Extension Of Data Envelopment Analysis Research Articles

Cross-efficiency aggregation based on interval conditional entropy: An application to forest carbon sink efficiency

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA), which can effectively distinguish between decision-making units (DMUs) through self- and peer-evaluation. The cross-efficiency of each DMU in a set of DMUs is measured in terms of intervals when the input–output data are represented by the number of intervals. Based on the interval cross-efficiency matrix, the interval entropy is defined in terms of the likelihood. Then, considering the influence of peer evaluation, the interval conditional cross-efficiency entropy is proposed and an aggregation model of the interval conditional cross-efficiency entropy is presented to create a ranking index for DMUs. Finally, a simple example is provided to illustrate the effectiveness of the proposed method, which is applied to the evaluation of forest carbon sink efficiency in China. The results indicate that the final cross-efficiencies of all 30 provinces range from 0 to 0.6. Among these provinces, those with a relatively high efficiency include Guangdong, Guizhou, Hainan, Shandong, and Qinghai.

Social network analysis for cross‐evaluation in data envelopment analysis

AbstractAs one of the important extensions of data envelopment analysis (DEA) methodology, cross‐evaluation combines self‐evaluation and peer‐evaluation processes for each decision making unit (DMU) to effectively eliminate unrealistic weight schemes and differentiate all the units for ranking. Differing from previous research, which mainly pays attention to either secondary goals for generating weights for peer evaluation or aggregation of self and peer‐evaluation efficiencies, our study focuses on evaluating the relationships among all DMUs. If we view each unit as a node to be evaluated, then peer‐evaluation among pairs of DMUs forms a bidirectional network among all the DMUs. Based on this idea, we introduce a data‐driven tool combining social network analysis and cross‐evaluation to examine self‐evaluated and peer‐evaluated scores in the network. Using the hyperlink‐induced topic search algorithm, we develop the concepts of self‐evaluation and peer‐evaluation objectivity coefficients based on how well DMUs accept the analysis results. The rankings based on our self‐evaluation and peer‐evaluation scores adjusted with objectivity coefficients are shown to be consistent. Our study provides a novel perspective for cross‐evaluation and DEA research. An application case study illustrates our new method.

Combining Data Envelopment Analysis and Machine Learning

Data Envelopment Analysis (DEA) is one of the most used non-parametric techniques for technical efficiency assessment. DEA is exclusively concerned about the minimization of the empirical error, satisfying, at the same time, some shape constraints (convexity and free disposability). Unfortunately, by construction, DEA is a descriptive methodology that is not concerned about preventing overfitting. In this paper, we introduce a new methodology that allows for estimating polyhedral technologies following the Structural Risk Minimization (SRM) principle. This technique is called Data Envelopment Analysis-based Machines (DEAM). Given that the new method controls the generalization error of the model, the corresponding estimate of the technology does not suffer from overfitting. Moreover, the notion of ε-insensitivity is also introduced, generating a new and more robust definition of technical efficiency. Additionally, we show that DEAM can be seen as a machine learning-type extension of DEA, satisfying the same microeconomic postulates except for minimal extrapolation. Finally, the performance of DEAM is evaluated through simulations. We conclude that the frontier estimator derived from DEAM is better than that associated with DEA. The bias and mean squared error obtained for DEAM are smaller in all the scenarios analyzed, regardless of the number of variables and DMUs.

An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternatives.

Evaluation of the Efficiency of Basic Sanitation Integrated Management in Brazilian Municipalities.

This study aims to evaluate the level of technical efficiency of companies that perform the integrated management of basic sanitation in Brazilian municipalities. A Multiple Data Envelopment Analysis (M-DEA) model was applied to estimate the performance of water supply and sewage services in municipalities covering more than of the Brazilian population, identifying the factors that most influence the efficiency of the sector in the years 2008 and 2016. The M-DEA methodology is an extension of Data Envelopment Analysis (DEA) with multiple DEA executions considering all combinations of inputs and outputs to calculate efficiency scores. The methodology reduces possible biases in the selection of resources and products of the model, ability to support decision-making in favor of improvements in the sector′s efficiency based on national regulatory framework. The analyses show that the companies analyzed can increase their operating results and attendance coverage by more than , given the current levels of infrastructure, human and financial resources in the sector. Based on the simulation of potential efficiency gains in Brazilian basic sanitation companies, the estimates show that the coverage of the population with access to sanitary sewage would go from the current to . The evidence found provides indications to subsidize sanitation management in the country at the micro-analytical level, enabling a better competitive position in the sector for the integrated management of basic sanitation and its universalization in Brazil.

