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 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.     

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.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

基于逆数据包络分析法的中医方药评价与药量计算研究

针对中医组方的药量推算建模问题,提出了基于证候上下文分析的逆数据包络分析（IDEA）算法。该算法以证侯的典型方剂为依据,以数据包络分析为评价工具,建立起反映证候演化的方药评价模型;依据代表证候状态的评价值,给相应的证型症状信息赋值,以完成“词计算”过程。最后,把具体的辨证过程植入到证侯发展的上下文环境中,以典型证型的“词计算”为依据,给出具体案例的证侯状态评价,再采用IDEA算法推算出药量数据。该模型的推算结果表明,它能够反映中医的一般用药规律,这将对辨证论治组方环节的数值化、客观化研究提供一种可能的思路。     

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.     

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.     

Robust data envelopment analysis approaches for evaluating algorithmic performance

Recent advances in state-of-the-art meta-heuristics feature the incorporation of probabilistic operators aiming to diversify search directions or to escape from being trapped in local optima. This feature would result in non-deterministic output in solutions that vary from one run to another of a meta-heuristic. Consequently, both the average and variation of outputs over multiple runs have to be considered in evaluating performances of different configurations of a meta-heuristic or distinct meta-heuristics. To this end, this work considers each algorithm as a decision-making unit (DMU) and develops robust data envelopment analysis (DEA) models taking into account not only average but also standard deviation of an algorithm’s output for evaluating relative efficiencies of a set of algorithms. The robust DEA models describe uncertain output using an uncertainty set, and aim to maximize a DMU’s worst-case relative efficiency with respect to that uncertainty set. The proposed models are employed to evaluate a set of distinct configurations of a genetic algorithm and a set of parameter settings of a simulated annealing heuristic. Evaluation results demonstrate that the robust DEA models are able to identify efficient algorithmic configurations. The proposed models contribute not only to the evaluation of meta-heuristics but also to the DEA methodology.     

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.     

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.     

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。     

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.     

A hybrid data envelopment analysis and multi-attribute decision making approach to sustainability assessment

The concept of sustainability consists of three main dimensions: environmental, techno-economic, and social. Measuring the sustainability status of a system or technology is a significant challenge, especially when it needs to consider a large number of attributes in each dimension of sustainability. In this study, we first propose a hybrid approach, involving data envelopment analysis (DEA) and a multi-attribute decision making (MADM) methodologies, for computing an index for each dimension of sustainability, and then we define the overall sustainability index as the mean of the three measured indexes. Towards this end, we define new concepts of efficiency and cross-efficiency of order (p, q) where p and q are the number of inputs and outputs, respectively. For a given (p, q) , we address the problem of finding efficiency of order (p, q) by developing a novel DEA-based selecting method. Finally, we define the sustainability index as a weighted sum of all possible cross-efficiencies of order (p, q) . Form a computational viewpoint, the proposed selecting model significantly decreases the computational burden in comparison with the successive solving of traditional DEA models. A case study of the electricity-generation technologies in the United Kingdom is taken as a real-world example to illustrate the potential application of our method.     

An enumeration algorithm for integer‐valued data envelopment analysis

Data envelopment analysis (DEA) models assume real‐valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision‐making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming (MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real‐valued data.     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

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.     

Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.     

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.     

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.