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Data envelopment analysis (DEA) is a linear programming method for measuring the performance and efficiency of units called decision-making units (DMUs). In many real-world performance measurement problems, the input and output data are not precisely known. Furthermore, the data may include dual-role factors that can be considered an input and output factor simultaneously. We propose a novel DEA model in the presence of imprecise data and imprecise dual-role factors by developing a new pair of mixed binary linear epsilon-based DEA models. The proposed models estimate the lower and upper bound efficiency scores in the presence of interval input, output, and dual-role factors by considering a fixed and unified production frontier for all DMUs. We then extend our models by including the weak ordinal dual-role factors. In contrast to the existing methods that exclude the dual-role factors, we include the dual-role factors and find a strictly positive value for the lower bound of the weights of inputs, outputs, and dual-role factors. We present a case study to demonstrate the applicability and exhibit the superiority of our approach over the existing methods.

Park proposed a pair of mathematical data envelopment analysis (DEA) models to estimate the lower and upper bound of efficiency scores in the presence of imprecise data. This article illust...

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.

This paper deals with imprecise data in data envelopment analysis (DEA). We construct a new pair of mathematical programming models by using the concepts of ‘inf’ and ‘sup’ to calculate the exact values of the lower- and upper-bound efficiency scores in the presence of interval and ordinal data. The method proposed in this study is motivated by the approach introduced by Kao (Eur J Oper Res 174(2):1087–1099, 2006) where a pair of two-level mathematical DEA models are converted into linear programming (LP) models to calculate the lower- and upper-bound efficiency scores in the presence of pure ordinal data. We show that the LP model proposed by Kao (2006) for finding the lower-bound efficiency score yields the upper-bound efficiency score. We propose an improved model that overcomes this drawback and successfully calculates the lower- and upper-bound efficiency scores. We demonstrate the applicability of our models with a numerical example and exhibit its efficacy through comparison with Kao’s (2006) 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 methods have been proposed in data envelopment analysis (DEA) for measuring efficiency in problems with interval or ordinal data. In this study, we review the weaknesses and drawbacks of these methods and show how converting ordinal or interval data into precise data can lead to violations of established DEA axioms. One of the axioms violated by these conversion processes is the inclusion of observations axiom, which requires a consistent definition of the production possibility set. We describe the special properties of ordinal and interval data together with their effect on the DEA-based rankings using a theorem and an example. We also propose a new algorithm and apply random dataset generation to overcome the problems arising from violations of the inclusion of observations axiom in DEA settings with ordinal or internal data. Several numerical examples are presented to demonstrate the applicability and exhibit the efficacy of the proposed method.

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.

This paper improves the integrated data envelopment analysis (DEA) model proposed by Asosheh et al. [1], for evaluating and ranking information technology (IT) projects in presence of both cardinal and ordinal data. They used balanced scorecard (BSC) for defining IT projects evaluation criteria and introduced a new DEA model to obtain most efficient IT project by considering imprecise data. This paper shows that their model randomly selects one efficient decision making unit (DMU) or IT project as the most efficient and the selection depends on the program or method is used for solving the problem. We develop their idea and propose a modified model to determine the most efficient DMU. In addition, this paper proposes a new algorithm for finding and ranking other efficient DMUs. The capability and usefulness of the proposed model is indicated by a numerical example.