Ranking All Units in DEA

Data Envelopment Analysis (DEA) is a methodology to compare efficiency of Decision Making Units (DMUs). DEA is an extension of Charnes, Cooper and Rhodes work by introducing CCR model in 1978. Ranking DMUs is one of the main purposes of DEA in management and engineering. DEA evaluates some DMUs with efficiency score one as efficient DMUs and we therefore need to produce a reliable method for fully ranking DMUs. Some methods have been proposed in this concept and newly Khodabakhshi and Aryavash (2012) ranked DMUs relative to their combined maximum and minimum efficiency scores where efficiency is defined as ratio of weighted sum of outputs to weighted sum of inputs. Due to some obtained weights (multipliers) in DEA may be zero, previous methods have low ability in ranking DMUs because of eliminating the effect of corresponding input and outputs on DEA evaluations. We expand their method by assigning lower bounds on multipliers using facet analysis and then we propose an equitable and precise method for ranking all DMUs based on the modified CCR. Keywords: Data envelopment analysis, decision making unit, rank.