具有阶段最终产出的链式网络DEA模型

针对具有阶段最终产出的链式网络提出了阶段最终产出为期望产出和非期望产出的概念并建立了相应的网络模型.给出了网络决策单元的网络DEA有效性与阶段DEA有效性的关系,给出了判别的充分必要条件.可以判断当网络决策单元不为网络DEA有效时,它在哪个阶段出现了无效率的情况.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.     

具有偏好锥的链式网络DEA模型

对链式网络DEA模型进行推广,将"偏好锥"引入网络DEA模型.针对中间产出重要性以及决策者评价时的偏好,建立带有产出锥和投入锥相应的两阶段生产可能集,对具有"偏好锥"的链式网络DEA模型,证明了决策单元为网络DEA有效的充要条件,给出了网络DEA有效性与各阶段弱DEA有效性的关系.另外,文章结合具体算例说明了偏好锥的变化对效率评价的影响.关于两阶段的模型以及相关结论可以推广到多阶段网络结构.     

只有产出(投入)BC~2模型中决策单元效率的几何刻画

在DEA方法中,DEA有效和弱DEA有效的决策单元位于生产前沿面上,非弱DEA有效的DEA无效决策单元位于生产可能集的内部而非生产前沿面上.通过引入生产可能集与生产前沿面移动的思想,证明只有产出(投入)的BC²模型评价下的决策单元的最优值与相应的生产前沿面的移动值存在倒数关系,以双产出(投入)情形图示说明,明确了决策单元在生产可能集中所处的位置.     

非期望产出的DEA效率评价

将非期望产出作为投入应用到传统DEA模型上,解决了非期望产出生产活动的效率评价问题.结合生产可能集,将非期望产出直接反映到生产可能集中,建立了基于投入导向的径向和非径向两种DEA模型.并对两种DEA模型效率值的大小关系、相对有效性的等价性问题进行了证明,指出非径向DEA模型更能准确的实现效率定量评价.     

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.     

考虑非期望产出的我国对外开放机场生产效率评估北大核心

针对已有对机场生产效率评估中忽视非期望产出这一问题,研究构建了非期望产出模型SBM-Undesirable,选择我国对外开放机场为研究对象,对其机场生产效率进行评估,并在此基础上对对外开放机场投入产出要素进行定量调整.研究结果表明:在机场生产运营过程中存在非期望产出的情况下,采用SBM-Undesirable模型对其进行效率评价,能够避免传统DEA模型的缺陷,提高效率评价的准确性.通过模型分析发现我国62个对外开放机场中有18个机场生产效率有效,而采用传统CCR模型进行机场生产效率评估时,只有12个机场生产效率有效,说明非期望产出对外开放机场生产效率有显著的影响;我国对外开放机场的生产效率有显著的区域特征,我国区域对外开放机场生产效率得分排序为华中、西南、西北、华南、华东、华北、东北;通过对我国生产效率无效的对外开放机场分析,发现各个对外开放机场普遍存在投入冗余、效益产出不足和非期望产出过多的情况,优化投入产出配置能力、减少机场投诉数量等非期望产出和增加机场有效产出是改善机场生产效率的现实途径.     

考虑非期望产出的我国对外开放机场生产效率评估

针对已有对机场生产效率评估中忽视非期望产出这一问题,研究构建了非期望产出模型SBM-Undesirable,选择我国对外开放机场为研究对象,对其机场生产效率进行评估,并在此基础上对对外开放机场投入产出要素进行定量调整.研究结果表明:在机场生产运营过程中存在非期望产出的情况下,采用SBM-Undesirable模型对其进行效率评价,能够避免传统DEA模型的缺陷,提高效率评价的准确性.通过模型分析发现我国62个对外开放机场中有18个机场生产效率有效,而采用传统CCR模型进行机场生产效率评估时,只有12个机场生产效率有效,说明非期望产出对外开放机场生产效率有显著的影响;我国对外开放机场的生产效率有显著的区域特征,我国区域对外开放机场生产效率得分排序为华中、西南、西北、华南、华东、华北、东北;通过对我国生产效率无效的对外开放机场分析,发现各个对外开放机场普遍存在投入冗余、效益产出不足和非期望产出过多的情况,优化投入产出配置能力、减少机场投诉数量等非期望产出和增加机场有效产出是改善机场生产效率的现实途径.     

