Calculating scale elasticity in DEA models

In the data envelopment analysis (DEA) efficiency literature, qualitative characterizations of returns to scale (increasing, constant, or decreasing) are most common. In economics it is standard to use the scale elasticity as a quantification of scale properties for a production function representing efficient operations. Our contributions are to review DEA practices, apply the concept of scale elasticity from economic multi-output production theory to DEA piecewise linear frontier production functions, and develop formulas for scale elasticity for radial projections of inefficient observations in the relative interior of fully dimensional facets. The formulas are applied to both constructed and real data and show the differences between scale elasticities for the two valid projections (input and output orientations). Instead of getting qualitative measures of returns to scale only as was done earlier in the DEA literature, we now get a quantitative range of scale elasticity values providing more information to policy-makers.     

企业技术创新能力评价新方法的研究

企业发展的核心竞争力是技术创新能力,公正客观的评价企业的技术创新能力十分必要,研究新型的企业技术创新能力评价方法对企业的成长和可持续发展有所帮助。本文较为全面的分析了企业技术创新能力的概念、内涵与特征,并对现有的评价方法进行了调研和对比分析。提出企业技术创新能力评价分析时应将企业持续创新能力和经济效益作为评价的重要内容,研究并构建了包括创新支撑和创新主体两个二级指标在内的新的企业技术创新能力评价指标体系,并对指标的重要性进行了划分,以期为企业评价技术创新能力提供参考。     

Measuring returns to scale in DEA models when the firm is regulated

In the standard framework of data envelopment analysis (DEA) models, the returns to scale are fully characterized using the multiplier on the convexity constraint of inefficient decision making units (DMU) using the projection of the input–output vector on the frontier. In this note, we investigate how the returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constraints change the role played by the convexity constraint. In order to avoid biased estimation of the returns to scale, we show that the interaction between the regulatory and the convexity constraints has to be taken into account.     

基于生产结构视角的高新技术产业技术扩散影响研究

基于奥地利学派生产结构视角探讨高新技术产业外部技术扩散的影响路径,提出技术扩散通过生产结构的迂回性作用于技术创新,进而影响产出绩效。基于2005~2014年我国四个高新技术产业的面板数据,利用stata14软件进行数据分析,并对所提假设进行检验。结果表明:外部技术扩散对生产结构迂回性具有正向影响,但迂回性负向影响企业技术自主创新能力。研究结论对企业提升产业竞争力、增强技术创新和创新扩散效率具有重要的理论和实践启示。     

基于主成分分析的新能源储能企业技术创新能力研究

基于科技创新投入、产出、支撑和转化等四个影响因素,构建新能源储能企业科技创新能力评价模型,并运用主成分分析法和聚类分析法,对我国主要新能源储能企业的科技创新能力进行分析和评价．分析表明,我国新能源储能企业科技创新的能力主要取决于经费投入和科研能力两大因素．新能源企业科技创新的研发经费投入、科研人员配备、科研成果等方面,与国外企业相比差距大,科技创新能力亟待提高．     

A directional distance based super-efficiency DEA model handling negative data

This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input–output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input–output data are non-negative or not. It successfully addresses the infeasibility issue of both the conventional radial super-efficiency DEA model and the Nerlove–Luenberger super-efficiency DEA model under the assumption of variable returns to scale. Moreover, it can project each DMU onto the super-efficiency frontier along a suitable direction and never leads to worse target inputs or outputs than the original ones for inefficient DMUs. Additional advantages of the proposed model include monotonicity, units invariance and output translation invariance. Two numerical examples demonstrate the practicality and superiority of the new model.     

DEA方法进行规模收益分析的几点注记

自从 Banker等人 ( 1 984)用 DEA方法进行规模收益分析 ,已有越来越多的学者也在进行相关的研究 .研究主要从两个方面进行 :基于 DEA输入模型的方法和基于 DEA输出模型的方法 .这两类方法所应用的模型、条件、结论都有所不同 ,但在应用中有些文章将它们混淆在一起 .本文针对应用中容易出现的错误 ,给出反例和正确的判别规模收益状况的充分必要条件 .并由规模收益的定义 ,建议使用 DEA—输出模型进行规模收益分析 .     

Linear programming solutions and distance functions under a constant returns to scale technology

In this paper, we investigate the various relationships among the linear programming solutions of data envelopment analysis (DEA) models under a constant returns to scale technology. We derive the analytical relationships among the efficiency measures and the activity variables for four separate models: the input-based, the output-based, the hyperbolic, and the proportional distance functions. We apply our results in order to derive a test of consistency that can be used in assessing the returns to scale among differing DEA models.     

A new non-oriented model for classifying flexible measures in DEA

In conventional data envelopment analysis (DEA), measures are classified as either input or output. However, in some real cases there are variables which act as both input and output and are known as flexible measures. Most of the previous suggested models for determining the status of flexible measures are oriented. One important issue of these models is that unlike standard DEA, even under constant returns to scale the input- and output-oriented model may produce different efficiency scores. Also, can be expected a flexible measure is selected as an input variable in one model but an output variable in the other model. In addition, in all of the previous studies did not point to variable returns to scale (VRS), but the VRS assumption is prevailed on many real applications. To deal with these issues, this study proposes a new non-oriented model that not only selects the status of each flexible measure as an input or output but also determines returns to scale status. Then, the aggregate model and an extension with the negative data related to the proposed approach are presented.     

Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs

This paper develops a DEA (data envelopment analysis) model to accommodate competition over outputs. In the proposed model, the total output of all decision making units (DMUs) is fixed, and DMUs compete with each other to maximize their self-rated DEA efficiency score. In the presence of competition over outputs, the best-practice frontier deviates from the classical DEA frontier. We also compute the efficiency scores using the proposed fixed sum output DEA (FSODEA) models, and discuss the competition strategy selection rule. The model is illustrated using a hypothetical data set under the constant returns to scale assumption and medal data from the 2000 Sydney Olympics under the variable returns to scale assumption.     

