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1

Schumacher, Christin. "Data Envelopment Analysis (DEA)." Controlling 25, no. 6 (2013): 336–37. http://dx.doi.org/10.15358/0935-0381_2013_6_336.

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2

Bhat, Ramesh, Bharat Bhushan Verma, and Elan Reuben. "Data Envelopment Analysis (DEA)." Journal of Health Management 3, no. 2 (October 2001): 309–28. http://dx.doi.org/10.1177/097206340100300207.

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3

Pereira, José Veiga. "Data Envelopment Analysis." Review of Business and Legal Sciences, no. 6 (July 5, 2017): 29. http://dx.doi.org/10.26537/rebules.v0i6.811.

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A avaliação das organizações e a deterntinação da performance obtida pelo exercício da gestão, tem sido uma preocupação constante de gestores e accionistas, embora com objectivos diversos. Nos dias de hoje, a questão coloca-se com maior acuidade quer pela competitividade acrescida quer pela dimensão e complexidade actual das empresas. Pretendemos com este trabalho fazer uma descrição da metodologia DEA - Data Envelopment Analysis - nas suas formulações iniciais mais simples. A metodologia do DEA, pretende obter uma medida única e simples de avaliação da eficiência, combinando um conjunto de outputs e de inputs relativos às diferentes unidades homogéneas que se pretendem avaliar.O método DEA é um método não paramétrico que pelas suas características é particularmente adequado à avaliação de unidades homogéneas não necessariamente lucrativas.Concluímos, em geral, que são úteis e constituem um avanço importante, as informações obtidas através do DEA mas que outros métodos, designadamente rácios e análises de regressão, podem dar um contributo importante para complementar aquela análise.
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4

Shewell, Patricia, and Stephen Migiro. "Data envelopment analysis in performance measurement: a critical analysis of the literature." Problems and Perspectives in Management 14, no. 3 (November 10, 2016): 705–13. http://dx.doi.org/10.21511/ppm.14(3-3).2016.14.

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This study examines the benefits of data envelopment analysis (DEA) in evaluating the performance of decision making units (DMUs). DEA is a mathematical programming tool applied in performance measurement. The problem identified is establishing business support units as value adding business units. A case is made for applying DEA when evaluating the performance of such business support units. To this end, a literature review of the results of applications of DEA to the evaluation of information technology and purchasing supply chain management functions was conducted. The findings indicate the benefits of DEA are that the method identifies efficient performers in a given population and, therefore, allows for benchmarking against the ’best in class’ performer. This as opposed to more commonly used parametric methods, such as regression analysis, which result in a comparator that represents the average performance for a given population, therefore, allowing only for measurement against the average. In addition, the findings indicate that in respect of business support units, the DEA methodology allows for the incorporation of intermediate outcomes, which facilitates the measurement of the contribution of these units to overall company performance. Although the DEA methodology has been widely applied, it is still not as well known or generally applied as the more common approaches. The recommendations made in this paper will be beneficial in bringing DEA to the attention of decision-makers. The recommendations will also raise awareness of the potential benefits to be realised when applying the method in developing performance measurement frameworks for business support units. Keywords: performance measurement, data envelopment analysis, decision making units, business support units. JEL Classification: C61, L25
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5

Ji, Aibing, Hui Liu, Hong-jie Qiu, and Haobo Lin. "Data envelopment analysis with interactive variables." Management Decision 53, no. 10 (November 16, 2015): 2390–406. http://dx.doi.org/10.1108/md-11-2014-0631.

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Purpose – The purpose of this paper is to build a novel data envelopment analysis (DEA) model to evaluate the efficiencies of decision making units (DMUs). Design/methodology/approach – Using the Choquet integrals as aggregating tool, the authors give a novel DEA model to evaluate the efficiencies of DMUs. Findings – It extends DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form. At last, the authors use the numerical examples to illustrate the performance of the proposed model. Practical implications – The proposed DEA model can be used to evaluate the efficiency of the DMUs with multiple interactive inputs and outputs. Originality/value – This paper introduce a new DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form.
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Golpîra, Hêriş. "A Hybrid Clustering Method Using Balanced Scorecard and Data Envelopment Analysis." International Journal Of Innovation And Economic Development 1, no. 7 (2015): 15–25. http://dx.doi.org/10.18775/ijied.1849-7551-7020.2015.17.2002.

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This paper introduces a new hybrid clustering method using Data Envelopment Analysis (DEA) and Balanced Scorecard (BSC) methods. DEA cannot identify its’ input and output itself, and it is a major weakness of the DEA. In the proposed method, this gap is resolved by integrating DEA with BSC. Some decision-making units (DMUs) needed in DEA method, in compliance with some inputs and outputs is the major drawback of this integration. To deal with this disadvantage, the proposed method selects the most important strategic factors, attained from the BSC method. These data considered to be the input data for the DEA method to calculate relative closeness (RC) of each DMU to the ideal one. Plotting the screen diagram regarding RC index leads us to the final clustering method. Finally, computational results show the applicability and usefulness of the method.
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7

Li, Ling, and Fengshan Wang. "Hybrid Dynamic Network Data Envelopment Analysis." Discrete Dynamics in Nature and Society 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/989581.

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Conventional DEA models make no hypothesis concerning the internal operations in a static situation. To open the “black box” and work with dynamic assessment issues synchronously, we put forward a hybrid model for evaluating the relative efficiencies of a set of DMUs over an observed time period with a composite of network DEA and dynamic DEA. We vertically deal with intermediate products between divisions with assignable inputs in the network structure and, horizontally, we extend network structure by means of a dynamic pattern with unrelated activities between two succeeding periods. The hybrid dynamic network DEA model proposed in this paper enables us to (i) pry into the internal operations of DEA by another network structure, (ii) obtain dynamic change of period efficiency, and (iii) gain the overall dynamic efficiency of DMUs over the entire observed periods. We finally illustrate the calculation procedure of the proposed approach by a numerical example.
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8

WEI, QUANLING, HONG YAN, and LIYONG PANG. "COMPOSITE NETWORK DATA ENVELOPMENT ANALYSIS MODEL." International Journal of Information Technology & Decision Making 10, no. 04 (July 2011): 613–33. http://dx.doi.org/10.1142/s0219622011004488.

