Centralized Resource Allocation Using Data Envelopment Analysis

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.     

Reprint of "Performance evaluation of China's high-tech innovation process :Analysis based on the innovation value chain"

The Chinese high-tech industry has developed greatly since the beginning of China's “National High-tech R&D (863) Program” and “China Torch Program”. This paper introduces a conceptual model extended from the innovation value chain model to simultaneously estimate the R&D and commercialization efficiencies for the high-tech industries of 29 provincial-level regions in China. To match reality, a network DEA incorporating both shared inputs and additional intermediate inputs is constructed to open the “black box” view of decision making units used in single-stage DEA. This study is the first attempt to link the R&D and commercialization with a solid theoretical foundation and feasible mathematical methods. The empirical findings show that most of the 29 regions have low efficiency in the commercialization sub-process compared to the R&D sub-process, although there are regional differences in China's high-tech industry. Pearson correlation shows that the R&D sub-process is not closely correlated to the commercialization sub-process in terms of efficiency. Our analysis can provide information for the formulation of policies to achieve high innovation efficiency.     

Performance evaluation of China's high-tech innovation process: Analysis based on the innovation value chain

The Chinese high-tech industry has developed greatly since the beginning of China's “National High-tech R&D (863) Program” and “China Torch Program”. This paper introduces a conceptual model extended from the innovation value chain model to simultaneously estimate the R&D and commercialization efficiencies for the high-tech industries of 29 provincial-level regions in China. To match reality, a network DEA incorporating both shared inputs and additional intermediate inputs is constructed to open the “black box” view of decision making units used in single-stage DEA. This study is the first attempt to link the R&D and commercialization with a solid theoretical foundation and feasible mathematical methods. The empirical findings show that most of the 29 regions have low efficiency in the commercialization sub-process compared to the R&D sub-process, although there are regional differences in China's high-tech industry. Pearson correlation shows that the R&D sub-process is not closely correlated to the commercialization sub-process in terms of efficiency. Our analysis can provide information for the formulation of policies to achieve high innovation efficiency.     

Efficiency aggregation with enhanced Russell measures in data envelopment analysis

In aggregation for data envelopment analysis (DEA), a jointly determined aggregate measure of output and input efficiency is desired that is consistent with the individual decision making unit measures. An impasse has been reached in the current state of the literature, however, where only separate measures of input and output efficiency have resulted from attempts to aggregate technical efficiency with the radial measure models commonly employed in DEA. The latter measures are “incomplete” in that they omit the non-zero input and output slacks, and thus fail to account for all inefficiencies that the model can identify. The Russell measure eliminates the latter deficiency but is difficult to solve in standard formulations. A new approach has become available, however, which utilizes a ratio measure in place of the standard formulations. Referred to as an enhanced Russell graph measure (ERM), the resulting model is in the form of a fractional program. Hence, it can be transformed into an ordinary linear programming structure that can generate an optimal solution for the corresponding ERM model. As shown in this paper, an aggregate ERM can then be formed with all the properties considered to be desirable in an aggregate measure—including jointly determined input and output efficiency measures that represent separate estimates of input and output efficiency. Much of this paper is concerned with technical efficiency in both individual and system-wide efficiency measures. Weighting systems are introduced that extend to efficiency-based measures of cost, revenue, and profit, as well as derivatives such as rates of return over cost. The penultimate section shows how the solution to one model also generates optimal solutions to models with other objectives that include rates of return over cost and total profit. This is accomplished in the form of efficiency-adjusted versions of these commonly used measures of performance.     

Incorporating quality into the measurement of hospital efficiency: a double DEA approach

This paper uses “double DEA” to assess how accounting for quality influences DEA technical efficiency scores of a sample of 1,074 US hospitals. In the first use of DEA, quality indices are estimated using a variety of process and outcome measures of quality. In the second use of DEA, technical efficiency is assessed while controlling for quality. A variety of DEA quality indices and a DEA variety of efficiency models are compared to determine how the treatment of quality influences findings regarding technical efficiency. Controlling for efficiency does matter, with outcome measures having an apparently greater impact than process measures. Given the call for improved quality and better cost containment, controlling for quality is an important contribution to efficiency analysis.     

Cross redundancy and sensitivity in DEA models

Data envelopment analysis (DEA) measures the efficiency of each decision making unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effect of such a dependency on DEA is not clear. In this paper, we call such a dependency a cross redundancy and examine the effect of a cross redundancy on DEA. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models. Furthermore, we present a sensitivity analysis to examine the effect of an imperfect cross redundancy on DEA by using accounting data obtained from United States exchange-listed companies.     

