IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v114y2023ics0305048322001359.html
   My bibliography  Save this article

Bargaining approach for efficiency assessment and target setting with fixed-sum variables

Author

Listed:
  • Lozano, Sebastián

Abstract

There are many Data Envelopment Analysis (DEA) applications in which an input or output variable is such that the total amount for all the units in the sample is fixed. In this paper, such situations are modelled as a bargaining problem in which the players correspond to each of the variables for each of the units. All the players try to improve their utility as much as possible, where utility improvement implies a reduction in the case of an input variable or an undesirable output and an increase in the case of a desirable output. The Feasible Set of the bargaining problem derives from the corresponding fixed-sum DEA technology. A centralized DEA model is formulated for computing the Nash bargaining solution, which determines the efficient targets of all the units. From these targets, a modified Enhanced Russell Graph efficiency measure (ERM) is proposed to compute the corresponding efficiency scores. The proposed approach has been validated on different datasets corresponding to a variety of situations involving fixed-sum variables.

Suggested Citation

  • Lozano, Sebastián, 2023. "Bargaining approach for efficiency assessment and target setting with fixed-sum variables," Omega, Elsevier, vol. 114(C).
    • Handle: RePEc:eee:jomega:v:114:y:2023:i:c:s0305048322001359
    DOI: 10.1016/j.omega.2022.102728
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048322001359
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2022.102728?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. Contreras, I. & Lozano, S., 2020. "Allocating additional resources to public universities. A DEA bargaining approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    2. Li, Yongjun & Liu, Jin & Ang, Sheng & Yang, Feng, 2021. "Performance evaluation of two-stage network structures with fixed-sum outputs: An application to the 2018winter Olympic Games," Omega, Elsevier, vol. 102(C).
    3. Wang, Ke & Zhang, Xian & Wei, Yi-Ming & Yu, Shiwei, 2013. "Regional allocation of CO2 emissions allowance over provinces in China by 2020," Energy Policy, Elsevier, vol. 54(C), pages 214-229.
    4. I. Contreras & S. Lozano & M. A. Hinojosa, 2021. "A DEA cross-efficiency approach based on bargaining theory," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(5), pages 1156-1167, May.
    5. E G Gomes & M P E Lins, 2008. "Modelling undesirable outputs with zero sum gains data envelopment analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 616-623, May.
    6. Zhu, Qingyuan & Aparicio, Juan & Li, Feng & Wu, Jie & Kou, Gang, 2022. "Determining closest targets on the extended facet production possibility set in data envelopment analysis: Modeling and computational aspects," European Journal of Operational Research, Elsevier, vol. 296(3), pages 927-939.
    7. Lins, Marcos P. Estellita & Gomes, Eliane G. & Soares de Mello, Joao Carlos C. B. & Soares de Mello, Adelino Jose R., 2003. "Olympic ranking based on a zero sum gains DEA model," European Journal of Operational Research, Elsevier, vol. 148(2), pages 312-322, July.
    8. Asmild, Mette & Paradi, Joseph C. & Pastor, Jesus T., 2009. "Centralized resource allocation BCC models," Omega, Elsevier, vol. 37(1), pages 40-49, February.
    9. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    10. Yang, Min & Li, Yong Jun & Liang, Liang, 2015. "A generalized equilibrium efficient frontier data envelopment analysis approach for evaluating DMUs with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 246(1), pages 209-217.
    11. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    12. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    13. Sun, Jiasen & Li, Guo & Wang, Zhaohua, 2018. "Optimizing China’s energy consumption structure under energy and carbon constraints," Structural Change and Economic Dynamics, Elsevier, vol. 47(C), pages 57-72.
    14. Sebastián Lozano & Gabriel Villa, 2004. "Centralized Resource Allocation Using Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 22(1), pages 143-161, July.
    15. Zhu, Qingyuan & Li, Xingchen & Li, Feng & Wu, Jie & Zhou, Dequn, 2020. "Energy and environmental efficiency of China's transportation sectors under the constraints of energy consumption and environmental pollutions," Energy Economics, Elsevier, vol. 89(C).
    16. Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2019. "Extending the bargaining approach to DEA target setting," Omega, Elsevier, vol. 85(C), pages 94-102.
    17. Yang, Feng & Wu, Desheng Dash & Liang, Liang & O'Neill, Liam, 2011. "Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 212(3), pages 560-569, August.
    18. J-L Hu & C-Y Fang, 2010. "Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 647-657, April.
    19. Yang, Min & Li, Yongjun & Chen, Ya & Liang, Liang, 2014. "An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 239(2), pages 479-489.
    20. Jie Wu & Panpan Xia & Qingyuan Zhu & Junfei Chu, 2019. "Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output," Annals of Operations Research, Springer, vol. 275(2), pages 731-749, April.
    21. Hamzeh Amirteimoori & Alireza Amirteimoori & Mahdi Karbasian, 2020. "Performance measurement of gas companies with fixed-sum inputs: a DEA-based model," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 47(7), pages 1591-1603, April.
    22. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    23. Lozano, Sebastián, 2016. "Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector," Omega, Elsevier, vol. 60(C), pages 73-84.
    24. Cecilio Mar-Molinero & Diego Prior & Maria-Manuela Segovia & Fabiola Portillo, 2014. "On centralized resource utilization and its reallocation by using DEA," Annals of Operations Research, Springer, vol. 221(1), pages 273-283, October.
    25. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    26. 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.
    27. Gongbing Bi & Chenpeng Feng & Jingjing Ding & Liang Liang & Feng Chu, 2014. "The linear formulation of the ZSG-DEA models with different production technologies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(8), pages 1202-1211, August.
    28. Lei Fang, 2016. "A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 412-420, March.
    29. Alireza Amirteimoori & Simin Masrouri & Feng Yang & Sohrab Kordrostami, 2017. "Context-based competition strategy and performance analysis with fixed-sum outputs: an application to banking sector," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1461-1469, November.
    30. Chen, Lifan & Guo, Mengyu & Li, Yongjun & Liang, Liang & Salo, Ahti, 2021. "Efficiency intervals, rank intervals and dominance relations of decision-making units with fixed-sum outputs," European Journal of Operational Research, Elsevier, vol. 292(1), pages 238-249.
    31. Qingyuan Zhu & Jie Wu & Malin Song & Liang Liang, 2017. "A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1483-1490, December.
    32. Tingting Liu & Zichen Zheng & Yuneng Du, 2021. "Evaluation on regional science and technology resources allocation in China based on the zero sum gains data envelopment analysis," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1729-1737, August.
    33. Trevor Collier & Andrew L. Johnson & John Ruggiero, 2011. "Measuring Technical Efficiency in Sports," Journal of Sports Economics, , vol. 12(6), pages 579-598, December.
    34. Chenpeng Feng & Feng Chu & Nan Zhou & Gongbing Bi & Jingjing Ding, 2019. "Performance evaluation and quota allocation for multiple undesirable outputs based on the uniform frontier," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(3), pages 472-486, March.
    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. Sebastián Lozano & Gabriel Villa, 2023. "Multiobjective centralized DEA approach to Tokyo 2020 Olympic Games," Annals of Operations Research, Springer, vol. 322(2), pages 879-919, March.
    2. Yu, Ming-Miin & Rakshit, Ipsita, 2023. "Target setting for airlines incorporating CO2 emissions: The DEA bargaining approach," Journal of Air Transport Management, Elsevier, vol. 108(C).

