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In traditional data envelopment analysis (DEA) the uncertainty of inputs and outputs is not considered when evaluating the performance of a unit. In other words, effects of uncertainty on optimality and feasibility of models are ignored. This paper introduces a new model for measuring the efficiency of decision making units (DMUs) having interval inputs and outputs. The proposed model is based on interval DEA (IDEA) in which the inputs and outputs are limited to be within uncertainty bounds. In this model, the inputs and outputs take fixed values for each DMU such that the sum of efficiencies is maximized. The DMUs are evaluated by the same production possibility set (PPS). The efficiency is measured based on the proposed conservatism level for each input and output. Indeed, the inputs and outputs are defined by the presented conservatism level. The proposed model is integrated measuring all the DMUs efficiencies simultaneously. These efficiency scores lie between the optimistic and pessimistic cases introduced by Despotis and Similar (2002) [11].

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Here, scalarization techniques for multi-objective optimization problems are addressed. A new scalarization approach, called unified Pascoletti-Serafini approach, is utilized and a new algorithm to construct the Pareto front of a given bi-objective optimization problem is formulated. It is shown that we can restrict the parameters of the scalarized problem. The computed efficient points provide a nearly equidistant approximation of the whole Pareto front. The performance of the proposed algorithm is illustrated by various test problems and its effectiveness with respect to some existing methods is shown.

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Cost efficiency models evaluate the ability of decision-making units (DMUs) to produce current
outputs at minimal cost. In real applications, the observed values of the input-output data and
their corresponding input prices are imprecise and vague. This paper employs a fuzzy data
envelopment analysis (Fuzzy DEA) method to study cost efficiency of DMUs. In previous studies
on the cost efficiency, no attention has been paid to the issue of ranking problem in fuzzy
environment. In addition, adequate accuracy is ignored in regards to appropriate range of fuzzy
cost efficiency scores. In this study, the proposed method is applied to assess fuzzy cost efficiency
in accordance with the  -level based approach. In this method, data information is considered
as triangular fuzzy numbers. The main idea is to convert the fuzzy DEA model into a family of
parametric crisp models to estimate the lower and upper bounds of the a-cut of the membership
functions of the cost efficiency measures. Moreover, the problem of ranking DMUs is investigated
based on the fuzzy cost efficiency, using a new method. Finally, the proposed method is illustrated
applying a numerical example, and then comparisons between the proposed method and previous
approaches are carried out.
 

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Using the experiences of successful and unsuccessful companies can be a criterion for predicting the situation of emerging companies. Each company can have a vector include both financial and non-financial characteristics. Accordingly, for an active or emerging company, it is possible to determine the characteristic vector and predict which group it is likely to belong to. The techniques used in this research are discriminant analysis and data envelopment analysis. Based on this technique, discriminant functions are designed to separate known sets. The main idea for finding discriminant functions is from data envelopment analysis, which makes a limit of efficiency for separating efficient units from inefficient ones. The discriminant functions of this method are used to predict the state of the company. Hyper planes are obtained as discriminant functions to separate companies. These hyper planes are based on multiple indicators. Each of these indicators can also apply in certain situations. The modeling used in this paper was used on oil companies listed on the Iran Stock Exchange. 15 indicators and criteria have been defined for each company. The data were for 2015 and 2016, and the number of oil companies was 18, of which 9 were successful and 9 were bankrupt. In this paper, with the help of data envelopment analysis and discriminant analysis, a new modeling was designed to find hyper planes for separating two sets. Modeling has been performed based on the different criteria that have existed, and each one applies in certain circumstances. In the following, the properties of the designed model are expressed and proved. The specific conditions of the criteria have become limitations that have been added to the multiplicative form of the designed model.

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In this paper, two non-linear technologies are proposed based on weak disposability definitions: weak disposability with non-uniform abatement factors and new weak disposability. Both technologies are applied to Spanish airport systems and the existing technologies are modified. To remove the computational complexity of non-linear approaches, the linearization methods are proposed. Then, in order to evaluate the efficiency measure of decision making units (DMUs), a directional distance function (DDF) is applied to the linear technologies and the analysis of the results is presented.

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A branch of researches is devoted to semiparametric and nonparametric estimation
of stochastic frontier models to employ the advantages in the operations research
technique of data envelopment analysis. The stochastic frontier model is the
parametric competition of data envelopment technique. This paper focused on a
nonlinear autoregressive stochastic frontier production model that covers dynamic
technical inefficiency. We consider a semiparametric method for the model ‎by
combining a parametric regression estimator with a nonparametric adjustment‎. The
unknown parameters are estimated using the full maximum likelihood and pairwise
composite likelihood methods‎. After the parameters are estimated by parametric
methods‎ , ‎ the obtained regression function is adjusted by a nonparametric factor‎, ‎and
the nonparametric factor is obtained through a natural consideration of the local -
fitting criterion‎. ‎Some asymptotic and simulation results for the semiparametric
method are discussed
 

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New concepts of -feasibility and -efficiency of solutions for fuzzy mathematical programming problems are used, where  is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted many interests. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts it to a Multi-Parametric Linear Programing (MPLP) problem, and then in phase II using the convenient optimal solution with the higher feasibility degree is concluded. Using this concept, we have solved the problem of the animal diet. In the process of milk production, the highest cost relates to animal feed. Based on reports provided by the experts, around seventy percent of dairy livestock costs included feed costs. In order to minimize the total price of livestock feed, according to the limits of feed sources in each region or season, and also the transportation and maintenance costs and ultimately milk price reduction, optimization of the livestock nutrition program is an essential issue. Because of the uncertainty and lack of precision in the optimal food ration done with existing methods based on linear programming, there is a need to use appropriate methods to meet this purpose. Therefore, in this study formulation of completely mixed nutrient diets of dairy cows is done by using a fuzzy linear programming in early lactation. Application of fuzzy optimization method and floating price make it possible to formulate and change the completely mixed diets with adequate safety margins. Therefore, applications of fuzzy methods in feed rations of dairy cattle are recommended to optimize the diets. Obviously, it would be useful to design suitable software, which provides the possibility of using floating prices to set feed rations by the use of fuzzy optimization method.

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This research uses Network Data EnvelopmentAanalysis (NDEA) by  undesirable factors to analyze and evaluate the performance of automotive industry. The modeling used is applied to five production lines of an automobile company by 16 indicators. The data used are for the year 2019. The main purpose is to provide a model to improve the quality of the product by evaluating the performance of quality health in production lines able  to rank by providing appropriate quality indicators to identify, formulate and achieve corrective measures. Accompanied with accurate problem solving and operational scheduling according to the most efficient organization/production line and so investigating the source of the problem and preventing the occurrence of the problem. Because determining the direction of performance and key performance indicators (KPI) of the organization and measuring them to increase its health efficiency requires an efficient and integrated system. On the other hand, creating a homogeneous and orderly development process between the elements of the organization as a common language to solve the quality problems by aiming the improvement of the performance, customer satisfaction, sustainable production and cost management has been proposed.

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Data Envelopment Analysis (DEA) is a nonparametric approach for evaluating the relative efficiency of a homogenous set of Decision Making Units (DMUs). To evaluate the relative efficiency of all DMUs, DEA model should be solved once for each DMU. Therefore, by increasing the number of DMUs, computational requirements are increased. The Cerebellar Model Articulation Controller (CMAC) is a neural network that resembles a part of the brain known as cerebellum. The CMAC network with a simple structure is capable of estimating nonlinear functions, system modelling and pattern recognition. Meanwhile, the CMAC approach has fast learning convergence and local generalization in comparison to other networks. The present paper is concerned with assessing the efficiency of DMUs by the CMAC neural network for the first time. The proposed approach is applied to a large set of 600 Iranian bank branches. The efficiency results are analyzed and compared with the Multi-layer Perceptrons (MLP) network outcomes. Based on the results, it can be seen that the DEA-CMAC results tend to be similar to those of DEA-MLP in terms of accuracy. In addition, the Mean Squared Error (MSE) in DEA-CMAC decreases much faster than that in DEA-MLP. The DEA-CMAC model takes 1008 and 1107 iterations to reach MSE errors of 2.03×〖10〗^(-4) and of 6.01×〖10〗^(-4), respectively, while the DEA-MLP model takes 1190 iterations keeping the MSE error stable at 2.07×〖10〗^(-1). Moreover, DEA-CMAC requirements for CPU time are far less than those needed by DEA-MLP.