DEA Malmquist productivity index based on a double-frontier slacks-based model: Iranian road safety assessment

Many governments in the developing world face the social and economic consequences of road accidents and mortalities. Hence, more precise evaluation of regional programs to reduce road fatalities has been a concern for many safety professionals.Road safety performance is often measured using various extensions of Data Envelopment Analysis (DEA), in particular the model proposed by Charnes, Cooper and Rhodes (CCR), which deals only with the radial efficiency as the objective function neither taking into account input excesses nor output shortfalls. The Slacks-Based Measure (SBM) of efficiency overcomes this shortcoming by taking both measurements mentioned above simultaneously. In this regard, the current study aims to employ the SBM in analyzing road safety performance. It is noteworthy that the efficiency of each Decision Making Unit (DMU) can be pessimistically measured using the slacks-based measure of inefficiency such that the anti-efficient DMUs provide the anti-efficient frontier. The results obtained from the optimistic and pessimistic frontiers are nonlinearly aggregated by means of the Evidential Reasoning (ER) algorithm.Furthermore, a Double-Frontier SBM-based Malmquist Productivity Index (DF-SBM- MPI) is provided to analyze the efficiency and technological changes in safety performance from 2014 to 2016. For this purpose, the standard SBM and Super-SBM models are used to compute the optimistic Malmquist Productivity Index (MPI); similarly, the pessimistic MPI is determined by means of the inverted SBM and Super-SBM models. Finally, the obtained MPIs from the two different points of view are geometrically combined to obtain the overall MPI.

A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance

Road traffic fatalities have long been a main concern of road safety experts in developing countries. Such countries annually lose a large number of their citizens due to road crashes. Globally, the Data Envelopment Analysis (DEA) has been successfully applied in road safety assessment as a powerful decision making method. It is noteworthy that all of the current studies optimistically measured the efficiency score of each Decision Making Unit (DMU) based on its position relative to only the efficient frontier. However, the efficiency value can be pessimistically determined on the basis of the anti-efficient frontier. A double-frontier model will lead to more realistic results. Meanwhile, many studies have recently implemented Cross-Efficiency Method (CEM) as a DEA extension for performance evaluation because of the unique ranking results without requiring unrealistic weight restrictions.In this regard, the present study aims to assess Iranian road safety performance by proposing a novel double-frontier CEM taking into account both optimistic and pessimistic points of view, simultaneously. Therefore, two cross-efficiency matrices are constructed by applying the standard and the inverted input-oriented CCR (Charnes, Cooper, Rhodes) models, respectively. Evidential Reasoning Approach (ERA) is then employed as a nonlinear method of combination to aggregate the transformed cross-efficiency scores to pieces of evidence. Finally, the findings confirm that the presented procedure results in a more realistic and comprehensive assessment, which is relatively in agreement with the evaluation results obtained considering both the efficient and anti-efficient frontiers.

A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion

Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing the relative efficiency of decision making units (DMUs). The cross-efficiency evaluation is an extension of DEA that provides a ranking method and eliminates unrealistic DEA weighting schemes on weight restrictions, without requiring a prior information. The cross-efficiency evaluation may have some shortages, e.g. the cross-efficiency scores may not be unique due to the presence of several optima. To rectify this issue, several secondary goals have been proposed in the literature. Some scholars have proposed several cross-efficiency evaluations based on maximising (minimising) the total deviation from their ideal point as an aggressive (benevolent) perspective. In some cases, minimising (maximising) the number of DMUs that achieve their target efficiencies, is more important than maximising (minimising) the total deviation from the ideal point. We propose some alternative models for the cross-efficiency evaluation based on the cardinality of the set of “satisfied DMUs”, i.e. the DMUs that achieve their maximum efficiencies. For aggressive (benevolent) cross-efficiency evaluation, among all the optimal weights for a specific unit, we choose the weights which can maximise its efficiency, and at the same time minimise (maximise) the number of satisfied units. We demonstrate how the proposed method can be implemented and illustrate the method using two examples.

Integrated approach for computing aggregation weights in cross-efficiency evaluation

Cross-efficiency evaluation is an extension of data envelopment analysis that has been widely used in many different applications aimed at producing a ranking of the set of decision making units. Besides the traditional self-appraisal of units, cross-evaluation methods also take into account peer-appraisals, which are then summarized into an overall performance measure. The standard approach for this aggregation process relies on an equally-weighted average that disregards that some cross-efficiency scores might be considered more relevant or reliable than others. This paper focuses on the aggregation process of cross-efficiency scores and proposes a new approach for deriving meaningful aggregation weights for a more comprehensive evaluation of the units. Our method integrates two complementary perspectives that weights should reflect: the discriminatory ability of the information contained in the cross-efficiency matrix and the relative importance that can be attributed to each of the peer-appraisals. In this sense, the approach presented here provides a more accurate evaluation of the units than previous approaches and therefore it is likely to produce more meaningful rankings. Some numerical examples are provided that validate the approach proposed and examine the results obtained in comparison with previous known methods.

