IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v43y2021i4d10.1007_s00291-021-00643-y.html
   My bibliography  Save this article

Fixed cost allocation in two-stage system using DEA from a noncooperative view

Author

Listed:
  • Qingxian An

    (Central South University)

  • Ping Wang

    (Central South University)

  • Honglin Yang

    (Hunan University)

  • Zongrun Wang

    (Central South University)

Abstract

This paper uses the data envelopment analysis (DEA) approach to solve the issue of allocating fixed costs among a set of decision-making units (DMUs) with two-stage network structure. Fixed cost allocation is a prominent issue that is encountered by organizations, and it is one of the most important applications of DEA. It exists not only in single-stage systems but in two-stage network systems, such as bank systems in real situations, which comprises the deposits process and lending process. However, branch banks often compete with one another out of self-interest. The objective of this paper is to design a fair allocation scheme for two-stage network systems and considering the noncooperative game relationship among DMUs. The idea of satisfaction degree and noncooperative game theory is integrated into the proposed allocation model. In the noncooperative framework, we define a DMU’s payoff as the product of two substage satisfaction degree, and every member is noncooperative and selfishly seeks to maximize its own payoff. The allocation plan to DMUs and substages is determined by the final competition payoff. A real case is analyzed to illustrate the applicability of the proposed approaches.

