Original Data Envelopment Analysis Research Articles

Linear robust data envelopment analysis: CCR model with uncertain data

Data envelopment analysis (DEA) traditionally assumes that input and output data of the different decision making units (DMUs) are measured with precision. However, in many real applications inputs and outputs are often imprecise. This paper proposes a linear robust data envelopment analysis (LRDEA) model using imprecise data represented by an uncertainty set. The method is based on the robust optimisation approach of Bertsimas and Sim to seek maximisation of efficiency under uncertainty (as does the original DEA model). In this approach, it is possible to vary the degree of conservatism to allow for a decision maker to understand the tradeoff between a constraint's protection and its efficiency. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. Application of the proposed model (LRDEA) to analyse the technical and scale efficiency of potato production in 23 Iranian provinces demonstrates the reliability and flexibility of the model.

A cross evaluation-based measure of super efficiency in DEA with interval data

Purpose – The traditional data envelopment analysis (DEA) model as a non-parametric technique can measure the relative efficiencies of a decision-making units (DMUs) set with exact values of inputs and outputs, but it cannot handle the imprecise data. The purpose of this paper is to establish a super efficiency interval data envelopment analysis (IDEA) model, an IDEA model based on cross-evaluation and a cross evaluation-based measure of super efficiency IDEA model. And the authors apply the proposed approach to data on the 29 public secondary schools in Greece, and further demonstrate the feasibility of the proposed approach. Design/methodology/approach – In this paper, based on the IDEA model, the authors propose an improved version of establishing a super efficiency IDEA model, an IDEA model based on cross-evaluation, and then present a cross evaluation-based measure of super efficiency IDEA model by combining the super efficiency method with cross-evaluation. The proposed model cannot only discriminate the performance of efficient DMUs from inefficient ones, but also can distinguish between the efficient DMUs. By using the proposed approach, the overall performance of all DMUs with interval data can be fully ranked. Findings – A numerical example is presented to illustrate the application of the proposed methodology. The result shows that the proposed approach is an effective and practical method to measure the efficiency of the DMUs with imprecise data. Practical implications – The proposed model can avoid the fact that the original DEA model can only distinguish the performance of efficient DMUs from inefficient ones, but cannot discriminate between the efficient DMUs. Originality/value – This paper introduces the effective method to obtain the complete rank of all DMUs with interval data.

An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.

Evaluation of the energy-saving and emission-reduction potential for Chinese provinces based on regional difference coefficients

Rapid economic growth has resulted in a severe energy shortage and extensive environmental pollution in China. The question of how to save energy and reduce emissions has become a popular topic not only in economic but also in political and social circles. Most of the previous studies on the subject were conducted to evaluate the potential for energy savings and emission reductions. As an indispensable factor, each region's external environment has a strong impact on evaluating its potential for energy savings and emission reductions. However, the prior studies seldom considered each region's external environment, which resulted in research findings that are not rationally convincing. Hence, in this paper, a regional difference coefficient is introduced and calculated by applying technique for order preference by similarity to ideal solution to represent the external environment from two perspectives: (1) each region's economic and technical ability and (2) each region's resource reserves and supplies ability. Based on the regional difference coefficients, the original data envelopment analysis model was modified to calculate the potential for energy savings and emission reductions for 30 provincial administrative regions in China from the year 2001–2011. The results show that the gaps in the energy-saving and emission-reduction potential among these 30 regions are large and still increasing. Each region has its own causes for changes in energy savings and emission reductions. Thus, the important factors influencing regional energy savings and emission reductions are analyzed. The paper finds that technical progress and economic strength are the main factors impacting the regional energy-saving performance, especially in the underdeveloped provinces, while the industrial structure and energy mix are important factors influencing China's emission-reduction performance.

