A “calculus” for data envelopment analysis

DEA models are not amenable to differential arguments for extreme efficient units. Consequently, function representations of the approximating technology are not differentiable in the usual sense. Dually, this nondifferentiability is manifested by multiple optima to the Charnes et al. (Eur J Oper Res 2:429–444, 1978) DEA problem. This paper shows how a “calculus” can be applied to DEA, and, in particular, how this “calculus” resolves the resulting weight choice problem uniquely. The “calculus” is based on the concept of willingness to pay and well-known results in the convex analysis literature (Rockafellar, Convex analysis, 1970) for directional derivatives and their associated superdifferentials.     

Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification

The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.     

Different orders of one-sided scale elasticities in multi-output production

In this paper we explore properties of different orders of one-sided scale elasticities in multi-input multi-output production using the theoretical framework developed by Hadjicostas and Soteriou (Eur J Oper Res 168:425–449, 2006), Krivonozhko et al. (J Oper Res Soc 55:1049–1058, 2004), and others. That framework includes as a special case the well-known operations research method of data envelopment analysis (DEA). A special case of the theory in this paper is the Banker-Morey (Oper Res 34:513–521, 1986a) DEA model for data that include both discretionary and non-discretionary inputs and outputs. Several inequalities among different orders of one-sided scale elasticities are presented. An example is used to illustrate many of the results and ideas of the paper. Finally, we show how the theory and results of this paper can be used to shed some light on implicit Hicks input technical change.     

Social entrepreneurship orientation and performance in non-profit organizations

With the downturn in the global socioeconomic panorama, the social entrepreneurship orientation (SEO) and the social performance of non-profit organizations (NPOs) have become subject to growing levels of attention. The objective of this study is to analyze the influence of SEO on the performance of NPOs. To this end, we deployed a quantitative methodology based on the application of a survey of NPOs, which received a total of 135 valid responses. Our results demonstrate a positive effect for the dimensions of social innovation and social proactivity even while reporting no effect for the acceptance of social risks on performance. These results hold important implications across two different levels: in terms of the NPOs and policy-makers.

     

Using data envelopment analysis to evaluate efficiency in the economic performance of Chinese cities

This paper studies the use of DEA (data envelopment analysis) as a tool for possible use in evaluating and planning the economic performance of China's cities (28 in all) which play a critical role in the government's program of economic development. DEA promises advantages which include the absence of any need for the assignment of weights on an a priori basis (to reflect the supposed relative importance of various outputs or inputs) when evaluating technical efficiency. It is also unnecessary to explicitly specify underlying functions that are intended to prescribe the analytical form of the relations between inputs and outputs. Finally, as is illustrated in the paper, DEA can be used to identify sources, and estimate amounts of inefficiencies in each city's performance as well as to identify returns-to-scale possibilities in ways that seem well-suited to the mixture of centralized and decentralized planning and performance that China is currently trying to use.     

Using DEA to evaluate the state of society as measured by multiple social indicators

This paper presents an approach for discussing the state of society, which is measured by multiple social indicators, using data envelopment analysis (DEA). Replacing inputs and outputs in DEA with negative and positive social indicators respectively, we analyze the desirability of living in the 47 prefectures of Japan. This is also a proposal for the potential use of DEA in multi-dimensional evaluation analysis other than the standard DEA efficiency analysis. The results using eight social indicators identify 26 DEA desirable prefectures out of the 47 and present other useful knowledge and information. It is concluded that DEA, which can avoid uniform evaluation by an a priori weighting system, provides availability as a comprehensive evaluation tool different from traditional ones.     

Unemployment and employment offices’ efficiency: What can be done?

Regional employment offices provide placement services to job-seekers and employers and organize active labor market programs. In this paper, we carry out a quantitative evaluation of the employment offices’ performance in Switzerland based on production efficiency measures. We use Data Envelopment Analysis (DEA) to estimate the performance of all employment offices and then account for factors in the local operating environment that are outside managerial control. This approach, and the ranking of employment offices, may easily be interpreted by policymakers and provides guidelines for raising the efficiency of the public employment service. Our findings suggest that there is considerable room for improved efficiency in employment service, which could lead to a lower level of structural unemployment. We also find that differences in the external operating environment have a significant influence upon the efficiency of employment offices.     

