Recently, using the data envelopment analysis (**DEA**) with **double** **frontiers** **approach**, Wang and Chin (2009) proposed a new **approach** for the selection of advanced manufacturing technologies: **DEA** with **double** **frontiers** and a new measure for the selection of the best advanced manufacturing technologies (AMTs). In this note, we show that their proposed overall performance measure for the selection of the best AMT has an additional computational burden. Moreover, we propose a new measure for developing a complete ranking of AMTs. Numerical examples are examined using the proposed measure to show its simplicity and usefulness in the AMT selection and justification.

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[4] Wang, Y.M., Chin, K.S., 2007. Discriminating **DEA** efficient candidates by considering their least relative total scores. Journal of Computational and Applied Mathematics 206, 209–215. [5] Wang, Y.M., Chin, K.S., 2009. A new **approach** for the selection of advanced manufacturing technologies: **DEA** with **double** **frontiers**. International Journal of Production Research 47, 6663–6679. [6] Wang, Y.M., Lan, Y.X., 2011. Measuring Malmquist productivity index: a new **approach** based on **double** **frontiers** data envelopment analysis. Mathematical and Computer Modelling 54, 2760–2771.

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model is the extension of Farrel measure used for multiple inputs and outputs and it deals with the calculation of radial efficiency in PPS under Constant returns to scale ( CRS ) and it has two characteristics of input orientation (envelopment form), and output orientation (multiplier form), that all the input and output values are non negative, whereas in many applications, the negative inputs and outputs could be appear as loss when the net profit is an output variable. Later on, various approaches presented which have the way for using negative data in this model and other models like the Semi-Oriented measurement. The **DEA** was presented based on the need for scientific method to analyze economic unit’s performance. Therefore, returns to scale ( RTS ) as an economical concept could be evaluated under **DEA** models. Indeed, returns to scale is related to the economical interpretation of the efficiencies of **DEA** . Returns to scale is the effect of means of production over production and has three type of “increasing”, “decreasing” and “constant”. In special case, if a DMU has a Constant returns to scale ( CRS ) – when any multi of inputs, Produce the same multi of outputs, than the DMU in this state, has the highest MPSS which represent a very important in **DEA** and connected with the RTS . The

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In real applications, there are many situations in which measures can play either the role of input or output while measures are vague. For this pur- pose, the present paper has been proposed two models to evaluate the performance and to deter- mine the status of fuzzy flexible measures where flexible and fuzzy data exist. Actually, fuzzy **DEA** models have been modified and extended. In the proposed models, similar to the prior mod- els for evaluating the efficiency of DMUs and clas- sifying flexible measures, selecting suitable M is a significant subject for calculating accurate effi- ciency. Numerical examples have been provided to illustrate the technique.

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High IPRI countries which are also rich in terms of GDP/c are better fitted to our model. That means, such countries have little uncertainty gaining wealth through heightening property rights. As we can see, in Table 6, they just have to give money to creative people that need protection from copyright piracy. We see more uncertainty, technically as **double**, in other clusters. Taking our study into the fuzzy side, we look at the subsequent error for each cluster. We took IPRI components as inputs of economic engine and evaluated the efficiency of each country using data envelopment analysis. US and China were two countries with very high IPRI efficiency relative to other countries. This indicates that US, which has high IPRI and high GDP has efficiently utilized IPRI components to enhance the economic performance and shall follow GA recommendation to perform even better. China which does not have a high IPRI ranking is also showing a perfect IPRI efficiency related to other countries. This indicated the China’s adequate quality of property rights policy making and suggests this country to follow GA recommendation foe Low cluster.

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There is a plethora of research measuring the efficiency of the SMEs of different countries. Most of the research is based on developed countries. Reverte and Guzman (2010) have measured the relative efficiency of 1939 Spanish SMEs using **DEA** as a measuring tool. In the literature, there are also studies calculating the efficiency of SMEs in Turkey with **DEA**. Bayraktar, Demirbag, Koh, Tatoglu, and Zaim (2009) have compared the supply chain management application efficiencies of Turkish and Bulgarian SMEs via **DEA**. In the study of supply chain management, Günay (2015) has measured the efficiency of 10 food companies processed in BIST SME market with the use of the BCC model of input-oriented **DEA**. Akin (2010) has measured the relative efficiencies of 115 small enterprises conducting activities in the Western Mediterranean Region of Turkey with **DEA**. Most of the research focused on firm-level analysis. Some examples in- clude Pitt and Lee (1981) on weaving firms in Indonesia; Little, Mazumdar, and Page (1987) on five industrial sectors in India; and Cortes (1987) on metalworking and food processing firms in Colombia. Determining entrepreneurial efficiency as a whole is miss- ing in previous literatures. Very little studies have worked on country-based entrepreneur- ial efficiency that compares countries on the basis of their efficiency in consuming the resources and producing the outputs. Without proper combination of available input fac- tor, a country will be off of the production possibilities frontier. A sufficient number of re- search now exists on distance functions (Cooper, Seiford, & Zhu, 2011), but positioning a country in terms of efficiency score, understanding the efficiency differences at a country level, and identifying an appropriate benchmark for each county, to the best of our know- ledge, are empirically untested.