Using panel data dea to measure CEOs' focus of attention: An application to the study of cognitive group membership and performance

In this study, we examine the existence and performance of cognitive groups. In accordance with the attention-based view of managerial cognition, cognitive groups are defined as groups of firms in which the CEOs focus their attention on similar strategic elements when seeking to maximize their firm's competitive advantage. We developed a panel data extension of the original Data Envelopment Analysis to gauge CEOs' focus of attention and then clustered firms into groups. We compared our approach with other approaches that use content analysis of CEOs' letters to shareholders and CEOs' demographic characteristics to measure CEOs' attention. Although the different approaches are related, indicating the existence of a common underlying construct (i.e., mental models), our approach explains a higher proportion of the variation in organizational performance. Copyright (C) 2014 John Wiley & Sons, Ltd.

Advances in data envelopment analysis

Since its introduction in 1978, data envelopment analysis (DEA) has become one of the preeminent nonparametric methods for measuring efficiency and productivity of decision making units (DMUs). Charnes et al. (1978) provided the original DEA constant returns to scale (CRS) model, later extended to variable returns to scale (VRS) by Banker et al. (1984). These ‘standard’ models are known by the acronyms CCR and BCC, respectively, and are now employed routinely in areas that range from assessment of public sectors, such as hospitals and health care systems, schools, and universities, to private sectors, such as banks and financial institutions (Emrouznejad et al. 2008; Emrouznejad and De Witte 2010). The main objective of this volume is to publish original studies that are beyond the two standard CCR and BCC models with both theoretical and practical applications using advanced models in DEA.

Dimension-Specific Efficiency Measurement Using Data Envelopment Analysis

Data envelopment analysis (DEA) is a powerful tool for evaluating and improving the performance of a set of decision-making units (DMUs). Empirically, there are usually many DMUs exhibiting “efficient” status in multi-input multioutput situations. However, it is not appropriate to assert that all efficient DMUs have equivalent performances. Actually, a DMU can be evaluated to be efficient as long as it performs best in a single dimension. This paper argues that an efficient DMU of a particular input-output proportion has its own specialty and may also perform poorly in some dimensions. Two DEA-based approaches are proposed to measure the dimension-specific efficiency of DMUs. One is measuring efficiency in multiplier-form by further processing the original multiplier DEA model. The other is calculating efficiency in envelopment-form by comparing with an ideal DMU. The proposed approaches are applied to 26 supermarkets in the city of Nanjing, China, which have provided new insights on efficiency for the managers.

A Comparative Study of Towing Performance of Illegally Parked Vehicles

The study uses Data Envelopment Analysis (DEA) to establish a measurement model of towing performance of illegally parked vehicles. As the model can simultaneously deal with performance indicators with multiple input cost items and multiple output benefit items, it is a more objective performance evaluation model. Besides, using Analytic Hierarchy Process (AHP), and through the weights of the various input items and output items determined by experts and scholars, the paper sets the weight ratio of the original DEA model. In order to explore the practicability and effectiveness of the model developed, the paper carries out a case study of the towing operation of illegally parked vehicles in Taipei City. The analytic results can be referential for making comparison of towing performance of illegally parked vehicles amongst different impound lots.

Evaluation of decision making units in the presence of fuzzy and non-discretionary

In original data envelopment analysis (DEA) models, input and output are measured by exact values on a ratio scale. However, this assumption may not be always valid. For example some data may be only known as in forms of fuzzy and non–discretionary data. In this paper we try to suggest a generalized model when some inputs and outputs are fuzzy and non-discretionary data.

Dealing with missing data based on data envelopment analysis and halo effect

This research attempts to solve the problem of dealing with missing data via the interface of Data Envelopment Analysis (DEA) and human behavior. Missing data is under continuing discussion in various research fields, especially those highly dependent on data. In practice and research, some necessary data may not be obtained in many cases, for example, procedural factors, lack of needed responses, etc. Thus the question of how to deal with missing data is raised. In this paper, modified DEA models are developed to estimate the appropriate value of missing data in its interval, based on DEA and Inter-dimensional Similarity Halo Effect. The estimated value of missing data is determined by the General Impression of original DEA efficiency. To evaluate the effectiveness of this method, the impact factor is proposed. In addition, the advantages of the proposed approach are illustrated in comparison with previous methods.

