An Integrated Approach Using Cross-Efficiency and Shapley Value in Performance Evaluation

Ranking decision making units (DMUs) for performance evaluation is an important issue in data envelopment analysis (DEA). This paper develops an integrated approach for ranking DMUs in DEA cooperative game, where DMUs are evaluated according to their Shapley values. For this purpose, a new characteristic function with DMUs is firstly defined; then, both aggressive and benevolent model formulations, which corresponding to aggressive or benevolent strategy in cooperative game, are utilized to obtain cross-efficiency scores of DMUs. Subsequently, the Shapley values are calculated in terms of the cross-efficiency scores by a simple formulation. An empirical study concerning assessment of nine container ports in China is examined using the developed approach. Comparisons and analyses with previous similar methods are also discussed.