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improving energy use efficiency of greenhouse cucumber production using DEA approach. Optimization of energy consumption[r]

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Supplier selection is a multi-Criteria problem. This study proposes a hybrid model for supporting the suppliers’ selection and ranking. This research is a two-stage model designed to fully rank the suppliers where each supplier has multiple Inputs and Outputs. First, the supplier evaluation problem is formulated by Data Envelopment Analysis (**DEA**), since the regarded decision deals with uncertainly and ambiguity of data as well as experts and manager linguistic judgment the proposed model is equipped with Fuzzy **approach**, then in this research we use of Fuzzy **DEA** for first stage. In the second stage, efficient suppliers are ranked with Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) model. Fuzzy **DEA** PROMETHEE ranking does not replace the **DEA** classification model; rather it furthers the analysis by providing full ranking in **DEA** context for efficient suppliers.

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We presented in this paper an alternative model for two-stage **DEA** under the assumption of series relationship between the two stages. Our modeling **approach** is based on the selection of an output orientation for the first stage and an input orientation for the second stage. In this manner, the intermediate measures are used as pivot that links the efficiency assessment models for the two stages in a single linear program. The proposed CRS model is straightforwardly extended to fit VRS situations. The additive efficiency decomposition **approach** coined in this paper is straightforward and, thus, free of the weighting assumption made in the original additive model [5]. Testing our models with data sets taken from previous studies, shows that the results obtained are comparable to those reported in the literature.

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Data Envelopment Analysis (**DEA**) is widely used in banking sector to measure the efficiency of the banks. This paper evaluates the performance of the banks in India using cost, revenue and profit models of **DEA** and comes out with a comprehensive efficiency index for banks, by combing the efficiency scores of various **DEA** models, using the Shannon entropy. In general, the banks included in this study are sound in terms of total assets, manpower, branch network etc., and they have been ranked based on their performance, which depends on optimal utilization of select variables. In order to measure the degree of agreement between rankings of banks based on three different models, namely cost, revenue and profit model, Kendall’s coefficient of concordance have been used. The study observes that Shannon-**DEA** **approach** provides a comprehensive efficiency index for banks and a reasonable way of ranking.

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Data Envelopment Analysis (**DEA**) is a nonparametric method used in operations research and economics to estimate the production **frontiers**. It is a linear programming method used performance of homogeneous organizational units and is widely used in banking industries, where the bank branch will be the unit of measurement (Thanassoulis, 1999). **DEA** is not only used in banking, but also to analyze the ctors such as industrial firms, universities, military operations, banking, and healthcare or hospitals. In a study, it is used to evaluate the management of 60 Missouri Commercial Banks for the period from 1984 to three cost indices of the UK Department of Health to benchmark NHS Trusts. He compares the efficiency rankings from the cost indices with those obtained by the use of **DEA** and Stochastic Cost Frontier (SCF) Analysis. In this study, the **DEA** was applied to rank the states within Indian Territory based on some inputs and outputs of Factor Sector taken from the Economic Appraisal of Tamil Nadu. The procedure for ranking of states using **DEA** **approach** is clearly described in the flow chart presented in the next

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DOI: 10.4236/tel.2017.76111 1651 Theoretical Economics Letters In the above equations denotes the elasticity measure and D denotes the values of objective function in the corresponding linear programing formulation of the VRS model. The subscript o is for output orientation. Values of ξ are obtained from the solutions of the linear program formulation of the **DEA**. We have calculated elasticities using above formula for each firm, in each time pe- riod and for the two output scenario. In this way, we obtained not only returns to scale characteristics but also a scale elasticity measure. A value of equal to (or very close to) 1 corresponds to constant returns to scale scenario, a value less than 1 corresponds to decreasing returns to scale scenario and a value greater than 1 corresponds to increasing returns to scale scenario. This is a quantitative estimate of returns to scale. We emphasize that for scale elasticity estimation we have used output oriented **DEA** because the formula for input oriented **DEA** may fail to give finite elasticity measure when the value of objective function of the **DEA** linear program and the scale characteristic variable ξ are equal in magnitude but ξ is negative in sign [30]. Next we partitioned our dataset, with two outputs, in three categories (Large, Medium and Small sized respectively), using k-means clustering for each year, in order to establish relationship be- tween firm size and RTS estimate.