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.     

外源投入型两阶段制造系统网络DEA效率分析研究

制造过程评价是改善制造系统效率的重要一环,传统的评价方法将每个制造系统决策单元视为黑箱来研究整体效率,忽略了中间产品转化信息及投入要素在各子过程中的配置信息。针对两阶段(第二阶段有外源性新投入)制造系统的效率评估问题,分别在固定规模报酬和可变规模报酬假设下,充分利用制造系统中间产品的转化及外源投入要素的配置信息,建立了制造系统网络DEA效率测度及分解模型,建模方法遵循客观评价原则,无需事先主观确定子效率和系统效率之间的组合关系。并将其应用于钢铁制造系统效率测度与分解,研究结果表明该方法能够挖掘决策单元内部子单元的效率情况,帮助决策者发现复杂制造过程非有效的根源,为复杂制造过程的整体效率测度及分解提供了有效的分析方法。     

Malmquist指数法对西部地区技术创新效率的评价——基于两阶段关联DEA方法

文章利用两阶段关联DEA模型计算Malmqusit指数及其分解指数,并用于评价西部地区技术创新效率,研究发现,当Malmqusit的一种分解指数对技术创新效率起促进作用时,另一种分解指数总会起制约作用。同时,在与传统DEA模型计算得到的结果相比,两阶段DEA方法得到的指数更能反映客观实际。     

The directional distance function and measurement of super-efficiency: an application to airlines data

In a recent paper published in this Journal, Lovell and Rouse (LR) proposed a modification of the standard data envelopment analysis (DEA) model that overcomes the infeasibility problem often encountered in computing super-efficiency. In the LR procedure one appropriately scales up the observed input vector (scale down the output vector) of the relevant super-efficient firm thereby usually creating its inefficient surrogate. By contrast, Chen suggested a different procedure that replaces input–output bundles that are found to be inefficient in standard DEA by their efficient projections. An alternative procedure proposed in this paper uses the directional distance function and the resulting Nerlove–Luenberger measure of super-efficiency. The fact that the directional distance function combines, by definition, features of both an input-oriented and an output-oriented model, generally leads to a complete ranking of the observations and is easily interpreted. A dataset on international airlines is utilized in an illustrative empirical application.     

Technical efficiency and economies of scale: A non-parametric analysis of REIT operating efficiency

This study measures technical efficiency and economies of scale for real estate investment trusts (REITs) by employing data envelopment analysis (DEA), a linear-programming technique. Using data from the National Association of Real Estate Investment Trusts (NAREITs) for the years 1992–1996, we find that REITs are technically inefficient, and the inefficiencies are a result of both poor input utilization and failure to operate at constant returns to scale. With respect to scale inefficiency, most REITs are operating at increasing returns to scale, suggesting that REITs could improve performance through expansion. Moreover, we employ regression analysis to determine what characteristics influence the efficiency measures obtained. The results show that internal REIT management is positively related to all measures of efficiency. Increasing leverage is negatively related to REIT input utilization. Finally, increasing REIT diversification across property types enhances scale efficiency (SE) but reduces input usage efficiency.     

两阶段视角下高技术产业技术创新效率及影响因素研究

基于两阶段视角,将规模报酬可变网络SBM模型和DEA.窗口分析方法相结合,分析了中国高技术产业17个细分行业2002-2011年间技术创新效率的变动趋势和行业差异,并利用面板Tobit,模型检验了技术创新效率的影响因素.结果表明:高技术产业技术创新效率值总体偏低,半数以上行业两阶段效率均处于低位区间,改进和提升空间很大.技术转化效率一直显著高于技术研发效率,两阶段效率失衡问题非常明显.行业集中度、开放度和所有制结构因素均对研发效率和总效率有显著影响,而行业集中度和企业规模对技术转化效率有显著影响.     

Data envelopment analysis with imprecise data

In original data envelopment analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. Cooper et al. [Management Science, 45 (1999) 597–607] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a non-linear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.     

基于云模型和证据理论的科技创新与持续发展能力评价

为科学合理地对企业科技创新与持续发展能力进行评估,文章从科技创新基础与现状情况、科技创新组织管理能力和科技创新持续发展能力三个方面入手建立企业科技创新与持续发展评估的指标体系,并针对指标的不确定性构建一种基于云模型和证据理论的科技创新与持续发展能力评价模型。首先应用云模型对评价指标转化为区间数并应用区间熵权法确定指标权重,其次运用证据理论对指标的置信度等进行计算得出评价对象的评估结果。最后以国网某省公司为例,分别应用基于云模型和证据理论的评估模型和区间证据推理方法进行评估研究,验证评价模型的可行性、准确性、科学性和合理性。研究结论为在企业科技创新与持续发展中应加强科技创新持续发展能力等方面的建设。     

Measurement of returns to scale using non-radial DEA models

There are some specific features of the non-radial data envelopment analysis (DEA) models which cause some problems for the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions from optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate as optimal, solutions contradicting optimization theory. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the non-radial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.     

Super-efficiency infeasibility and zero data in DEA

Lee et al. (2011) and Chen and Liang (2011) develop a data envelopment analysis (DEA) model to address the infeasibility issue in super-efficiency models. In this paper, we point out that their model is feasible when input data are positive but can be infeasible when some of input is zero. Their model is modified so that the new super-efficiency DEA model is always feasible when data are non-negative. Note that zero data can make the super-efficiency model under constant returns to scale (CRS) infeasible. Our discussion is based upon variable returns to scale (VRS) and can be applied to CRS super-efficiency models.