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Developing realistic models for the evaluation of sustainable supply chains has turned into a major challenge facing managers. The decision-making approaches proposed here consist of two stages. At the first stage, a dynamic-network data envelopment analysis (DNDEA) model is established for the first time, wherein the current efficiency of a business can be influenced by its prior social and environmental activities, as two main dimensions of sustainability. The second stage correspondingly presents, for the first time, a model in which total efficiency is calculated based on the value of historical data. Sensitivity analysis is exploited to determine the more effective factors of sustainability in efficiency evaluations. To validate the model, it is used to assess the sustainability of the suppliers of an auto spare parts manufacturer. The study results reveal that the model is well-able to evaluate the performance of dynamic network structures, with a very high discriminating power. Following the implementation of this model, only the supplier(KARAN) is found to reach the efficiency limit, and  SIRIN S.N. is recognized as the most inefficient supplier with an efficiency score of 0.6409. The sensitivity analysis outcomes demonstrate that the least amount of efficiency change is related to the economic pillar; however, the rising trend in wage costs, compared with other economic factors, brings a better effect on augmenting the efficiency of some inefficient suppliers. The highest efficiency changes during sensitivity analysis are further observed in both social and environmental dimensions. Therefore, it is claimed that investing in these two pillars can have a significant impact on the efficiency of suppliers.
 

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Due to the changes of performance measures, a vital aspect for decision makers is finding optimal scale sizes of entities. Moreover, there are undesirable measures in many investigations. In the existing data envelopment analysis (DEA) approaches, optimal scale sizes (OSSs), average-cost efficiency (ACE) and average-revenue efficiency (ARE) of decision making units (DMUs) with desirable measures under strong disposability have been estimated while undesirable factors are presented in many real world examinations. Accordingly, in this research, OSSs and ARE of DMUs with undesirable outputs are addressed under managerial disposability. ARE is defined as the composite of scale and output allocative efficiencies under managerial disposability. To illustrate in detail, a two-stage DEA-based approach is rendered to estimate ARE and OSSs in the presence of undesirable outputs. A numerical example and an illustrative case are given to explain the proposed approach in this study.

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In the traditional cost-efficiency model, the information about each decision unit includes inputs, outputs, and the input prices are fixed and specific. In practice, the price of the inputs often fluctuates at different times, and these prices for the decision-making unit are time-dependent. By the traditional method, the efficiency of decision units is impossible in the presence of time-dependent input prices. On the other hand, the exact method of cost-efficiency calculation is also difficult and time-consuming. In this study, a new method for calculating cost efficiency of decision making units with time-dependent prices during a period of time using numerical integral is presented. As  the information of the decision-making units varies over time, a method for calculating their cost efficiency accurately is presented. however,  the exact method is difficult or impossible to be solved  in some cases. Therefore, in this study, an approximate method for calculating the cost efficiency in the given state is presented. This is a suitable replacement for the precise method. The efficiency of decision making units at different time is measured and the units are ranked using the proposed method. Finally, a numerical example is provided to indicate the method and compare it with the precise method. This study shows that the efficiency obtained by the approximate method is very close to the efficiency obtained by the exact method, and at the same time, the calculation speed increases.
 

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Data Envelopment Analysis (DEA) is a nonparametric approach for evaluating the relative efficiency of a homogenous set of Decision Making Units (DMUs). To evaluate the relative efficiency of all DMUs, DEA model should be solved once for each DMU. Therefore, by increasing the number of DMUs, computational requirements are increased. The Cerebellar Model Articulation Controller (CMAC) is a neural network that resembles a part of the brain known as cerebellum. The CMAC network with a simple structure is capable of estimating nonlinear functions, system modelling and pattern recognition. Meanwhile, the CMAC approach has fast learning convergence and local generalization in comparison to other networks. The present paper is concerned with assessing the efficiency of DMUs by the CMAC neural network for the first time. The proposed approach is applied to a large set of 600 Iranian bank branches. The efficiency results are analyzed and compared with the Multi-layer Perceptrons (MLP) network outcomes. Based on the results, it can be seen that the DEA-CMAC results tend to be similar to those of DEA-MLP in terms of accuracy. In addition, the Mean Squared Error (MSE) in DEA-CMAC decreases much faster than that in DEA-MLP. The DEA-CMAC model takes 1008 and 1107 iterations to reach MSE errors of 2.03×10-4  and of 6.01×10-4 , respectively, while the DEA-MLP model takes 1190 iterations keeping the MSE error stable at 2.07×10-1 . Moreover, DEA-CMAC requirements for CPU time are far less than those needed by DEA-MLP.
 

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Cost efficiency in which cost coefficients are given for some inputs (cost coefficients can be different for disparate decision-making units (DMUs)) is one of the most important concepts in data envelopment analysis (DEA) to analyze the performance. Moreover, in some occasions, the cost performance and changes of input measures should be addressed while the convexity property is violated. Therefore, in this paper, first a DEA model is provided to assess cost efficiency based on the free disposal hull (FDH) model. Then, by considering cost and technical efficiencies achieved, a multi-objective problem called the inverse FDH cost model is presented to determine input values based on output changes while the cost and technical efficiency levels are preserved. The multi-objective problem is computed applying two approaches. Also, a dataset from the literature is presented to show the performance of the proposed method. For this purpose, we used the data of six banks in different countries. We added 2% to the outputs and analyzed the inputs with two models. In the first model, we used cost coefficients for weights, and in the second model, we used the same weights. Contrary to forecasts, some entries have decreased and others have increased. But from the results, we have noticed that the first model is more realistic because most of the solutions have increased in this model.
 

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Tone [29] proposed a method of super-efficiency slack-based measures (SBM) for ranking efficient decision-making units (DMUs), so that this model would rank efficient DMUs. The established model was able to measure radially. It calculates and measuring the efficiency of inefficient DMUs and the amount of super-efficiency of efficient DMUs. Du et al. [11] developed the Charens et al. [6] model in to the additive DEA model, as well as the additive super performance model. Turn et al. [32] used a linear SBM and S-SBM integrated model that had the properties of both models and reduced the time factor compared to previous models. In order to be able to calculate the amount of additive super efficiency; First we identify the efficient DMUs and then apply the additive super-efficiency model to the efficient DMUs. In this paper, the proposed model obtains the additive efficiency value of inefficient DMUs and the additive super efficiency value of efficient DMUs with less computation time. The amount of DMUs calculated from the integrated model in this article can be compared to the Guo et al. [15] article in comparison with the time table of the text of the article.
 

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Data Envelopment Analysis is one of the most appropriate methods in Evaluation of decision-making units in the real world. That is why researchers have always tried to improve and develop existing methods and approaches in this field. Network Data Envelopment Analysis is used to evaluate the efficiency of network systems by considering processes within divisions. In the evaluation of network systems, one of the challenges is the presence of undesirable and non-discretionary data in the system. Not many conducted have been done about the simultaneous presence of these factors in general two-stage network systems. For this reason, by extending CCR model and combining some methods in this study, we presented a model that is able to evaluate two-stage systems with the mentioned conditions. One of the strengths of the proposed model in this study is the achievement of the efficiency of the system and divisions simultaneously. At the end of the article, we analyzed the results with a numerical example. The results show the ability of the presented model in evaluating the systems under investigation.

 

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In cost efficiency models, the capability of producing observed outputs of a target decision making unit (DMU) is evaluated by its minimum cost. Traditional cost efficiency models are considered for situations where data set is known for each DMU, while, some of them are imprecise in practice. Several studies have carried out to evaluate cost efficiency using fuzzy data envelopment analysis (DEA) methods for dealing with the imprecise data that have drawbacks. The issue of presenting improve strategy is ignored for inefficient units, as well as the applied models are not easily implemented. This paper proposes a new extension to evaluate fuzzy cost efficiency using fuzzy extended multiplication and division operations. This method offers a fully fuzzy model with triangular fuzzy input-output data along with triangular fuzzy input prices. In the proposed extension, a new definition of fuzzy cost efficiency is suggested based on the extended operations. Finally, a numerical example is provided to show the applicability of the proposed models.
 

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In the evaluation of decision making units with classical models of data envelopment analysis, it is assumed that the factors are deterministic. In some decision-making problems, the amount of inputs or outputs of the units is not exactly known and it is a three-parameter interval in grey form. In this case, it is recommended to choose the factors from their center of gravity. In the classic models of data envelopment analysis, all factors are also considered desirable, but in real problems there are undesirable factors too which cannot be used to evaluate problems with undesirable inputs and undesirable outputs. In this paper, a model is presented for calculating the efficiency of decision making units in the presence of the center of gravity of undesirable three-parameter interval grey undesirable factors based on the combination of strong and weak disposability principles. To this end, the proposed method is discussed with a practical example.