Context-dependent data envelopment analysis with cross-efficiency evaluation

To address some problems with the original context-dependent data envelopment analysis (DEA), this paper proposes a new version of context-dependent DEA; this version is based on cross-efficiency evaluations. One of the problems with the original context-dependent DEA is that the attractiveness and progress measures only represent the radial distance between the decision-making unit (DMU) under evaluation and the evaluation context. This representation only shows how distinct the DMU is from a single specific DMU on the evaluation context, not from the entire evaluation context overall. Another problem is that the magnitude of attractiveness and progress scores in the original context-dependent DEA may not have significant meanings. It may not be proper to say that a DMU is more attractive simply because it has a higher attractiveness score for the same reason that the performance of inefficient DMUs cannot be compared with one another simply based on their efficiency scores. We incorporate cross-efficiency evaluations into the context-dependent DEA to overcome the preceding shortcomings of the original context-dependent DEA. We also demonstrate the proposed model's appropriateness and usefulness with an illustrative example.

Multiple Variable Proportionality in Data Envelopment Analysis

Data envelopment analysis (DEA) provides an optimization methodology for deriving an efficiency score for each member of a set of peer decision-making units. Under the original DEA model it was assumed that there is constant returns to scale (CRS). This idea was later extended to the more general case that allowed for variable returns to scale (VRS). In both of these structures, it is assumed that the returns to scale (RTS) classification, consistent with the classical definition, applies to the entire (input, output) bundle. In many settings it can be the case that the output bundle can be separated into distinct subsets or business units wherein an RTS-type behavior may be different for one subgroup than for another. We refer to such situations as involving multiple variable proportionality (MVP). Examples of MVP can occur when there are different product subgroupings in a company, different wards in hospitals, different programs in a university, and so on. Identification of such differential behavior can provide management with important insights regarding the most productive proportionality size (MPPS) in each of those subgroups. In the current paper we introduce DEA-based tools that address those situations where MVP exists.

The examination of pseudo-allocative and pseudo-overall efficiencies in DEA using shadow prices

The original Data Envelopment Analysis (DEA) models developed by Charnes et al. (Eur J Oper Res 2:429–444, 1978), Banker et al. (Manag Sci 30:1078–1092, 1984) were both radial models. These models and their varied extensions have remained the most popular DEA models in terms of utilization. The benchmark targets they determined for inefficient units are primarily based on the notion of maintaining the same input and output mixes originally employed by the evaluated unit (i.e. disregarding allocative considerations). This paper presents a methodology to investigate allocative and overall efficiency in the absence of defined input and output prices. The benchmarks determined from models based on this methodology will consider all possible input and/or output mixes. Application of this methodology is illustrated on a model of the financial intermediary function of a bank branch network.

Measuring Hotel Performance Using the Game Cross-Efficiency Approach

This study evaluates the comparative operating efficiencies of 23 international tourist hotels in Taipei by means of data envelopment analysis (DEA). A game cross-efficiency extension of the original DEA method is applied to provide reliable and comprehensive evaluation results. The main advantage of this approach is that it not only assesses hotel efficiency effectively based on self- and peer evaluation but also takes the competition among decision-making units (DMUs) into account. A star-rating system is also proposed to rate the performance of the international hotels under study based on their DEA efficiency scores over different periods. The results reveal that the mode of hotel operation significantly affects efficiency, in that hotels operated by international chains are more efficient than independent hotels. However, the level achieved in the traditional Taiwanese plum-rating system by hotels had no significant impact on hotel operational efficiency.