Suggested Citation

  • Qingxian An & Ping Wang & Honglin Yang & Zongrun Wang, 2021. "Fixed cost allocation in two-stage system using DEA from a noncooperative view," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1077-1102, December.
    • Handle: RePEc:spr:orspec:v:43:y:2021:i:4:d:10.1007_s00291-021-00643-y
    DOI: 10.1007/s00291-021-00643-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-021-00643-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00291-021-00643-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wu, Jie & Zhu, Qingyuan & Ji, Xiang & Chu, Junfei & Liang, Liang, 2016. "Two-stage network processes with shared resources and resources recovered from undesirable outputs," European Journal of Operational Research, Elsevier, vol. 251(1), pages 182-197.
    2. Du, Juan & Liang, Liang & Chen, Yao & Cook, Wade D. & Zhu, Joe, 2011. "A bargaining game model for measuring performance of two-stage network structures," European Journal of Operational Research, Elsevier, vol. 210(2), pages 390-397, April.
    3. Cook, Wade D. & Kress, Moshe, 1999. "Characterizing an equitable allocation of shared costs: A DEA approach," European Journal of Operational Research, Elsevier, vol. 119(3), pages 652-661, December.
    4. Beasley, J. E., 2003. "Allocating fixed costs and resources via data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 147(1), pages 198-216, May.
    5. Gonzalez-Padron, Tracy & Akdeniz, M. Billur & Calantone, Roger J., 2014. "Benchmarking sales staffing efficiency in dealerships using extended data envelopment analysis," Journal of Business Research, Elsevier, vol. 67(9), pages 1904-1911.
    6. Chen, Yao & Du, Juan & David Sherman, H. & Zhu, Joe, 2010. "DEA model with shared resources and efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(1), pages 339-349, November.
    7. Lee, Chia-Yen, 2016. "Nash-profit efficiency: A measure of changes in market structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 659-663.
    8. M. Khodabakhshi & K. Aryavash, 2014. "The fair allocation of common fixed cost or revenue using DEA concept," Annals of Operations Research, Springer, vol. 214(1), pages 187-194, March.
    9. Ruiyue Lin & Zhiping Chen & Zongxin Li, 2016. "An equitable DEA-based approach for assigning fixed resources along with targets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1373-1381, November.
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    12. Menghan Chen & Sheng Ang & Lijing Jiang & Feng Yang, 2020. "Centralized resource allocation based on cross-evaluation considering organizational objective and individual preferences," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 529-565, June.
    13. Jiawen Liu & Yeming Gong & Joe Zhu & Jinlong Zhang, 2018. "A DEA-based approach for competitive environment analysis in global operations strategies," Post-Print hal-02312151, HAL.
    14. An, Qingxian & Yan, Hong & Wu, Jie & Liang, Liang, 2016. "Internal resource waste and centralization degree in two-stage systems: An efficiency analysis," Omega, Elsevier, vol. 61(C), pages 89-99.
    15. Lozano, S. & Villa, G. & Brännlund, R., 2009. "Centralised reallocation of emission permits using DEA," European Journal of Operational Research, Elsevier, vol. 193(3), pages 752-760, March.
    16. Liu, Jiawen & Gong, Yeming (Yale) & Zhu, Joe & Zhang, Jinlong, 2018. "A DEA-based approach for competitive environment analysis in global operations strategies," International Journal of Production Economics, Elsevier, vol. 203(C), pages 110-123.
    17. Jiasen Sun & Yelin Fu & Xiang Ji & Ray Y. Zhong, 2017. "Allocation of emission permits using DEA-game-theoretic model," Operational Research, Springer, vol. 17(3), pages 867-884, October.
    18. Feng Li & Ali Emrouznejad & Guo-liang Yang & Yongjun Li, 2020. "Carbon emission abatement quota allocation in Chinese manufacturing industries: An integrated cooperative game data envelopment analysis approach," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(8), pages 1259-1288, August.
    19. Guo, Chuanyin & Zhu, Joe, 2017. "Non-cooperative two-stage network DEA model: Linear vs. parametric linear," European Journal of Operational Research, Elsevier, vol. 258(1), pages 398-400.
    20. Mahdiloo, Mahdi & Ngwenyama, Ojelanki & Scheepers, Rens & Tamaddoni, Ali, 2018. "Managing emissions allowances of electricity producers to maximize CO2 abatement: DEA models for analyzing emissions and allocating emissions allowances," International Journal of Production Economics, Elsevier, vol. 205(C), pages 244-255.
    21. Tao Ding & Ya Chen & Huaqing Wu & Yuqi Wei, 2018. "Centralized fixed cost and resource allocation considering technology heterogeneity: a DEA approach," Annals of Operations Research, Springer, vol. 268(1), pages 497-511, September.
    22. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    23. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    24. Weiwei Zhu & Qian Zhang & Haiqing Wang, 2019. "Fixed costs and shared resources allocation in two-stage network DEA," Annals of Operations Research, Springer, vol. 278(1), pages 177-194, July.
    25. Cook, Wade D. & Zhu, Joe & Bi, Gongbing & Yang, Feng, 2010. "Network DEA: Additive efficiency decomposition," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1122-1129, December.
    26. 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, vol. 197(1), pages 389-401, August.
    27. Chaoqun Ma & Debin Liu & Zhongbao Zhou & Wei Zhao & Wenbin Liu, 2014. "Game Cross Efficiency for Systems with Two-Stage Structures," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, March.
    28. M. C. Gouveia & L. C. Dias & C. H. Antunes & M. A. Mota & E. M. Duarte & E. M. Tenreiro, 2016. "An application of value-based DEA to identify the best practices in primary health care," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 743-767, July.
    29. Yongjun Li & Feng Li & Ali Emrouznejad & Liang Liang & Qiwei Xie, 2019. "Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game," Annals of Operations Research, Springer, vol. 274(1), pages 373-394, March.
