IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v52y2015icp92-100.html
   My bibliography  Save this article

Set-valued DEA production games

Author

Listed:
  • Lozano, S.
  • Hinojosa, M.A.
  • Mármol, A.M.

Abstract

In this paper, a generalization of the linear production model is considered on the basis of a DEA-inspired technology in which the maximization of the production levels is formulated as a multi-objective linear programming problem. When multiple decision-makers cooperate by pooling their resources and sharing their technologies in the production process, the final production must then be divided between the agents involved, and a multi-commodity game arises. Such a game is referred to as a set-valued DEA production game. It is shown that, by adopting two different excess functions to measure the dissatisfaction of the coalitions, two different core concepts emerge, namely the preference core and the dominance core. Moreover, we provide the procedure to determine allocations in the respective least cores and show how to compute the nucleolus in the case of the excess function leading to the preference core. Finally, the results are illustrated with a case study.

Suggested Citation

  • Lozano, S. & Hinojosa, M.A. & Mármol, A.M., 2015. "Set-valued DEA production games," Omega, Elsevier, vol. 52(C), pages 92-100.
    • Handle: RePEc:eee:jomega:v:52:y:2015:i:c:p:92-100
    DOI: 10.1016/j.omega.2014.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048314001236
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2014.10.002?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. J. Timmer & P. Borm & J. Suijs, 2000. "Linear Transformation of Products: Games and Economies," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 677-706, June.
    2. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    3. Fernandez, F. R. & Hinojosa, M. A. & Puerto, J., 2004. "Set-valued TU-games," European Journal of Operational Research, Elsevier, vol. 159(1), pages 181-195, November.
    4. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min & Lin, Bruce J.Y., 2013. "A survey of DEA applications," Omega, Elsevier, vol. 41(5), pages 893-902.
    5. Nishizaki, Ichiro & Sakawa, Masatoshi, 2001. "On computational methods for solutions of multiobjective linear production programming games," European Journal of Operational Research, Elsevier, vol. 129(2), pages 386-413, March.
    6. 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.
    7. K Tone, 2002. "A strange case of the cost and allocative efficiencies in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1225-1231, November.
    8. Tone, Kaoru & Tsutsui, Miki, 2010. "Dynamic DEA: A slacks-based measure approach," Omega, Elsevier, vol. 38(3-4), pages 145-156, June.
    9. Lozano, S., 2013. "DEA production games," European Journal of Operational Research, Elsevier, vol. 231(2), pages 405-413.
    10. Joe Zhu, 2014. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 1, pages 1-9, Springer.
    11. Rogge, Nicky & De Jaeger, Simon, 2013. "Measuring and explaining the cost efficiency of municipal solid waste collection and processing services," Omega, Elsevier, vol. 41(4), pages 653-664.
    12. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    13. Fukuyama, Hirofumi & Weber, William L., 2010. "A slacks-based inefficiency measure for a two-stage system with bad outputs," Omega, Elsevier, vol. 38(5), pages 398-409, October.
    14. Cook, Wade D. & Tone, Kaoru & Zhu, Joe, 2014. "Data envelopment analysis: Prior to choosing a model," Omega, Elsevier, vol. 44(C), pages 1-4.
    15. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    16. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2013. "Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA," European Journal of Operational Research, Elsevier, vol. 231(2), pages 443-451.
    17. Kao, Chiang & Liu, Shiang-Tai, 2014. "Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks," Omega, Elsevier, vol. 47(C), pages 90-98.
    18. Lozano, S. & Moreno, P. & Adenso-Díaz, B. & Algaba, E., 2013. "Cooperative game theory approach to allocating benefits of horizontal cooperation," European Journal of Operational Research, Elsevier, vol. 229(2), pages 444-452.
    19. Cook, Wade D. & Liang, Liang & Zhu, Joe, 2010. "Measuring performance of two-stage network structures by DEA: A review and future perspective," Omega, Elsevier, vol. 38(6), pages 423-430, December.
    20. Hinojosa, M.A. & Mármol, A.M., 2011. "Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences," Omega, Elsevier, vol. 39(2), pages 159-167, 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. Nishizaki, Ichiro & Hayashida, Tomohiro & Sekizaki, Shinya & Okabe, Junya, 2022. "Data envelopment analysis approaches for two-level production and distribution planning problems," European Journal of Operational Research, Elsevier, vol. 300(1), pages 255-268.
    2. M. G. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. A. Mosquera, 2020. "On benefits of cooperation under strategic power," Annals of Operations Research, Springer, vol. 288(1), pages 285-306, May.
    3. Zhang, Ganggang & Wu, Jie & Zhu, Qingyuan, 2020. "Performance evaluation and enrollment quota allocation for higher education institutions in China," Evaluation and Program Planning, Elsevier, vol. 81(C).
    4. Contreras, I. & Lozano, S., 2022. "Size efficiency, splits and merger gains, and centralized resource reallocation of Spanish public universities," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    5. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    6. Jie Wu & Qingyuan Zhu & Junfei Chu & Qingxian An & Liang Liang, 2016. "A DEA-based approach for allocation of emission reduction tasks," International Journal of Production Research, Taylor & Francis Journals, vol. 54(18), pages 5618-5633, September.
    7. An, Qingxian & Wen, Yao & Ding, Tao & Li, Yongli, 2019. "Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method," Omega, Elsevier, vol. 85(C), pages 16-25.
    8. Li, Yongjun & Xie, Jianhui & Wang, Meiqiang & Liang, Liang, 2016. "Super efficiency evaluation using a common platform on a cooperative game," European Journal of Operational Research, Elsevier, vol. 255(3), pages 884-892.