Efficiency of DMUs with Interval Data under the Hypotheses of Weak Data Consistency

The original data envelopment analysis (DEA) measures the efficiencies of decision making units（DMUs） with exact values of inputs and outputs. For interval data, some methods have been developed to calculate the interval efficiencies, however, the result of classic method always have high uncertainties. This paper proposes the hypothesis of weak data consistency in DEA. LP (linear programming) models to solve the upper and lower bounds of interval efficiencies are established. Lengths of efficiency intervals under the hypotheses are shorter the its limiting case is the result of DEA model under the hypotheses of data consistency

Should the US clean air act include CO 2 emission control?: Examination by data envelopment analysis

This study proposes a new use of Data Envelopment Analysis (DEA) to measure the operational, environmental and both-unified efficiency measures of US coal-fired power plants. The power plants produce not only desirable outputs (e.g., electricity) but also undesirable outputs (e.g., CO 2 and NO x ) as a result of their plant operations. A Range-Adjusted Measure (RAM) is used as an original non-radial DEA model. Then, it is reformulated for handling undesirable (bad) outputs. The proposed use of DEA models measures the environmental and unified performance of power plants under two variable alternatives (with and without CO 2 emission control) in order to examine both the influence of US Clean Air Act (CAA) on the acid rain causing gases (NO x and SO 2) and its extension to the CO 2 regulation. This study finds that the acid rain program under the CAA has been effective on the emission control of SO 2 and NO x produced at US coal-fired power plants. Moreover, additional regulation on CO 2 may enhance their environmental and unified performance. Thus, it is recommended that the US federal and state governments need to expand the legal scope of CAA to the emission control on CO 2 because the gas is considered as a main source of global warming and climate change.

A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data. In this paper, we propose a semi-oriented radial measure, which permits the presence of variables which can take both negative and positive values. The model is applied to data on a notional effluent processing system to compare the results with those yielded by two alternative methods for dealing with negative data in DEA: The modified slacks-based model suggested by Sharp et al. [Sharp, J.A., Liu, W.B., Meng, W., 2006. A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of Operational Research Society 57 (11) 1–6] and the range directional model developed by Portela et al. [Portela, M.C.A.S., Thanassoulis, E., Simpson, G., 2004. A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of Operational Research Society 55 (10) 1111–1121]. A further example explores the advantages of using the new model.

Efficiency Analysis and Target Setting of Spanish Airports

In this paper an efficiency analysis of 41 Spanish airports is carried out. A description of the physical infrastructure of the airports, namely total runway area, apron capacity, passenger throughput capacity, number of baggage belts, number of check-in counters and number of boarding gates, is used as inputs. Air Traffic Movements, Passenger Movements and Cargo handled are used as outputs. An output-oriented, Variable-Returns-to-Scale, non-radial Data Envelopment Analysis (DEA) model is used to compute the Russell measure of output technical efficiency. Half of the airports are found technically efficient. Scale efficiency and local Returns to Scale have also been assessed, indicating that except for a few airports that operate at their Most Productive Scale Size, for most Spanish airports Increasing Returns to Scale prevail. An original DEA model for target setting and scenario analysis is also proposed. The model uses two parameters (Plane Load Factor and Passenger/Cargo Ratio) that allow the relating of two of the outputs to the third. The model computes efficient targets given the value of these two parameters and the vector of available inputs. The results of this target-setting DEA model for Seville airport for different values of the two parameters and different future input scenarios are presented.

Fuzzy context-dependent data envelopment analysis

The original context-dependent Data Envelopment Analysis (DEA) is developed to measure the attractiveness and progress of Decision-Making Units (DMUs) based on a given evaluation context and different strata of efficient frontiers, rather than the traditional first-level efficient frontier, are used as evaluation contexts. It is limited to crisp data. To deal with imprecise data, this paper introduces the notion of fuzziness and develops a procedure to provide finer evaluation results of DMUs with fuzzy observations based on the original context- dependent DEA by using a ranking method based on the comparison of α-cuts. The proposed approach is an extension to the fuzzy environment of the original context-dependent DEA; it represents some real-life processes more appropriately. A numerical example is used to illustrate the approach.