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Mathematical Problems in Engineering
Volume 2015, Article ID 710264, 7 pages
Research Article

Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

School of Management, Shenyang University of Technology, Shenyang, Liaoning 110870, China

Received 26 April 2015; Accepted 5 July 2015

Academic Editor: Jurgita Antucheviciene

Copyright © 2015 Qiang Hou and Xue Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method.