Allocating the fixed cost based on data envelopment analysis in view of the Shapley value

This paper considers fixed cost allocation in view of cooperative game theory and proposes an approach based on data envelopment analysis while incorporating the perspectives of coalition efficiency and the Shapley value. To do this, we first build two models to evaluate coalition efficiencies before and after cost allocation, and we prove that all coalitions can be efficient after fixed cost allocation. Then, following the premise that each coalition makes itself efficient without reducing the efficiencies of other decision-making units' preallocation efficiency, we propose a model that determines the acceptable range of each coalition's allocated fixed cost. Furthermore, a model is constructed to determine the final cost allocation based on three principles: efficiency, monotonicity, and similarity. Moreover, the Shapley value is employed to obtain the cost allocated to each decision-making unit (DMU). The proposed approach considers the relationships among DMUs across their forming coalitions to determine their interaction types and then generates a fixed cost allocation result that possesses the features of the Shapley value. This process makes the fixed cost allocation more acceptable. Finally, a simple numerical example and an empirical case are provided to illustrate the calculation process of the proposed approach and compare our approach with the traditional methods.