IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v283y2020i2p662-675.html
   My bibliography  Save this article

Fixed cost allocation based on the principle of efficiency invariance in two-stage systems

Author

Listed:
  • An, Qingxian
  • Wang, Ping
  • Emrouznejad, Ali
  • Hu, Junhua

Abstract

Fixed cost allocation among groups of entities is a prominent issue in numerous organisations. Addressing this issue has become one of the most important topics of the data envelopment analysis (DEA) methodology. In this study, we propose a fixed cost allocation approach for basic two-stage systems based on the principle of efficiency invariance and then extend it to general two-stage systems. Fixed cost allocation in cooperative and noncooperative scenarios are investigated to develop the related allocation plans for two-stage systems. The model of fixed cost allocation under the overall condition of efficiency invariance is first developed when the two stages have a cooperative relationship. Then, the model of fixed cost allocation under the divisional condition of efficiency invariance wherein the two stages have a noncooperative relationship is studied. Finally, the validation of the proposed approach is demonstrated by a real application of 24 nonlife insurance companies, in which a comparative analysis with other allocation approaches is included.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:2:p:662-675
    DOI: 10.1016/j.ejor.2019.11.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309427
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.11.031?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. Du, Juan & Cook, Wade D. & Liang, Liang & Zhu, Joe, 2014. "Fixed cost and resource allocation based on DEA cross-efficiency," European Journal of Operational Research, Elsevier, vol. 235(1), pages 206-214.
    2. 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.
    3. 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.
    4. Emrouznejad, Ali & Yang, Guo-liang, 2018. "A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 4-8.
    5. Dariush Khezrimotlagh & Yao Chen, 2018. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 217-234, Springer.
    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. 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.
    8. 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.
    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. Joe Zhu, 2014. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 4, pages 61-92, Springer.
    13. Li, Haitao & Chen, Chialin & Cook, Wade D. & Zhang, Jinlong & Zhu, Joe, 2018. "Two-stage network DEA: Who is the leader?," Omega, Elsevier, vol. 74(C), pages 15-19.
    14. Cook, Wade D. & Hababou, Moez, 2001. "Sales performance measurement in bank branches," Omega, Elsevier, vol. 29(4), pages 299-307, August.
    15. 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.
    16. Jie Wu & Jun-Fei Chu & Liang Liang, 2016. "Target setting and allocation of carbon emissions abatement based on DEA and closest target: an application to 20 APEC economies," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(1), pages 279-296, November.
    17. 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.
    18. 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.
    19. 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.
    20. Li, Yongjun & Chen, Yao & Liang, Liang & Xie, Jianhui, 2012. "DEA models for extended two-stage network structures," Omega, Elsevier, vol. 40(5), pages 611-618.
    21. 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.
    22. 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.
    23. 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.
    24. Li, Yongjun & Yang, Min & Chen, Ya & Dai, Qianzhi & Liang, Liang, 2013. "Allocating a fixed cost based on data envelopment analysis and satisfaction degree," Omega, Elsevier, vol. 41(1), pages 55-60.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. Gholam Reza Jahanshahloo & Jafar Sadeghi & Mohammad Khodabakhshi, 2017. "Proposing a method for fixed cost allocation using DEA based on the efficiency invariance and common set of weights principles," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 223-240, April.
    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. Wang, Miao & Feng, Chao, 2021. "The consequences of industrial restructuring, regional balanced development, and market-oriented reform for China's carbon dioxide emissions: A multi-tier meta-frontier DEA-based decomposition analysi," Technological Forecasting and Social Change, Elsevier, vol. 164(C).
    2. Feng Yang & Ruochen Hu & Qiong Xia & Dawei Wang, 2024. "A DEA-based method of watershed ecological compensation allocation and liability sharing and its application: a case study of the Xin’an River," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(11), pages 28161-28186, November.
    3. Xu, Guangcheng & Wu, Jie & Zhu, Qingyuan & Pan, Yinghao, 2024. "Fixed cost allocation based on data envelopment analysis from inequality aversion perspectives," European Journal of Operational Research, Elsevier, vol. 313(1), pages 281-295.
    4. Yu Shi & Anyu Yu & Huong Ngo Higgins & Joe Zhu, 2021. "Shared and unsplittable performance links in network DEA," Annals of Operations Research, Springer, vol. 303(1), pages 507-528, August.
    5. Yongjun Li & Wenhui Hou & Weiwei Zhu & Feng Li & Liang Liang, 2021. "Provincial carbon emission performance analysis in China based on a Malmquist data envelopment analysis approach with fixed-sum undesirable outputs," Annals of Operations Research, Springer, vol. 304(1), pages 233-261, September.
    6. Dariush Akbarian, 2021. "Network DEA based on DEA-ratio," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.
    7. Dai, Qianzhi & Li, Yongjun & Lei, Xiyang & Wu, Dengsheng, 2021. "A DEA-based incentive approach for allocating common revenues or fixed costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 675-686.
    8. Pan, Yuling & Dong, Feng, 2022. "Design of energy use rights trading policy from the perspective of energy vulnerability," Energy Policy, Elsevier, vol. 160(C).
    9. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.
    10. 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.

    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. 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.
    2. 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.
    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. 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.
    5. 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.
    6. Chu, Junfei & Wu, Jie & Chu, Chengbin & Zhang, Tinglong, 2020. "DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches," Omega, Elsevier, vol. 94(C).
    7. 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.
    8. Dai, Qianzhi & Li, Yongjun & Lei, Xiyang & Wu, Dengsheng, 2021. "A DEA-based incentive approach for allocating common revenues or fixed costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 675-686.
    9. 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.
    10. 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).
    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. 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.
    13. 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.
    14. Yu, Ming-Miin & Chen, Li-Hsueh & Hsiao, Bo, 2018. "A performance-based subsidy allocation of ferry transportation: A data envelopment approach," Transport Policy, Elsevier, vol. 68(C), pages 13-19.
    15. Jianhui Xie & Qiwei Xie & Yongjun Li & Liang Liang, 2021. "Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique," Annals of Operations Research, Springer, vol. 304(1), pages 453-480, September.
    16. 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.
    17. Chao, Shih-Liang & Yu, Ming-Miin, 2022. "Applying data envelopment analysis to allocate incentive bonuses for container terminal operators," Transport Policy, Elsevier, vol. 125(C), pages 231-240.
    18. Xu, Guangcheng & Wu, Jie & Zhu, Qingyuan & Pan, Yinghao, 2024. "Fixed cost allocation based on data envelopment analysis from inequality aversion perspectives," European Journal of Operational Research, Elsevier, vol. 313(1), pages 281-295.
    19. 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.
    20. 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).

    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:eee:ejores:v:283:y:2020:i:2:p:662-675. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.