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.     

Online banking performance evaluation using data envelopment analysis and principal component analysis

This paper presents a hybrid approach to conducting performance measurements for Internet banking by using data envelopment analysis (DEA) and principal components analysis (PCA). For each bank, DEA is applied to compute an aggregated efficiency score based on outputs, such as web metrics and revenue; and inputs, such as equipment, operation cost and employees. The 45 combinations of DEA efficiencies of the studied banks are calculated, and used as a ranking mechanism. PCA is used to apply relative efficiencies among the banks, and to classify them into different groups in terms of operational orientations, i.e., Internet banking and cost efficiency focused orientations. Identification of operational fitness and business orientation of each firm, in this way, will yield insights into understanding the weaknesses and strengths of banks, which are considering moving into Internet banking.     

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.     

Benchmarking of service quality with data envelopment analysis

This paper proposes a data envelopment analysis (DEA) approach to measurement and benchmarking of service quality. Dealing with measurement of overall service quality of multiple units with SERVPERF as multiple-criteria decision-making (MCDM), the proposed approach utilizes DEA, in particular, the pure output model without inputs. The five dimensions of SERVPERF are considered as outputs of the DEA model. A case study of auto repair services is provided for the purpose of illustration. The current practice of benchmarking of service quality with SERVQUAL/SERVPERF is limited in that there is little guidance to whom to benchmark and to what degree service quality should be improved. This study contributes to the field of service quality benchmarking by overcoming the above limitations, taking advantage of DEA’s capability to handle MCDM problems and provide benchmarking guidelines.     

Uncertain network data envelopment analysis with undesirable outputs to evaluate the efficiency of electricity power production and distribution processes

In this paper, a customized network data envelopment analysis model is developed to evaluate the efficiency of electric power production and distribution processes. In the production phase, power plants consume fuels such as oil and gas to generate the electricity. In the distribution phase, regional electricity companies transmit and distribute the electricity to the customers in houses, industries, and agriculture. Although, the electricity is assumed to be a clean type of energy, several types of emissions and pollutions are produced during electricity generation. The generated emissions are considered as an undesirable output. A customized network data envelopment analysis (NDEA) approach is proposed to evaluate the efficiency of these processes Each decision making unit (DMU) includes two serially connected sub-DMUs, i.e., production and distribution stages. The models are extended using interval data to address the considerable uncertainty in the problem. The efficiency scores of main process, and each sub-process are determined. The final ranking of DMUs and sub-DMUs are achieved using a multi-attribute decision making (MADM) method. The whole approach is applied in a real case study in electrical power production and distribution network with 14 DMUs. The proposed approach has the following innovations in comparison with existing methods: (1) Both production and distribution process are evaluated in a unique model; (2) Undesirable outputs and uncertainty of data are considered in proposed approach; (3) Properties of proposed models are discussed through several theorems; (4) The efficiencies of production and distribution phases are determined distinctively; (5) A full ranking approach is proposed; (6) A real case study of electrical power production and distribution network is surveyed. The results of proposed approach are adequate and interesting. This approach can be customized for application in similar systems such as water production-supply management, Oil and fuel production–distribution systems, and supply chains.     

Measuring the relative performance for leading fabless firms by using data envelopment analysis

IC Design (fabless) is critical for the global semi-conductor industry. The total revenue of all global fabless firms in 2003 was about US$20 billion, with the top 30 firms earning accounting for 96% of the market share. To examine the leaders in the field, this research analyzes the relative performances of those top 30 fabless firms. Fabless firms are often evaluated based on subjective judgments, and an overall scheme to measure the performance involving objective, multi-input and multi-output criteria is yet to be established. There is also a need for identifying and determining suggestions of how specific firms could improve their performance. Data Envelopment Analysis (DEA) method has been employed in this paper to satisfy the above needs. Using the input and output data of 2003, this study used the DEA method to build a model to evaluate the performance of those global top 30 fabless firms. The current research used four efficiency models: CCR, A&P, BCC, and Cross-Efficiency. To offer a comparison of efficiencies and associated discussions, an analysis of the Scale-Return is provided. Finally, the performance of various fabless firms in 2003 is analyzed. According to the CCR and A&P models, the results showed that the top ten Decision Management Units (DMUs) achieved better operation performance among the 30 leading global fabless firms.     

