A slack-based measure of efficiency in context-dependent data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). In the DEA literature, a context-dependent DEA is developed to provide finer evaluation results by examining the efficiency of DMUs in specific performance levels based upon radial DEA efficiency scores. In DEA, non-zero input and output slacks are very likely to present after the radial efficiency score improvement. Often, these non-zero slack values represent a substantial amount of inefficiency. Therefore, in order to fully measure the inefficiency in DMU's performance, it is very important to also consider the inefficiency represented by the non-zero slacks in the context-dependent DEA. This study proposes a slack-based context-dependent DEA which allows a full evaluation of inefficiency in a DMUs performance. By using slack-based efficiency measure, we obtain different frontier levels and more appropriate performance benchmarks for inefficient DMUs.     

基于偏好DEA模型的中国纺织业效率评价

基于具有输入输出指标偏好信息的数据包络分析模型评价中国纺织工业的效率,给出了描述规模报酬不变和规模报酬可变假设的DEA模型及其对偶规划的一种形式。模型克服传统DEA模型应用中常见的决策单元权重为零进而高估决策单元效率的不合理现象,有效地测算了中国31个地区纺织工业的经济运行效率,并分析了地区间效率水平差异的原因。利用各决策单元在经验生产前沿面上的投影点,估计了中国纺织工业的随机生产前沿函数,最后用效率弹性线性递减模型分析了销售收入、人均资产、台港澳和外商投资对各地区效率的微观影响关系。     

Additive slacks-based measure: Computational strategy and extension to network DEA

The current paper visits a set of data envelopment analysis (DEA) models that identify inefficiency by optimizing input and output slacks. These slacks are aggregated either in an additive or ratio form. Only the ratio slacks-based DEA models can be solved as a linear program and generate a DEA score between zero and unity. The additive slacks-based model can be equivalent to the Russell graph measure and converted into a second order cone programming (SOCP) problem whose solving procedure has become a mature technology. As such, the additive slacks-based model can also yield a DEA score between zero and unity. This study shows that the additive slacks-based model can be applied to modelling network DEA where the internal structures of decision making units (DMUs) are of interest. The additive slacks-based network DEA can be solved using SOCP technique and adapted to the preference of the decision maker by choosing the weights for aggregating individual components in the network structures. It is shown that the additive slacks-based approach can yield divisional efficiencies of Pareto optimal equivalences to be selected by the decision maker when compared to the existing ratio slacks-based measure. An example and solving codes are provided in the current study.     

CCR or BCC: what if we are in the wrong model?

The CCR model by Charnes et al. (Eur J Oper Res 2:429–444, 1978) together with the BCC model by Banker et al. (Manag Sci 30:1078–1091, 1984) are the most popular approaches of measuring efficiency among a group of decision making units, DMUs, in data envelopment analysis, DEA. The right choice of a DEA model—CCR or BCC—often, if not always, is a difficult decision. To evaluate a DMU’s efficiency for both models might be helpful, but it does not always capture the essential issues at stake. In this paper we propose a comparative analysis of both concepts: How does activity scaling under constant BCC-efficiency influence CCR-efficiency. And inversely, how does BCC-efficiency behave when activity scaling under constant CCR-efficiency is applied. Such findings of mutual effects improve a DMU’s ability to reassess upsizing and downsizing of activities. Moreover, it allows for exact calculations of the resulting economic effects, and these effects give new insights beyond classical DEA. Finally, scale efficiency turns out to be the ideal concept to control these activity changes, rather than just CCR- or BCC-efficiency. We use a little numerical example to emphasize advantages of the new concept and sketch the new findings for a theater scenery.     

Konsensuale Effizenzbewertung und -verbesserung mittels DEA

This contribution is a new DEA approach in as much as it permits the decision making units (DMUs) to improve their respective efficiencies from the view of a peer rather than form their own self-appraisal attitudes. These authors study the output oriented model under constant scale efficiencies and first develop how a DMU can improve its performance by radial output increase or even by free output variation??in the light of the weight system of an arbitrary peer. The results are an improved cross-efficiency matrix and a maximum cross-efficiency matrix. Either of these matrices may serve as an appropriate instrument for a consensual choice of a peer??consensual among all DMUs. Input oriented models as well as simultaneous input/output considerations amend the so far developed results. A suitable example demonstrates all aspects of the new approach.     

