A new integrated AR-IDEA model to find the best DMU in the presence of both weight restrictions and imprecise data

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.