DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection

Data envelopment analysis (DEA) has been extended to cross-efficiency evaluation to provide better discrimination and ranking of decision-making units (DMUs). However, the non-uniqueness of optimal weights in the traditional DEA models (CCR and BCC models) has reduced the usefulness of the DEA cross-efficiency evaluation method. To solve this problem, we introduce the concept of the satisfaction degree of a DMU towards a set of optimal weights for another DMU. Then, a new DEA cross-efficiency evaluation approach, which contains a maxmin model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. Our maxmin model and algorithm 1 can obtain for each DMU an optimal set of weights that maximises the least satisfaction degrees among all the other DMUs. Further, our algorithm 2 can then be used to guarantee the uniqueness of the optimal weights for each DMU. Finally, our approach is applied to a real-world case study of technology selection.