Journal of Operational Research and Its Applications ( Applied Mathematics ) - Lahijan Azad University

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Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of peer decision making units (DMUs) with multiple input and outputs. Traditional data envelopment analysis (DEA) models require crisp input and output data. In real world situations, however, crisp input and output data may not always be available, especially when a set of decision-making units (DMUs) contains missing data, judgment data, or predictive data. In this paper, a new model of Data Envelopment Analysis is provided to enable the user to decide the unit performance with regard to fuzziness data. The new fuzzy DEA models are formulated as LP models without the need of making any assumptions and too much computational effort. In addition, this paper, an analytical fuzzy ranking approach is developed to compare and rank the fuzzy efficiencies of the DMUs

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In today's competitive world, many manufacturing and service companies, have been forced to proceed new management approaches. Among these approaches, can be noted new methods of performance evaluation that have an important role in improvement of organization performance. Balanced scorecard is one of the recent management innovations that evaluated organization from the four major management perspectives with the aim of providing a comprehensive view of business for executives. But a key component to any BSC is the baseline or benchmark against which performance is measured. Without a standard or a baseline, evaluation is impossible. However, standards are hard to determine and can be misleading. To solve this problem, integrated DEA and BSC model is proposed. Data envelopment analysis model is method based on mathematical programming and a non-parametric approach that used in evaluating the relative efficiency of decision making units with multiple same inputs and outputs. Since DEA is based on relative analysis, the decision unites evaluated against each other thus by combining the BSC with DEA we overcome one of the major obstacles of BSC, namely, the need to determine standards. In this paper a new model of balanced DEA-BSC is offered. The main advantages of the proposed model are providing a comprehensive insight of business for executives, a balanced assessment based on all BSC Indicators, and creation balance between them, linearity and flexibility of model and high separation power. Finally, the experience of using the proposed model in performance evaluation of Yazd Tile and Ceramic Companies is presented.

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Data envelopment analysis (DEA) does not provide more information about the efficient decision making units (DMUs). A method to rank efficient DMUs is common set of weights (CSW). This research proposes some simple methods to find common set of weights CSW for the performance indices of DEA efficient DMUs. These methods use the results of the standard DEA models to determine the CSW. Unlike the existing methods, the resulted CSW is determined without deleting or rounding the weights and put all weights in computation.

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In data envelopment analysis the use of peer set to assess individual or best practice performance, detecting outliers is critical for achieving accurate results. In these deterministic frontier models, statistical tests are now mostly available. This paper deals with two statistical tests for detecting outliers in data envelopment analysis. In the presented methods, each observation is deleted from the sample once and the resulting DEA model is solved, leading to a distribution of efficiency estimates; before and after elimination. Based on the achieved distribution, two statistical tests are then designed to identify the potential outlier(s). We illustrate the method through a real data set. The method could be used in a first step before using any frontier estimation

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In current research, energy efficiency and technical efficiency of wheat farmers were calculated in Mazandaran province. To estimate technical efficiency the Stochastic Nonparametric Envelopment of Data (StoNED) was used. The model incorporating nonparametric data envelopment analysis model which contain the smoothness and concavity constraints with stochastic frontier analysis model. The requirement data for this study was include 375 farmers in 2012. The results showed that in production of wheat, nitrogen, seed and fuel with 41.7, 25.4 and 20.5 percent have the largest proportion of input energy and manpower with 0.21 percent and herbicides with 0.53 percent have the lowest percentage of energy. A total of 15761.5 MJ of energy input and 62.8 MJ output energy in wheat production systems was calculated. About 20.7% of the input energy in wheat production systems was direct energy and 79.2% of its energy was indirect form. Renewable energy sources is about 25/6% of the total input energy and non-renewable energy sources is about 74.3%. Energy productivity is 0/29 MJ/ kg and means that each unit of energy can produce just 0/29 kg of product. Average energy efficiency per hectare obtained 3/99 for wheat. The net and specific energy were 47066.9 MJ/ha and 3.4 MJ/Kg respectively. The average technical efficiency, pure technical efficiency and scale efficiency was 0.46, 0.45 and 0.43, respectively. About 46.4% of the farms have constant returns to scale, 24.8% of the farms have diminishing returns to scale, and 28/8 percent is increasing returns to scale.

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Nowadays, one of the key issues in many organizations, especially in institutions such as banks with many branches, is that is the method for evaluating their performance is not a rational and correct method. Conventional techniques, used to evaluate performance, are single-level and cannot provide enough managerial information to identify the inefficient factors of the inefficient units and attain the benefits and disadvantages of competitive strategies. However, the multilevel data envelopment analysis can overcome this problem. One of the most important problems with classical models is to ignore the internal relations of each unit in performance evaluation. In this paper, a multilevel mathematical model is designed to evaluate the performance of bank branches using the Stokklberg game concept and multivariate programming, which solves the problems of previous models and is able to provide a more realistic assessment of the efficiency of bank branches

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In this article, centralized resource allocation (CRA) models based on the value efficiency in DEA and DEA-R are recommended. In general, if the input and output data of decision-making units are available, DEA models provide targets of units on the efficiency frontier in addition to the efficiency of units. However, if only a ratio of the input data to output data, or vice versa, is available, DEA models cannot determine the efficiency and target of units. In order to overcome this problem, DEA-R models are utilized. With a linear programming problem, centralized resource allocation models can achieve the projection of all decision-making units on the efficiency frontier. Therefore, in the present article the projection of inefficient units in DEA and DEA-R is achieved using the CRA models based on the value efficiency (considering units that the manager defines as MPS). In the end, as applied research, a case study is carried out for clothing companies of a specific brand.

