Performance measurement with classification information: an enhanced additive DEA model

This paper presents an improved measurement tool for evaluating performance of branches within a major Canadian bank. While there have been numerous previous studies of performance in the banking industry, particularly at the branch level, this study is different in a very significant way: specifically two kinds of data are used to develop the model. The first type of data is that related to standard transactions, available from any bank; such have formed the basis of numerous previous studies. The second type of data, obtained from the site studied, is classification information, based on branch consultant/expert judgment as to good and poor performance of branches. The purpose herein is to present a modified version of an existing benchmarking model, data envelopment analysis (DEA), and to show how this tool is applied in the banking industry. The mechanism used herein to incorporate expert knowledge within the DEA framework is to first apply a discriminant or classification tool, to quantify the functional relation that best captures the expert's mental model for performance. The outcome of this first phase is an orientation of variables to aid in the definition of inputs and outputs. The resulting orientation then defines the DEA model that makes up the second phase of the model.     

Two-stage evaluation of bank branch efficiency using data envelopment analysis

There are two key motivations for this paper: (1) the need to respond to the often observed rejections of efficiency studies’ results by management as they claim that a single-perspective evaluation cannot fully reflect the operating units’ multi-function nature; and (2) a detailed bank branch performance assessment that is acceptable to both line managers and senior executives is still needed. In this context, a two-stage Data Envelopment Analysis approach is developed for simultaneously benchmarking the performance of operating units along different dimensions (for line managers) and a modified Slacks-Based Measure model is applied for the first time to aggregate the obtained efficiency scores from stage one and generate a composite performance index for each unit. This approach is illustrated by using the data from a major Canadian bank with 816 branches operating across the nation. Three important branch performance dimensions are evaluated: Production, Profitability, and Intermediation. This approach improves the reality of the performance assessment method and enables branch managers to clearly identify the strengths and weaknesses in their operations. Branch scale efficiency and the impacts of geographic location and market size on branch performance are also investigated. This multi-dimensional performance evaluation approach may improve management acceptance of the practical applications of DEA in real businesses.     

A survey on bank branch efficiency and performance research with data envelopment analysis

The banking industry has been the object of DEA analyses by a significant number of researchers and probably is the most heavily studied of all business sectors. Various DEA models have been applied in performance assessing problems, and the banks' complex production processes have further motivated the extension and improvement of DEA techniques. This paper surveys 80 published DEA applications in 24 countries/areas that specifically focus on bank branches. Key issues related to the design of DEA models in these studies are discussed. Much advice is included on how to design future experiments and studies in this domain. A number of areas where further research could be fruitful are suggested.     

考虑环境因素的三阶段半参数效率评价模型与实证研究

数据包络分析方法自提出以来,因其在评价决策单元相对有效性的诸多优势而得到了广泛应用,但其局限性之一在于要求决策单元具有相同的投入和产出性质。为了突破这一局限性,本文将参数方法引入DEA评价模型,以考虑外部环境因素对生产系统的影响;构建了一个新的三阶段半参数效率评价模型,其突出特点在于对"环境变量"和"非自由处置变量"的有效处理;选取国内某石油企业下属的各大油田作为分析对象,对上述三阶段模型进行了实证研究,证明了该三阶段模型的实用性和有效性。     

DEA target setting approach within the cross efficiency framework

Target setting is an important reason that data envelopment analysis (DEA) is widely applied to analyze efficiency. However, the efficiency overestimation of traditional DEA may affect the rationality of target setting, and even may make this method invalid in target setting. This paper innovatively proposes the definition of cross efficient, and develops two new target setting approaches for individual decision-making unit (DMU) and global optimization to improve the cross efficiency of DMUs in different decision-making situations. Then the influence of decision maker's preference on the improvement direction is discussed, and then these approaches are further extended. This paper solves the limitations of traditional DEA in target setting, and provides different directions to improve cross efficiency for meeting decision makers’ needs. Finally, two examples are provided to illustrate the effectiveness of these approaches.     

商业银行分理处效率对效益的影响程度分析

在运用数据包络分析方法对商业银行分理处进行效益和效率的评价的基础上,提出分析效率对盈利性影响程度的方法,通过对某商业银行支行的12个分理处的实证分析,初步证明了该方法的有效性。     

基于机会约束随机Index-DEA的投资组合效率评价

传统DEA和分散化DEA是两种常见的非参数评价方法,二者也被广泛应用于投资组合效率评价。已有相关研究通常将风险和期望收益视为投资组合的投入和产出指标,但该投入-产出假设与实际投资过程并不吻合。在实际投资过程中,真实投入应为投资组合的初始财富,产出则是其终端财富。基于新的投入-产出假设,本文对投资组合初始财富进行标准化,将终端财富转化为收益率形式,进而构造随机生产可能集和相应的机会约束随机Index-DEA模型。当投资组合收益率服从联合正态分布时,随机Index-DEA模型被转化为等价的确定性模型,从理论上证明该等价模型的凸凹性,并提出相应的求解算法。最后,利用该随机Index-DEA模型对我国30只开放式基金进行效率评价,验证所提出DEA模型和求解算法的有效性。     

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.     

Ensuring units invariant slack selection in radial data envelopment analysis models,and incorporating slacks into an overall efficiency score

This paper introduces a new methodology ensuring units invariant slack selection in radial DEA models and incorporating the slacks into an overall efficiency score. The CCR and BCC models are units invariant in their radial component, but not in their slack component, thus changing the units of measurement of one or more variables can change the models' solution. The proposed Full Proportional Slack (FPS) methodology improves the slack selections of the CCR and BCC models by producing slack selections that (a) are units invariant, thus producing fully units invariant models, (b) maximize the relative improvements represented by the slacks, and not their values, and (c) measure the full slacks that need to be removed from their corresponding variables. The FPS methodology is a fully oriented methodology first maximizing the improvements in the variables on the side of the orientation of the model. The Proportional Slack Adjusted (PSA) methodology incorporates the FPS slacks into an overall efficiency score, making it easier to interpret and use the results. The FPS and PSA methodologies are illustrated using an input oriented VRS Loan Quality DEA model with data from the retail branch network of one of Canada's largest banks.     

