Ranking Decision Making Units with Negative and Positive Input and Output

Data envelopment analysis (dea) is a nonparametric method for measuring the efficiency of decision making units (dmus) which was first introduced by charnes, cooper and rhodes in1978 as the ccr model .one of the most important topics in management science is determining the efficiency of dmus. dea technique is employed for this purpose. in many dea models, the best performance of a dmu is indicated by an efficiency score of one. there is often more than one dmu with this efficiency score. to rank and compare efficient units, many methods have been introduced .moreover, the main assumption in all dea models was that all input and output values are positive, but practically, we encounter many cases that violate this term and we ultimately have negative inputs and outputs.