sensitivity analysis to determine the performance security margin of decision making units with the optimistic and pessimistic frontiers

Data envelopment analysis is a non-parametric method used to evaluate the relative efficiency of homogeneous units, consists of multiple inputs for producing multiple outputs. since the calculated efficiencies for the dmus are relative, each dmu attempts to improve its performance and not to miss the position of efficiency in competition with the other dmus. the part of data envelopment analysis surveys the sensitivity of the set of efficient dmus with their simultaneous perturbations. in this paper we focus one on the important topic of the sensitivity analysis is called “the relative efficiency security margin” and propose an algorithm to determine value of it. moreover, we proceed the pessimistic frontier and called it “the inefficiency improvement margin”. then we present two numerical examples with optimistic and pessimistic frontiers and an applied example of the15pharmaceutical companies in tehran stock exchange were used to illustrate the advantages and capabilities of our proposed algorithm. so, with this information, the managers of companies can identify their closest threat and improve their performance in order to keep their position at increasing complexity of business and the significant technological advancement of technology and not to miss their efficient position in ranking.