Cross efficiency based heuristics to rank decision making units in data envelopment analysis

This paper proposes two cross-efficiency based heuristics (CEHs) for ranking decision making units (DMUs) in Data Envelopment Analysis (DEA). This paper also suggests a stratification-based consistency evaluation framework (SCEF) to evaluate the performance of the proposed heuristics and several DEA-based full ranking methods in terms of consistency. Several cross-efficiency (CE) methods have been developed as a DEA extension to rank efficient and inefficient DMUs with the main idea of using DEA to do peer evaluation. However, it has been well known that they all suffer from lack of discrimination since efficiency scores from those methods may not be unique due to the non-uniqueness of the DEA optimal weights in the Linear Programming (LP) models. The proposed CEH methods overcome this issue since they do not use any LP models but show comparable consistency level to other DEA-based full ranking methods based on SCEF. Numerical examples from the literature and simulation indicate that CEHs are a good surrogate for CE method.

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.

Productivity and its determinants in microfinance institutions (MFIs): Evidence from South Asian countries

This study investigates the productivity of 50 South Asian microfinance institutions (MFIs) by deploying a Malmquist Productivity Index (an extension of Data Envelopment Analysis) with a panel data covering the years 2007 to 2012. The empirical results indicate that South Asian MFIs have improved their annual average productivity by 2.1% largely due to changes in technical efficiency. However, the overall level of technological change is shown to remain static. Further decomposition of technical efficiency change indicates that overall productivity progress is mainly due to scale efficiency. In the course of investigating the determinants of productivity, this study found that the productivity of South Asian MFIs is significantly affected by financial, economic and institutional factors. Policy implications are further discussed.

Fuzzy cross-efficiency evaluation: a possibility approach

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA) aimed at ranking decision making units (DMUs) involved in a production process regarding their efficiency. As has been done with other enhancements and extensions of DEA, in this paper we propose a fuzzy approach to the cross-efficiency evaluation. Specifically, we develop a fuzzy cross-efficiency evaluation based on the possibility approach by Lertworasirikul et al. (Fuzzy Sets Syst 139:379---394, 2003a) to fuzzy DEA. Thus, a methodology for ranking DMUs is presented that may be used when data are imprecise, in particular for fuzzy inputs and outputs being normal and convex. We prove some results that allow us to define "consistent" cross-efficiencies. The ranking of DMUs for a given possibility level results from an ordering of cross-efficiency scores, which are real numbers. As in the crisp case, we also develop benevolent and aggressive fuzzy formulations in order to deal with the alternate optima for the weights.

Book Reviews

In Book Reviews, we review an extensive and diverse range of books. They cover theory and applications in operations research, statistics, management science, econometrics, mathematics, computers, and information systems. In addition, we include books in other fields that emphasize technical applications. The editor will be pleased to receive an email from those willing to review a book, with an indication of specific areas of interest. If you are aware of a specific book that you would like to review, or that you think should be reviewed, please contact the editor. The following books are reviewed in this issue of Interfaces, 46(1), January–February 2016: Operations Planning: Mixed Integer Optimization Models, Joseph Geunes; Extension of Data Envelopment Analysis with Preference Information: Value Efficiency, Tarja Joro and Pekka J. Korhonen; and Rational Action: The Sciences of Policy in Britain and America, 1940–1960, William Thomas.

Evaluation of vendors ranking by EATWOS approach

Purpose– In order to improve the supply chain performance, organizations need to improve the efficiency of vendors. Although many techniques are used for vendor efficiency measurement, there is a lack of research about defining satisficing level to analyze improvement potential of vendors. The purpose of this paper is to incorporate satisficing level of some outputs to determine efficiency improvement potential of existing vendors.Design/methodology/approach– Method used in this paper is an extension of Data Envelopment Analysis, which has been used frequently for efficiency measurement of Decision Making Units. This method is known as Efficiency Analysis Technique with Output Satisficing (EATWOS), which has been mainly used in the field of economics for efficiency measurement.Findings– A case illustration of a National Capital Region of Delhi, India, based manufacturer and distributor of packaged drinking water is depicted to portray the practical application of EATWOS in vendor efficiency evaluation and their relative ranking. This method has helped in evaluating the improvement potential in performance of given vendors and helping in strategic decision making for the given organizationResearch limitations/implications– In case of more variables, this method becomes more complex to get the solution. Second, sometimes difference in vendors ranking without and with satisficing concept is very less, as in this case. Therefore, recording and analysis of output data of vendors should be done very carefully.Practical implications– Major implications of this study is that while selecting vendors, organizations should also try to understand improvement potential for given vendors by applying satisficing concept as given in this research. This approach helps in analyzing improvement potentials of suppliers.Originality/value– This paper explores an innovative approach to rank vendors on basis of certain criteria after considering the satisficing concept and improvement potentials of vendors.

