Ranking Decision Making Units based on their profit in competition to reach a ‎standard level

The full ranking or complete ranking of decision making units is one of the main ‎issues in data envelopment analysis. A full ranking is a ranking that considers all ‎efficient and inefficient units simultaneously and finds a ranking for them. Almost all ‎of the developed ranking methods consider only the efficient units. On the other hand, ‎ranking inefficient units by traditional data envelope analysis models are also ‎inaccurate due to ignoring the role of slacks. In the present paper two novel methodologies are proposed in order to fully ranking of decision making units. In the presented ‎approach, all of the decision making units participate in a competition in a way that all ‎are projected onto the efficient frontier considering common weights. Then, according ‎to the profit that each unit attains to reach this standard level, a rank order of all ‎decision making units are obtained.In the first method , the satisfaction of units is measured in the competition and the satisfaction of the units that have the lowest satisfaction is improved. in the second method, by setting up the cross - profit table, the optimal weights of all units are taken into account in competition. After all, the proposed methods are applied on sample problems.