Performance measurement and classification data in DEA: Input-oriented model

This paper presents an improved efficiency measurement tool by modifying the existing data envelopment analysis methodology to permit the incorporation of expert knowledge. A previous paper examined the inclusion of such knowledge within the additive model. This information appeared in the form of a binary classification of a subset of the decision making units under study (e.g. good versus poor performers). In the current paper, we extend this logic to the input-oriented radial projection model. We demonstrate that the inclusion of this and other forms of expert judgment can improve the performance of the DEA tool in the sense that the efficiency scores are more in line with expert/management beliefs.     

Benchmarking firm performance from a multiple-stakeholder perspective with an application to Chinese banking

We know very little about how a firm would compare against its peers when evaluated from a multiple-stakeholder perspective where the same variables are interpreted differently. Since most medium-to-large organizations acknowledge the multi-dimensional nature of their operations, finding out the performance evaluations of various stakeholders can inform managerial decision-making. Thus, the main motivation for this study is to capture the interactions among different perceptions on a common set of performance measures. Using data envelopment analysis (DEA), we work with an approach that allows a flexible designation of inputs and outputs based on varying perspectives of five key stakeholders in banking. The versatile approach demonstrates that different views from the stakeholder universe can be summarily captured in DEA scores. A numerical example on Chinese commercial banks identifies the compliant (efficient) banks versus rigid (inefficient) banks, as well as the amenable stakeholders (those evaluating banks as efficient) versus the recalcitrant stakeholders (those evaluating banks as inefficient). The aligned views held by management and shareholders as evidenced by significant correlation among performance rankings imply reduced agency costs. Similarly, shared perceptions between customers and employees may encourage management to examine how this important business interface can be improved.     

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.     

A network DEA quantity and quality-orientated production model: An application to Australian university research services

The motivation for this analysis is the recently developed Excellence in Research for Australia (ERA) program developed to assess the quality of research in Australia. The objective is to develop an appropriate empirical model that better represents the underlying production of higher education research. In general, past studies on university research performance have used standard DEA models with some quantifiable research outputs. However, these suffer from the twin maladies of an inappropriate production specification and a lack of consideration of the quality of output. By including the qualitative attributes of peer-reviewed journals, we develop a procedure that captures both quality and quantity, and apply it using a network DEA model. Our main finding is that standard DEA models tend to overstate the research efficiency of most Australian universities.     

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.     

Measuring efficiency with products,by-products and parent-offspring relations: A conditional two-stage DEA model

In the usual data envelopment analysis (DEA) setting, as pioneered by Charnes et al. (1978) [1], it is assumed that a set of decision making units (DMUs) is to be evaluated in terms of their relative efficiencies in converting a bundle of inputs into a bundle of outputs. The usual assumption in DEA is that each output is impacted by each and every member of the input set. One particular area of recent research is that relating to partial input to output impacts where the main issue addressed is that in many settings not all inputs impact all outputs. In that situation the authors view the DMU as consisting of a set of mutually exclusive subunits, with each subunit having its own unique bundle of inputs and outputs. Examined as well in this area, is the presence of multiple processes for generating sets of outputs. Missing from that earlier work is consideration of the presence of outputs in the form of by-products, giving rise to a parent-offspring phenomenon. One of the modeling complications there is that the parent assumes two different roles; as an input affecting the offspring, while at the same time being the dominant output. This gives rise to a model that we refer to as conditional two-stage. Another complication is that in the presence of multiple processes, by-products often arise out of only a subset of those processes. In the current paper we develop a DEA-type of methodology to handle partial input to output impacts in the presence of by-products.     

Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences

In this paper we introduce the class of axial solutions for multiple objective optimization problems in contexts in which partial information on preference weights is available. These solutions combine the use of an improvement axis to direct the search of the most preferred result with the concept of efficiency with respect to preference information.     

Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA

Measuring and improving the efficiency of the Chinese commercial banking system has recently attracted increasing interest. Few studies, however, have adopted the two-stage network DEA to explore this issue in the Chinese context. Because the entire operational process of the banking system could be divided into two sub-processes (deposit producing and profit earning), the evaluation of the sub-process efficiencies could be used to assist in identifying the sources of the inefficiency of the entire banking system. In this study, we utilize the network DEA approach to disaggregate, evaluate and test the efficiencies of 16 major Chinese commercial banks during the third round of the Chinese banking reform period (2003–2011) with the variable returns to scale setting and the consideration of undesirable/bad output. The main findings of this study are as follows: (i) the two-stage DEA model is more effective than the conventional black box DEA model in identifying the inefficiency of banking system, and the inefficiency of the Chinese banking system primarily results from the inefficiency of its deposit producing sub-process; (ii) the overall efficiency of the Chinese banking system improves over the study period because of the reform; (iii) the state-owned commercial banks (SOBs) appear to be more overall efficient than the joint-stock commercial banks (JSBs) only in the pre-reform period, and the efficiency difference between the SOBs and the JSBs is reduced over the post-reform period; (iv) the disposal of non-performing loans (NPLs) from the Chinese banking system in general explains its efficiency improvement, and the joint-equity reform of the SOBs specifically increases their efficiencies.     

How to better identify the true managerial performance: State of the art using DEA

Our motivation is to detail a potential improvement on the three-stage analysis published by Fried et al. [Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis 2002;17:157–74] that can distinguish true performers from those that may be advantaged by favourable environments or measurement errors. The method starts with data envelopment analysis (DEA), and continues with stochastic frontier analysis to explain the variation in organisational performance in terms of the operating environment, statistical noise and managerial efficiency. It concludes with DEA again using adjusted data to reveal a measure of performance based on management efficiency only. Our proposed contributions include (i) a comprehensive approach where total input and output slacks are identified simultaneously for non-radial inefficiencies before levelling the playing field, (ii) identifying percent adjustments attributable to the environment and statistical noise, and (iii) using a fully units-invariant DEA model.     

Indirect elicitation of non-linear multi-attribute utility functions. A dual procedure combined with DEA

This paper proposes a non-interactive method to elicit non-linear multi-attribute utility functions which is based on duality results. The idea is to obtain a utility function which is compatible with the observed behavior of decision makers. The paper builds on a previous work by André and Riesgo [A non-interactive method to elicit non-linear multi-attribute utility functions. Theory and application to agricultural economics. European Journal of Operational Research 2008;181:793–807] but it eliminates an important shortcoming: the necessity to have an analytical expression of the efficient set or an estimation of it. The alternative approach presented in this paper consists in using a method of projection onto the true efficient set, based on data envelopment analysis (DEA). In a simulation exercise we check the ability of the method to recover true preference parameters in the presence of errors made by decision makers.     

Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.     

Association of DEA super-efficiency estimates with financial ratios: Investigating the case for Chinese banks

The great majority of applications of the popular frontier technique data envelopment analysis (DEA) do not test for the association of efficiency estimates with key performance indicators used by industry observers. Nevertheless, identifying efficiency estimates’ associations with commonly accepted financial measures of performance could guide benchmarking activities, pricing decisions, and regulatory monitoring. Thus, the current paper investigates to what extent bank DEA super-efficiency estimates are associated with key financial ratios. A low correlation may present an opportunity to address inefficiencies that were not obvious in financial ratio analysis, thus enabling an update of inferences drawn from ratios. Regressing ratios on efficiency estimates may also help predict financial ratios. Where an input–output specification is comprised of key financial ratios, DEA can also be used to objectively identify benchmarks for ratio analysis based on actual observed data collected from peers. Nine super-efficiency DEA formulations across two profitability models are systematically tested. The slacks-based measure of DEA with a parsimonious profitability efficiency model emerges as the most significant combination explaining the variation in the two industry ratios, post-tax profit/average total assets and return on average equity.     