Firm efficiency and stock returns

In this paper, we investigate the role of firm efficiency in asset pricing using a sample of US publicly listed companies for the period 1988–2007. We employ non-parametric data envelopment analysis (DEA) on various input/output combinations, focusing on sales and market value as output measures in the construction of the frontier technologies. Using these performance measures, we examine whether efficient firms perform differently from inefficient firms following standard financial analysis procedures. First, we employ performance attribution regressions, by forming portfolios based on efficiency scores and tracking the performance of the various portfolios over time. Second, we perform cross-sectional/panel regressions to determine whether firm efficiency indeed has explanatory power for the cross-section of stock returns. Our results suggest that firm efficiency plays an important role in asset pricing and that efficient firms significantly outperform inefficient firms even after controlling for known risk factors.     

Weak congestion in output additive data envelopment analysis

Our earlier work [Wei QL, Yan H. Congestion and returns to scale in data envelopment analysis. European Journal of Operational Research 2004;153:641–60] discussed necessary and sufficient conditions for the existence of congestion together with aspects of returns to scale under an output-oriented DEA framework. In line with this work, the current paper investigates the issue of “weak congestion”, wherein congestion occurs when the reduction of selected inputs causes some, rather than all, outputs to increase, without a worsening of others. We define output efficiency for decision making units under a series of typical DEA output additive models. Based on this definition, we offer necessary and sufficient conditions for the existence of weak congestion. Numerical examples are provided for purposes of illustration.     

基于DEA的先进制造技术无形效益评价研究

根据输入输出指标数据值进行数据包络分析(DEA)计算,对先进制造技术(AMT)投资方案的输入数据进行相对效率评价,避免单纯考虑输出指标的不确定性和不可度量性,做到无形效益价值输出指标的量化分析。将DEA中的C2R模型与BC2模型进行改变,结合对偶理论,提出AMT无形效益价值是一种新型影子价格的观点,分析AMT无形效益价值的相对有效性,对无效的方案提出了输入输出指标数据的改进方法。最后通过一个实例,验证了方法的可行性和实用性。     

Identifying bank outputs and inputs with a directional technology distance function

The bank efficiency literature lacks an agreed definition of bank outputs and inputs. This is problematic given the long-standing controversy concerning the status of deposits, but also because bank efficiency estimates are known to be affected by the inclusion of additional outputs such as non-traditional (fee-based) activities or risk measures. This paper proposes a data-driven identification of bank outputs and inputs using the directional technology distance function. While previous applications of this tool used symmetric expansion or contraction directions, we focus on a set of orthogonal directions, each corresponding to an assumption on the input/output status of an individual variable. These directions correspond to a set of different specifications, whose estimated coefficients can be used to determine the input or output status of all variables except the regressand. Our empirical analysis revealed a very consistent pattern across the alternative specifications estimated. There is strong evidence that customer deposits are an input, and that non-performing loans are an important undesirable output. Finally, the orthogonal expansions/contractions we consider avoid the simultaneity problem raised by the “convenient normalization” commonly used to impose linear homogeneity in stochastic frontier estimation.     

Two-Stage DEA: An Application to Major League Baseball

We show how to use DEA to model DMUs that produce in two stages, with output from the first stage becoming input to the second stage. Our model allows for any orientation or scale assumption. We apply the model to Major League Baseball, demonstrating its advantages over a standard DEA model. Our model detects inefficiencies that standard DEA models miss, and it can allow for resource consumption that the standard DEA model counts towards inefficiency. Additionally, our model distinguishes inefficiency in the first stage from that in the second stage, allowing managers to target inefficient stages of the production process.     

