In this paper, the fixed cost allocation problem among the decision making units (DMU) with two stages is considered. First, the fixed cost is treated as an additional input to DMUs, and an additive two-stage DEA model is established. Then, some important theorems are proven:1. each DMU could find at least one allocation plan to make its total and each stage Pareto efficient; 2. there is at least one allocation plan for all DMUs and their stages to be Pareto efficient under a set of common weight; 3. the efficient fixed cost allocation set is provided. These theorems are also founded when it is expanded to the two-stage system with shared inputs. In order to obtain an equitable allocation, the satisfaction degree of each DMU's stage is defined. Through maximizing the minimal satisfaction degree, the final allocation plan is gotten. The numerical example shows that our approach is feasible and valid. Since the efficiency and fairness is considered together, the fixed cost allocation obtained from our approach is fair and valid. Our approach can give managers supports when they face cost allocation problems.
ZHANG Ran, RAN Lun, DU Tao, LI Jin-lin
. A Fixed Cost Allocation Based on Two-stage DEA and Satisfaction Degree[J]. Chinese Journal of Management Science, 2019
, 27(2)
: 138
-149
.
DOI: 10.16381/j.cnki.issn1003-207x.2019.02.014
[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 2(6):429-444.
[2] Cook W D, Kress M. Characterizing an equitable allocation of shared costs:A DEA approach[J]. European Journal of Operational Research, 1999, 119(3):652-661.
[3] Beasley J E. Allocating fixed costs and resources via data envelopment analysis[J]. European Journal of Operational Research, 2003, 147(1):198-216.
[4] 李勇军,梁樑.一种基于DEA与Nash讨价还价博弈的固定成本分摊方法[J]. 系统工程, 2008, 26(6):73-77.
[5] 李勇军, 梁樑, 凌六一. 基于DEA联盟博弈核仁解的固定成本分摊方法研究[J]. 中国管理科学, 2009, 17(1):58-63.
[6] Li Yongjun, Yang Min, Chen Ya, et al. Allocating a fixed cost based on data envelopment analysis and satisfaction degree[J]. Omega, 2013, 41(1):55-60.
[7] Du Juan, Cook W D, Liang Liang, et al. Fixed cost and resource allocation based on DEA cross-efficiency[J]. European Journal of Operational Research, 2014, 235(1):206-214.
[8] Cook W D, Zhu J. Allocation of shared costs among decision making units:A DEA approach[J].Computers & Operations Research, 2005, 32(8):2171-2178.
[9] 雷西洋, 戴前智, 李勇军,等. 考虑系统内部平行结构的DEA资源分摊方法[J]. 中国管理科学, 2015, 23(1):50-55.
[10] Kao C, Hwang S N. Efficiency decomposition in two-stage data envelopment analysis:An application to non-life insurance companies in Taiwan[J]. European Journal of Operational Research, 2008, 185(1):418-429.
[11] Chen Yao, Cook W D, Li Ning, et al. Additive efficiency decomposition in two-stage DEA[J]. European Journal of Operational Research, 2009, 196(3):1170-1176.
[12] 毕功兵, 梁樑, 杨锋. 两阶段生产系统的DEA效率评价模型[J]. 中国管理科学, 2007, 15(2):92-96.
[13] 孙玉华, 曾庆铎. 基于DEA的二阶段网络系统的固定成本分摊方法[J]. 经济数学, 2013,30(1):33-36.
[14] Yu M M, Chen L H, Hsiao B. A fixed cost allocation based on the two-stage network data envelopment approach[J]. Journal of Business Research, 2016, 69(5):1817-1822.
[15] Golany B, Tamir E. Evaluating efficiency-effectiveness-equality trade-offs:A data envelopment analysis approach[J]. Management Science, 1995, 41(7):1172-1184.
[16] Chen Yao, Du Juan, Sherman H D, et al. DEA model with shared resources and efficiency decomposition[J]. European Journal of Operational Research, 2010, 207(1):339-349.
