General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.     

A generalized multiplicative directional distance function for efficiency measurement in DEA

For measuring technical efficiency relative to a log-linear technology, a generalized multiplicative directional distance function (GMDDF) is developed using the framework of multiplicative directional distance function (MDDF). Furthermore, a computational procedure is suggested for its estimation. The GMDDF serves as a comprehensive measure of efficiency in revealing Pareto-efficient targets as it accounts for all possible input and output slacks. This measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity, unit invariance, translation invariance, and positive affine transformation invariance. This measure can be easily implemented in any standard DEA software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision-making preferences. Finally, to demonstrate the ready applicability of our proposed measure, an illustrative empirical analysis is conducted based on real-life data set of 20 hardware computer companies in India.     

Short-run and long-run efficiency measures for multiplant firms

The usual Data Envelopment Analysis (DEA) model for measuring the relative efficiency assumes that all plants belong to distinct firms superior to them. For firms with more than one plant, Koopmans proposes a procedure for deriving the short-run production frontier for each firm. Modifying his idea, a DEA model is constructed in this paper for measuring the short-run efficiency of each plant within a firm. Based on the theory of production economics that the long-run production frontier is an envelop super-imposed upon all short-run production frontiers, another DEA model is constructed to measure the long-run efficiency of every plant. The long-run efficiency is always smaller than or equal to the short-run efficiency. Consequently, it is possible that an inefficient plant can only be improved in the long-run. With the models constructed in this paper, a decision-maker is able to distinguish between what can be achieved in the short-run and what in the long-run. To clarify the idea, an example of Taiwan forests is adopted for illustration. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cartan geometries and multiplicative forms

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures.     

On value efficiency

Value efficiency analysis (VEA) is a data envelopment analysis (DEA)-based approach that measures the efficiency of decision-making units, incorporating the decision maker's preferences explicitly. If the functional form of the value function is assumed pseudoconcave, then a tangent cone where the most preferred point is its vertex can be used to recognize value inefficient points. In this article, we consider the value function assumptions and show that the pseudoconcavity assumption can be extended to also cover nonsmooth value functions in VEA using a known class of limiting subdifferentials in nonsmooth analysis. The focus of this article is to show that the tangent cone approach to recognize value inefficient points is a valid approach even if the value function assumptions are more general than pseudoconcavity. Moreover, we show that continuity is needed in the case of true value efficiency.     

An efficiency measurement framework for multi-stage production systems

We develop an efficiency measurement framework for systems composed of two subsystems arranged in series that simultaneously computes the efficiency of the aggregate system and each subsystem. Our approach expands the technology sets of each subsystem by allowing each to acquire resources from the other in exchange for delivery of the appropriate (intermediate or final) product, and to form composites from both subsystems. Managers of each subsystem will not agree to ‘`vertical integration’' initiatives unless each subsystem will be more efficient than what each can achieve by separately applying conventional efficiency analysis. A Pareto Efficient frontier characterizes the acceptable set of efficiencies of each subsystem from which the managers will negotiate to select the final outcome. Three proposals for the choice for the Pareto efficient point are discussed: the one that achieves the largest equiproportionate reduction in the classical efficiencies; the one that achieves the largest equal reduction in efficiency; and the one that maximizes the radial contraction in the aggregate consumption of resources originally employed before integration. We show how each choice for the Pareto efficient point determines a derived measure of aggregate efficiency. An extensive numerical example is used to illustrate exactly how the 2 subsystems can significantly improve their operational efficiencies via integration beyond what would be predicted by conventional analysis.     

Implementing and interpreting a data envelopment analysis model to assess the efficiency of health systems in developing countries

This paper presents a data envelopment analysis model that canbe implemented by public sector management for assessing theefficiency of a health system within a developing country. Toillustrate the practical implementation and interpretation ofthe model this study compares health systems across 51 developingcountries using 1998–99 data. The results of the analysisgenerated empirical indicators of efficiency, and we demonstratehow these may then be used by management in order to understandthe factors associated with good performance of a health system.     

Improving weak efficiency frontiers in the fuzzy data envelopment analysis models

Evaluating the performance of activities or organization by common data envelopment analysis models requires crisp input/output data. However, the precise inputs and outputs of production processes cannot be always measured. Thus, the data envelopment analysis measurement containing fuzzy data, called “fuzzy data envelopment analysis”, has played an important role in the evaluation of efficiencies of real applications. This paper focuses on the fuzzy CCR model and proposes a new method for determining the lower bounds of fuzzy inputs and outputs. This improves the weak efficiency frontiers of the corresponding production possibility set. Also a numerical example illustrates the capability of the proposed method.     

Essentially finite algorithms for minimizing a class of convex piecewise polynomial functions

We consider minimax problems of the type min _t[a,b] max _i p _t (t), where thep _i (t) are real polynomials which are convex on an interval [a, b]. Here, the function max _i p _i (t) is a convex piecewise polynomial function. The main result is an algorithm yielding the minimum and the minimizing point, which is efficient with respect to the necessary number of computed polynomial zeros. The algorithms presented here are applicable to decision problems with convex loss. While primarily of theoretical interest, they are implementable for quadratic loss functions with finitely many states of nature. An example of this case is given. The algorithms are finite when polynomial zeros need not be approximated.The author is indebted to T. E. S. Raghavan for many stimulating discussions.     