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This paper extends the DEA model to considering the decision-making unit (DMU) with the network structure. We define the network DMU and its network DEA efficiency based on the postulate system. On the series structure of the DMU, we further discuss a sequential optimization model originally proposed by Sexton and Lewis.1,2 Based on their work, we extend to the DMU with general network of k stages and propose a composite network DEA model which evaluate the network DEA efficiency by solving only one linear programming. We show that the network efficiency obtained from the composite model is equivalent to that obtained by the sequential optimization model. We show that a network DMU is network-efficient if and only if it is efficient at all stages. That is, the network-efficient DMU follows the "Bellman Optimal Principle." Our model shows that if a network DMU is not DEA-efficient, then it is not efficient at one stage at least. We also define the projection of the network DMU on the corresponding production possibility set of network DMUs. Finally, we discuss other basic structures of the network DMU and show that the overall network DEA model can be extended to the general network DMU.
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9

UEDA, Toru. "Data Envelopment Analysis and Fuzzy DEA." Journal of Japan Society for Fuzzy Theory and Systems 10, no. 2 (1998): 193–99. http://dx.doi.org/10.3156/jfuzzy.10.2_13.

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10

Oral, Muhittin. "E-DEA: Enhanced data envelopment analysis." European Journal of Operational Research 207, no. 2 (December 2010): 916–26. http://dx.doi.org/10.1016/j.ejor.2010.05.035.

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11

TONE, Kaoru. "Data Envelopment Analysis." Journal of Japan Society for Fuzzy Theory and Systems 8, no. 1 (1996): 11–14. http://dx.doi.org/10.3156/jfuzzy.8.1_11.

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12

Fenyves, Veronika, and Tibor Tarnóczi. "Data envelopment analysis for measuring performance in a competitive market." Problems and Perspectives in Management 18, no. 1 (March 31, 2020): 315–25. http://dx.doi.org/10.21511/ppm.18(1).2020.27.

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In today’s increasingly competitive markets, it is essential to be able to determine the position of a company as opposed to its competitors. Today the traditional financial ratios are most widely used to measure corporate performance, but more and more authors begin to criticize their use. It is difficult to use financial ratios as a complex measurement tool. It is crucial to use an appropriate method or tool to measure corporate performance, which can measure the company’s performance in a complex way represented by one indicator. In this study, the Data Envelopment Analysis (DEA) method is used, which is one of the potential tools available. Several researchers have used the DEA method to measure corporate performance. Many authors consider DEA as a useful tool for measuring corporate performance, while others criticize it. The authors analyze the performance of retail food companies in Hungary’s Northern Great Plain region. The companies analyzed were chosen from the region investigated, and they have “food retail grocery store” as their main activity, and they had six cleared annual reports in the period 2012–2017. There was a total of 887 companies in the region examined, and 563 (63.5%) met the conditions. The analysis was made using the time-series data of companies for 2012–2017 based on their financial reports, and the authors dealt with various possibilities for extending DEA, which can support its more accurate use. Based on evaluating the retail food companies’ performance in the Northern Great Plain region, one can state that the efficiency of companies shows a very mixed picture over the years examined. The study suggests solutions to the indicated problem. The findings indicate that the application of extended DEA methods gives better results; that is, one can get better estimates of the efficiency of companies.
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13

PHILLIPS, FRED. "25 YEARS OF DATA ENVELOPMENT ANALYSIS." International Journal of Information Technology & Decision Making 04, no. 03 (September 2005): 317–23. http://dx.doi.org/10.1142/s021962200500157x.

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This retrospective by an early DEA researcher recalls the people, the setting, the formative philosophies, and early implementation experiences with Data Envelopment Analysis. It is a tribute to the founders of DEA, a historical chronicle, and a perspective on the nature and value of this important operations research methodology.
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14

Feroz, Ehsan H., Sungsoo Kim, and Raymond L. Raab. "Analytical Procedures: A Data Envelopment Analysis Approach." Journal of Emerging Technologies in Accounting 2, no. 1 (January 1, 2005): 17–31. http://dx.doi.org/10.2308/jeta.2005.2.1.17.

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In this paper, we demonstrate the usefulness of Data Envelopment Analysis (DEA) as an analytical procedure for auditors, especially in the planning stage of the audit, to determine the extent of audit and to assess the preliminary risk level of the client. We believe that DEA can also be used in the overall review stage to detect any anomalies and to assess the reasonableness of financial statements. DEA-based analytical procedures can provide consistent and reliable red ags and benchmarks for auditors to compare a client to other firms in the same industry. We provide an illustrative use of DEA as an analytical procedure for auditing a client in the oil and gas industry. We also provide validation for DEA as an analytical procedure.
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15

DIKE, IJ. "Modified Fuzzy Data Envelopment Analysis Models." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 3, no. 3b (November 15, 2020): 208–21. http://dx.doi.org/10.46912/napas.186.

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This paper examines the use of data envelopment analysis (DEA) in the conduct of efficiency measurement involving fuzzy (interval) input-output values. Data envelopment analysis is a linear programming method for comparing the relative productivity (or efficiency) of multiple service units. Standard DEA models assume crisp data for both the input and output values. In practice however, input and output values may be uncertain, vague, imprecise or incomplete. A new pair of fuzzy DEA models is presented which differs from existing fuzzy DEA models handling uncertain data. In this approach, upper bound interval data are used exclusively to obtain the upper frontier values while lower bound interval data are used exclusively to obtain the lower frontier values. The outcome, when compared with the outcome of existing approach, based on the same set of data, shows a swap in the upper and lower frontier values with exactly the same number of efficient decision making units (DMUs). This new approach therefore clears the ambiguity occasioned by the mixture of upper and lower bound values in the determination of the upper and lower frontier efficiency scores respectively.
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16

Sihotang, Hengki Tamando, Syahril Efendi, Muhammad Zarlis, and Herman Mawengkang. "Data driven approach for stochastic data envelopment analysis." Bulletin of Electrical Engineering and Informatics 11, no. 3 (June 1, 2022): 1497–504. http://dx.doi.org/10.11591/eei.v11i3.3660.

