Supplier Ranking Using Data Envelopment Analysis and New Cross Efficiency Evaluation in the Presence of Undesirable Outputs

Data envelopment analysis is a linear programming-based approach used to evaluate the relative performance of decision making units (DMU's) that perform the same tasks with multiple inputs and multiple outputs. Due to the optimistic view of the DEA in evaluating the performance of homogeneous decision making units, multiple units with a maximum relative efficiency score (equal to unit) are highly likely. Therefore, ranking models were presented to distinguish between efficient units. Cross efficiency evaluation is one of the most useful tools for ranking DMUs in data envelopment analysis. This model has two major flaws in implementation. First, it yields different results in the presence of optimal alternatives; and second, there is no compelling reason to use the arithmetic mean to integrate the cross-performance matrix results. In this paper, a new approach, inspired by the preferential voting process and the idea proposed in the TOPSIS method, is presented to combine cross-performance results in the presence of undesirable outputs. The results are then used to rank suppliers in the presence of undesirable outputs.