Improving the discrimination power and weights dispersion in the data envelopment analysis

Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of peer decision making units (DMUs) with multiple input and outputs. Beside of its popularity, DEA has some drawbacks such as unrealistic input–output weights and lack of discrimination among efficient DMUs. In this study, two new models based on a multi-criteria data envelopment analysis (MCDEA) are developed to moderate the homogeneity of weights distribution by using goal programming (GP). These goal programming data envelopment analysis models, GPDEA-CCR and GPDEA-BCC, also improve the discrimination power of DEA.     

A note on a new method based on the dispersion of weights in data envelopment analysis

In a very recent paper by Bal et al. (Bal, H., Örkcü, H. H., & Çelebioğlu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Computers & Industrial Engineering, 54(3), 502–512), a data envelopment analysis (DEA) model which incorporates the coefficients of variations (CVs) of input–output weights was proposed to improve the discrimination power of DEA and balance input–output weights. This note points out that the input and output weights in DEA are of different dimensions and units. The weights with different dimensions and units cannot be simply added together and averaged. In other words, the DEA model with the inclusion of CVs of input–output weights, which was referred to as CVDEA model for short, makes no sense if input and output data are not normalized to eliminate their dimensions and units. This note also illustrates the facts that the CVDEA model can cause significant efficiency changes when a scale transformation is performed for an input or output and may produce multiple local optimal solutions due to its nonlinearity, leading to totally different assessment conclusions. These facts reveal that the CVDEA model suffers from serious drawbacks and its applications for efficiency assessment should be very cautious.     

A new method based on the dispersion of weights in data envelopment analysis

One of the drawbacks of the data envelopment analysis (DEA) is the problem of lack of discrimination among efficient decision making units (DMUs) and hence yielding many numbers of DMUs as efficient. The main purpose of this study is to overcome this inability. In the case in which the minimization of the coefficient of variation (CV) for input–output weights is added to the DEA model, more reasonable and more homogeneous input–output weights are obtained. For this new proposed model based on the CV it is observed that the number of efficient DMUs is reduced, improving the discrimination power. When this new approach is applied to two well-known examples in the literature, and a real-world data of OECD countries, it has been seen that the new model yielded a more balanced dispersion of input–output weights and reduced the number of efficient DMUs. In addition, the applicability of the new model is tested by a simulation study.     

Indian thermal power plant challenges and remedies via application of modified data envelopment analysis

This paper evaluates the performance of coal‐fired thermal power plants in India for the year 2008–2009 using data envelopment analysis (DEA); subdividing the power plants into three categories depending on their scale—small, medium, and large. The classical DEA model is analyzed to identify the efficient ones from the whole gamut of plants run by various organizations of the central government, state government, and private sector. Slack analysis is carried out to explore the specific areas that need to be focused on, in quantitative terms, for the overall efficiency improvement. Further efficiency evaluation is extended from a single criterion‐based conventional approach to a multiple criteria oriented approach, and the resulting DEA models are more efficient and flexible in many aspects, particularly in discriminant and weight analysis. Results of multicriteria DEA (MCDEA) are substantiated with cross‐efficiency analysis by deploying the weights obtained by the MCDEA in the cross‐efficiency analysis. On the basis of the insights provided by the outcome of the analysis, both qualitative and quantitative measures are proposed for improvement of the plant performances. The result of this analysis may assist the management of the power plants to introspect and review their systems and processes for optimal use of resources. The methodology adopted in the present work can also be employed for deeper understanding of power plants in other parts of India as well as in other countries.     

A generalized multiple layer data envelopment analysis model for hierarchical structure assessment: A case study in road safety performance evaluation

Data envelopment analysis (DEA) is a powerful analytical research tool for measuring the relative efficiency of a homogeneous set of decision making units (DMUs) by obtaining empirical estimates of relations between multiple inputs and multiple outputs related to the DMUs. To further embody multilayer hierarchical structures of these inputs and outputs in the DEA framework, which are prevalent in today’s performance evaluation activities, we propose a generalized multiple layer DEA (MLDEA) model. Starting from the input-oriented CCR model, we elaborate the mathematical deduction process of the MLDEA model, formulate the weights in each layer of the hierarchy, and indicate different types of possible weight restrictions. Meanwhile, its linear transformation is realized and further extended to the BCC form. To demonstrate the proposed MLDEA model, a case study in evaluating the road safety performance of a set of 19 European countries is carried out. By using 13 hierarchical safety performance indicators in terms of road user behavior (e.g., inappropriate or excessive speed) as the model’s input and 4 layered road safety final outcomes (e.g., road fatalities) as the output, we compute the most optimal road safety efficiency score for the set of European countries, and further analyze the weights assigned to each layer of the hierarchy. A comparison of the results with the ones from the one layer DEA model clearly indicates the usefulness and effectiveness of this improvement in dealing with a great number of performance evaluation activities with hierarchical structures.     