Efficiency persistence of bank and thrift CEOs using data envelopment analysis

We examine the performance of chief executive officers (CEOs) of US banks and thrifts. We apply data envelopment analysis (DEA) to measure the performance of CEOs on a yearly basis over the 1997–2004 period, and find evidence that best-practice CEOs who have a DEA efficiency score of one are rewarded with higher compensation compared to under-performing CEOs who have a DEA efficiency score greater than one. We find DEA efficiency score to be a highly significant predictor of CEO compensation, even after adjusting for firm size. In addition, we find that DEA efficiency scores of CEOs have decreased over the observation period. We also find that best-practice CEOs tend to be persistent on a yearly basis, but we find little evidence of multi-period persistence. The results of this study can serve as a benchmark for CEOs wishing to evaluate their performance relative to their peers, and as a new measure of CEO performance.     

Fuzzy data envelopment analysis and its application to location problems

In this paper, fuzzy DEA (data envelopment analysis) models are proposed for evaluating the efficiencies of objects with fuzzy input and output data. The obtained efficiencies are also fuzzy numbers that reflect the inherent ambiguity in evaluation problems under uncertainty. An aggregation model for integrating fuzzy attribute values is provided in order to rank objects objectively. Using the proposed method, a case study involving a restaurant location problem is analyzed in detail. Rent of establishment, traffic amount, level of security, consumer consumption level and competition level are identified as the primary factors in determining an ideal location for a Japanese-style rotisserie restaurant. Based on field investigation, the uncertain information on primary factors is represented by fuzzy numbers. Using the fuzzy aggregation model, the best location of restaurant is determined. The case study shows that fuzzy DEA models can be quite useful for solving business problems under uncertainty.     

An integrated data envelopment analysis and free disposal hull framework for cost-efficiency measurement using rough sets

Traditional cost-efficiency analysis methods require exact and precise values for inputs, outputs and input prices. However, this is not the case in many real-life applications. This study proposes a rough cost-efficiency approach to the problem of ranking efficient decision making units (DMUs). Based on rough set theory, a nonparametric methodology for cost-efficiency analysis is developed. The merits of this methodology include computational ease and the capacity to incorporate data uncertainty. Furthermore, it applies to both convex data envelopment analysis (DEA) and non-convex free disposal hull (FDH) technologies under different returns-to-scale assumptions. A numerical example and a real-life case study in the Japanese banking industry demonstrate the applicability of the proposed framework. In particular, the rankings of the DMUs resulting from the proposed models are compared with those obtained using the maximum technical efficiency loss index.     

Right and left returns to scales in data envelopment analysis: Determining type and measuring value

This study identifies types and values of right and left returns to scales (RTSs) of efficient decision making units (DMUs) in data envelopment analysis (DEA). In this research, we first introduce a new approach to estimate types of right and left returns to scales of efficient DMUs and then, values of right and left returns to scales of these DMUs are measured by presenting two new DEA models.     

A new mixed integer linear model for selecting the best decision making units in data envelopment analysis

In a recent paper by Amin (Amin, Gholam R. (2009). Comment on finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 56, 1701–1702), he proposed an improved approach to determine a single efficient DMU as the most (or the best) efficient DMU. It will be shown that this nonlinear mixed integer model may fail to produce a solution since it can be infeasible in some cases. In this paper, a linear mixed integer model is proposed which is feasible and can produce a single efficient DMU as well. The model can also be extended to rank all extreme efficient DMUs. Some properties and advantages of the model will be explained. The contents of the paper will be illustrated by some numerical examples including a real data set of nineteen facility layout alternatives.     