基于超效率DEA模型的我国各省水运业效率分析

应用超效率DEA模型并结合CCR模型和BCC模型对我国各省水运业效率加以分析。通过BCC模型求得各省水运业的纯技术效率和规模效率,分析各省水运业管理现状和所处规模报酬阶段;对比分析了CCR模型和超效率DEA模型得到的效率值差异,从中也反映了应用超效率DEA获得效率值的真实性。实证结果表明,天津、河北、辽宁、上海、海南、贵州、云南和青海8个地区的综合效率、纯技术效率和规模效率都达到有效;CCR模型和超效率DEA模型各省总体均值分别为0.606和1.556,差异很大;最后应用CCR模型松弛变量分析了投入冗余额和产出不足额,给出了各投入产出指标的改进值。     

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis (DEA). In this study, we focus on a “big data” problem related to the considerably large dimensions of the input-output data. The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation, including principal component analysis (PCA-DEA), which is based on the idea of aggregating input and output, efficiency contribution measurement (ECM), average efficiency measure (AEC), and regression-based detection (RB), which is based on the idea of variable selection. We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test. In addition, we discuss the effect of initial variable selection in RB for the first time. Based on the results, we offer guidelines that are more reliable on how to choose an appropriate method.     

关于DEA有效性理论的一点探索

给出经典的基于输入和输出的DEA模型,把基于DEA模型相结合的相对效率模型引入评价证券相对有效性,以风险作为输入,期望收益率作为输出,便可以用DEA模型评价每只证券相对有效性。     

基于超DEA的皖江九市产业用地效率评价

本文以皖江九市作为研究区,在采用传统DEA评价方法 C2R模型评价2001至2010年10年间皖江九市总体产业用地投入产出效率的基础上,采用超效率DEA评价法对2010年皖江九市各市产业用地投入产出效率进行评价排序。结果表明:2001年至2010年10年间,皖江九市总体上仅2008及2010年两年产业用地投入产出为DEA有效,其余年份均存在产业用地投入冗余、产出不足现象;2010年,产业用地投入产出达到DEA有效的城市有六个,运用超DEA模型排序产业用地投入产出效率,结果从高到低依次为合肥、马鞍山、滁州、芜湖、巢湖及池州。     

The Application of Mathematical Programming Approaches to Estimating Container Port Production Efficiency

Container terminal production is both an important and complicated element in the contemporary global economy. This paper aims to evaluate the efficiency of the world’s most important container ports and terminals using the two alternative techniques of Data Envelopment Analysis (DEA) and the Free Disposal Hull (FDH) model. The results give an insight into the current efficiency ranking of the world’s major container ports and terminals. They also confirm expectations that the available mathematical programming methodologies lead to different results and that appropriate variable definition of input and output factors is a crucial element in meaningful applications of DEA and FDH. It is also concluded that the availability of panel data, rather than cross-sectional data would greatly improve the validity of the efficiency estimates derived from all the mathematical programming techniques applied.JEL Classification:C61, D24, E23, L23, L25, L92     

基于DEA模型的企业员工绩效考评研究

利用数据包络分析(DEA)方法对企业员工进行绩效考评,目的是真实、客观地反映员工的工作表现。本文提出运用只有输出(输入)和二次相对有效性的DEA模型对企业员工进行静态与动态的绩效考评,并结合实例进行实证研究,为人力资源管理提供了有价值的方法。     

Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis

In this paper we propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on data envelopment analysis (DEA). The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only, to obtain initial measures of producer performance. In the second stage, stochastic frontier analysis (SFA) is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance. An application to nursing homes is provided to illustrate the power of the three-stage methodology.     

稳增长和调结构双重目标下的我国产业投资战略导向研究

本文基于投入产出理论,从稳增长和调结构的视角,将产业投资决策表现为产业投资依赖度、产业投资效率两个状态指标,从而使产业投资决策成为一个具备完全时间内容和空间意义的系统决策。通过变结构控制动态投入产出模型识别各产业对投资的依赖度,通过DEA(数据包络分析)模型识别各产业当前的投资效率,并通过BCG(波士顿矩阵)模型综合分析产业的外部投资环境依赖度和内部投资效率,进一步判断在投资环境发生变化时如何采取合适的产业投资战略。     

Environmental efficiency measurement and the materials balance condition

The materials balance condition is a fundamental adding up condition, which essentially says that: “what goes in must come out”. In this paper we argue that a number of the recently developed methods of incorporating pollution measures into standard productive efficiency models may be inconsistent with this fundamental condition. We propose an alternative method that involves the incorporation of the materials balance concept into the production model in a similar manner to which price information is normally incorporated. This produces a new environmental efficiency measure that can be decomposed into technical and allocative components, in a similar manner to the conventional cost efficiency decomposition. The approach is illustrated with the case of phosphorus emission on Belgian pig-finishing farms, using data envelopment analysis (DEA) methods. Our results indicate that a substantial proportion of nutrient pollution on these farms can be abated in a cost reducing manner.