Ranking units in DEA based on efficiency intervals and decision‐maker's preferences

Data Envelopment Analysis (DEA) uses the best favorable weight set for the inputs and outputs of each decision‐making unit (DMU) to obtain its best possible score. Hence, this score can be considered as an upper bound of the real efficiency score. If we also use the least favorable weight set of each DMU, then a lower bound of the efficiency score can also be obtained. So, instead of one score, we can find an interval that gives all possible values of the efficiency score for each DMU. The aim of this paper is to propose an approach for determining efficiency intervals and setting up a full ranking of DMUs based on these intervals. We incorporate explicitly the decision‐maker's preferences in two phases. The first phase is for obtaining efficiency intervals, by introducing some restrictions on the input and output weights. The second one is for ranking the intervals based on the combination of the lower and the upper bounds of the efficiency intervals. The developed formulations will be illustrated through some numerical examples.     

Evaluating the efficiency of a two-stage production process using data envelopment analysis

Data envelopment analysis (DEA) has been widely used to evaluate the comparative efficiencies of production processes. Most of the DEA applications assume that production processes consist of one stage. However, many production processes such as IT investments have more than one stage. In a two‐stage production process, the first stage inputs produce intermediate outputs, which are used as inputs to the second stage to produce the final outputs. In such cases, using single‐stage DEA may result in inaccurate efficiency evaluation. To address such problems, DEA models assuming two‐stage production processes have been developed. In this paper, we extend two‐stage DEA models by considering input and output slacks. We apply our model to the data from the banking industry and compare the results with those of the previous two‐stage DEA models. Our model can identify weakly efficient units of evaluation that could not be identified by the previous models.     

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.     

Minimizing deviations of input and output weights from their means in data envelopment analysis

In this paper, we propose a model that minimizes deviations of input and output weights from their means for efficient decision-making units in data envelopment analysis. The mean of an input or output weight is defined as the average of the maximum and the minimum attainable values of the weight when the efficient decision making unit under evaluation remains efficient. Alternate optimal weights usually exist in the linear programming solutions of efficient decision-making units and the optimal weights obtained from most of the linear programming software are somewhat arbitrary. Our proposed model can yield more rational weights without a priori information about the weights. Input and output weights can be used to compute cross-efficiencies of decision-making units in peer evaluations or group decision-making units, which have similar production processes via cluster analysis. If decision makers want to avoid using weights with extreme or zero values to access performance of decision-making units, then choosing weights that are close to their means, may be a rational choice.     

An integer‐valued data envelopment analysis model with bounded outputs

Integer‐valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced “natural augmentability” axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision‐making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer‐valued DEA models for including bounded output variables. Some model variants are achieved by introducing a new axiom of “boundedness” over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model

Data Envelopment Analysis (DEA) is one of the best-known efficiency evaluation methods due to its advantages in selection of weights. Many research papers have extensively discussed the issue of weight restrictions, rather than those implied in the model itself. However, this often leads to a failure to represent the relations of certain weights, as well as underestimation of the efficiency of Decision Making Units (DMUs). When analyzing the medical sectors of Taiwan with the developed models and CCR, it is found that efficiency underestimation by efficient DMUs is more serious than that of inefficient DMUs. In addition, underestimation occurs when weights are concentrated in the same output, however, every output of referenced DMU is the same times of corresponding output of targeted DMU.     

A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real life applications, undesirable outputs may be present in the production process which needs to be minimized. The present study endeavors to propose a DEA model with undesirable outputs and further to extend it in fuzzy environment in view of the fact that input/output data are not always available in exact form in real life problems. We propose a fuzzy DEA model with undesirable fuzzy outputs which can be solved as crisp linear program for each α in (0, 1] using α-cut approach. Further, cross-efficiency technique is applied to increase the discrimination power of the proposed models and to rank the efficient DMUs at every α in (0, 1]. Moreover, for better understanding of the proposed methodology, we present a numerical illustration followed by an application to the banking sector in India. This is the first study which attempts to measure the performance of public sector banks (PuSBs) in India using fuzzy input/output data for the period 2009–2011. The results obtained from the proposed methodology not only depict the impact of undesirable output on the performance of PuSBs but also analyze efficiently the influence of the presence of uncertainty in the data over the efficiency results. The findings show that the efficiency results of many PuSBs vary with the variation in α during the selected period.     