具有非期望产出的随机DEA模型研究

为解决含有不确定信息的非期望产出效率评价问题,建立了一个非期望产出的随机DEA模型.该模型将非期望产出作为负期望产出进行处理,引入了期望效率值、显著性水平来刻画随机问题,并通过机会约束规划的相关知识将模型转化为确定形式.对模型的最优值的相关性质进行了探讨,说明最优值与期望效率值、显著性水平之间的关系.最后给出数值实验说明该模型的有效性.     

考虑投入和产出指标偏好的广义DEA模型

广义DEA是一种基于决策单元和非决策单元自由选择参考集的扩展DEA模型.传统DEA模型的最优解大多是由线性规划随机计算的,未能充分考虑投入和产出指标的重要程度.将投入和产出指标的决策者偏好引入到广义DEA模型约束条件中,首先定义投入和产出指标偏好矩阵,再将该矩阵纳入广义DEA模型的约束条件,构建了带投入和产出指标偏好的广义DEA模型(GDEA-IP).接下来给出决策单元GDEA-IP有效性与评价指标的量纲选择无关性的证明,以及决策单元为GDEA-IP弱有效和有效的理论证明.算例分析说明GDEA-IP模型的有效性,通过和其它经典模型的对比分析,进一步说明该模型比广义DEA模型具有更大的灵活性和通用性,拓展了DEA方法的理论研究.     

A new approach in modelling undesirable output in DEA model

With an increasing attention on the environment, one of the major research thrusts in Data Envelopment Analysis (DEA) based performance evaluation is the undesirable output in the conventional DEA model. There is considerable research published on the undesirable aspects of production outputs. However, the economic implications and the suitability of the DEA models for incorporating the undesirable outputs are less carefully investigated and discussed. In this paper, a comparative study is conducted of typical eco-DEA models to illustrate this issue. We propose a ratio model to evaluate the undesirable as well as the desirable outputs simultaneously. We apply the specially developed model to investigate the impact of production pollutants while conducting the efficiency evaluation in the textile industry of China. The results reveal that the production output-oriented efficiency evaluation can be significantly altered once the environmental aspects are factored into the model.     

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.     

Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs

In this paper, the inverse data envelopment analysis (DEA) with the preference of cone constraints will be discussed in a way that in the decision-making units, the undesirable inputs and outputs exist simultaneously. Supposing that the efficiency level does not change, if the unit under assessment increases the level of the desirable outputs and decreases the level of the undesirable outputs, how will it affect the amount of the desirable input level and the undesirable input level? To answer this question, the application of the inverse DEA with preference of cone constraints is suggested. The suggested approach, while maintaining the efficiency level, increases the level of its undesirable input and decreases the level of its desirable input by selection of strongly efficient solutions or some weakly efficient solutions of the multiple objective linear programming (MOLP) model. While maintaining the efficiency level, the suggested approach by selection of strongly efficient solution or some of the weakly efficient solutions of the MOLP model can increase the undesirable input level and decrease the desirable input level. Similarly, the suggested approach can be applied if the decision-making unit increases its undesirable input level and decreases the desirable input level so that the undesirable output level decreases and the desirable output level increases while maintaining the efficiency level. As an illustration, two numerical examples are rendered.     

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.     

Network DEA efficiency in input–output models: With an application to OECD countries

We undertake network efficiency analysis within an input–output model that allows us to assess potential technical efficiency gains by comparing technologies corresponding to different economies. Input–output tables represent a network where different sectoral nodes use primary inputs (endowments) to produce intermediate input and outputs (according to sectoral technologies), and satisfy final demand (preferences). Within the input–output framework it is possible to optimize primary inputs allocation, intermediate production and final demand production by way of non-parametric data envelopment analysis (DEA) techniques. DEA allows us to model the different subtechnologies corresponding to alternative production processes, to assess efficient resource allocation among them, and to determine potential output gains if inefficiencies were dealt with. The proposed model optimizes the underlying multi-stage technologies that the input–output system comprises identifying the best practice economies. The model is applied to a set of OECD countries.     

Characteristics and structures of weak efficient surfaces of production possibility sets

This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration.     

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.