Ratio-based RTS determination in weight-restricted DEA models

This paper provides computationally efficient approaches for determining to which returns to scale (RTS) class a unit belongs in weight-restricted Data Envelopment Analysis (DEA) models. A non-traditional computational algorithm is introduced. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. Some theorems and algorithms are given. Computational advantages of the provided results are discussed and one of the algorithms is illustrated using real world data.     

Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis

An issue which has received widespread attention in rapidly growing field of DEA is the sensitivity of the results of analysis to perturbations in the data.     

基于SFA与DEA模型的创新型城市科技创新效率实证研究

分别运用SFA模型和DEA模型对10个样本城市2001-2010年的科技创新效率进行定量测度,并对两种方法测度出的创新型城市科技创新效率值排序进行相关分析和一致性检验.结果表明两种方法测度出的创新型城市科技创新效率在数值上有显著差异,但在效率排序上具有很好的一致性.     

基于SMAA和公共权重的决策单元效率评价与排序

在数据包络分析(DEA)中,公共权重模型是决策单元效率评价与排序的常用方法之一。与传统DEA模型相比,公共权重模型用一组公共的投入产出权重评价所有决策单元,评价结果往往更具有区分度且更为客观。本文考虑决策单元对排序位置的满意程度,提出了基于最大化最小满意度和最大化平均满意度两类新的公共权重模型。首先,基于随机多准则可接受度分析(SMAA)方法,计算出每个决策单元处于各个排名位置的可接受度;然后,通过逆权重空间分析,分别求得使最小满意度和平均满意度最大化的一组公共权重;最后,利用所求的公共权重,计算各决策单元的效率值及相应的排序。算例分析验证了本文提出的基于SMAA的公共权重模型用于决策单元效率评价与排序的可行性。     

Testing over-representation of observations in subsets of a DEA technology

This paper proposes a test for whether data are over-represented in a given production zone, i.e. a subset of a production possibility set which has been estimated using the non-parametric Data Envelopment Analysis (DEA) approach. A binomial test is used that relates the number of observations inside such a zone to a discrete probability weighted relative volume of that zone. A Monte Carlo simulation illustrates the performance of the proposed test statistic and provides good estimation of both facet probabilities and the assumed common inefficiency distribution in a three dimensional input space. Potential applications include tests for whether benchmark units dominate more (or less) observations than expected.     

不确定环境下基于交叉评价的模糊综合评价方法

由于环境的不确定性,多属性决策中客观数据和主观因素并存,决策者很难做出精准的评判.借鉴DEA交叉评价的思想,将量化数据用交叉评价方法进行处理,得出平均交叉效率值作为模糊综合评价的指标进行二次评价.建立了不确定环境下基于交叉评价的模糊综合评价模型,并通过评价实例验证了模型的客观、全面性.     

用DEA估计生产力进步的探讨

有关生产力进步的概念与计算,文［１］、［２］基于规模报酬不变的生产前沿面来研究,本文推广到基于一般生产前沿面来研究．因此本文在讨论中用面向输出的Ｃ２ＧＳ２模型而不是文［１］、［２］中所用的面向输入的Ｃ２Ｒ模型．     

只有输出(入)的DEA改进模型及其应用

研究了只有输出(入)的DEA分析方法,针对只有输出(入)DEA模型的不足,重新定义了只有输出(入)的DEA评价方法的有效性,并改进了模型。相对已有的只有输出(入)的DEA模型,该模型充分利用了决策单元的诸输出(入),提高了DEA评价的效果。作为应用,运用新模型对武警防暴队形优选问题进行了有效性分析。     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

引入特征AHP的PDEA评价模型研究

提出了基于特征AHP的带偏好DEA评价模型,该模型充分利用了带偏好约束锥的DEA方法能反映决策者对各准则的偏好程度,具备研究多个同类样本的"相对优劣性"评价的优势,并可有效地避免了由于引入偏好带来的主观性.最后,通过模型仿真、分析,验证了提出的评价模型的优点.     

Chapter 11 Simulation studies of efficiency,returns to scale and misspecification with nonlinear functions in DEA

Using statistically designed experiments, 12,500 observations are generated from a 4-pieced Cobb-Douglas function exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes ofn=50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at corner points), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances — which suggests that COLS may have previously unidentified robustness properties — while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted.     

论“打开黑箱评价”的网络DEA模型

讨论了两阶段网络DEA模型KH,复合网络DEA模型WYP,以及两个模型之间的关系.并指出了上述两个模型能够打开"黑箱".     

基于AHP和DEA联用的城市交通环境可持续发展评价方法研究

将层次分析法(AHP)和数据包络分析(DEA)相结合构建了两种方法的联用评价模式,对使用该方法评价城市交通环境可持续发展水平和后续决策指导方面进行了探讨.该方法对AHP法在多个决策单元定量对比分析和DEA体现决策者偏好方面进行了改善.从影响城市交通环境可持续发展水平的城市综合发展、道路设施水平、交通运输功能和交通环境质量等方面出发,建立了城市交通环境可持续发展评价体系,并应用于深圳市实证分析,通过AHP分析认为深圳市2000～2007年城市交通环境可持续发展水平在波动中缓慢上升,再通过27个城市2005年数据DEA有效性分析和投影分析,得到深圳市在城市交通环境可持续发展方面的总体效率为0.9729,并得到了其要达到DEA有效的调整方案和部分政策建议.     