Improved data envelopment analysis models for evaluating interval efficiencies of decision-making units

In a recent article, Wang et al. [Wang, N. S., Yi, R. H., & Wang, W. (2008). Evaluating the performances of decision-making units based on interval efficiencies. Journal of Computational and Applied Mathematics, 216, 328–343] proposed a pair of interval data envelopment analysis (DEA) models for measuring the overall performances of decision-making units (DMUs) with crisp data. In this paper, we demonstrate that interval DEA models face problems in determining the efficiency interval for each DMU when there are zero values for every input. To remedy this drawback, we propose a pair of improved interval DEA models which make it possible to perform a DEA analysis using the concepts of the best and the worst relative efficiencies. Two numerical examples will be examined using the improved interval DEA models. One of the examples is a real-world application about 42 educational departments in one of the branches of the Islamic Azad University in Iran that shows the advantages and applicability of the improved approach in real-life situations.     

A comprehensive fuzzy DEA model for emerging market assessment and selection decisions

The changing economic conditions have challenged many financial institutions to search for more efficient and effective ways to assess emerging markets. Data envelopment analysis (DEA) is a widely used mathematical programming technique that compares the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. In the conventional DEA model, all the data are known precisely or given as crisp values. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. In addition, performance measurement in the conventional DEA method is based on the assumption that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some input variables should be maximized and/or some output variables should be minimized. Moreover, real-world problems often involve high-dimensional data with missing values. In this paper we present a comprehensive fuzzy DEA framework for solving performance evaluation problems with coexisting desirable input and undesirable output data in the presence of simultaneous input–output projection. The proposed framework is designed to handle high-dimensional data and missing values. A dimension-reduction method is used to improve the discrimination power of the DEA model and a preference ratio (PR) method is used to rank the interval efficiency scores in the resulting fuzzy environment. A real-life pilot study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms in assessing emerging markets for international banking.     

基于群决策的加权动态网络SBM-DEA模型

传统的DEA模型在实际应用时主要存在三个问题：一是如何体现评价者的主观态度;二是评价有限个决策单元的动态网络效率时如何提高模型的分辨力;三是如何合理地确定子时期的权重。对此,提出了“过渡期”这一概念,首先在已有数据的基础上对过渡期的投入产出数据进行主观预测,接着提出指数衰减法来确定子时期的权重,然后构建了一个基于群决策的加权动态网络SBM-DEA模型,最后应用此模型评价了我国16家上市银行的相对效率。结果表明,改进后的模型不仅有效解决了现有问题,而且得到的评价结果更加客观。     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

Measurement of overall performances of decision-making units using ideal and anti-ideal decision-making units

Data envelopment analysis (DEA) is a method for evaluating relative efficiencies of decision-making units (DMUs) which perform similar functions in a production system, consuming multiple inputs to produce multiple outputs. The conventional form of DEA evaluates performances of DMUs only from the optimistic point of view. In other words, it chooses the most favorable weights for each DMU. There is another approach that measures efficiency of a DMU from the pessimistic point of view. This approach chooses the most unfavorable weights for evaluation of each DMU. In this paper, we propose to integrate both efficiencies in the form of an interval in order to measure the overall performance of a DMU. The proposed DEA models for evaluation of efficiencies are called bounded DEA models. The proposed approach will be compared using a numerical example. Another example regarding performance evaluation of 50 bank branches in Iranian cities will be presented to demonstrate the advantages, simplicity, and utility of this approach in real-life situations.     

Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. Conventional DEA models assume that inputs and outputs are measured by exact values on a ratio scale. However, the observed values of the input and output data in real-world problems are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Several researchers have proposed various fuzzy methods for dealing with the ambiguous and random data in DEA. In this paper, we propose three fuzzy DEA models with respect to probability-possibility, probability-necessity and probability-credibility constraints. In addition to addressing the possibility, necessity and credibility constraints in the DEA model we also consider the probability constraints. A case study for the base realignment and closure (BRAC) decision process at the U.S. Department of Defense (DoD) is presented to illustrate the features and the applicability of the proposed models.     

Data envelopment analysis of reservoir system performance

In long-term performance analyses of water systems with surface reservoirs for different operating scenarios, the analyst (or decision maker) is faced with two connected problems: (1) how to handle the extensive output of the simulation model and derive information on the scenarios scores for a prescribed set of performance criteria, and (2) how to compare scenarios in a multi-criterial sense while identifying the most desired. The data sets may overburden the analyst, while an evaluating procedure may be subjective due to personal preferences, attitudes, knowledge and miscellaneous factors. The data envelopment analysis (DEA) approach proposed here seems to be reliable in treating these situations, and sufficiently objective in evaluating and ranking the scenarios. Certain performance indices are defined as evaluating criteria in a standard multi-criterial sense, and then virtually divided into scenarios' output and input measures. By considering scenarios as product units, the DEA optimizes the weights of inputs and outputs, computes productivity efficiency for each unit, and rank them appropriately. Omitting the analyst's personal judgment on the technical parameters that describe system's performance restricts, in this way, the influence of the decision maker. A case study application on the reservoir system in Brazil proved that a methodological connection for solving decision problems with discrete alternatives really exists between the DEA and standard multi-criteria methods.