On ratio-based RTS determination: An extension

This technical note extends the results of our recent paper [Korhonen, Soleimani-damaneh, Wallenius, EJOR 215 (2011) 431–438], for determining the RTS status of Decision Making Units in Weight-Restricted DEA models.     

Finding the efficiency score and RTS characteristic of DMUs by means of identifying the efficient frontier in DEA

Data envelopment analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as decision-making units (DMUs), where the presence of multiple inputs and outputs makes comparisons difficult. The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, a method for identifying the efficient frontier is introduced. Then, the efficiency score and returns to scale (RTS) characteristic of DMUs will be produced by means of the equation of efficient frontier.     

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.     

Avoiding infeasibility in DEA models with weight restrictions

The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs.     

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.     

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.     

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.     

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．     

A dual simplex-based method for determination of the right and left returns to scale in DEA

This study reviews the concept of the “right” and the “left” returns to scale (RTS) in data envelopment analysis (DEA), and a dual simplex-based method, for determining these two notions in RTS, is proposed, which has computational advantages as compared to the customary method.     

Measurement of simultaneous scale and mix changes in inputs and outputs using DEA facets and RTS

We show a new use of the efficient facets in DEA. Specifically, once we have identified all facets of the DEA technology, we are able to estimate the potential changes in some inputs and outputs, while fixing other inputs and outputs, ranges of simultaneous scale and mix changes in inputs and outputs, while proportionally increasing or decreasing other inputs and outputs, and, finally, the RTS. The proposed algorithms are applied to corporate planning processes of chemical companies.     

DEA congestion and returns to scale under an occurrence of multiple optimal projections

Economic implications of congestion have been recently discussed in many DEA (data envelopment analysis) studies. In addition, several previous research efforts have explored a theoretical linkage between returns to scale (RTS) and the concept of congestion, because the two economic concepts are closely connected to each other. Tone and Sahoo [Tone, K., Sahoo, B.K., 2004. Degree of scale economies and congestion: A unified DEA approach. European Journal of Operational Research 158, 755–772] have published the theoretical linkage in this journal. All of the previous studies, including their research (2004), assume a unique optimal solution in the investigation on DEA-based congestion. When multiple solutions occur in DEA-based congestion measurement, the economic implications of congestion obtained from the previous research are all problematic from both theoretical and practical perspectives. To deal with the issue, this study explores how to deal with the occurrence of multiple solutions in the DEA-based congestion measurement. This study proposes a new approach for the congestion measurement and theoretically compares the proposed approach with Tone and Sahoo (2004).     

Re-examining scale elasticity in DEA

We propose a new scheme for measuring scale elasticity of production based on a new cost efficiency model developed in Tone (2002). Comparing our model with classical model we establish the superiority of our model over the latter based on the premise that the classical estimates of cost efficiency and scale elasticity can be illusory.     

Computation of efficient targets in DEA models with production trade-offs and weight restrictions

Recently new models of data envelopment analysis (DEA) were introduced that incorporate production trade-offs between inputs and outputs or based on them weight restrictions. In this paper, we develop a computational procedure suitable for the practical application of such models. We show that the standard two-stage optimisation procedure used in DEA to test the full efficiency of units and identify their efficient targets may work incorrectly in the new models. The modified procedure consists of three stages: the first evaluates the radial efficiency of the unit, the second identifies its efficient target, and the third its reference set of efficient peers. Each stage requires solving one linear program for each unit.     

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.     

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.     

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.     

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.     

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。     

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。     

Constant and variable returns to scale DEA models for socially responsible investment funds

In order to evaluate the performance of socially responsible investment (SRI) funds, we propose some models which use data envelopment analysis (DEA) and can be computed in all phases of the business cycle. These models focus on the most crucial elements of an investment in mutual funds.