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Allocating a fixed cost based on data envelopment analysis and satisfaction degree

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  • Li, Yongjun
  • Yang, Min
  • Chen, Ya
  • Dai, Qianzhi
  • Liang, Liang
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    Abstract

    This paper uses the Data Envelopment Analysis (DEA) technique to solve the problem of allocating a fixed cost across a set of comparable decision making units (DMUs) in a fair way. It first investigates the effect of the fixed cost on each DMU and on the collection of DMUs. Next we prove that there exist some cost allocations which can make each DMU and the collection of DMUs efficient. We show that such a cost allocation is unique and equivalent to the proportional sharing method if the fixed cost allocation problem is a one-dimensional case. In a multidimensional case, the fixed cost allocations may not be unique. This paper defines the concept of satisfaction degree, and proposes a maxmin model and a corresponding algorithm to generate a unique fixed cost allocation. Finally, the proposed approach has been applied to a data set from prior literature.

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    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 41 (2013)
    Issue (Month): 1 ()
    Pages: 55-60

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    Handle: RePEc:eee:jomega:v:41:y:2013:i:1:p:55-60

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    Keywords: Data envelopment analysis (DEA); Cost allocation; Efficiency; Maxmin model; Satisfaction degree;

    References

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    1. Wang, Yun-Tong & Zhu, Daxin, 2002. "Ordinal proportional cost sharing," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 215-230, May.
    2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 1009-37, September.
    3. Moulin, Herve, 1994. "Serial Cost-Sharing of Excludable Public Goods," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 305-25, April.
    4. Li, Yongjun & Yang, Feng & Liang, Liang & Hua, Zhongsheng, 2009. "Allocating the fixed cost as a complement of other cost inputs: A DEA approach," European Journal of Operational Research, Elsevier, Elsevier, vol. 197(1), pages 389-401, August.
    5. Cook, Wade D. & Liang, Liang & Zhu, Joe, 2010. "Measuring performance of two-stage network structures by DEA: A review and future perspective," Omega, Elsevier, Elsevier, vol. 38(6), pages 423-430, December.
    6. Cook, Wade D. & Kress, Moshe, 1999. "Characterizing an equitable allocation of shared costs: A DEA approach," European Journal of Operational Research, Elsevier, Elsevier, vol. 119(3), pages 652-661, December.
    7. Beasley, J. E., 2003. "Allocating fixed costs and resources via data envelopment analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 147(1), pages 198-216, May.
    8. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, Elsevier, vol. 2(6), pages 429-444, November.
    9. Du, Juan & Liang, Liang & Chen, Yao & Bi, Gong-bing, 2010. "DEA-based production planning," Omega, Elsevier, Elsevier, vol. 38(1-2), pages 105-112, February.
    10. Wu, Jie & Liang, Liang & Chen, Yao, 2009. "DEA game cross-efficiency approach to Olympic rankings," Omega, Elsevier, Elsevier, vol. 37(4), pages 909-918, August.
    11. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, Elsevier, vol. 46(1-2), pages 73-91.
    12. Avkiran, Necmi K., 2011. "Association of DEA super-efficiency estimates with financial ratios: Investigating the case for Chinese banks," Omega, Elsevier, Elsevier, vol. 39(3), pages 323-334, June.
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