    30. Liang Liang & Wade D. Cook & Joe Zhu, 2008. "DEA models for two‐stage processes: Game approach and efficiency decomposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 643-653, October.
    31. Yu, Ming-Miin & Chen, Li-Hsueh & Hsiao, Bo, 2016. "A fixed cost allocation based on the two-stage network data envelopment approach," Journal of Business Research, Elsevier, vol. 69(5), pages 1817-1822.
    32. Chia -Yen Lee & Andrew L. Johnson, 2015. "Measuring Efficiency in Imperfectly Competitive Markets: An Example of Rational Inefficiency," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 702-722, February.
    33. Feng Li & Jian Song & Alexandre Dolgui & Liang Liang, 2017. "Using common weights and efficiency invariance principles for resource allocation and target setting," International Journal of Production Research, Taylor & Francis Journals, vol. 55(17), pages 4982-4997, September.
    34. Yang, Zhihua & Zhang, Qianwei, 2015. "Resource allocation based on DEA and modified Shapley value," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 280-286.
    35. A Mostafaee, 2013. "An equitable method for allocating fixed costs by using data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(3), pages 326-335, March.
    36. Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Majid Azadi & Balal Karimi & William Ho & Reza Farzipoor Saen, 2022. "Assessing green performance of power plants by multiple hybrid returns to scale technologies," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1177-1211, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. An, Qingxian & Wang, Ping & Emrouznejad, Ali & Hu, Junhua, 2020. "Fixed cost allocation based on the principle of efficiency invariance in two-stage systems," European Journal of Operational Research, Elsevier, vol. 283(2), pages 662-675.
    2. Li, Feng & Zhu, Qingyuan & Chen, Zhi, 2019. "Allocating a fixed cost across the decision making units with two-stage network structures," Omega, Elsevier, vol. 83(C), pages 139-154.
    3. Yang, Jiawei & Li, Dan & Li, Yongjun, 2024. "A generalized data envelopment analysis approach for fixed cost allocation with preference information," Omega, Elsevier, vol. 122(C).
    4. Feng Li & Qingyuan Zhu & Liang Liang, 2019. "A new data envelopment analysis based approach for fixed cost allocation," Annals of Operations Research, Springer, vol. 274(1), pages 347-372, March.
    5. Tatiana Bencova & Andrea Bohacikova, 2022. "DEA in Performance Measurement of Two-Stage Processes: Comparative Overview of the Literature," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 5, pages 111-129.
    6. An, Qingxian & Tao, Xiangyang & Xiong, Beibei & Chen, Xiaohong, 2022. "Frontier-based incentive mechanisms for allocating common revenues or fixed costs," European Journal of Operational Research, Elsevier, vol. 302(1), pages 294-308.
    7. Li, Yongjun & Lin, Lin & Dai, Qianzhi & Zhang, Linda, 2020. "Allocating common costs of multinational companies based on arm's length principle and Nash non-cooperative game," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1002-1010.
    8. Ang, Sheng & Liu, Pei & Yang, Feng, 2020. "Intra-Organizational and inter-organizational resource allocation in two-stage network systems," Omega, Elsevier, vol. 91(C).
    9. Xie, Qiwei & Xu, Qifan & Zhu, Da & Rao, Kaifeng & Dai, Qianzhi, 2020. "Fair allocation of wastewater discharge permits based on satisfaction criteria using data envelopment analysis," Utilities Policy, Elsevier, vol. 66(C).
    10. Mehdi Soltanifar & Farhad Hosseinzadeh Lotfi & Hamid Sharafi & Sebastián Lozano, 2022. "Resource allocation and target setting: a CSW–DEA based approach," Annals of Operations Research, Springer, vol. 318(1), pages 557-589, November.
    11. Yongjun Li & Feng Li & Ali Emrouznejad & Liang Liang & Qiwei Xie, 2019. "Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game," Annals of Operations Research, Springer, vol. 274(1), pages 373-394, March.
    12. Yu, Ming-Miin & Chen, Li-Hsueh & Hsiao, Bo, 2016. "A fixed cost allocation based on the two-stage network data envelopment approach," Journal of Business Research, Elsevier, vol. 69(5), pages 1817-1822.
    13. Xiong, Xi & Yang, Guo-liang & Zhou, De-qun & Wang, Zi-long, 2022. "How to allocate multi-period research resources? Centralized resource allocation for public universities in China using a parallel DEA-based approach," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    14. Xi Jin & Bin Zou & Chan Wang & Kaifeng Rao & Xiaowen Tang, 2019. "Carbon Emission Allocation in a Chinese Province-Level Region Based on Two-Stage Network Structures," Sustainability, MDPI, vol. 11(5), pages 1-24, March.
    15. Lim, Dong-Joon & Kim, Moon-Su, 2022. "Measuring dynamic efficiency with variable time lag effects," Omega, Elsevier, vol. 108(C).
    16. Tao Ding & Ya Chen & Huaqing Wu & Yuqi Wei, 2018. "Centralized fixed cost and resource allocation considering technology heterogeneity: a DEA approach," Annals of Operations Research, Springer, vol. 268(1), pages 497-511, September.
    17. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    18. Chu, Junfei & Hou, Tianteng & Li, Feng & Yuan, Zhe, 2024. "Dynamic bargaining game DEA carbon emissions abatement allocation and the Nash equilibrium," Energy Economics, Elsevier, vol. 134(C).
    19. Weiwei Zhu & Qian Zhang & Haiqing Wang, 2019. "Fixed costs and shared resources allocation in two-stage network DEA," Annals of Operations Research, Springer, vol. 278(1), pages 177-194, July.
    20. Li, Feng & Zhang, Danlu & Zhang, Jinyu & Kou, Gang, 2022. "Measuring the energy production and utilization efficiency of Chinese thermal power industry with the fixed-sum carbon emission constraint," International Journal of Production Economics, Elsevier, vol. 252(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:orspec:v:43:y:2021:i:4:d:10.1007_s00291-021-00643-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.