A DEA Based Model for Ranking Air Freighters Operational Efficiency

This paper proposes a benchmarking model useful to rank and select aircraft used in the freight industry. The decision-making problem of aircraft ranking and selection is addressed by implementing an extension of Data Envelopment Analysis (DEA), i.e. the cross-efficiency calculation. DEA efficiency is a useful indicator to evaluate the value for money of an aircraft in the freight industry and its extension - the cross-efficiency measurement makes it possible to rank aircraft according to this value for money measurements. A sample of 22 air freighters is used to analyze the model validity. DEA scores show that 4 aircraft models only are evaluated as being full 100% efficient, and some old models (i.e., DC 9-10F) are as efficient as the recent aircraft models sold in the market (A300F and A330-200F).

Data envelopment analysis with discrete‐valued inputs and outputs

AbstractThe conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units, which has real‐valued inputs and outputs. In many real occasions, there are cases in which some inputs and/or outputs must only take some particularised real or integer values. These values are referred to as discrete data. The need to deal with discrete‐valued data in DEA naturally occurs when we use real‐valued or integer‐valued DEA, but the reduced inputs and outputs of an inefficient decision making unit are restricted to some particular real or integer values. In this case, axioms such as unbounded ray, convexity and free disposability as discussed in the conventional DEA are violated. In this paper, an alternative extension of DEA in the case of discrete‐valued data has been faced. An axiomatic foundation is proposed to define the new production possibility set. In order to exemplify the method, a case of 25 Iranian gas companies' activities are illustrated.

Best-practice benchmarking using clustering methods: Application to energy regulation

Data envelopment analysis (DEA) is widely used as a benchmarking tool for improving productive performance of decision making units (DMUs). The benchmarks produced by DEA are obtained as a side-product of computing efficiency scores. As a result, the benchmark units may differ from the evaluated DMU in terms of their input–output profiles and the scale size. Moreover, the DEA benchmarks may operate in a more favorable environment than the evaluated DMU. Further, DEA is sensitive to stochastic noise, which can affect the benchmarking exercise. In this paper we propose a new approach to benchmarking that combines the frontier estimation techniques with clustering methods. More specifically, we propose to apply some clustering methods to identify groups of DMUs that are similar in terms of their input–output profiles or other observed characteristics. We then rank DMUs in the descending order of efficiency within each cluster. The cluster-specific efficiency rankings enable the management to identify not only the most efficient benchmark, but also other peers that operate more efficiently within the same cluster. The proposed approach is flexible to combine any clustering method with any frontier estimation technique. The inputs of clustering and efficiency analysis are user-specified and can be multi-dimensional. We present a real world application to the regulation of electricity distribution networks in Finland, where the regulator uses the semi-nonparametric StoNED method (stochastic non-parametric envelopment of data). StoNED can be seen as a stochastic extension of DEA that takes the noise term explicitly into account. We find that the cluster-specific efficiency rankings provide more meaningful benchmarks than the conventional approach of using the intensity weights obtained as a side-product of efficiency analysis.

Selecting suppliers for a long-term relationship

The purpose of this paper is to develop a quantitative methodology based on data envelopment analysis (DEA), including the constraint of ‘self-efficiency’ for supplier selection. This paper considers not only both product and process characteristics as outputs of the suppliers but also suppliers' self-efficiency, a prerequisite for the survival of the supplier in a competitive environment. Three extensions of DEA are employed and combined for ranking and selecting among self-efficient suppliers. A real example illustrates the applicability and discriminating power of the proposed model compared to a similar study.

The effect of quality and socio-demographic variables on efficiency measures in primary health care

This paper aims to extend the literature on measuring efficiency in primary health care by considering the influence of quality indicators and environmental variables conjointly in a case study. In particular, environmental variables are represented by patients' characteristics and quality indicators are based on technical aspects. In order to deal with both aspects, different extensions of data envelopment analysis (DEA) methodology are applied. Specifically, we use weight restrictions to ensure that the efficiency scores assigned to the evaluated units take quality data into account, and a four-stage model to identify which exogenous variables have impact on performance as well as to compute efficiency scores that incorporate this information explicitly. The results provide evidence in support of the importance of including information about both aspects in the analysis so that the efficiency measures obtained can be interpreted as an accurate reflection of performance.