An improved cross-ranking method in data envelopment analysis. Issue 1 (2nd January 2016) - Jin, Minyue
ABSTRACT: Cross-efficiency evaluation is an extension of data envelopment analysis methodology for fully ranking decision-making units (DMUs). Based on the idea that ranking order is much more meaningful than the individual efficiency score in several circumstances, a cross-ranking matrix was recently introduced. The matrix was built by replacing the efficiency score in the conventional cross-efficiency matrix with the ranking order of that efficiency score in each row. However, the non-uniqueness issue in the cross-efficiency scores in the cross-efficiency evaluation may result in different ranking orders in the matrix and may thus limit the usefulness of cross-ranking method. This study improves the cross-ranking method by introducing an interval cross-efficiency matrix in cross-efficiency evaluation. The interval cross-efficiency matrix can reveal all possible cross-efficiency scores through self-evaluation and peer evaluation. Therefore, the derived cross-ranking matrix based on the interval cross-efficiency matrix can show all information on possible ranking orders for all DMUs. The improved method is illustrated by two numerical examples.