Ranking of decision making units: a review and development of new model using data envelopment analysis approach

A key limitation of Data Envelopment Analysis (DEA) models is their inability to rank the decision making units (DMUs) particularly efficient ones. In this paper a systematic review of literature concerned to ranking of DMUs is presented. Thereafter a new model has been developed by extending the DEA model using merger methodology. According to this methodology in a set of n DMUs, one DMU is merged in another DMU simply by adding their inputs and outputs linearly while keeping the inputs and outputs of unmerged DMUs unaltered. These DMUs are then reanalyzed to get the relative efficiency of newborn DMU (achieved by merging two DMUs) and revised efficiencies of unmerged DMUs. Thereafter the same merging process is iterated for all possible combinations of mergers in a systematic manner. By doing this process we obtain ⁿC2 total number of efficiencies for each DMU. Out of this set of results the frequency of occurrences of 100% efficiency for each DMU is counted. The DMU which has the maximum frequency of such occurrence has been assigned the top rank and others are put under lower rankings in order of occurrence of frequencies. In this approach maximum numbers of DMUs are assigned the ranking except few DMUs where there is a tie in the frequency. The ranking of such DMUs is decided on the basis of frequency of occurrences of higher efficiency scores.