    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. Bouzidis, Thanasis & Karagiannis, Giannis, 2022. "An alternative ranking of DMUs performance for the ZSG-DEA model," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    2. Thanasis Bouzidis & Giannis Karagiannis, 2021. "An Alternative Ranking of DMUs Performance for the ZGS-DEA Model," Discussion Paper Series 2021_12, Department of Economics, University of Macedonia, revised Oct 2021.
    3. Yu, Shasha & Lei, Ming & Deng, Honghui, 2023. "Evaluation to fixed-sum-outputs DMUs by non-oriented equilibrium efficient frontier DEA approach with Nash bargaining-based selection," Omega, Elsevier, vol. 115(C).
    4. 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).
    5. Ding, Tao & Zhang, Yun & Zhang, Danlu & Li, Feng, 2023. "Performance evaluation of Chinese research universities: A parallel interactive network DEA approach with shared and fixed sum inputs," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    6. Lozano, Sebastián & Contreras, Ignacio, 2022. "Centralised resource allocation using Lexicographic Goal Programming. Application to the Spanish public university system," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    7. Xi Xiong & Guo-liang Yang & Kai-di Liu & De-qun Zhou, 2022. "A proposed fixed-sum carryovers reallocation DEA approach for social scientific resources of Chinese public universities," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(7), pages 4097-4121, July.
    8. 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.
    9. Zhu, Qingyuan & Li, Xingchen & Li, Feng & Wu, Jie & Zhou, Dequn, 2020. "Energy and environmental efficiency of China's transportation sectors under the constraints of energy consumption and environmental pollutions," Energy Economics, Elsevier, vol. 89(C).
    10. Thanasis Bouzidis & Giannis Karagiannis, 2022. "Extending the Zero-Sum Gains Data Envelopment Analysis Model," Discussion Paper Series 2022_06, Department of Economics, University of Macedonia, revised Aug 2022.
    11. Thanasis Bouzidis & Giannis Karagiannis, 2022. "Extending the zero-sum gains data envelopment analysis model," Journal of Productivity Analysis, Springer, vol. 58(2), pages 171-184, December.
    12. Sebastián Lozano & Gabriel Villa, 2023. "Multiobjective centralized DEA approach to Tokyo 2020 Olympic Games," Annals of Operations Research, Springer, vol. 322(2), pages 879-919, March.
    13. Jie Wu & Panpan Xia & Qingyuan Zhu & Junfei Chu, 2019. "Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output," Annals of Operations Research, Springer, vol. 275(2), pages 731-749, April.
    14. Lucas Assunção & Andréa Cynthia Santos & Thiago F. Noronha & Rafael Andrade, 2021. "Improving logic-based Benders' algorithms for solving min-max regret problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 23-57.
    15. Thanasis Bouzidis & Giannis Karagiannis, 2022. "A note on the zero-sum gains data envelopment analysis model," Operational Research, Springer, vol. 22(3), pages 1737-1758, July.
    16. Li, Yongjun & Liu, Jin & Ang, Sheng & Yang, Feng, 2021. "Performance evaluation of two-stage network structures with fixed-sum outputs: An application to the 2018winter Olympic Games," Omega, Elsevier, vol. 102(C).
    17. Tingting Liu & Zichen Zheng & Yuneng Du, 2021. "Evaluation on regional science and technology resources allocation in China based on the zero sum gains data envelopment analysis," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1729-1737, August.
    18. Contreras, I. & Lozano, S., 2020. "Allocating additional resources to public universities. A DEA bargaining approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    19. Qingyuan Zhu & Jie Wu & Malin Song & Liang Liang, 2017. "A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1483-1490, December.
    20. Alireza Amirteimoori & Simin Masrouri & Feng Yang & Sohrab Kordrostami, 2017. "Context-based competition strategy and performance analysis with fixed-sum outputs: an application to banking sector," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1461-1469, November.

    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:jomega:v:114:y:2023:i:c:s0305048322001359. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.