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.     

存在保证域的模糊超效率DEA模型

模糊DEA模型是用于解决存在模糊数据的决策单元(DMUs)效率评价问题的,然而现有的模糊DEA模型分辨率低,本文构建了存在保证域的模糊超效率DEA模型,并给出了一种基于截集的求解方法并进行了证明,该模型有效地解决了输入和输出全部或部分为模糊数的决策单元全排序问题。最后给出了一个银行效率评价的实例说明了方法的有效性。     

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。     

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     

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16家高科技上市公司为应用实例,研究其相对经营效率.     

Performance Effects of Using the Balanced Scorecard: A Note on the Dutch Experience

This article aims to contribute to understanding how to use the Balanced Scorecard (BSC) effectively. The BSC lends itself to various interpretations. This article explores how the way in which the BSC is used affects performance. Empirical evidence from Dutch firms suggests BSC use will not automatically improve company performance, but that the manner of its use matters: BSC use that complements corporate strategy positively influences company performance, while BSC use that is not related to the strategy may decrease it. We discuss the findings and offer managers guidance for optimal use of the BSC.     

Common benchmarking and ranking of units with DEA

This paper develops a common framework for benchmarking and ranking units with DEA. In many DEA applications, decision making units (DMUs) experience similar circumstances, so benchmarking analyses in those situations should identify common best practices in their management plans. We propose a DEA-based approach for the benchmarking to be used when there is no need (nor wish) to allow for individual circumstances of the DMUs. This approach identifies a common best practice frontier as the facet of the DEA efficient frontier spanned by the technically efficient DMUs in a common reference group. The common reference group is selected as that which provides the closest targets. A model is developed which allows us to deal not only with the setting of targets but also with the measurement of efficiency, because we can define efficiency scores of the DMUs by using the common set of weights (CSW) it provides. Since these weights are common to all the DMUs, the resulting efficiency scores can be used to derive a ranking of units. We discuss the existence of alternative optimal solutions for the CSW and find the range of possible rankings for each DMU which would result from considering all these alternate optima. These ranking ranges allow us to gain insight into the robustness of the rankings.     

资源约束型两阶段生产系统的DEA效率评价模型

经典的数据包络分析(DEA)模型将决策单元看作"黑箱",忽视决策单元的内部过程,必然会高估决策单元的效率。本文研究了一种资源约束型两阶段生产系统的DEA效率评价方法,针对此类生产过程的内部过程,研究其内部运行机制对整体效率的影响。本文提出的模型实质上是一类特殊的网络DEA模型,其评价原理有别于已有的研究成果,但更有助于管理者确定生产过程的非有效来源及其效率改进方向。实例证实本文方法的合理性。     

Measuring performance of two-stage network structures by DEA: A review and future perspective

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). An important area of development in recent years has been devoted to applications wherein DMUs represent two-stage or network processes. One particular subset of such processes is those in which all the outputs from the first stage are the only inputs to the second stage. The current paper reviews these models and establishes relations among various approaches. We show that all the existing approaches can be categorized as using either Stackelberg (leader-follower), or cooperative game concepts. Future perspectives and challenges are discussed.     

Malmquist productivity index based on common-weights DEA: The case of Taiwan forests after reorganization

The performance of a decision making unit (DMU) can be evaluated in either a cross-sectional or a time-series manner, and data envelopment analysis (DEA) is a useful method for both types of evaluation. In order to eliminate the inconsistency caused by using different frontier facets to calculate efficiency, common-weights DEA models have been developed, under which a group of DMUs can be ranked for a specific period. This study proposes a common-weights DEA model for time-series evaluations to calculate the global Malmquist productivity index (MPI) so that the productivity changes of all DMUs have a common basis for comparison. The common-weights global MPI not only has sound properties, but also produces reliable results. The case of Taiwan forests after reorganization shows that the MPIs calculated from the conventional DEA model produce misleading results. The common-weights global MPI approach, on the other hand, correctly identifies districts with unsatisfactory performance before the reorganization and those with unsatisfactory productivity improvement after the reorganization.     

矩阵型网络DEA模型及其实证检验

针对传统DEA模型无法有效的评价矩阵型网络系统的效率,本文构建了矩阵型网络决策单元的生产可能集,建立了矩阵型网络DEA模型。在此基础上证明了决策单元在矩阵型网络DEA模型下为弱DEA有效的充分必要条件为其每个子系统均为弱DEA有效。最后,选用美国的十个电力公司作为决策单元对模型进行实证检验,得出结论:矩阵型网络DEA模型弥补了传统DEA模型无法反映内部有效性从而可能得到错误结果的缺陷,并能精确地计算出各个子过程的效率,辨识出具体需要改进的子过程。同时新模型为评价复杂系统的效率提供了新的思路。     

