A complete ranking of DMUs with undesirable outputs using restrictions in DEA models

Ranking DMUs is an important issue in DEA studies. Traditional DEA model usually leads to the failure to ranking all DMUs when DMUs get the same efficiency score, such as efficient DMUs or inefficient DMUs with the same efficiency score. For the sake of comparing and improving capabilities of DMUs, many researchers have sought to fully rank both efficient, as well as inefficient DMUs. In this paper, an extended DEA model considering undesirable outputs using restrictions is presented to realize a unique ranking of DMUs through the new “Maximal Balance Index” based on the optimal shadow prices. Meanwhile, a numerical example and an empirical example are provided to illustrate the difference from previous work and the application of the extended model. In the empirical study, the complete ranking of DMUs incorporating undesirable outputs is proved to be useful and unique.