Determining the inefficient space and ranking of DMUs with undesirable outputs

One of the applications of Data Envelopment Analysis (DEA) is in ranking of Decision Making Units (DMUs). When some DMUs are the same in efficiency score, this ranking results in failure. Various methods are introduced to rank efficient and inefficient DMUs and attempt to give a fully ranking in order to improve the evaluation. Many articles are published in this field so that have some problems. In this paper, by considering undesirable outputs and extending the inefficient space, a complete ranking of DMUs is presented. On the other hands using facet as a complement of previous methods leads to a fully ranking.