Survey on rank preservation and rank reversal in data envelopment analysis

• We demonstrated the occurrence of rank reversal in different ranking models in DEA.
• Certain ranking methods are surveyed in DEA focusing on rank preservation and rank reversal phenomena.
• We discussed three other models in which the phenomenon does not occur when a copy of a DMU is added to the PPS.

In most data envelopment analysis (DEA) models, the best performers have the full efficient status denoted by unity (or 100), and, from experience, we know that usually plural decision making units (DMUs) have this efficient status. Discriminating between these efficient DMUs is an interesting subject, and a large number of methods have been proposed for fully ranking both efficient and inefficient DMUs. This paper demonstrates the fact that the rank reversal phenomenon may occur in most DEA ranking methods; however, this study introduces some ranking methods which do not follow the procedure and lack this taint. Numerical examples are provided to clearly illustrate the above mentioned phenomenon in some DEA ranking methods. In fact, certain ranking methods are surveyed in DEA focusing on rank preservation and rank reversal phenomena.