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Decision making based on data driven deals with a large amount of data will evaluate the process's effectiveness. Evaluate effectiveness in this paper is measure of performance efficiency of data envelopment analysis (DEA) method in this study is the approach with uncertainty problems. This study proposed a new method called the robust stochastic DEA (RSDEA) to approach performance efficiency in tackling uncertainty problems (i.e., stochastic and robust optimization). The RSDEA method develops to combine the stochastics DEA (SDEA) formulation method and Robust Optimization. The numerical example demonstrates the performance efficiency of the proposed formulation method, with the results performing confirmed that the efficiency value is 89%.
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Papatheodorou, Theodore, John Giannatsis, and Vassilis Dedoussis. "Evaluating 3D Printers Using Data Envelopment Analysis." Applied Sciences 11, no. 9 (May 5, 2021): 4209. http://dx.doi.org/10.3390/app11094209.

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Data Envelopment Analysis (DEA) is an established powerful mathematical programming technique, which has been employed quite extensively for assessing the efficiency/performance of various physical or virtual and simple or complex production systems, as well as of consumer and industrial products and technologies. The purpose of the present study is to investigate whether DEA may be employed for evaluating the technical efficiency/performance of 3D printers, an advanced manufacturing technology of increasing importance for the manufacturing sector. For this purpose, a representative sample of 3D printers based on Fused Deposition Modeling technology is examined. The technical factors/parameters of 3D printers, which are incorporated in the DEA, are investigated and discussed in detail. DEA evaluation results compare favorably with relevant benchmarks from experts, indicating that the suggested DEA technique in conjunction with technical and expert evaluation could be employed for evaluating the performance of a highly technological system, such as the 3D printer.
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WONG, PHILIP Y. L., STEPHEN C. H. LEUNG, and JOHN D. GILLEARD. "PORTFOLIO PERFORMANCE BENCHMARKING WITH DATA ENVELOPMENT ANALYSIS." Asia-Pacific Journal of Operational Research 30, no. 05 (October 2013): 1350011. http://dx.doi.org/10.1142/s0217595913500115.

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This paper proposes data envelopment analysis (DEA) as a suitable data analysis tool to overcome facility management (FM) benchmarking difficulties: FM performance benchmarking analysis is often unsophisticated, relying heavily on simple statistical representation, linking hard cost data with soft customer satisfaction data is often problematic. A case study is presented to show that DEA can provide FM personnel with an objective view on performance improvements. An objective of the case study is to investigate the relative efficiency of nine facilities with the same goals and to determine the most efficient facility. The case is limited to nine buildings in FM on four inputs and nine output criteria. The paper concludes by demonstrating that DEA-generated improvement targets can be applied when formulating FM outsourcing policies, strategies and improvements. Facility manager can apply DEA-generated improvement targets in formulating FM outsourcing policies, specifications development, FM strategy and planning. FM benchmarking with DEA can enhance continuous improvement in service efficiency and cost saving. This will help reduce utility cost as well as pollution. This paper fills the gap in the research of FM benchmarking by applying DEA which studies both soft and hard data simultaneously. It also contributes to a future research of a trade-off sensitivity test between FM cost, services performance and reliability.
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Abdullah, Dahlan, Hartono, and Cut Ita Erliana. "Hesitant Fuzzy-Stochastic Data Envelopment Analysis (HF-SDEA) Model for Benchmarking." JOIV : International Journal on Informatics Visualization 5, no. 1 (March 31, 2021): 94. http://dx.doi.org/10.30630/joiv.5.1.405.

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The Data Envelopment Analysis (DEA) method is a method commonly used in benchmarking. The Dynamic Data Envelopment Analysis (DDEA) method was proposed to improve the DEA method in the benchmarking process. The DDEA method proposed can determine the effectiveness of the Decision Making Unit (DMU). The disadvantage of the DDEA model is that it cannot handle problems that involve benchmarking for stochastic data. To improve the DDEA method, the Stochastic Data Envelopment Analysis (SDEA) method is proposed which can be used for benchmarking involving stochastic data. The SDEA method itself has weaknesses in dealing with noise and uncertainty problems that will appear in the assessment process. The purpose of the research conducted by the researcher was to use the Hesitant Fuzzy method in optimizing the SDEA method so that the Hesitant Fuzzy model - Stochastic Data Envelopment Analysis (HF-SDEA) could be carried out benchmarking process in a situation where the assessment contained many elements of uncertainty. The results of this study are benchmarking methods that can do benchmarking for stochastic data on conditions that contain elements of uncertainty.
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Vieira Junior, Hélcio. "Multicriteria approach to data envelopment analysis." Pesquisa Operacional 28, no. 2 (August 2008): 231–42. http://dx.doi.org/10.1590/s0101-74382008000200004.

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With the aim of making Data Envelopment Analysis (DEA) more acceptable to the managers' community, the Weights Restrictions approaches were born. They allow DEA to not dispose of any data and permit the Decision Maker (DM) to have some management over the method. The purpose of this paper is to suggest a Weights Restrictions DEA model that incorporates the DM preference. In order to perform that, we employed the MACBETH methodology as a tool to find out the bounds of the weights to be used in a Weights Restrictions approach named Virtual Weights Restrictions. Our proposal achieved an outcome that has an expressive correlation with three widely used decision-aids methodologies: the ELECTRE III, the SMART and the PROMETHEE I and II. In addition, our approach was able to join the most significant outcomes of all the above three Multicriteria decision-aids methodologies in one unique outcome.
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21

CHEN, YAO. "ON PREFERENCE STRUCTURE IN DATA ENVELOPMENT ANALYSIS." International Journal of Information Technology & Decision Making 04, no. 03 (September 2005): 411–31. http://dx.doi.org/10.1142/s0219622005001647.

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The paper studies the result of Zhu21 and establishes a relationship between the efficiency in data envelopment analysis (DEA) and the pareto optimality under multiple objective linear programming (MOLP). It is shown that the DEA/preference structure models in Zhu21 can be derived by traditional MOLP techniques. Incorporation of tradeoffs or value judgments is a direct result of using MOLP techniques. New uses of DEA are developed and described. The approach is applied to a set of Chinese cities.
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22

Lu, Chung-Cheng Jason, and Yen-Chun Jim Wu. "Evaluation of Heuristics Using Data Envelopment Analysis." International Journal of Information Technology & Decision Making 13, no. 04 (July 2014): 795–810. http://dx.doi.org/10.1142/s0219622014500606.