Calculation of scale elasticities in DEA models: direct and indirect approaches

The qualitative characterisation of returns to scale in DEA has been a research issue the last decade. However, quantitative information provides the ultimate information. This paper presents two ways of obtaining numerical values of scale elasticity by an indirect approach using efficiency scores and dual variables for radial projections of inefficient points to the frontier, and a direct approach that is more general and powerful and directly evaluates numerically scale elasticity at any point on the DEA surface along intersections with planes. The direct and indirect approaches are compared using real data and a very high correspondence is found.     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.     

Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates

Many studies devoted to efficiency performance evaluation in the education sector are based on measures of central tendency at school level as, for example, the average values of students belonging to the same school. Although this is a common and accepted way of summarizing data from the original observations (students), it is not less true that this approach neglects the existing dispersion of data, which may become a serious problem if variability across schools is high. Additionally, imprecision may arise when experts on each evaluated subject select the battery of questions, with different levels of difficulty, which will be the base for the final questionnaires completed by students. This paper uses data from US students and schools participating in PISA (Programme for International Student Assessment) 2015 to illustrate that schools' efficiency measures based on aggregate data and imprecision may reflect an inaccurate picture of their performance if they are compared to measures estimated accounting for broader information provided by all students of the same school. In order to operationalize our approach, we resort to Fuzzy Data Envelopment Analysis. This methodology allows us to deal with the notion of fuzziness in some variables such as the socio-economic status of students or test scores. Our results indicate that the estimated measures of performance obtained with the fuzzy DEA approach are highly correlated with those calculated with traditional DEA models. However, we find some relevant divergences in the identification of efficient units when we account for data dispersion and vagueness.     

Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry

The banking industry in Canada is essentially an oligopoly with five large participants controlling about 90% of the market. To evaluate the industry's performance over time, we need to deal with the problem of a small number of DMU's compared to the number of relevant inputs and outputs. To overcome this problem we use data envelopment analysis (DEA) window analysis, whereby efficiency scores for the 20 year period 1981–2000 are obtained. To measure productivity changes over time, Malmquist indices can be calculated from DEA scores. Using DEA window analysis scores, however, raise the question of how to define the same period frontier in a DEA window analysis. We show that for both the adjacent and the base period Malmquist index and for all suggested definitions of same period frontier, the standard decomposition into frontier shift and catching up effects gives inappropriate results when Malmquist indices are based on DEA window analysis scores.     

我国银行业市场结构、效率及绩效关系研究

文章以国际上较流行的数据包络方法为测度工具,利用由CCR模型衍变而来的VRS及NIRS效率模型,对我国商业银行1997、1999、2001、2003年等4年的技术效率、规模效率、纯技术效率进行测算。根据所测得的效率数据,对有效结构假说和结构行为绩效假说进行实证检验,结果显示,效率和市场集中度与银行绩效正相关,而市场份额则与绩效负相关,该结论表明这两个假说都不适合中国银行业市场。同时,我们必须充分重视银行效率的提高。     

Detecting Outliers in Frontier Models: A Simple Approach

In frontier analysis, most of the nonparametric approaches (DEA, FDH) are based on envelopment ideas which suppose that with probability one, all the observed units belong to the attainable set. In these deterministic frontier models, statistical theory is now mostly available (Simar and Wilson, 2000a). In the presence of super-efficient outliers, envelopment estimators could behave dramatically since they are very sensitive to extreme observations. Some recent results from Cazals et al. (2002) on robust nonparametric frontier estimators may be used in order to detect outliers by defining a new DEA/FDH deterministic type estimator which does not envelop all the data points and so is more robust to extreme data points. In this paper, we summarize the main results of Cazals et al. (2002) and we show how this tool can be used for detecting outliers when using the classical DEA/FDH estimators or any parametric techniques. We propose a methodology implementing the tool and we illustrate through some numerical examples with simulated and real data. The method should be used in a first step, as an exploratory data analysis, before using any frontier estimation.     

Another Approach to Data Envelopment Analysis in Noisy Environments: DEA+

In this paper a DEA+ labeled approach for efficiency measurement in the stochastic case is presented along with a consistency proof and some preliminary evidence illustrating the small sample performance. DEA+ can basically handle multi-output technologies like standard DEA but allows to filter noise, that might have disturbed production and unlike a related approach does not require panel data. Consistency of DEA+ relies on the assumption of i.i.d. distributed and bounded noise and requires radial efficiency measurement. First Monte Carlo experiments show that a DEA+ based average inefficiency estimator performs well for samples of size n=100 in one-output, two-input settings compared to the corresponding Stochastic Frontier Estimator. Sensitivity of DEA+ performance with respect to parametrization of noise is weak, but higher noise contribution requires much larger sample size for satisfactory results.     