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In Data envelopment analysis choice of too many inputs and too many outputs manifest in too many efficient production units, forcing **DEA** to loose its discriminatory power. Small number of inputs and outputs mask the truly efficient production plans as inefficient. In the envelopment models degrees of freedom increase with sample size as we notice in statistical theory of estimation. However, degrees of freedom decrease with increase in the number of inputs and/or outputs. A rule of thumb that serves as a guide to select the sample size is,

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456 reductions in one or more inputs can be associated with increases in one or more outputs-without worsening any other input or output. Proceeding in reverse, congestion occurs when increases in one or more inputs can be associated with decreases in one or more outputs-without improving any other input or output. According to the inefficiency definition, inefficiency refers to waste which represents an unnecessary expenditure of resources for some input that could have been avoided without having had to augment other inputs or reduce any outputs. And congestion is a severe form of inefficiency in the sense that benefits in both inputs and outputs could be secured by reducing the congesting input amounts [4]. Consequently for a DMU evaluated to be fully (100%) **DEA** efficient, there must be evidences to show that it is not possible to improve any of its inputs or outputs without worsening some of its other inputs or outputs [5]. Hence, for a DMU to be fully efficient there must be no waste [22].

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The study uses the **DEA** **approach** to investigate the determinants of performance efficiency of 19 selected banks in Nigeria for the year 2009. In order to have a robust empirical analysis, three **DEA** performance efficiency measure are employed to include the constant returns to scale (CRS), variable returns to scale (VRS) and scale. The independent variables (determinants) of bank efficiency used in the study include Bank size, Bank age, Board independence and Bank ownership structure. The measurement of the variables is demonstrated below in the table below.

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The main limitation of this study derives from not considering all Iberian seaports in the analysis and hence preventing any conclusions onsmaller seaports. Therefore, the conclusions presented here are limited to the selected sample of the most representative Iberian seaports. As **DEA** analysis cal- culates the efficiency based on the selected DMU ’ s, the results probably would be different if the sample was different. In this sense, we would suggest the study be applied to all Iberian seaports. We would also recommend that the study be applied to the same seaports for the period since 2009 to analyse and compare i) the effects of the global financial crisisand the recovery, or otherwise, of seaports, ii) the effect of the latest restructurings, for example, Aveiro seaport’s link to the national railway network, operational in 2010, provides for the movement of around 600,000 t, and iii) the effects of the enlargement of the Panama Canal from 2013 that will impact on the world’s shipping routes and the positioning of Iberian seaports.

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That is, **DEA** seeks to determine which of the N DMUs determine an envelopment surface or an efficient frontier. DMUs lying on the surface are deemed efficient, while DMUs that do not lie on the frontier are termed inefficient, and the analysis provides a measure of their relative efficiency. As mentioned, the solution of the model dictates the solution of (N) linear programming problems, one for each DMU. It provides us with an efficiency measure for each DMU and shows by how much each of a DMU’s ratios should be improved if it were to perform at the same level as the best performing prefectures in the sample. In this way we extract an efficiency ratio for each prefecture, which shows us by how much the ratios of each prefecture could be improved so as to reach the same level of efficiency with that of the most efficient prefectures in the sample.

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Efficiency evaluation plays an important role in improving quality and equity and decision support services, [6]. It can better mobilize available resources and provide decision makers and health managers with the information and evidence they need. Efficiency seeks to determine the extent to which the inputs (resources) of the health system are used to achieve health system objectives, [7]. According to Thoral, [8], in a context where medicine is becoming more complex, medical technologies are rapidly developing and diffusing, and economic constraints are increasing, the aim of the evaluation is to maximize efficiency under the constraint of resource allocation. Thus, the pursuit of efficiency should be a central objective of policy makers and managers, and to this end better tools for measuring and understanding efficiency are needed, [7]. As a result, in this work, we assess the efficiency of MENA countries health systems using the nonparametric **approach**, data envelopment analysis **DEA**.

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Data Envelopment Analysis (**DEA**) is becoming an increasingly popular tool for assessing the relative performance of industries and companies. By apply- ing **DEA** theory to the non-financial sector, the relative efficiency of 27 listed corporations in the United Arab Emirates (UAE) has been analyzed in this paper. The focus of the study has been on the impact of the financial crisis and the recovery thereafter. Further, the productivity change was decomposed into technical efficiency change and technological change by using the non-para- metric Malmquist Productivity Index (MPI) over the period from 2007 to 2014. Based on Malmquist analysis, we find that the most efficient industries during the post-crisis period were food and beverages, telecommunication and pharmaceuticals. In contrast, the sectors that were adversely affected by the crisis were services, real estate, construction and cements. The break-up of the TFP indicated that the efficiency indices in the top performing industries were driven by technological improvements or frontier effects. The top-per- forming companies in the UAE during the 2007-14 period demonstrated in- novation-led growth, aided by the use of better technology, investments in capital equipment, and adoption of new production processes.

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in **DEA** by using tchebycheff norm; since, inputs and outputs are fuzzy. Therefore, it may be obtained a fuzzy rank for decision making units hence we developed this method for ranking DMUs with fuzzy data. We illustrated our model by a numerical example and compared with fuzzy 𝐿 1 norm proposed by Jahanshahloo et al. [9]. We proposed our model for triangular fuzzy

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