Ranking of Non-Extreme Efficient units based on multi ideal DMUs in PPS

Data envelopment analysis (DEA) is a body of research methodologies to evaluate overall efficiencies, identify the sources, and estimate the amounts of inefficiencies in inputs and outputs. In DEA, the best performers are called DEA efficient and the efficiency score of a DEA efficient unit is denoted by a unity. The standard DEA method assigns an efficiency score less than one to inefficient decision-making units (DMUs), from which a ranking can be derived. However, efficient DMUs all have an efficiency of one, so that for these units no ranking can be given. Since in evaluating by traditional DEA models many DMUs are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In the last decade, ranking DEA efficient units has become the interests of many DEA researchers and a variety of models (called super- efficiency models) were developed to rank DEA efficient units. Super efficiency data envelopment analysis model can be used in ranking the performance of efficient DMUs. While the models developed in the past are interesting and meaningful, they have the disadvantages of being infeasible or instable occasionally. But the main problem of super- efficient models is lack of differentiation between non- extreme efficient DMUs, so these models cannot rank these DMUs. In this paper, we propose a new method for Ranking Non- Extreme Efficient Decision making units in Data Envelopment Analysis based on benchmark. One of the main advantages of our approach is that, this method doesn’t apply any new models, rather this model applies a combination of the well-known models for ranking DMUs. Therefore, understanding our proposed method is easy for readers. One numerical example is examined to illustrate the potential applications of the proposed method.