A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

基于交叉评价策略的DEA全局协调相对效率排序模型

在DEA(数据包络分析)研究领域,建构在交叉效率概念基础上的现有决策单元排序方法仅以定义的方式给出了用于决策单元排序的交叉效率评价值。对于这种方法构建方式,分别基于管理学的效率概念和多属性决策理论,分析指出其中的交叉效率评价值从本质上讲既与效率的管理学概念不符,也与决策单元的优劣不存在理性逻辑联系。为克服现有决策单元排序方法所存在的上述问题,基于交叉评价策略和效率的管理学概念内涵给出了DEA全局协调相对效率的新概念,在此基础上利用优化理论给出了可以用于决策单元优劣排序的DEA全局协调相对效率测度模型,并通过理论分析和数值案例验证解释了该模型相对于现有决策单元排序方法所拥有的比较优势。     

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.     

Efficiency measurement for hierarchical network systems

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.     

Multi-valued measures in DEA in the presence of undesirable outputs

Data envelopment analysis (DEA) evaluates the relative efficiency of a set of comparable decision making units (DMUs) with multiple performance measures (inputs and outputs). Classical DEA models rely on the assumption that each DMU can improve its performance by increasing its current output level and decreasing its current input levels. However, undesirable outputs (like wastes and pollutants) may often be produced together with desirable outputs in final products which have to be minimized. On the other hands, in some real-world situations, we may encounter some specific performance measures with more than one value which are measured by various standards. In this study, we referee such measures as multi-valued measures which only one of their values should be selected. For instance, unemployment rate is a multi-valued measure in economic applications since there are several definitions or standards to measure it. As a result, selecting a suitable value for a multi-valued measure is a challenging issue and is crucial for successful application of DEA. The aim of this study is to accommodate multi-valued measures in the presence of undesirable outputs. In doing so, we formulate two individual and summative selecting directional distance models and develop a pair of multiplier- and envelopment-based selecting approaches. Finally, we elaborate applicability of the proposed method using a real data on 183 NUTS 2 regions in 23 selected EU-28 countries.     

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.     

Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA

In benchmarking, organizations look outward to examine others’ performance in their industry or sector. Often, they can learn from the best practices of some of them and improve. In order to develop this idea within the framework of Data Envelopment Analysis (DEA), this paper extends the common benchmarking framework proposed in Ruiz and Sirvent (2016) to an approach based on the benchmarking of decision making units (DMUs) against several reference sets. We refer to this approach as cross-benchmarking. First, we design a procedure aimed at making a selection of reference sets (as defined in DEA), which establish the common framework for the benchmarking. Next, benchmarking models are formulated which allow us to set the closest targets relative to the reference sets selected. The availability of a wider spectrum of targets may offer managers the possibility of choosing among alternative ways for improvements, taking into account what can be learned from the best practices of different peer groups. Thus, cross-benchmarking is a flexible tool that can support a process of future planning while considering different managerial implications.     

两阶段DEA前沿面投影问题研究——兼对我国上市银行运营绩效进行评价

DEA方法,即数据包络分析方法,是一种用于评价决策单元(Decision Making Units,DMUs)相对有效性的实证方法。近年来DEA方法已经广泛的应用于各行各业的绩效评价中,并发展出两阶段DEA方法。两阶段DEA方法相对于传统DEA方法的优势在于,它不但可以提供被评价对象的总体效率值,还可以分别生成每一阶段的效率值。但正是由于中间要素的存在,按照传统的DEA方法来调整两阶段DEA投入、产出要素的优化过程已不能成功投影在有效前沿面上。本文基于两阶段DEA方法,通过加入"虚拟中间要素"在两阶段DEA中嵌入一个"虚拟阶段",这样不但完善了两阶段DEA的逻辑结构,而且成功的将被评价单元投影到有效前沿面。最后本文应用以上方法对我国上市银行的运营绩效进行了实证分析。实证结果令我们意外的是,国有商业银行运营绩效优于股份制银行。     

随机环境下的多投入多产出生产前沿面估计

传统的DEA模型假设观测样本的投入产出都是确定型数据, 这使得DEA在实际应用中受到限制, 本文提出的基于拟似然估计的多投入多产出随机非参数包络数据 (PLE-StoNED) 方法拓展了这个假设, 能够估计随机环境下的生产前沿面.本文证明, 生产可能集假设条件下的前沿面可以用一个有凹凸性和单调性限制的函数来表示.相较之前的StoNED方法, 本文提出的方法可以估计随机环境下多投入多产出决策单元 (DMU) 的前沿面.通过Monte Carlo实验, 多投入多产出PLE-StoNED方法的有效性得到验证, 它可纠正DEA等传统方法产生的偏误.最后, 实证研究部分运用这一新提出的方法估计了中国大陆商业银行的生产前沿面和效率.本文提出的方法弥补了DEA缺乏统计性的不足, 可为决策者在随机环境下对多投入多产出决策单元进行生产力和效率评估提供决策参考.