    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 & Wen, Yao & Ding, Tao & Li, Yongli, 2019. "Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method," Omega, Elsevier, vol. 85(C), pages 16-25.
    2. Simar, Leopold & Zelenyuk, Valentin, 2018. "Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores," LIDAM Discussion Papers ISBA 2018020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    4. Ruiz, José L. & Sirvent, Inmaculada, 2019. "Performance evaluation through DEA benchmarking adjusted to goals," Omega, Elsevier, vol. 87(C), pages 150-157.
    5. Avkiran, Necmi Kemal, 2015. "An illustration of dynamic network DEA in commercial banking including robustness tests," Omega, Elsevier, vol. 55(C), pages 141-150.
    6. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    7. Zha, Yong & Liang, Nannan & Wu, Maoguo & Bian, Yiwen, 2016. "Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach," Omega, Elsevier, vol. 60(C), pages 60-72.
    8. Kadziński, Miłosz & Labijak, Anna & Napieraj, Małgorzata, 2017. "Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports," Omega, Elsevier, vol. 67(C), pages 1-18.
    9. Park, Jaehun & Lee, Dongha & Zhu, Joe, 2014. "An integrated approach for ship block manufacturing process performance evaluation: Case from a Korean shipbuilding company," International Journal of Production Economics, Elsevier, vol. 156(C), pages 214-222.
    10. Toloo, Mehdi & Hančlová, Jana, 2020. "Multi-valued measures in DEA in the presence of undesirable outputs," Omega, Elsevier, vol. 94(C).
    11. Babak Daneshvar Rouyendegh & Asil Oztekin & Joseph Ekong & Ali Dag, 2019. "Measuring the efficiency of hospitals: a fully-ranking DEA–FAHP approach," Annals of Operations Research, Springer, vol. 278(1), pages 361-378, July.
    12. Kaffash, Sepideh & Azizi, Roza & Huang, Ying & Zhu, Joe, 2020. "A survey of data envelopment analysis applications in the insurance industry 1993–2018," European Journal of Operational Research, Elsevier, vol. 284(3), pages 801-813.
    13. Cook, Wade D. & Ruiz, José L. & Sirvent, Inmaculada & Zhu, Joe, 2017. "Within-group common benchmarking using DEA," European Journal of Operational Research, Elsevier, vol. 256(3), pages 901-910.
    14. Wei, Guiwu & Chen, Jian & Wang, Jiamin, 2014. "Stochastic efficiency analysis with a reliability consideration," Omega, Elsevier, vol. 48(C), pages 1-9.
    15. Dyckhoff, Harald & Souren, Rainer, 2022. "Integrating multiple criteria decision analysis and production theory for performance evaluation: Framework and review," European Journal of Operational Research, Elsevier, vol. 297(3), pages 795-816.
    16. Chowdhury, Hedayet & Zelenyuk, Valentin, 2016. "Performance of hospital services in Ontario: DEA with truncated regression approach," Omega, Elsevier, vol. 63(C), pages 111-122.
    17. Ruiyue Lin & Zhiping Chen & Qianhui Hu & Zongxin Li, 2017. "Dynamic network DEA approach with diversification to multi-period performance evaluation of funds," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 821-860, July.
    18. Tüselmann, Heinz & Sinkovics, Rudolf R. & Pishchulov, Grigory, 2016. "Revisiting the standing of international business journals in the competitive landscape," Journal of World Business, Elsevier, vol. 51(4), pages 487-498.
    19. González, Eduardo & Cárcaba, Ana & Ventura, Juan, 2015. "How car dealers adjust prices to reach the product efficiency frontier in the Spanish automobile market," Omega, Elsevier, vol. 51(C), pages 38-48.
    20. Färe, Rolf & Fukuyama, Hirofumi & Grosskopf, Shawna & Zelenyuk, Valentin, 2016. "Cost decompositions and the efficient subset," Omega, Elsevier, vol. 62(C), pages 123-130.

    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:52:y:2015:i:c:p:92-100. 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.