEA效率评价方法.该方法充分考虑了不同结构DMU的主观偏好,较好地规避了传统DEA方法在结构异质DMU效率评价过程中的不公平性.随后,该方法分别被拓展至投入结构异质和多重结构异质的情境中.最后,通过两个算例来说明本文方法的有效性与实用性.     

Target setting in data envelopment analysis using MOLP

Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods.