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  We suggest a method for finding the non-dominated points of the production possibility set (PPS) with variable returns to scale (VRS) technology in data envelopment analysis (DEA). We present a multiobjective linear programming (MOLP) problem whose feasible region is the same as the PPS under variable returns to scale for generating non-dominated points. We demonstrate that Pareto solutions of the MOLP produce efficient units in DEA, and vice versa. We solve the MOLP problem by using a finite number of weights which are extreme rays of the cone generated by the efficient solutions. We obtain new efficient points by changing weights, and thus the efficient solutions set is produced.

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Here, we examine the capability of artificial neural networks (ANNs) in sensitivity analysis of the parameters of efficiency analysis model, namely data envelopment analysis (DEA). We are mainly interested to observe the required change of a group of parameters when another group goes under a managerial change, maintaining the score of the efficiency. In other words, this methodology provides a platform for simulating the level of some parameters against the remaining parameters for generating different scenarios, as being in demand for managers.

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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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     One of the most reliable indicators of the evaluation of the same units is the use of mathematical programming based method called data envelopment analysis (DEA). DEA measures the efficiency score of a set of homogeneous decision making units (DMUs) based on observed input and output. The DEA method has been added to the literature by integrating Farrell's method in such a way that each evaluation unit has multiple inputs and multiple outputs. With the advancement and evolution of this approach, DEAis now one of the active areas of research in measuring performance and has been dramatically welcomed by world researchers. Charnes, Cooper, and Rhodes (CCR) [1] first proposed DEA method to evaluate the relative efficiency for not-for-profit organizations. So far, many studies and researches have been carried out in various associations and universities around the world about DEA and its applications. The simplicity of understanding and implementing the DEA method, along with its high precision and wide application in various political, cultural, social and economic fields has led many researchers to use this method to achieve their goals. So far, more than 50,000 articles, books, theses and more have been published on DEA theories and applications, calculations and issues.

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Resource allocation is a problem that commonly appears in organization with a centralized decision making (CDM), who controls the units. The aim of central decision making is to allocate resources in such a way that the organization get the most benefit. Some Data Envelopment Analysis (DEA) researchers presented DEA-based resource allocation models by paying attention to energy saving and environmental pollution reduction. In this paper, we expanded a resource allocation model for 25 branches of an Iranian Tejarat bank, so that determined how much decision making (DM) can save on energy and manpower hours, so that undesirable outputs like non-performing loans are significantly reduced in a way that achieve the minimum reduction of desirable outputs while unchanged the performance of each unit after re-allocation. The result of the implementation of the model shows that in total with a 10% and 23% reduction in staff and costs respectively can result in the 0.09% reduction of deposits and 56% of non-performing loans.

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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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Predictive analytics is an area of statistics that deals with extracting information from data and using
that to predict trends and behavioral patterns. Many mathematical models have been developed and
used for prediction, and in some cases, they have been found to be very strong and reliable. This
paper studies different mathematical and statistical approaches for events prediction. The main goal
of this research is to design and construct a hybrid prediction method for events prediction, based on
Logistic Regression (LR) method and Data Envelopment Analysis (DEA) technique. In this study, a
novel hybrid algorithm was developed, and considering the kind of collected data, LR method was
applied for input selection, and the capability of the additive (ADD) model of DEA was examined to
predict the occurrence or non-occurrence of the events. To apply the proposed approach, the selected
disease for the case study was a stroke. The results showed that any patient who was placed on the
frontier has had a stroke by one or more risk factors. On the other hand, the observations that were
not on the frontier had not suffered from a stroke. The overall accuracy of 88.5 percentages was
obtained for the developed 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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This paper develops slacks-based measure (SBM) and additive SBM (ASBM) to evaluate efficiency of decision making units (DMUs) in a two-stage structure with undesirable outputs and feedback variables from the internal perspective. The SBM model is linearized  for a specific weight and the ASBM model is reformulated as a second order cone program. The target values for all inputs, outputs (both desirable and undesirable) and intermediate products are  provided. This study shows that unlike the SBM model, ASBM can be adapted to the preference of the decision maker by selecting the weights to aggregate stages in the network.
 

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Data envelopment analysis (DEA), as a well-established nonparametric method, is used to meet efficiency evaluation purposes in many businesses, organizations, and decision units. This paper aims to present a novel integrated approach to fuzzy interpretive structural modeling (FISM) and dynamic network data envelopment analysis (DNDEA) for the selection and ranking of sustainable suppliers. First, suppliers' efficiency values in a supply chain are determined, using the dynamic network data envelopment analysis (DNDEA) model developed for this purpose. Then, a heuristic method is presented based on the fuzzy interpretive structural modeling (FISM) to find a common set of weights (CSWs) for the variables involved. Depending on the data conditions, two approaches, viz. centralized and decentralized, are proposed for efficiency measurement. To illustrate the model's capability, the proposed methodology is further applied to the real data of a company, named Nirou Moharekeh Industries (NMI). The results of a study on 12 suppliers within the DNDEA model accordingly reveal that one unit (i.e. KARAN) obtains an efficient value, but an inefficient score is observed in 11 units, whose technical efficiency value is in the range of 0.6409 to 0.9983. After utilizing the weights gained from the heuristic method, the efficiency value of the most inefficient supplier (that is, SIRINS.N.) dwindles from 0.6409 to 0.6319.

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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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One of the most useful tools in Operations Research (OR) which is essentially applied to evaluate the performance of treated Decision-Making Units (DMUs) is Data Envelopment Analysis (DEA). Because of in the current decades, DEA models have been used and extended in many disciplines and hence attracted much interests. The traditional DEA treats DMUs as black boxes and calculates their efficiencies by considering their initial inputs and their final outputs. Since, in the real situations, input data are included some uncertainties, hence in this study we consider a DEA with fuzzy stochastic data and suggest a three-stage DEA model by taking into account undesirable output. To achieve this aim, an extended probability approach is applied to the reform of three-stage DEA models. Finally, we give an illustrative example by considering a case study on the banking industry.

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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.