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This paper focuses on identifying relatively efficient configurations of algorithmic operators among a set of configurations in the development of heuristics or meta-heuristics. Each configuration is considered as a decision-making unit with multiple inputs and outputs. Then, data envelopment analysis (DEA) is adopted to evaluate relative and cross-efficiencies of a set of algorithmic configurations. The proposed approach differs from existing methods based on statistical tests in that multiple inputs and outputs are simultaneously considered in an integrated framework for the evaluation of algorithmic efficiency. A case study is presented to demonstrate the application of DEA for determining the efficient configurations of genetic algorithm operators. The evaluation results of two DEA models are also compared. The DEA evaluation results are consistent with those obtained by a commonly used statistical method.
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23

Wen, Meilin, Linhan Guo, Rui Kang, and Yi Yang. "Data Envelopment Analysis with Uncertain Inputs and Outputs." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/307108.

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Data envelopment analysis (DEA), as a useful management and decision tool, has been widely used since it was first invented by Charnes et al. in 1978. On the one hand, the DEA models need accurate inputs and outputs data. On the other hand, in many situations, inputs and outputs are volatile and complex so that they are difficult to measure in an accurate way. The conflict leads to the researches of uncertain DEA models. This paper will consider DEA in uncertain environment, thus producing a new model based on uncertain measure. Due to the complexity of the new uncertain DEA model, an equivalent deterministic model is presented. Finally, a numerical example is presented to illustrate the effectiveness of the uncertain DEA model.
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Zhang, Bao, Chenpeng Feng, Min Yang, Jianhui Xie, and Ya Chen. "Bounded and discrete data in data envelopment analysis with assurance regions." Journal of Modelling in Management 15, no. 3 (February 20, 2020): 1017–36. http://dx.doi.org/10.1108/jm2-09-2019-0225.

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Purpose The purpose of this paper is to evaluate design performance of 51 gear shaping machines by using data envelopment analysis (DEA). Design/methodology/approach Existing studies extend traditional DEA by handling bounded and discrete data based on envelopment models. However, value judgment is usually neglected and fail to be incorporated in these envelopment models. In many cases, there is a need for prior preferences. Using existing DEA approaches as a backdrop, the current paper presents a methodology for incorporating assurance region (AR) restrictions into DEA with bounded and discrete data, i.e. the assurance region bounded discrete (AR-BD) DEA model. Then, the AR-BD DEA model is combined with a context-dependent DEA to obtain an efficiency stratification. Findings The authors examine different AR restrictions and calculate efficiency scores of five scenarios of AR restrictions by using the proposed AR-BD DEA model. It shows that AR restrictions have a great impact on the efficiency scores. The authors also identify nine efficient frontiers in total. For each decision-making unit, it could set benchmarks and improve its performance based on each higher efficient frontier. Originality/value This paper first evaluates efficiency of gear shaping machines by considering different (bounded and discrete) variable types of data and including AR restrictions. The AR-BD DEA model and context-dependent AR-BD DEA model proposed in this paper further enrich the DEA theory. The findings in this paper certainly provide useful information for both producers and consumers to make smart decisions.
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Покушко, М. В., А. А. Ступина, А. А. Истомина, and Р. И. Кузьмич. "APPLICATION OF THE CHARNES-COOPER-RHODES MODEL OF THE DATA ENVELOPMENT ANALYSIS METHOD TO IMPROVE THE EFFICIENCY OF BOILER AND COMBINED HEAT AND POWER PLANTS." СИСТЕМЫ УПРАВЛЕНИЯ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ, no. 4(90) (December 1, 2022): 9–12. http://dx.doi.org/10.36622/vstu.2022.90.4.002.

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Проанализирован метод Data Envelopment Analysis (DEA) для оценки эффективности сложных систем. Описана базовая модель Charnes-Cooper-Rhodes (CCR). Представлена методология применения метода DEA в системе отопления. Проведены эксперименты по использованию модели CCR с ориентацией на вход и ориентацией на выход, а также рассчитаны показатели эффективности. The method of data envelopment analysis for assessing the efficiency of complex systems is analyzed. The basic Charnes-Cooper-Rhodes (CCR) model is described. The methodology of Data Envelopment Analysis (DEA) method application in a heating system is presented. Experiments on the use of input-oriented and output-oriented CCR model are conducted and performance indicators are calculated.
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Martić, Milan, Marina Novaković, and Alenka Baggia. "Data Envelopment Analysis - Basic Models and their Utilization." Organizacija 42, no. 2 (March 1, 2009): 37–43. http://dx.doi.org/10.2478/v10051-009-0001-6.

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Data Envelopment Analysis - Basic Models and their UtilizationData Envelopment Analysis (DEA) is a decision making tool based on linear programming for measuring the relative efficiency of a set of comparable units. Besides the identification of relatively efficient and inefficient units, DEA identifies the sources and level of inefficiency for each of the inputs and outputs. This paper is a survey of the basic DEA models. A comparison of DEA models is given. The effect of model orientation (input or output) on the efficiency frontier and the effect of the convexity requirements on returns to scale are examined. The paper also explains how DEA models can be used to assess efficiency.
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Guerrero, Nadia M., Juan Aparicio, and Daniel Valero-Carreras. "Combining Data Envelopment Analysis and Machine Learning." Mathematics 10, no. 6 (March 11, 2022): 909. http://dx.doi.org/10.3390/math10060909.

