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.     

Improving the discrimination of data envelopment analysis models in multiple time periods

The trade‐offs approach is an advanced tool for the improvement of the discrimination of data envelopment analysis (DEA) models; this can improve the traditional meaning of efficiency as a radial improvement factor for inputs or outputs. Therefore, the Malmquist index – the prominent index for measuring the productivity change of decision making units (DMUs) in multiple time periods that use DEA models with variable returns to scale and constant returns to scale technologies – can be improved by using the trade‐offs technology. Hence, an expanded Malmquist index can be defined as an improved method of a traditional Malmquist index that uses the production possibility set, which could present more discrimination of DMUs, in the presence of the trade‐offs technology. In addition, similar to a traditional Malmquist index, it breaks down into different components. An illustrative example is presented to show the ability of the suggested method of presenting the Malmquist index from a computational point of view.     

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.     

Common set of weights in data envelopment analysis under prospect theory

Data envelopment analysis (DEA) is a data‐driven tool for performance evaluation, measuring decision‐making units (DMUs) and designating them with specific weightings. The standard DEA model typically sets up that decision‐makers (DMs) are wholly rational to select the most favourable weights to obtain the maximum performance score, but does not take into account their attitude toward risk during the assessment. The prospect theory generally matches humans' psychological behaviours. Thus, our study captures the non‐rational behaviours of DMs, performing under risk scenarios, in order to construct a novel common‐weights DEA model that maximizes the total prospect value, which can vary more steeply for losses than for gains, hence obtaining a more realistic common weight scheme. Our proposed model not only generates DMUs, with higher total prospect values, but also greater degrees of satisfaction. The current study shows that the prospect theory can be aptly extended to the DEA research area, supplying a proper guideline for future DEA research.     

Common weights data envelopment analysis with uncertain data: A robust optimization approach

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.     

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.     

基于公共权重数据包络分析的军事训练绩效排序

针对传统数据包络分析(DEA)公共权重生成方法不同时具备线性、规模无关优点的问题,根据军事训练绩效评估需求,提出了一种新的DEA公共权重生成方法。该方法以DEA有效单位为计算基础,首先对训练数据进行归一化,然后运用多目标规划模型求解,绩效排序结果更加公平合理,并且同时具有线性、规模无关的优点。最后,通过一个军事应用,证明了该方法科学、有效。     

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.     

数据包络分析研究热点综述

数据包络分析是面向多输入多输出决策单元的有效性评估方法。在介绍数据包络分析的基本思想和模型基础之上,总结了近年来国内外的研究热点,包括两阶段DEA、效率排序DEA、随机DEA和相关扩展问题,旨在围绕以上研究热点,对DEA近年来的理论研究及其扩展模型进行梳理和分类。最后对数据包络分析进一步研究提出展望。     

Value of the stochastic efficiency in data envelopment analysis

This article examines the potential benefits of solving a stochastic DEA model over solving a deterministic DEA model. It demonstrates that wrong decisions could be made whenever a possible stochastic DEA problem is solved when the stochastic information is either unobserved or limited to a measure of central tendency. We propose two linear models: a semi-stochastic model where the inputs of the DMU of interest are treated as random while the inputs of the other DMUs are frozen at their expected values, and a stochastic model where the inputs of all of the DMUs are treated as random. These two models can be used with any empirical distribution in a Monte Carlo sampling approach. We also define the value of the stochastic efficiency (or semi-stochastic efficiency) and the expected value of the efficiency.     

Multiparametric sensitivity analysis of the additive model in data envelopment analysis

In this paper, we study multiparametric sensitivity analysis of the additive model in data envelopment analysis using the concept of maximum volume in the tolerance region. We construct critical regions for simultaneous and independent perturbations in all inputs/outputs of an efficient decision making unit. Necessary and sufficient conditions are derived to classify the perturbation parameters as “focal” and “nonfocal.” Nonfocal parameters can have unlimited variations because of their low sensitivity in practice and these parameters can be deleted from the final analysis. For focal parameters a maximum volume region is characterized. Theoretical results are illustrated with the help of a numerical example.     

Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale

The classic Data Envelopment Analysis (DEA) models developed with the assumption that all inputs and outputs are non-negative, whereas, we may face a case with negative data in the actual business world. So, the need to adapt the DEA models so that they are applicable to cases includes inputs and outputs which can take both negative and non-negative values has been an issue. It can be readily demonstrated that the assumption of constant returns to scale (CRS) is not possible in technologies under negative data. So, one of the interesting and challenge questions is how to determine the state of RTS in the presence of negative data under variable returns to scale (VRS) technology. Accordingly, in this contribution, we first address the efficiency measure and then suggest a method to discover the state of returns to scale (RTS) in the presence of negative input and output values which has not been discussed much enough so far in DEA literature. Finally, the main results are elaborated by some illustrative examples.     

模糊机会约束数据包络分析模型及其应用

为求解模糊环境下输出倾向的数据包络分析（DEA）模型,利用可信性测度建立了一类新的输出倾向的可信性DEA（CDEA）模型,其中目标函数采用了模糊机会约束规划的概念,且所有的约束条件中都含有模糊输入和模糊输出数据。当模糊输入和模糊输出数据为相互独立的梯形模糊变量时,把所建立的CDEA模型转化为其清晰等价形式,进而研究了模型的两个基本性质;通过一个应用实例来说明所建立CDEA模型的有效性。     

Cone ratio data envelopment analysis and multi-objective programming

A new ‘cone ratio’ data envelopment analysis (DEA) model that substantially generalizes the Charnes-Cooper-Rhodes (CCR) model and the Charnes-Cooper-Thrall approach characterizing its efficiency classes is developed and studied. It allows for infinitely many decision-making units (DM Us) and arbitrary closed convex cones for the virtual multipliers as well as the cone of positivily of the vectors involved. Generalizations of linear programming and polar cone equalizations arc the analytical vehicles employed.     

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.     

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.     

Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

Multiobjective target setting in data envelopment analysis using AHP

In this paper two new target setting DEA approaches are proposed. The first one is an interactive multiobjective method that at each step of the process asks the decision maker (DM) which inputs and outputs he wishes to improve, which ones are allowed to worsen and which ones should stay at their current level. The local relative priorities of these inputs and outputs changes are computed using the analytic hierarchy process (AHP). After obtaining the candidate target, the DM can update his preferences for improving, worsening or maintaining current inputs and outputs levels and obtain a new candidate target. Thus continuing, until a satisfactory operating point is computed. The second method proposed uses a lexicographic multiobjective approach in which the DM specifies a priori a set of priority levels and, using AHP, the relative importance given to the improvements of the inputs and outputs at each priority level. This second approach requires solving a series of models in order, one model for each priority level. The models do not allow for worsening of neither inputs nor outputs. After the lowest priority model has been solved the corresponding target operating point is obtained. The application of the proposed approach to a port logistics problem is presented.