基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。     

Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools

Public sector output provision is influenced not only by discretionary inputs but also by exogenous environmental factors. In this paper, we extended the literature by developing a conditional DEA estimator of allocative efficiency that allows a decomposition of overall cost efficiency into allocative and technical components while simultaneously controlling for the environment. We apply the model to analyze technical and allocative efficiency of Dutch secondary schools. The results reveal that allocative efficiency represents a significant 37 percent of overall cost efficiency on average, although technical inefficiency is still the dominant part. Furthermore, the results show that the impact of environment largely differs between schools and that having a more unfavorable environment is very expensive to schools. These results highlight the importance of including environmental variables in both technical and allocative efficiency analysis.     

A joint measurement of efficiency and effectiveness for non-storable commodities: Integrated data envelopment analysis approaches

Efficiency and effectiveness for non-storable commodities represent two distinct dimensions and a joint measurement of both is necessary to fully capture the overall performance. This paper proposes two novel integrated data envelopment analysis (IDEA) approaches, the integrated Charnes, Cooper and Rhodes (ICCR) and integrated Banker, Charnes and Cooper (IBCC) models, to jointly analyze the overall performance of non-storable commodities under constant and variable returns to scale technologies. The core logic of the proposed models is simultaneously determining the virtual multipliers associated with inputs, outputs, and consumption by additive specifications for technical efficiency and service effectiveness terms with equal weights. We show that both ICCR and IBCC models possess the essential properties of rationality, uniqueness, and benchmarking power. A case analysis also demonstrates that the proposed novel IDEA approaches have higher benchmarking power than the conventional separate DEA approaches. More generalized specifications of IDEA models with unequal weights are also elaborated.     

A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis

The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.     

Solving the puzzles of structural efficiency

Since the concept of “structural efficiency” first appeared in Farrell [Farrell, M.J., 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, Part III 120, 253–281], attempts have been made to derive measures for the performance of a group of production units (often referred to an industry with many firms). Many empirical studies used the technical efficiency of an average unit to measure the structural efficiency of a group, but researchers have been puzzled by the discrepancies between the average of individual efficiency scores and the performance of the group as a whole. In this paper, we point out that the “shadow price model” provides a useful framework for understanding the economic meaning of the structural efficiency as well as its components. By recognizing these components, the puzzles related to the inconsistencies between the individual and group performance can be solved readily.     

Stability of efficiency evaluations in data envelopment analysis

Efficiency evaluations in data envelopment analysis are shown to be stable for arbitrary perturbations in the convex hulls of input and output data. Also, the corresponding restricted Lagrange multiplier functions are shown to be continuous. The results are proved using point-to-set mappings and a particular region of stability from input optimization.Research partly supported by National Science Foundation Grants, Office of Naval Research Grant, and by the Natural Sciences and Engineering Council of Canada.     

技术进步效率测度模型的构建及应用

技术进步是影响经济增长的决定性因素,因此,技术进步的测度成为一个重要的研究问题。然而,技术进步的测度到目前为止还没有统一和令人信服的方法。本文使用DEA方法,基于理想生产前沿面构建了技术进步效率测度模型。技术进步效率测度模型是技术进步度量的一种新方法,是一个相对量的测量,规避了技术进步总量测算模型的一些缺陷。将模型用于测算我国1999～2008年的技术进步效率,测算结果表明我国大多数地区技术进步效率呈逐年上升的趋势,经济产出较高而同时消耗了较低资源投入的省份具有较高的技术进步效率。这说明低消耗的技术进步才是有效的,能够有效支撑经济的可持续发展。     

Monitoring managerial efficiency in the performing arts: A regional theatres network perspective

Managerial efficiency within the performing arts programming can be understood as the technical efficiency of transforming the resources cultural managers have available into a determined cultural output. Through this explanation different conceptions on the finished performance product it leads us to select two different output variables (number of performances, and number of attendances). In this way, three different models are considered regarding those conceptual points of view. Data on the Circuït Teatral Valencià, a Spanish regional theatres network, is used to develop empirically the concept of Managerial Efficiency and set up a framework to allow us to monitor it.     

指标可取负值的基于输入与输出的DEA模型

有关基于输入与输出的DEA模型,本文与现有文献的不同之处,一是模型中的评价指标可取负值,二是被评的决策单元可以不是所给的n个决策单元之一,三是模型并非由多目标规划模型推得.此外,给出了有关此模型的三个定理.因此,可知有关此模型的最优解存在的充分条件;在求解此模型后就能在判断决策单元的DEA有效性的同时计算出其相对效率,并能计算出其在DEA相对有效面上的"投影".     

Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks

Conventional data envelopment analysis (DEA) for measuring the efficiency of a set of decision making units (DMUs) requires the input/output data to be constant. In reality, however, many observations are stochastic in nature; consequently, the resulting efficiencies are stochastic as well. This paper discusses how to obtain the efficiency distribution of each DMU via a simulation technique. The case of Taiwan commercial banks shows that, firstly, the number of replications in simulation analysis has little effect on the estimation of efficiency means, yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions. Secondly, the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation. Thirdly, the interval-data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information. In conclusion, when multiple observations are available for each DMU, the stochastic-data approach produces more reliable and informative results than the average-data and interval-data approaches do.