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Data Envelopment Analysis (DEA) is one of the most used non-parametric techniques for technical efficiency assessment. DEA is exclusively concerned about the minimization of the empirical error, satisfying, at the same time, some shape constraints (convexity and free disposability). Unfortunately, by construction, DEA is a descriptive methodology that is not concerned about preventing overfitting. In this paper, we introduce a new methodology that allows for estimating polyhedral technologies following the Structural Risk Minimization (SRM) principle. This technique is called Data Envelopment Analysis-based Machines (DEAM). Given that the new method controls the generalization error of the model, the corresponding estimate of the technology does not suffer from overfitting. Moreover, the notion of ε-insensitivity is also introduced, generating a new and more robust definition of technical efficiency. Additionally, we show that DEAM can be seen as a machine learning-type extension of DEA, satisfying the same microeconomic postulates except for minimal extrapolation. Finally, the performance of DEAM is evaluated through simulations. We conclude that the frontier estimator derived from DEAM is better than that associated with DEA. The bias and mean squared error obtained for DEAM are smaller in all the scenarios analyzed, regardless of the number of variables and DMUs.
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Hatami-Marbini, Adel, Saber Saati, and Madjid Tavana. "Data Envelopment Analysis with Fuzzy Parameters." International Journal of Operations Research and Information Systems 2, no. 3 (July 2011): 39–53. http://dx.doi.org/10.4018/joris.2011070103.

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Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Previous methods have not considered the preferences of the decision makers (DMs) in the evaluation process. This paper proposes an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. The authors construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different a levels. Then, the DM identifies his or her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is used to develop a ranking order of the DMUs. This study allows the DMs to use their preferences or value judgments when evaluating the performance of the DMUs.
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29

Cook, Wade D., and Larry M. Seiford. "Data envelopment analysis (DEA) – Thirty years on." European Journal of Operational Research 192, no. 1 (January 2009): 1–17. http://dx.doi.org/10.1016/j.ejor.2008.01.032.

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30

Du, Juan, Jiazhen Huo, and Joe Zhu. "Data Envelopment Analysis with Output-Bounded Data." Asia-Pacific Journal of Operational Research 33, no. 06 (December 2016): 1650050. http://dx.doi.org/10.1142/s0217595916500500.

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In conventional data envelopment analysis (DEA), data are usually assumed to be non-negative with no specific bounds. However, many practical applications require some data, and thus their projections, to fall within certain limits. For example, percentage data such as the satisfactory rate cannot exceed 100% to make sense. This data characteristic is very likely to be violated under the assumption of constant returns to scale (CRS), due to its ray expansion property. In order to tackle this issue under CRS, a series of radial models are developed to constrain DEA projections within imposed bounds from the output side. Then efficient decision making units (DMUs) can be further discriminated simply by eliminating it from the reference set, avoiding the infeasibility problem existing in the VRS super-efficiency measures. The methodology is demonstrated with data consisting of 119 general acute care hospitals located in Pennsylvania, USA.
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McCabe, Brenda, Viet Tran, and Joseph Ramani. "Construction prequalification using data envelopment analysis." Canadian Journal of Civil Engineering 32, no. 1 (February 1, 2005): 183–93. http://dx.doi.org/10.1139/l04-073.

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Contractor prequalification is essential in most construction projects, and the process has been performed by many different methods in practice. Data envelopment analysis (DEA) had been recognized as a useful technique to prequalify contractors by assigning relative efficiency scores. Data envelopment analysis, however, usually requires a large amount of data and has not been fully developed to achieve reliable results. An enhanced contractor prequalification model using DEA was developed together with a methodology for determining a "practical frontier" of best contractors. The established practical frontier can be used as a regional performance standard for the owner in prequalification and as improvement guidelines for contractors.Key words: contractor prequalification, construction engineering, data envelopment analysis, practical frontier.
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Ahn, Heinz, and Nadia Vazquez Novoa. "Effects of Data Envelopment Analysis on Performance Assessment." International Journal of Business Analytics 2, no. 1 (January 2015): 1–22. http://dx.doi.org/10.4018/ijban.2015010101.

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This paper examines the Data Envelopment Analysis (DEA) methodology from a cognitive perspective. Specifically, it analyzes (a) the role of DEA scores as an overall efficiency measure and (b) to what extent the presence of DEA scores for a non-financial performance appraisal influences a posterior financial performance assessment. The study confirms that the efficiency score acts as a strong performance marker when deciding on which decision making units (DMUs) should be awarded for their non-financial performance. Furthermore, it shows that the results of the non-financial performance evaluation may act as an anchor which significantly influences a posterior financial assessment. These insights have practical consequences for planning, reporting, and controlling processes that incorporate DEA efficiency scores.
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Ketabi, Saeedeh, Hamid Ganji, Samireh Shahin, Mehdi Mahnam, Marzieh Soltanolkottabi, and Shirin Alsadat Hadian Zarkesh Moghadam. "Surgical services efficiency by data envelopment analysis." Benchmarking: An International Journal 22, no. 6 (August 3, 2015): 978–93. http://dx.doi.org/10.1108/bij-02-2013-0022.

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Purpose – Different surgical services demand operating rooms (OR) to treat elective patients, each competing for a limited supply of OR time. The purpose of this paper is to obtain empirical measures of performance in the management of OR. The current research compares technical efficiency of 11 specialties in elective operating theatre of Alzahra Hospital in Isfahan, Iran in autumn of 2009. Design/methodology/approach – Data envelopment analysis (DEA) can be used as tools in management control and planning. First, the input oriented and variable returns to scale model of DEA technique has been applied and separate benchmarks for possible reductions in resources used has been derive, and significant savings are possible on this account. Findings – The efficiency scores of inefficient specialties are between 0.62 and 0.96. Neurosurgery and general surgery are the best and the worst units. DEA results determine by how much hospitals can increase elective inpatient surgeries for each specialty. Originality/value – The originality of this study is to obtain empirical measures of performance in the management of OR. DEA has not been applied to measure the efficiency of different department in an organization. The measures are common in different units and have been collected in a similar way.
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Zýková, Petra. "Comparison Between Data Envelopment Analysis Models with Penalties." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 67, no. 6 (2019): 1665–69. http://dx.doi.org/10.11118/actaun201967061665.

