Abstract— Data envelopment analysis (DEA) has been a popular approach in performance measure. However, alternate optimal solutions exist in most linear programming solutions of an efficient decision making unit (DMU), and reduce the effectiveness of the DEA cross efficiency evaluation method in ranking DMUs. Some methods choosing different weight sets in the alternate optimal solutions to perform cross efficiency evaluation have been studied in the literature. This paper introduces an approach to find two weight sets with opposite secondary objectives: one minimizes the number of efficient DMUs and the other maximizes the number of efficient DMUs, in the alternate optimal solutions, for cross efficiency evaluation. Both weight sets are used to compute cross efficiency evaluation in DEA. The intuition of this approach is that a “truly” efficient DMU is expected to perform well in any efficient weight sets in DEA. Therefore, a more efficient DMU is expected to have a higher evaluation than those of other less efficient DMUs when evaluated with weight sets that are different in their weight patterns. Computational results are provided to show the value of the proposed approach.