Group division based on common weights in cross efficiency evaluation

In the traditional cross efficiency procedure, each decision making unit (DMU) offers a set of selfish weights to maximise its own efficiency. However, it is often not easy to be accepted by all other decision making units (DMUs). Since the cross efficiency of a DMU not only has a significant relevance with its own evaluation but also with other peer DMUs' measurement, a DMU may choose to cooperate or compete with some other DMUs to obtain a higher cross efficiency. Secondary-goal strategies, such as benevolent and aggressive strategies, have been applied in groups in which the relationship between each DMU is determined. With the benevolent strategy, all of the DMUs are under the situations of cooperation while they will compete with each other with the aggressive strategy. Obviously in reality, there is a situation in which alliances are often uncertain. Pure aggressive or benevolent strategy may be not suitable for the case. To solve this problem, the current paper proposes a new cross efficiency approach based on a series of common weights of each two DMUs. An example is given to illustrate our method.