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The paper deals with Data Envelopment Analysis (DEA) models with advanced voting systems for ranking of candidates with penalties. The main aims of the system are to find a general winner and ranking of all candidates. Every voter gives the ranking of the first t-candidates and can give penalties to candidates who he/she surely does not want to vote for. Advanced voting systems are being used based on the use of data envelopment analysis models. The original contribution of the paper consists in the formulation of a new DEA/AR model with penalties. This model is derived from the DEA/AR model with penalties. The proposed models are illustrated on a simulated data set. This paper aims to compare DEA models with penalties.
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Shiraz, Rashed Khanjani, Madjid Tavana, and Debora Di Caprio. "Chance-constrained data envelopment analysis modeling with random-rough data." RAIRO - Operations Research 52, no. 1 (January 2018): 259–84. http://dx.doi.org/10.1051/ro/2016076.

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Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.
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Amirteimoori, Alireza, Hossein Azizi, and Sohrab Kordrostami. "Double Frontier Two-Stage Fuzzy Data Envelopment Analysis." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 01 (February 2020): 117–52. http://dx.doi.org/10.1142/s0218488520500063.

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Data envelopment analysis (DEA) is a mathematical programming approach with widespread applications in productivity and efficiency analysis. Compared with traditional DEA models, two-stage DEA models show the performance of each process and make available more information for decision making. In an article by Kao and Liu, models were proposed for combining a two-stage process to achieve overall fuzzy efficiency measures. Their method follows the simple geometric average approach and uses the product of two efficiencies. The present article applies a different angle for efficiency analysis in the two-stage fuzzy DEA. We suggest that the overall efficiency score of a decision-making unit (DMU) is defined as total weight of stage efficiencies, not as the simple product of their efficiency. Moreover, the proposed fuzzy DEA models are different from the model by Kao and Liu for fuzzy data in that our models are linear without the need for additional changes in variables and use the same set of constraints to measure the efficiency of DMUs with fuzzy input and output data. While the models by Kao and Liu are a nonlinear optimization problem that need additional changes in variables, and use different sets of constraints to measure fuzzy efficiencies. Additionally, our proposed approach evaluates the performance of DMUs from both optimistic and pessimistic viewpoints. Finally, using the proposed approach, the Taiwanese non-life insurance company problem will be investigated.
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Zagoruiko, Ivan, and Lesia Petkova. "DEA METHOD AS A TOOL FOR COMPARATIVE ANALYSIS OF THE EFFICIENCY OF NATIONAL ECONOMIES." Proceedings of Scientific Works of Cherkasy State Technological University Series Economic Sciences, no. 62 (September 27, 2021): 81–92. http://dx.doi.org/10.24025/2306-4420.62.2021.242067.

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The paper deals with the theory of comparative analysis of the efficiency of national economies using the nonparametric method of data envelopment analysis (DEA). The main works on the use of data envelopment analysis are studied. In order to develop the ideas of F. Caselli, W. J. Coleman II., J. Growiec it is proposed to take into account that the goal of producers in modern economy is not only to increase technical efficiency, which is expressed in reducing stock and labor intensity, but also to increase economic (in a narrow sense) efficiency that is reduction of the real prices of the used production factors. The subject of the research is an adequate representation of the interdependence of these "competing" goals in the theory of the efficiency frontiers. In the study, all efficiency frontiers were constructed in a purely nonparametric way reflecting a single period (in a standard form – a year). The goal is to solve the problem of incompleteness of a purely technological approach to the world efficiency frontiers that is to supplement the classical DEA model in a way to make it possible to build the boundaries of technical and economic efficiency using both methods – the envelopments of the actual states (points) of the countries and the envelopments of their national functions of the product distribution and its price. In accordance with the content of the proposed model of Paired Efficiency Frontier Model (PEF model), the geometric method is chosen as the main method for studying and interpreting the results obtained. Therefore, it is proven that it is possible to display a frontier using the envelopment method of functions distribution (straight lines) in one coordinate system as an envelopmentl of actual states (points) in an alternative system. This, in turn, significantly simplifies the range estimation to these borders. In the course of the research, the following goals are set: to determine the algebraic forms of linear programming problems that adequately represent the frontiers of technical and economic efficiency; to outline the main points of view regarding the construction of a global technological frontier and to justify the feasibility of complementing it with a global economic frontier. The proposed model contains four efficiency frontiers – technological and economic frontiers constructed using the envelopment method of the actual states, and similar frontiers representing the envelopments of the functions of the product distribution and its price. In accordance with the content of the proposed model, the geometric method is chosen as the main method for studying the frontiers of efficiency and interpreting the results obtained. Hence, it is possible to display a frontier using the envelopment method of functions distribution (straight lines) in one coordinate system as an envelopmentl of actual states (points) in an alternative system.
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Migiro, Stephen, and Patricia Shewell. "Finance Function Performance Measurement-A Data Envelopment Analysis Approach." Journal of Economics and Behavioral Studies 9, no. 6 (January 15, 2018): 109–21. http://dx.doi.org/10.22610/jebs.v9i6.2009.

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The practice of measuring performance of the finance function as a business support unit is not widespread. This study assessed the importance of measuring finance function performance, by ascertaining whether such measurement facilitates identification of the relative efficiency of business finance functions, and by establishing its impact, if any, on overall company performance. Focussing on a sample of companies in the South African Freight Forwarding industry, a performance metric was developed and implemented to measure finance function performance. Relative finance function efficiency was then evaluated using inputorientated data envelopment analysis (DEA) to identify ‘best in class’ performance and to benchmark participants’ performance. Further, value chain DEA (VC-DEA) was applied to evaluate finance function efficiency simultaneously with overall company efficiency. Results show that implementation of the performance metric together with DEA facilitated the benchmarking of the finance functions of the sample group and the establishment of improvement targets for the finance functions determined as inefficient. In addition, a link between overall company performance and finance function performance in terms of inputs was confirmed; however, this link was not conclusively established as regards finance function performance in terms of outputs. The contribution of the study includes confirmation that implementation of the performance metric together with DEA facilitates the critical evaluation of finance function performance, thus establishing the importance of measuring the performance of the finance functions. In addition, incorporating the use of DEA in a performance framework for the finance function as a business support unit has extended the range of applications of DEA.
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Natesan, Sarabjeet D., and Rahul Ratnakar Marathe. "Evaluation of MGNREGA: data envelopment analysis approach." International Journal of Social Economics 44, no. 2 (February 13, 2017): 181–94. http://dx.doi.org/10.1108/ijse-05-2015-0114.

