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Some input-output classifier data envelopment analysis (DEA) models in multiplier and envelopment forms were developed to designate the status of flexible measures, playing either input or output roles. These models ignore the role of non-Archimedean epsilon in the input-output classification process. We show that these epsilon-free models may ignore some flexible measures in the performance evaluation process and hence the status of such flexible measure(s) can be randomly and inappropriately identified. To fill this gap, we develop a pair of epsilon-based multiplier and envelopment classifier models. We also develop an approach to find a suitable epsilon value for our developed classifier models. A case study of the supplier selection problem in the Iranian Space Research Center (ISRC) is provided to illustrate the potential application of our new epsilon-based approach.

Data envelopment analysis (DEA) is a mathematical programming approach to efficiency measurement in many applications. In some real-life applications, three situations are established. First, the input and output data are imprecise. Second, it is necessary to use the weight restrictions in order to consider the management view. Third, the decision maker needs to find the best decision making units (DMUs). In the traditional DEA model, it is supposed that the input and output data are precise and the weights are free. This paper proposes a new mixed integer assurance-region imprecise DEA (AR-IDEA) model to find the best DMU by solving only one model. Also, a new algorithm is developed to find and rank the other efficient DMUs by using the proposed model. Indeed, the proposed approach can be used to find and rank the best DMUs in real-life applications. A numerical example of the supplier selection problem is provided to show the usefulness and effectiveness of the proposed approach.

To efficiency measure in real-life applications of data envelopment analysis (DEA) model, the inputs and outputs data are sometimes imprecise, and we need to use the weight restrictions in order to incorporate management’s views. For this purpose, the present paper investigates the problems of existing approaches in this area, and proposes a comprehensive DEA model which enables us to estimate the relative efficiency scores of real-life systems. The proposed model contains different types of imprecise data and general form of weight restrictions. A new simulation-based genetic algorithm (GA) is developed to estimate the expected values of relative efficiencies with the comprehensive DEA model. It is shown that the proposed model and the solution approach solves the drawbacks of existing models, and gives more informative and reliable results. Some numerical examples are provided to illustrate the theoretical content of the paper and to show the effectiveness of the new approach.

In basic data envelopment analysis (DEA) models the status of input and output measures are exactly known and given. However, in certain cases, some factors could play either input or output roles that are referred to as flexible measures. The existing approaches to deal with flexible measures solve two models for each DMU to rank the DMUs, one to classify flexible measures, and another to estimate efficiency scores. Moreover, these approaches ignore the role of non-Archimedean epsilon in the performance evaluation process. In this paper, we develop a novel mixed binary linear DEA model to classify the flexible measures and find the best DMU. Moreover, we propose an approach to find a suitable epsilon value for our developed model and suggest a new algorithm to find and rank all efficient units. An interesting case study in Tehran Stock Exchange is provided to illustrate the potential application of our new approach.

The efficiency measurement with traditional data envelopment analysis (DEA) requires precise input and output data. However, the input and output data is imprecise in many real-world problems. Various imprecise methods are developed to estimate the lower and upper bound efficiency scores in the presence of interval and weak ordinal data. We show the existing methods provide an estimation of the lower or upper bound efficiency score and cannot find their exact values in the presence of weak ordinal data. As a result, the ranking of decision making units (DMUs) may not be reliable since they are based on estimated efficiency scores. We propose a pair of DEA models to find the lower and upper bound efficiency scores. We prove the proposed models can find the exact values of the lower and upper bound efficiency scores in the presence of weak ordinal data. However, these exact values depend on a set of parameters in the presence of ordinal data. Therefore, we further propose a novel measure, fathoming the robustness of the efficiency function for the parameter space, to select the best practice DMUs in the presence of imprecise data. We present a real-world application in the space industry to demonstrate the applicability and superiority of the proposed method over the existing methods.

Several mixed binary linear programming models have been proposed in the literature to rank decision-making units (DMUs) in data envelopment analysis (DEA). However, some of these models fail to consider the decision-makers’ preferences. We propose a new mixed binary linear DEA model for finding the most efficient DMU by considering the decision-makers’ preferences. The model proposed in this study is motivated by the approach introduced by Toloo and Salahi (2018). We extend their model by introducing additional assurance region type I (ARI) weight restrictions (WRs) based on the decision-makers’ preferences. We show that direct addition of assurance region type II (ARII) and absolute WRs in traditional DEA models leads to infeasibility and free production problems, and we prove ARI eliminates these problems. We also show our epsilon-free model is less complicated and requires less effort to determine the best efficient unit compared with the existing epsilon-based models in the literature. We provide two real-life applications to show the applicability and exhibit the efficacy of our model.