Ranking Decision-Making Units Using Interval Data Envelopment Analysis: Extension and Application

In the current world, dealing with some problems with interval data is inevitable. In this case, the methods applied for real data could not be employed. To solve these problems, the modified version of previous methods or new methods should be presented. In this paper, the two-stage ranking method that already has been proposed by the authors is modified to solve the mentioned problems. In each stage, two optimistic and pessimistic attitudes are considered and their corresponding models are presented. Then, an appropriate algorithm for classifying the units based on their obtained interval efficiency is proposed. To demonstrate the applicability of the proposed method, 30 branches of the social security insurance organization in Iran are classified. Also, the validity and consistency of the proposed method are confirmed. The main contributions of this paper are as follows: Decision-making units (DMUs) are ranked with interval inputs and outputs. Inefficiency of the first projection (obtained in the first stage) is applied in the unit rank score. All units are classified in separate classes and all units of each class are ranked. Pareto-efficient projections (practical benchmarks) are obtained for all inefficient units. The proposed model is always feasible and unit invariant.