Methods and applications of DEA cross-efficiency: Review and future perspectives

The field of engineering management usually involves evaluation issues, such as program selection, team performance evaluation, technology selection, and supplier evaluation. The traditional self-evaluation data envelopment analysis (DEA) method usually exaggerates the effects of several inputs or outputs of the evaluated decision-making unit (DMU), resulting in unrealistic results. To address this problem, scholars have proposed the cross-efficiency evaluation (CREE) method. Compared with the DEA method, CREE can rank DMUs more completely by using reasonable weights. With the extensive application of this technique, several problems, such as non-unique weights and non-Pareto optimal results, have arisen in CREE methods. Therefore, the improvement of CREE has attracted the attention of many scholars. This paper reviews the theory and applications of CREE, including the non-uniqueness problem, the aggregation of cross-efficiency data, and applications in engineering management. It also discusses the directions for future research on CREE.