A Ranking Method Based on a Full-inefficient Frontier in the Presence of Undesirable Outputs

Data Envelopment Analysis (DEA) is an approach to assess similar-structured decision making units (DMUs) efficiency. As in DEAs it might be more than one efficient unit is assessed, some methods have been proposed for ranking efficient units. One of these methods is ranking method based on the completely inefficient boundary. This method has advantages over other ranking methods, including ability to determine the ranking of non-veritable units. Unlike the Andersen and Peterson method, this method has no problems or instability. In this method, a completely inefficient border is identified, which includes DMUs with the worst performance level. In the production process, in addition to desirable outputs, adverse emissions such as air pollution can also be generated. The presence of such outputs plays an important role in estimating the efficiency and determining the effective DMUs. In this paper, the unit position is evaluated based on a completely inefficient boundary, so that an inefficient DMU is depicted as an inadequate input and output, and a reduction in desirable outputs on a completely inefficient boundary. In this paper, an output-oriented radial model and a slack-based non-radial model are proposed to rank efficient units in the presence of undesirable outputs based on a completely inefficient boundary.