Abstract—In data envelopment analysis (DEA), all efficient decision making units (DMUs) have the same efficiency score which are difficult to discriminate. Cross-efficiency can be used to discriminate among efficient-DMUs. It also provides an alternative efficiency ranking for inefficient-DMUs. However, weight sets used for cross-efficiency may not be proper for ranking DMUs. The reason for this is that alternate optimal solutions for the weights exist for efficient-DMUs in DEA. The weight sets for efficient-DMUs are usually picked arbitrarily by linear programming (LP) software within the alternate optimal region. It is highly unlikely that those weight sets obtained from the LP software are the most suitable for performance measure. Therefore, some researchers have proposed using secondary objectives to search for more homogeneous or better weight sets within the alternate optimal regions. This paper examines four of those models and attempts to determine the accuracy of the four models in estimating the performance rankings for DMUs in DEA.

Index Terms—Cross-efficiency, DEA, efficiency score, performance measure.

Kim Fung Lam is with the Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong (e-mail: msblam@cityu.edu.hk).

Cite: Kim Fung Lam, "Using Cross-Evaluations in Data Envelopment Analysis," International Journal of Applied Physics and Mathematics vol. 4, no. 4, pp. 240-243, 2014.