Ranking decision-making units in data envelopment analysis by introducing the ideal unit

In recent years, Data Envelopment Analysis (DEA) has become one of the evaluation methods that researchers have widely analyzed. DEA is a non-parametric method to evaluate units under evaluation that produce multiple outputs by consuming multiple inputs. A significant issue in traditional DEA models is the introduce efficient units without discriminating against them. The process of discriminating efficient units, known as ranking, is a widely discussed topic. Considering that in the DEA literature, an efficient unit is one that has less input and more output, in this regard, the ideal unit is defined as a unit with the least input and the most output (usually virtual) and the distance between the efficient units and the ideal unit is considered the super efficient unit as a criterion for ranking the efficient units. The present study is an attempt to propose a new model for ranking efficient units by introducing an ideal unit and calculating the distance between each efficient unit and the ideal unit. In the following, by stating an important theorem, it is proved that the proposed model is always feasible, and in this way, one of the biggest challenges of the previous ranking models was solved. The results and advantages of the proposed model are further examined by solving some numerical examples, and the results obtained from some existing methods are compared.