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Purpose How can efficiency of a welfare scheme be measured? The purpose of this paper is to develop an efficiency evaluation model, the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) implementation efficiency model (MIEM), to evaluate the rural employment guarantee scheme in India. Design/methodology/approach MIEM employs data envelopment analysis (DEA) to compare relative efficiency of MGNREGA implementing states. It uses policy implementation process as a central “black-box” about which not much can be said, to account for state-wise implementation differences. Findings Based on administration, funds, expenditure, employment created, works executed and completed, women beneficiaries and households completing 100 days of employment, the MIEM captures current implementation efficiency and provides suggestions to propel inefficient states toward efficiency. Practical implications DEA has operationalized MGNREGA evaluation. As a decision support system, MIEM assists evaluators to develop guidelines from better performing states. It is anticipated that it will facilitate scaling up MGNREGA in inefficient states. Social implications The model developed here can be applied to diverse evaluation conditions thus leading to better utilization of scarce resources. Originality/value This paper is one of few to use DEA to evaluate MGNREGA, and is one of the first to evaluate all India implementing states on efficiency.
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Kim, Sun, and Jun. "Sustainable Technology Analysis Using Data Envelopment Analysis and State Space Models." Sustainability 11, no. 13 (June 29, 2019): 3597. http://dx.doi.org/10.3390/su11133597.

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To find sustainable technology in various areas, we propose an analytical methodology based on data envelopment analysis (DEA) and the state space model (SSM). DEA is an analytical method used to compare the efficiencies and performances of several items. In DEA, for sustainable technology analysis, the items of DEA can be the technological keywords or international patent classification (IPC) codes in patent documents. In this paper, the proposed method is used to find the relative performance of different patent keywords using comparison and evaluation. We apply this methodology to compare the technological efficiencies between patent keywords for sustainable technology analysis. We apply the additive model and directional distance function of DEA to develop the proposed methodology for building the technological structure of target technology. In addition, we forecast the future trend of target technology using the SSM and find the area of sustainable technology by its result. The SSM is well suited for time series forecasting on technology analysis. We extract the IPC codes from patent documents for the SSM. In our research, we combine the results of DEA and the SSM to find the area of technological sustainability. To illustrate the validity and performance of our research, we conduct a case study using the patent documents used and registered by Apple.
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Bai, Xuejie, Feng Zhang, and Yankui Liu. "Modeling fuzzy data envelopment analysis under robust input and output data." RAIRO - Operations Research 52, no. 2 (April 2018): 619–43. http://dx.doi.org/10.1051/ro/2017038.

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This paper offers a fuzzy optimization framework for data envelopment analysis (DEA) to evaluate the relative efficiency of decision making units (DMUs) with parametric interval-valued fuzzy variable-based inputs and outputs. The parametric interval-valued fuzzy variable-based inputs and outputs is employed to capture the uncertainty of data on the basis of professional judgements or empirical estimations. The DEA problem is formulated as fuzzy expectation model with credibility constraints. When the inputs and outputs are mutually independent parametric interval-valued triangular fuzzy variables, we investigate the parametric equivalent representations of expectation objective function and chance constraints. In order to find the optimal solution of our DEA model, a domain decomposition method is proposed. Finally, the numerical example on the sustainable supplier evaluation and selection problem is provided to demonstrate the efficiency of the proposed DEA model and domain decomposition method.
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Parichatnon, Surakiat, Kamonthip Maichum, and Ke-Chung Peng. "Measuring technical efficiency of Thai rubber production using the three-stage data envelopment analysis." Agricultural Economics (Zemědělská ekonomika) 64, No. 5 (May 14, 2018): 227–40. http://dx.doi.org/10.17221/19/2016-agricecon.

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The study investigated the technical efficiency of rubber production in Thailand. Secondary data were collected from the Thai rubber plantations in four regions from 2005 to 2014 by using a three-stage data envelopment analysis (DEA) model. The DEA was used to evaluate the technical efficiency levels and to remove undesirable environmental impacts. Furthermore, the Malmquist productivity index was used to measure the changes in the rubber production efficiency and estimate the rubber productivity trend. The findings indicate that the efficiency scores obtained using adjusted inputs in stage 3 of the DEA approach were higher than the efficiency scores in stage 1 of the DEA approach. Moreover, the results also showed that the Northern region has the worst scores of technical efficiency and declination of productivity among the four regions. However, the technical performance of the Thai rubber production has shown a good performance, an upward productivity trend, and has demonstrated the advantages of the method used. Findings from the study could provide crucial information to farmers, the Thai government, and agricultural planners for formulating effective strategies or plans to improve their technology and efficiency levels.
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Kordrostami, Sohrab, Alireza Amirteimoori, and Monireh Jahani Sayyad Noveiri. "Fuzzy integer-valued data envelopment analysis." RAIRO - Operations Research 52, no. 4-5 (October 2018): 1429–44. http://dx.doi.org/10.1051/ro/2018015.

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In conventional data envelopment analysis (DEA) models, the efficiency of decision making units (DMUs) is evaluated while data are precise and continuous. Nevertheless, there are occasions in the real world that the performance of DMUs must be calculated in the presence of vague and integer-valued measures. Therefore, the current paper proposes fuzzy integer-valued data envelopment analysis (FIDEA) models to determine the efficiency of DMUs when fuzzy and integer-valued inputs and/or outputs might exist. To illustrate, fuzzy number ranking and graded mean integration representation methods are used to solve some integer-valued data envelopment analysis models in the presence of fuzzy inputs and outputs. Two examples are utilized to illustrate and clarify the proposed approaches. In the provided examples, two cases are discussed. In the first case, all data are as fuzzy and integer-valued measures while in the second case a subset of data is fuzzy and integer-valued. The results of the proposed models indicate that the efficiency scores are calculated correctly and the projections of fuzzy and integer factors are determined as integer values, while this issue has not been discussed in fuzzy DEA, and projections may be estimated as real-valued data.
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RATNER, Svetlana V., and Artem M. SHAPOSHNIKOV. "Practical applications of Network Data Envelopment Analysis." Economic Analysis: Theory and Practice 22, no. 5 (May 30, 2023): 800–828. http://dx.doi.org/10.24891/ea.22.5.800.