Non-oriented slack-based decompositions of profit change with an application to Taiwanese banking

A change in profit can originate from the output side and the input side. In the spirit of work by Tone [1] and follows Grifell-Tatjé and Lovell's [2], we propose a non-oriented slacks-based measure (SBM) model to decompose the change in the operating profit into various meaningful components: quantity effect and a price effect. The quantity effect can be decomposed into a productivity effect and an activity effect. The productivity effect is further decomposed into a technical effect and an operating efficiency effect. Both of them include an output side, which will result in a change in revenue and an input side which will result in a change in cost. The activity effect can be decomposed into a product mix effect, a resource mix effect and a scale effect. We illustrate our decompositions to the Taiwanese banking sector during the period 1994-2002 using the average of the base and current prices to evaluate these contributions. We find ignoring input side effects on the decomposition of profit changes would cause misleading results in managerial issues.     

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.     

确定任意投入-产出组合规模弹性的DEA模型

本文探讨数据包络分析(DEA)对规模收益的定量分析.过去的研究文献只涉及全输入组合对全输出组合的产出弹性.本文通过建立一般模型来计算任意输入组合对任意输出组合的产出弹性,从而可以确定在产出弹性中占主导地位的最佳投入组合.按照最佳投入组合来扩展规模可避免盲目投资和浪费资源,达到以最小投入获取最大产出的效用.     

Statistical precision of DEA and Malmquist indices: A bootstrap application to Norwegian grain producers

Previous applications of data envelopment analysis (DEA) and its subsequent Malmquist indices to efficiency and productivity measurements have been criticised for not providing statistical inferences regarding the significance of observed results. In this paper, DEA and a Malmquist index are combined with a bootstrap method in order to provide succinct statistical inferences that determine the performance of grain producers in Eastern Norway. The data cover the period between 1987 and 1997. Results reveal: (i) a significant degree of inefficiency (approximately 11%) and an average productivity progress of 38% over the period considered; (ii) the formidable productivity progress observed is primarily explained by technical efficiency changes that enabled producers to catch up with front runners; and (iii) environmental factors, such as weather conditions, impact both efficiency and productivity. Finally, the analysis reveals that using bootstrapping to make statistical inferences suggests that researchers should be careful in making performance comparisons based on conventional DEA methods, as any discovered differences may not be significant.     

三阶段组合效率测度模型与技术研发效率测度

在系统梳理现有可调整环境因素或/与统计噪音影响的三阶段组合效率测度模型的基础上,利用幅度调整测度(RAM)与随机前沿分析(SFA)结合,构建了无需强制性调整环境因素与统计噪音影响的三阶段组合效率测度改进模型——RAM-SFA-RAM.相对现有模型,新的组合测度模型不但在估计影响与调整投入和产出时可实现较为客观地设定环境因素与松弛变量之间存在非线性生产函数关系,以降低效率估计偏误,而且充分利用了RAM模型全面测度无效的优点,为从投入和产出两个方面同时过滤环境因素与统计噪音的差异性影响提供了新的分析途径;更重要的是,选用的RAM具有平移不变性,可使组合测度模型克服现有模型只能通过最值强制性对投入和产出进行正向调整以适应选择的效率估计模型无法处理非正值的不足,避免了由此产生的效率估计偏误.实证研究部分用这一组合效率测度模型分析了中国省域层次上大中型工业企业的技术研发效率,为效率的客观比较提供了可行的模型方法.     

Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector

In this paper the efficiency assessment of general networks of processes that produce both desirable and undesirable outputs is addressed. This problem arises in many contexts (e.g. transportation, energy generation, etc.). A general networks slacks-based inefficiency (GNSBI) measure can be computed using a simple linear program that takes into account the weak disposability of the bad outputs. The slacks-based inefficiency (SBI) of each process is also calculated. Target values for all inputs, outputs (both desirable and undesirable) and even intermediate products are also provided. The proposed approach is rather general and can accommodate many different network topologies and returns to scale assumptions. Two applications to the banking sector are presented: one to assess banks efficiencies and another to assess bank branches.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.