Presenting DEA graphically

This paper introduces a methodology that permits presentation of the results of data envelopment analysis (DEA) graphically. A specialized form of multi-dimensional scaling, Co-Plot, enables presentation of the DEA results in a two-dimensional space, hence in a clear, understandable manner. When plotting ratios rather than original data, DEA efficient units can be visualized clearly, as well as their connections to specific variables and/or ratios. Furthermore, Co-Plot can be used in an exploratory data analysis to identify outliers, whose data require additional scrutiny, and potentially inconsequential variables that could be aggregated or removed from the analysis with little effect on the subsequent DEA results.     

Iterative Converging Algorithms for Computing Bounds on Durations of Activities in Pert and Pert-Like Models

Since its invention in 1958, Program Evaluation and Review Technique (PERT) has been widely used during the planning, design, and implementation of projects. Pert models the activities of a project as a single source-single sink directed acyclic graph where nodes represent events (end or beginning of activities) and arcs activities. The maximum amount by which an activity can be delayed without delaying the overall project is called the slack. Critical tasks have zero slack whereas all noncritical tasks have positive slacks. Pert is a valuable tool in the management of large projects since it allows to compute the slack of each activity of the project. Such information may be crucial in avoiding cost overruns that would be caused by delays to critical activities and/or excessive delays to noncritical activities. What Pert fails to provide is how one should go about distributing remaining slack on noncritical activities while taking into consideration properties of the activities as well as precedence relationships among them, so as to have reasonable upper bounds on duration of all activities, critical or noncritical. In this paper we propose several algorithms for the distribution of slack on non-critical activities. We show that if one desires to distribute the remaining slack proportionally to the initially assigned activity durations then the problem is in P, and propose an algorithm of linear time complexity. However if one desires to use distribution functions other than the initial durations of activities, then the problem of slack distribution becomes NP-complete. Finding the maximal bounds corresponding to zero-slack solution at the sink requires iterative application of exponential algorithm. For that case we introduce an approximation algorithm of linear time complexity on each iteration. The algorithm iteratively increases bounds on durations of activities and converges to the zero-slack solution on all paths from the source node to the sink node in the Pert-like graph. The algorithms described in this paper were successfully applied to solving timing bounds problems in VLSI design.     

基于可变权重的DEA效率评价模型

传统DEA模型将投入、产出权重视为固定变量。为了更合理地对决策单元的效率进行评价,本文研究了如何将有关投入、产出变量的权重的更多信息融入效率评价模型,提出了可变权重的概念,给出了一种基于可变权重的DEA效率评价模型。本文模型是CCR模型的推广。在有关权重信息可得的前提下,本文模型较之CCR模型中效率评价上更为合理。但是,如何准确度量投入、产出权重并将其函数化,是本文方法应用的难点。一个算例分析演示了本文模型。     

Evolving the latent variable model as an environmental DEA technology

This article tests several nonparametric DEA models for their ability to accurately decompose CO₂ emissions change using a Malmquist styled decomposition framework. This production oriented activity analysis involves panel data and two data sets from the literature for comparison. A new Latent Variable radial input-oriented technology is introduced that is closely associated with a Koopmans Efficient Slacks Based Model. The Latent Variable technology simultaneously reduces inputs and undesirable outputs in a single Multiple Objective Linear Program. This production theoretic methodology is adapted to preserve both scale efficiency and causality within the envelopment framework. Finally, the application studies demonstrate the internal consistency of the Latent Variable reduction coefficients, which overturns previous results and paves the way for further research into undesirable externalities.     

The enhanced Russell-based directional distance measure with undesirable outputs: Numerical example considering CO2 emissions

Following the spirit of the enhanced Russell graph measure, this paper proposes an enhanced Russell-based directional distance measure (ERBDDM) model for dealing with desirable and undesirable outputs in data envelopment analysis (DEA) and allowing some inputs and outputs to be zero. The proposed method is analogous to the output oriented slacks-based measure (OSBM) and directional output distance function approach because it allows the expansion of desirable outputs and the contraction of undesirable outputs. The ERBDDM is superior to the OSBM model and traditional approach since it is not only able to identify all the inefficiency slacks just as the latter, but also avoids the misperception and misspecification of the former, which fails to identify null-jointness production of goods and bads. The paper also imposes a strong complementary slackness condition on the ERBDDM model to deal with the occurrence of multiple projections. Furthermore, we use the Penn Table data to help us explore our new approach in the context of environmental policy evaluations and guidance for performance improvements in 111 countries.     

Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture

In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (J Oper Res Soc 2004;55:1311–22). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

A slacks-based inefficiency measure for a two-stage system with bad outputs

We model the performance of DMUs (decision-making units) using a two-stage network model. In the first stage of production DMUs use inputs to produce an intermediate output that becomes an input to a second stage where final outputs are produced. Previous black box DEA models allowed for non-radial scaling of outputs and inputs and accounted for slacks in the constraints that define the technology. We extend these models and build a performance measure that accounts for a network structure of production. We use our method to estimate the performance of Japanese banks, which use labor, physical capital, and financial equity capital in a first stage to produce an intermediate output of deposits. In the second stage, those deposits become an input in the production of loans and securities investments. The network estimates reveal greater bank inefficiency than do the estimates that treat the bank production process as a black box with all production taking place in a single stage.     

DEA博弈模型的分析与发展

数据包络分析(Data Envelopment Analysis,DEA)与博弈论之间关系密切.传统DEA模型忽略了决策单元(Decision Making Units,DMUs)之间的竞合关系,对权重的限制过于宽松,难以合理评价DMU效率值.为此,将博弈论方法引入至DEA模型,开展DEA的博弈研究,既是对DEA理论的重大发展,也将极大拓宽博弈论的应用研究.本文分三个阶段对现有的DEA博弈研究进行述评:(1)DEA的博弈论解释;(2)DEA Game模型及其应用;(3)DEA效率博弈;在深入分析重点模型基础上,总结其发展脉络,促进DEA理论与实践的发展.     

基于修正Russell方法的模糊决策单元的排序

文章首先建立基于修正Russell方法的超效率DEA模型,然后基于模糊数的比较,建立并求解模糊环境下的基于修正Russell方法的超效率DEA模型,从而解决了模糊决策单元的全排序问题。文末的算例将基于修正Russell方法的模糊超效率DEA模型,与基于CCR模型的模糊超效率DEA模型的结果进行了比较分析。     

Centralized resource allocation BCC models

In two recent papers, Lozano and Villa [Centralized resource allocation using data envelopment analysis. Journal of Productivity Analysis 2004;22:143–61. [1]] and Lozano et al. [Centralized target setting for regional recycling operations using DEA. OMEGA 2004;32:101–10. [2]] introduce the concept of “centralized” data envelopment analysis (DEA) models, which aim at optimizing the combined resource consumption by all units in an organization rather than considering the consumption by each unit separately. This is particularly relevant for situations where some variables are controlled by a central authority (e.g. Head Office) rather than individual unit managers. In this paper we reconsider one of the centralized models proposed by the above-mentioned authors and suggest modifying it to only consider adjustments of previously inefficient units. We show how this new model formulation relate to a standard DEA model, namely as the analysis of the mean inefficient point. We also provide a procedure that can be used to generate alternative optimal solutions, enabling a decision maker to search through alternate solution possibilities in order to select the preferred one. We then extend the model to incorporate non-transferable as well as strictly non-discretionary variables and illustrate the models using an empirical example of a public service organization.     

Verallgemeinerte DEA-Modelle zur Performanceanalyse

Dyckhoff and Allen derived a generalisation of Data Envelopment Analysis (DEA) in order to measure ecological efficiency. This approach distinguishes between inputs and outputs of an activity on the one hand and their impact on the relevant evaluation criteria—referred to as efforts and benefits—on the other hand. Thereby, the current framework of the DEA for analysing the relative performance of productive units is fundamentally extended. The relevance of this framework is not limited to ecological aspects because many essential problems of DEA application can be solved. Against this background, the paper presents a formalisation of the generalised DEA, applies it to the well-known basic DEA models, and concretises these models for linear effort and benefit functions.     

基于DEA的高等学校内部院系绩效评价

内部院系绩效评价是高等学校加强内部管理的关键。本文利用X大学的数据,采用数据包络分析法对有关院系的办学绩效进行评价,得出了各学院的总体技术效率、纯技术效率和规模效率值,对有关投入产出指标的松弛量进行了分析,从而指明了调整内部院系资源配置和改进绩效的方向,最后对研究模型的敏感性进行了分析,结果表明模型具有较高的效度。     

评价相对效率的投入—产出型DEA

传统 DEA只能在固定投入或产出的条件下 ,从产出或投入角度测算决策单元相对效率 ,因而不能综合地反映决策单元的投入产出效果 .基于双目标规划 ,本文将提出从投入及产出角度评价决策单元相对效率的投入—产出型 DEA,并研究其相对有效性 .最后以沪市 1 6家高科技上市公司为应用实例 ,研究其相对经营效率     

基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。