Corporate philanthropic selection using data envelopment analysis

This paper presents a case study involving quantitative models for the selection of corporate philanthropic projects. The four analytic techniques used by this company for ranking and selecting philanthropic projects are all based on Data Envelopment Analysis (DEA). Instead of relaying only on one traditional DEA model, the four approaches employed in this study enable the decision maker to identify the most deserving school.     

两阶段生产系统的DEA效率评价模型

数据包络分析(DEA)作为一种数学规划方法,已经被广泛用来评价一个决策单元相对于其它决策单元的效率。经典的DEA模型把决策单元看作一个“黑箱”,对决策单元的内部运行机制不作深入的研究。本文以一个两阶段生产系统为例,从生产系统的内部过程出发,提出一个基于DEA的模型以合理评估该决策单元的相对效率。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,但确实有助于管理者确定生产过程(如供应链)的非有效来源及其效率改进方向。     

MEASUREMENT OF MULTIPLE SITES IN SERVICE FIRMS WITH DATA ENVELOPMENT ANALYSIS

Data envelopment analysis (dea) has become an increasingly popular method to measure performance for service firms with multiple sites. DEA is superior to many traditional methods for firms that have multiple goals. The promise of DEA is that the complex, multi-objective problem of performance measurement can be reduced to a single number. Unfortunately, the practice of DEA often belies the promise. Misconceptions concerning the purpose and implementation of DEA can cause DEA applications to be less than successful. Here, the technique is explained, and a guide to the implementation of DEA is proposed, utilizing DEA studies of retail bank branches.     

A linear formulation of the two-level DEA model

In efficiency measurement, the input and output factors of similar characteristics can be grouped into input and output categories, respectively, using a weighted-average approach under the data envelopment analysis (DEA) framework to form a two-level DEA model. The resulting two-level model is nonlinear. This note transforms the nonlinear model into a linear one using a variable substitution technique. Linear models are easier to solve than their nonlinear counterparts. The linear transformation is applicable to the two-level model built from both the primal and dual forms of the conventional one-level DEA model. The linear model transformed from the nonlinear model developed from the primal form has a dual which is equivalent to the nonlinear model developed from the dual form.     

Data Envelopment Analysis for Managerial Control and Diagnosis*

Data envelopment analysis (DEA) is a linear programming-based technique that converts multiple input and output measures into a single comprehensive measure of productive efficiency. This is accomplished via the construction of an empirically based production frontier and by the identification of peer groups. Each unit is evaluated by comparison against a composite unit that is constructed as a convex combination of other units in its peer group. DEA has now been applied in a variety of managerial contexts. In this paper we draw on theories of decision making, measurement and control, the mathematical properties of DEA, prior reported applications, and our own experience, to assess the potential of DEA as a general management tool. We first make the distinction between managerial diagnosis and control. We show how measurement requirements differ for these two managerial decision contexts, and argue that DEA has the potential to provide support in each context. Measurement and decision support criteria for each activity are then developed by reference to the literature on diagnosis and control. Based on its mathematical definition and properties, the relevant attributes of DEA are then derived. The technique is evaluated in each capacity by comparison to the appropriate set of criteria. This evaluation is supported with evidence from our experience with DEA in a large public-sector organization. We argue that the structural properties of DEA, critical managerial choices in its application, and situationally specific factors, interact to determine the strengths and limitations of DEA in each decision context. Implications for research and practice are discussed.     

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。     

Stage efficiency evaluation in a two-stage network data envelopment analysis model with weight priority

Conventional DEA models treat the entire production system as a black box and ignore its internal structures. To address this issue, many studies have examined the DEA efficiencies of two-stage systems in which all outputs of the first stage are the only inputs to the second stage. Based on game theory, the non-cooperative model and centralized model were developed for such a two-stage network structure. However, for the centralized model with multiple optimal solutions and the non-cooperative model, an assumption is required as to whether the first or second stage should be assigned the absolute priority for optimization. In many cases, certain circumstances might exist in which one stage does not completely dominate the other stage. In this paper, we develop a methodology for assessing the overall and stage efficiencies by considering the different and DMU-specific degree of priority given to the stages. Particularly, the non-cooperative model and the centralized model can be deemed as special cases. Moreover, we compare the proposed approaches with the existing approaches, which indicates that our approaches can greatly reduce the computational burden. Two empirical examples are used to demonstrate the proposed approach.     

Target intermediate products setting in a two-stage system with fairness concern

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this paper, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.     

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.     

Production efficiency in Indian agriculture: An assessment of the post green revolution years

In this paper we use the nonparametric method of Data Envelopment Analysis (DEA) to obtain Pareto-Koopmans measures of technical efficiency of individual states over the years 1970–71 through 2000–01 in a multi-output, multi-input model of agricultural production. We disaggregate overall efficiency into two distinct components representing output and input efficiencies and identify the contribution of individual outputs and inputs to the measured level of overall efficiency. Because introduction of modern inputs has been a major component of the process of modernization of Indian agriculture, we examine to what extent different states succeeded in utilizing the modern inputs compared to the traditional inputs. Variations in the DEA efficiency scores across states and over years is explained in terms of differences in various institutional and demographic factors in a second stage regression analysis.     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.