数据包络分析模型的化工试验设计方法评价

数据包络分析(DEA)是以“相对效率评价”基于化工试验中反应物、生成物之间的投入、产出关系,探讨了化工试验设计,主要探讨了在化工试验设计中DEA作为评价正交试验设计方法的一种有效的分析工具的理论和应用。实例分析表明,将DEA方法运用于化工试验设计的评价具有计算简单,意义清楚的特点,是对正交试验设计的有益补充。     

Radial data envelopment analysis models with mixed orientation of input and output

This paper discusses parametric solutions and envelopment formulations of radial data envelopment analysis (DEA) models with mixed orientation of input and output. These solutions geometrically but not numerically lie between the two usual solutions from input and output orientations. The consequent results provide alternative optimal solutions between those from input‐ and output‐oriented CCR models for constant returns to scale DEA models and optimal scale efficiency in addition to technical efficient solutions from input‐ and output‐oriented BCC models for variable returns to scale DEA models.     

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.     

Data envelopment analysis based on maximin relative efficiency criterion

While gauging the performances of operating entities using imprecise information on the input and output importance weights, an entity is considered Farrell efficient as long as it outperforms its peers for at least one feasible combination of the weights for inputs and outputs. This paper argues that Farrell efficiency computations are based on an optimistic perspective and a Farrell-efficient entity may perform rather poorly when weights corresponding to realistic considerations are assigned to inputs and outputs. An entity is defined as robust efficient if its relative efficiency score reaches 1 in all feasible combinations of the input and output weights. A linear programming based approach is proposed to perform what is referred to as robust efficiency analysis to identify robust efficient entities. In contrast to Farrell efficiency analysis, robust efficiency analysis involves the computation of the lowest efficiency score that can be assigned to an entity relative to the highest score among all the entities where an identical combination of weights for inputs and outputs is applied. The production possibility set underlying the proposed approach is also defined and interpreted. An experimental study illustrates that when compared with Farrell efficiency analysis robust efficiency analysis has sharper discrimination capability and the entity it identifies as efficient has superior average performance.     

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.     

基于数据包络分析的虚拟企业知识评价方法

业知识对企业性能、竞争力有着重要的影响,通过对伙伴企业知识的评价,可以加强虚拟企业对知识的管理,从而提高虚拟企业性能。针对虚拟企业知识评价的问题,提出一种以企业模型为媒介的间接的知识评价方法——KP²RP,并结合它的五个元素：知识、产品、过程、资源、性能,定义了它们之间的关联矩阵,给出了关联矩阵的知识评价级别,最后提出基于数据包络分析的知识评价模型,并且利用实例分析了评价方法的可行性。     

A unified model for detecting efficient and inefficient outliers in data envelopment analysis

Data envelopment analysis (DEA) uses extreme observations to identify superior performance, making it vulnerable to outliers. This paper develops a unified model to identify both efficient and inefficient outliers in DEA. Finding both types is important since many post analyses, after measuring efficiency, depend on the entire distribution of efficiency estimates. Thus, outliers that are distinguished by poor performance can significantly alter the results. Besides allowing the identification of outliers, the method described is consistent with a relaxed set of DEA axioms. Several examples demonstrate the need for identifying both efficient and inefficient outliers and the effectiveness of the proposed method. Applications of the model reveal that observations with low efficiency estimates are not necessarily outliers. In addition, a strategy to accelerate the computation is proposed that can apply to influential observation detection.     

New analytical hierarchical process/data envelopment analysis methodology for ranking decision‐making units

The analytical hierarchical process/data envelopment analysis (AHP/DEA) methodology for ranking decision‐making units (DMUs) has some problems: it illogically compares two DMUs in a DEA model; it is not compatible with DEA ranking in the case of multiple inputs/multiple outputs; and it leads to weak discrimination in cases where the number of inputs and outputs is large. In this paper, we propose a new two‐stage AHP/DEA methodology for ranking DMUs that removes these problems. In the first stage, we create a pairwise comparison matrix different from AHP/DEA methodology; the second stage is the same as AHP/DEA methodology. Numerical examples are presented in the paper to illustrate the advantages of the new AHP/DEA methodology.     

A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.