CSR and service quality in nonprofit organizations: the case of a performing arts association

• The relationship between corporate social responsibility (CSR) and marketing performance has been widely investigated recently, but mostly in relation to for-profit companies. This paper highlights the importance of this topic for nonprofit organizations (NPOs). Focusing on an Italian NPO operating in the performing arts and entertainment industry, two empirical studies (a quantitative survey and a qualitative exploratory enquiry) prove the strategic relevance of CSR in nonprofit contexts. The results demonstrate that CSR can be considered an additional dimension of the customer perception of service quality in NPOs and reveal that customer perception of the social responsibility of the studied NPO is strongly linked to its institutional mission and to the modalities through which it pursues that mission.

Copyright © 2014 John Wiley & Sons, Ltd.     

A graphically based machine learning approach to predict secondary schools performance in Tunisia

The main purpose of this paper is to identify the key factors that impact schools' academic performance and to explore their relationships through a two-stage analysis based on a sample of Tunisian secondary schools. In the first stage, we use the Directional Distance Function approach (DDF) to deal with undesirable outputs. The DDF is estimated using Data Envelopment Analysis method (DEA). In the second stage we apply machine-learning approaches (regression trees and random forests) to identify and visualize variables that are associated with a high school performance. The data is extracted from the Program for International Student Assessment (PISA) 2012 survey. The first stage analysis shows that almost 22% of Tunisian schools are efficient and that they could improve their students’ educational performance by 15.6% while using the same level of resources. Regression trees findings indicate that the most important factors associated with higher performance are school size, competition, class size, parental pressure and proportion of girls. Only, school location appears with no impact on school efficiency. Random forests algorithm outcomes display that proportion of girls at school and school size have the most powerful impact on the predictive accuracy of our model and hence could more influence school efficiency. The findings disclose also the high non-linearity of the relationships between these key factors and school performance and reveal the importance of modeling their interactions in influencing efficiency scores.     

Environmental performance evaluation: A state-level DEA analysis

In recent years, the continuous development of every country's economic activities has generated undesirable impacts on the environment. Common problems are high water and energy consumption rates, jointly with harmful pollution levels. This situation has gained the research community's interest in exploring and analyzing the extent to which initiatives to reduce such environmental problems have succeeded. Therefore, it is relevant to have measures that encompass information on the results obtained by such initiatives. Using the data envelopment analysis (DEA) methodology, it is possible to measure the efficiency of an entity under evaluation, such as an industry, state, or country. DEA also allows one to compare the performance measures of entities operating in similar circumstances and identify which entities are performing best, given the inputs they use and the outputs they produce. This study evaluates different states in Mexico in terms of their environmental performance and provides a perspective on how environmental initiatives can contribute to protecting and preserving the environment. By addressing this problem, best-performers and practices are identified, and valuable insights are gained regarding how each state carries out such initiatives.     

基于DEA-AHP的港口物流绩效评价研究

基于层次分析法(AHP)和数据包络分析法(DEA),构建了适合港口物流绩效评价的新型指标体系,建立了AHP和DEA相结合的两阶段评价模型。该模型首先进行定性指标的层次分析,然后将分析结果作为DEA的输入输出项,并结合其他定量指标进行DEA评价,最后结合实例验证评价方法的可行性。     

Managerial Efficiency,Managerial Succession and Organizational Performance

Data envelopment analysis (DEA) is used to create a measure of managerial efficiency in an attempt to reassess the conflicting theories concerning the impact of organizational performance on manager succession, and the counter-theories concerning the impact of manager succession on organizational performance. The analysis uses data for 147 college basketball teams from 1984 to 1991. The results indicate that winning, not efficiency, is the key criterion used in determining managerial retention. Yet when managers of losing teams are dismissed the teams tend to do even worse. If, however, the efficiency of the new manager is greater than that of the former, the disruptive effect of succession is minimized. Because administrators appear to focus on winning, not efficiency, they will often select new managers who are less efficient than departed managers. These results are unique to this literature and indicate promise for the use of DEA in analyses of the internal efficiencies of organizations. © 1997 John Wiley & Sons, Ltd.