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This study intends to estimate bias corrected efficiency, technical efficiency, managerial efficiency and thus scale and confidence intervals associated with them, using input oriented data envelopment analysis approach and LSW algorithm. Results show the average of scale efficiency of our country’s industry section is 93% and except for recycling industry (code no. 37), furniture and unclassified artifacts (code no. 36), scale efficiency is more than 90% which indicates the main cause of technical inefficiency in industry sector is managerial inefficiency. Furthermore, almost 15% of our country’s industries are managerially 100% efficient and operate quite successfully and about 5% of industries operate with a managerial efficiency of less than 60% and the lowest managerial efficiency scores are of machinery industries (code no. 2922) and textiles finishing industries (code no. 1712) as lower than 0.3.

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 In this article, we analyzed the efficiency of food and beverage companies that were accepted in stock market, using a nonlinear model. This model eliminates the weak points of base Data Envelopment Models in high computing, lack of integration and too many numbers of zero weights. Taking into account that in this study we developed the base Data Envelopment Analysis model, the research method is developmental in terms of purpose. Also, due to using the suggested model in determining the efficiency of food and beverage companies is practical. The indices of the study were obtained from previous studies and in order to confirm these indices, the opinions of 5 stock market and university experts were considered. The data for the present study and the actual value of these indices was obtained from codal.ir website according to each company’s financial situation. In this study, by making use of coding in Lingo software, the efficiency of selected companies was calculated in CCR and two common weight methods. In order to validate the suggested model, by calculating Spearman correlation coefficient, it was indicated that the suggested model has significant correlation with two other models and it was confirmed in terms of validation. The average of proposed model is also equal to 0.81 that is reduced in comparison to CCR model and shows the distinguishability of the model in comparison to CCR base model. Results show that the proposed model in addition to elimination of weak points of classic base models, including high computing, lack of integration and too many numbers of zero weights, has a high authenticity and pretty good distinguishability.

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Gas refineries are one of the pivotal industries, have crucial role in economic development. Because of such an importance, there can be found a rich literature in evaluating and ranking these organizations. Data envelopment analysis is a popular non-parametric technique received much attention in the mentioned area. The current research addresses to evaluate 11 gas refineries in Iran between 1392-1394 using two-stage CCR based data envelopment analysis technique. In this regard, numerical results show that some of the refineries lie on the efficient frontier; Hence, Anderson-Peterson is employed to rank the efficient ones and phase 0 and 10 ASALUYE refinery is introduced as the strong efficient DMU. Malmquist measure is also applied to investigate the progression/ retrogression of the DMUs. 

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Communication plays an important role in the growth of societies and people. The Postal network is considered to be the largest physical link and network of exchanges among communities in the world, which is of particular importance for continuous communication with customers in these types of service units. In contrast, prediction, control and analysis have become an inevitable necessity in organizations and a great management tool for decision making. In this paper, baseline data envelopment analysis models for measuring and evaluating post offices’ efficiency in Guilan province in years 1392 & 1393 have been investigated. For this purpose, CCR input-axis is better than the BCC model. Because the traditional data envelopment analysis models are not capable of introducing the optimization model and the most efficient unit, we use Anderson-Peterson’s model, in which Rudsar & Anzali units are best at 92 and 93 consecutives. Finally, we use the neural network to integrate the data access approach for predicting the efficiency of postal units. The results show that this new model has good potential for prediction, and because of its high precision, it can replace traditional methods.

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Traditional DEA method considered decision making units (DMUs) as a black box, regardless of their internal structure and appraisal performance with respect to the final inputs and outputs of the units. However, in many real systems we have internal structure. For this reason, network DEA models have been developed. Parallel network DEA models are a special variation which inputs of unit allocated to several sub-processes, and the total output of these processes are the output of the relevant unit. Parallel network DEA model have been developed based on certain and confidence data and they do not have the ability to deal with uncertainty about inputs and outputs data. In this paper we are going to provide a robust parallel network DEA model and attempt to describe and analyze the new model with a real case study.
The proposed model can evaluate the performance of parallel structure and it has the ability to deal with uncertainty in the data. The results show that with increasing levels of uncertainty and decreasing of reliability, efficiency of decision-making units will be further reduced. Increasing of discrimination power is another advantage of the proposed model. Also traditional network models show more deviations in the results in compare with robust network model when the data are changed.

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The standard data envelopment analysis (DEA) method assumes that the values for inputs and outputs are exact. While DEA assumes exact data, the existing imprecise DEA (IDEA) assumes that the values for some inputs and outputs are only known to lie within bounded intervals, and other data are known only up to an order. In many real applications of DEA, there are cases in which some of the input and output variables belong to bounded and discrete sets and the others are known to lie within bounded intervals. In this paper a new variety of imprecise data in the DEA has been faced. The proposed approach transforms a nonlinear DEA model to an equivalent linear programming problem. Upper and lower bounds of efficiency scores of operational units are defined. A real case of commercial banks is provided to illustrate the applicability of the approach.