The common revenue allocation based on modified Shapley value and DEA cross-efficiency

How to design a fair and reasonable allocation plan for the common revenue of the alliance is considered in this paper. We regard the common revenue to be allocated as an exogenous variable which will not participate in the subsequent production process. The production organizations can cooperate with each other and form alliances. As the DEA cross-efficiency combines self- and peer-evaluation mechanisms, and the cooperative game allows fair negotiation among participants, we combine the cross-efficiency with the cooperative game theory and construct the modified Shapley value to reflect the contribution of the evaluated participant to the alliance. In addition, for each participant, both the optimistic and the pessimistic modified Shapley values are considered, and thus the upper and lower bounds of the allocation revenue are obtained, correspondingly. A numerical example is presented to illustrate the operation procedure. Finally, we apply the approach to an empirical application concerning a city commercial bank with 18 branches in China.