基于DEA联盟博弈核仁解的固定成本分摊方法研究

The Methodological Study of Allocating the Fixed Cost Based on the Nucleolus in Data Envelopment Analysis and Cooperative Game

本文结合DEA(Data Envelopment Analysis)和联盟博弈理论研究了固定成本分摊问题。本文首先证明了在固定成本作为决策单元(Decision Making Unit,DMU)新投入要素的条件下,那么DMU个体和整体将同为DEA有效,在此结论的基础上,本文结合联盟博弈理论,定义了联盟博弈的特征函数,提出了基于核仁解的固定成本分摊模型,并给出了相应的求解算法,最终通过算例说明了本文方法的合理性和求解算法的可行性。

Combining Data Envelopment Analysis and cooperative game theory, this paper has studied how to allocate the fixed cost among decision making units （DMU）. Firstly,it has proven that all DMU individuals and collectivity are DEA efficient, if the fixed cost can be treated as an additional input to DMUs. Then, combining the conclusion with cooperative game, it defines characteristic function, and proposes a nucleolus-based fixed cost allocation model, as well as its algorithms. Finally,a numerical experiment has shown that the proposed approach is reasonable and its algorithms are feasible.