Developing a step-by-step effectiveness assessment model for customer-oriented service organizations

Effectiveness involves more than simple efficiency, which is limited to the production process assessment of peer operational units. Effectiveness incorporates variables that are both controllable (i.e. efficiency) and non-controllable (i.e. perceived quality) by the operational units. It is a fundamental driver for the success of either a for-profit or a non-for-profit unit in a competitive environment that is customer/citizen- and goal-oriented. Additionally, with respect to the short-run production constraints, i.e. the resources available and controllable by the operational units, and the legal status, we go beyond the traditional effectiveness assessment techniques by developing a Modified or “rational” Quality-driven-Efficiency-adjusted Data Envelopment Analysis (MQE-DEA) model. This particular model provides in the short run a feasible effectiveness attainment path for every disqualified unit in order to meet high-perceived quality and high-efficiency standards. By applying the MQE-DEA model a new production equilibrium is determined, which is different from the equilibrium suggested by the mainstream microeconomic theory, in that it takes into account not only the need for operational efficiency but also the customer-driven market dynamics.     

Decomposing technical efficiency and scale elasticity in two-stage network DEA

The constant returns to scale assumption maintained by neoclassical theorists for justifying the black-box structure of production technology in long run does not necessarily allow one to infer that there are no scale benefits available in its sub-technologies. Most of real-life production technologies are multi-stage in nature, and the sources of increasing returns lie in the sub-technologies. It is, therefore, imperative to estimate the scale economies of a firm not only for the network technology but also for the sub-technologies. To accomplish this, two approaches are suggested in this contribution, based on the premise concerning whether a network technology construct considers allocative inefficiency. The first approach, which is ours, makes use of a single network technology for two interdependent sub-technologies. The second approach, which is due to Kao and Hwang (2011), however, assumes complete allocative efficiency by considering two independent sub-technology frontiers, one for each sub-technology. The distinction between these two approaches is important from a policy point of view since the network efficiencies revealed from these two approaches have distinctive causative factors that do not permit them to be used interchangeably.     

运用DEA方法评价地区科技资源配置的相对有效性

本文针对我国东部、中部和西部地区科技资源状况的差异性,运用数据包络分析方法(DEA方法)来评价区域科技资源配置的相对有效性,指出了区域科技资源配置状况的非均衡性,并揭示了影响科技资源配置相对效率的原因。     

An extension to data envelopment analysis with preference structure for estimating overall inefficiency

This paper extends data envelopment analysis (DEA) with preference structure by fully considering the substitution effects among different inputs or outputs. When the unit cost and price information on inputs and outputs are available, the generalized weighted CCR (GWCCR) models proposed in this paper can provide some scalar values for measuring the overall inefficiency. It is found that the GWCCR models focus on the relative aspects of overall inefficiency instead of the absolute aspects focused on by the weighted additive DEA model.     

How to measure the impact of environmental factors in a nonparametric production model

The measurement of technical efficiency allows managers and policy makers to enhance existing differentials and potential improvements across a sample of analyzed units. The next step involves relating the obtained efficiency estimates to some external or environmental factors which may influence the production process, affect the performances and explain the efficiency differentials. Recently introduced conditional efficiency measures (,  and ), including conditional FDH, conditional DEA, conditional order-m and conditional order-α, have rapidly developed into a useful tool to explore the impact of exogenous factors on the performance of Decision Making Units in a nonparametric framework. This paper contributes in a twofold fashion. It first extends previous studies by showing that a careful analysis of both full and partial conditional measures allows the disentangling of the impact of environmental factors on the production process in its two components: impact on the attainable set and/or impact on the distribution of the efficiency scores. The authors investigate these interrelationships, both from an individual and a global perspective. Second, this paper examines the impact of environmental factors on the production process in a new two-stage type approach but using conditional measures to avoid the flaws of the traditional two-stage analysis. This novel approach also provides a measure of inefficiency whitened from the main effect of the environmental factors allowing a ranking of units according to their managerial efficiency, even when facing heterogeneous environmental conditions. The paper includes an illustration on simulated samples and a real data set from the banking industry.     

An environment-adjusted evaluation of citizen satisfaction with local police effectiveness: Evidence from a conditional Data Envelopment Analysis approach

Hard data alone are not sufficient to evaluate local police effectiveness in the new age of community policing. Citizens can provide useful feedback regarding strengths and weaknesses of police operations. However, citizen satisfaction indicators typically fail to accurately convey the multidimensional nature of local policing and account for characteristics that are non-controllable for the local police departments. In this paper, we construct a measure of perceived effectiveness of community oriented police forces that accounts for both multidimensional aspects of local policing and exogenous influences. In specific, this paper suggests the use of a multivariate conditional, robust order-m version of a non-parametric Data Envelopment Analysis approach with no inputs. We show the potentiality of the method by constructing and analyzing perceived effectiveness indicators of local police forces in Belgium. The findings suggest that perceived police effectiveness is significantly conditioned by the demographic and socioeconomic environment.