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Subject. The article considers a methodology for assessing the comparative effectiveness of the activity of homogeneous economic agents, i.e. Data Envelopment Analysis. Objectives. The focus is on systematization and classification of modern practical applications of network Data Envelopment Analysis, identification of types of additional information that can be extracted from solving problems of network DEA for the strategic management of companies/organizations. Methods. The study rests on systematic literature review. Results. At present, multi-stage DEA models are most actively used to model and evaluate the performance of banks, supply chains consisting of a “supplier-manufacturer-distributor” link, innovative and high-tech companies (or territories), and companies whose activities are regulated by strict environmental standards. Least of all, multi-stage DEA models are so far used to model consumer behavior as a sequential process consisting of many stages, which is explained by the underdevelopment of approaches to measuring consumer behavior factors. Conclusions. The main difference between the types of multi-stage network models is the absence or presence of common inputs for several stages, which are divided in a certain proportion between the stages (subsystems). This factor significantly affects the type of optimization model and approaches to its solution. The presence of common inputs gives rise to the need to solve an additional optimization problem for the distribution of resources between subsystems.
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Gandhi, Aradhana, and Ravi Shankar. "Efficiency measurement of Indian retailers using Data Envelopment Analysis." International Journal of Retail & Distribution Management 42, no. 6 (June 3, 2014): 500–520. http://dx.doi.org/10.1108/ijrdm-10-2012-0094.

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Purpose – The purpose of this paper is to analyze the performance of Indian retailers in recent past and derive meaningful insight for practicing managers in this area. Design/methodology/approach – This paper analyses the economic efficiencies of select Indian retailers using three related methodologies: Data Envelopment Analysis (DEA), Malmquist Productivity Index (MPI) and Bootstrapped Tobit Regression. Findings – DEA analysis has shown that five retail firms out of selected 18 are found as efficient under the CCR model of DEA and seven out of 18 retail firms are efficient under the BCC model of DEA. MPI results indicate that 61 percent of the firms have progressed in terms of the MPI during the period under consideration. The Bootstrapped Tobit Regression shows that number of retail outlets and mergers and acquisitions can be considered as the driving forces influencing efficiency of retailers in India. Research limitations/implications – The paper has a limitation with reference to the availability of data for a few retail outlets, especially in the modeling through the Bootstrapped Tobit Regression. Originality/value – This study seems to be the first in applying productivity analysis using DEA, MPI and Bootstrapped Tobit Regression for the Indian retail sector.
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Kleine, Torben, Lena Robbenmenke, Elmar Reucher, and Norbert Meiners. "Effizienzbewertung von Arbeitsagenturen mittels Data Envelopment Analysis (DEA)." Sozialer Fortschritt 71, no. 2 (February 1, 2022): 119–37. http://dx.doi.org/10.3790/sfo.71.2.119.

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Die in Deutschland seit 2009 nahezu fortlaufend sinkenden Arbeitslosenquoten in Kombination mit steigenden Ausgaben der Bundesagentur für Arbeit ­legen die Frage nach der Effizienz der Arbeitsagenturen nahe. Verschiedene Studien haben sich in der Vergangenheit dieses Themas angenommen. In dem vorliegenden Beitrag wird auf Basis von Daten aus dem Jahr 2018 die Bewertung der relativen Effizienzen unter Anwendung der Data Envelopment Analysis (DEA) durchgeführt. Dies geschieht auf Basis realer In- und Outputs, was eine objektive Effizienzbewertung der Arbeitsagenturen verspricht. Für die Effi­zienzbewertungen werden insgesamt 16 ausgewählte Arbeitsagenturen der Regionaldirektion Niedersachen-Bremen herangezogenen. Die Analysen zeigen, dass die im Rahmen der vorliegenden Studie betrachteten Arbeitsagenturen ­relativ hohe Effizienzwerte aufweisen. Für ineffiziente Arbeitsagenturen werden Handlungsempfehlungen zur Steigerung ihrer Effizienz ausgesprochen. Eine allgemeine Aussage über die Effizienz einzelner Prozesse oder den Einsatz des Budgets der Arbeitsagenturen lässt sich auf Grundlage der Berechnungen (noch) nicht treffen. Efficiency Evaluation of Employment Agencies by Means of Data Envelopment Analysis (DEA) The almost continuous decline in unemployment rates in Germany since 2009, combined with rising expenditure by the Federal Employment Agency, suggests the question of the efficiency of the employment agencies. Various studies have addressed this issue in the past. This paper uses data from 2018 to assess relative efficiencies using Data Envelopment Analysis (DEA). This is done on the basis of real inputs and outputs, which promises an objective efficiency assessment of employment agencies. A total of 16 selected employment agencies of the Regional Directorate of Lower Saxony-Bremen are used for the efficiency evaluations. The analyses show that the employment agencies considered in this study have relatively high efficiency values. Recommendations for action to increase the efficiency of inefficient employment agencies are made. A general statement on the efficiency of individual processes or the use of the budget of the employment agencies cannot (yet) be made on the basis of the calculations.
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Reitzenstein, Constantin Freiherr von. "Benchmarking von Universitätsklinika mittels Data Envelopment Analysis (DEA)." WiSt - Wirtschaftswissenschaftliches Studium 36, no. 8 (2007): 405–11. http://dx.doi.org/10.15358/0340-1650-2007-8-405.

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Sherman, H. David, and George Ladino. "Managing Bank Productivity Using Data Envelopment Analysis (DEA)." Interfaces 25, no. 2 (April 1995): 60–73. http://dx.doi.org/10.1287/inte.25.2.60.

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Roll, Y., and Y. Hayuth. "Port performance comparison applying data envelopment analysis (DEA)." Maritime Policy & Management 20, no. 2 (January 1993): 153–61. http://dx.doi.org/10.1080/03088839300000025.

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Dyckhoff, H., and K. Allen. "Measuring ecological efficiency with data envelopment analysis (DEA)." European Journal of Operational Research 132, no. 2 (July 2001): 312–25. http://dx.doi.org/10.1016/s0377-2217(00)00154-5.

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