IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v77y2018icp180-188.html
   My bibliography  Save this article

Data envelopment analysis for bi-level systems with multiple followers

Author

Listed:
  • Zhou, Xiaoyang
  • Luo, Rui
  • Tu, Yan
  • Lev, Benjamin
  • Pedrycz, Witold

Abstract

This study aims to evaluate the performance of a bi-level system including two kinds of players: a leader positioned at the upper level and multiple followers located at the lower level. The overall system tries to use inputs to produce outputs in a cost-efficient way. However, each player in the bi-level system controls different decision variables and has varying objectives. Based on this, a novel bi-level data envelopment analysis model with multiple followers is developed, in order to evaluate the performance of overall bi-level system as well as each player in detail. Then the extended Kuhn–Tucker conditions are used to solve the proposed model. An illustrative example is presented to validate the proposed approach by evaluating supply chains with a single plant and two distribution centers. A comparative analysis is conducted to demonstrate that the developed model has stronger discriminating power and can provide more managerial insights. Several conclusions can be reached from this study: the lower level subsystem is cost-efficient if and only if every follower is cost-efficient, and the lower level cost efficiency lies between the smallest cost efficiency and the largest cost efficiency among all followers; being cost-efficient at both the upper level and the lower level results in an achievement of overall cost efficiency in a bi-level structure, and the overall cost efficiency falls in between the upper level and the lower level cost efficiencies.

Suggested Citation

  • Zhou, Xiaoyang & Luo, Rui & Tu, Yan & Lev, Benjamin & Pedrycz, Witold, 2018. "Data envelopment analysis for bi-level systems with multiple followers," Omega, Elsevier, vol. 77(C), pages 180-188.
    • Handle: RePEc:eee:jomega:v:77:y:2018:i:c:p:180-188
    DOI: 10.1016/j.omega.2017.06.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048317302918
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2017.06.007?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. Chen, Ci & Yan, Hong, 2011. "Network DEA model for supply chain performance evaluation," European Journal of Operational Research, Elsevier, vol. 213(1), pages 147-155, August.
    2. 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.
    3. 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.
    4. Despotis, Dimitris K. & Sotiros, Dimitris & Koronakos, Gregory, 2016. "A network DEA approach for series multi-stage processes," Omega, Elsevier, vol. 61(C), pages 35-48.
    5. Liang Liang & Feng Yang & Wade Cook & Joe Zhu, 2006. "DEA models for supply chain efficiency evaluation," Annals of Operations Research, Springer, vol. 145(1), pages 35-49, July.
    6. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    7. Liu, Wenbin & Zhou, Zhongbao & Ma, Chaoqun & Liu, Debin & Shen, Wanfang, 2015. "Two-stage DEA models with undesirable input-intermediate-outputs," Omega, Elsevier, vol. 56(C), pages 74-87.
    8. Calvete, Herminia I. & Galé, Carmen & Iranzo, José A., 2014. "Planning of a decentralized distribution network using bilevel optimization," Omega, Elsevier, vol. 49(C), pages 30-41.
    9. 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.
    10. Ray, Subhash, 2016. "Cost efficiency in an Indian bank branch network: A centralized resource allocation model," Omega, Elsevier, vol. 65(C), pages 69-81.
    11. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    12. Wu, Desheng Dash, 2010. "BiLevel programming Data Envelopment Analysis with constrained resource," European Journal of Operational Research, Elsevier, vol. 207(2), pages 856-864, December.
    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. Song, Xiaoling & Wang, Yudong & Zhang, Zhe & Shen, Charles & Peña-Mora, Feniosky, 2021. "Economic-environmental equilibrium-based bi-level dispatch strategy towards integrated electricity and natural gas systems," Applied Energy, Elsevier, vol. 281(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. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2020. "A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system," Omega, Elsevier, vol. 95(C).
    2. 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.
    3. Despotis, Dimitris K. & Koronakos, Gregory & Sotiros, Dimitris, 2016. "The “weak-link” approach to network DEA for two-stage processes," European Journal of Operational Research, Elsevier, vol. 254(2), pages 481-492.
    4. Galagedera, Don U.A. & Watson, John & Premachandra, I.M. & Chen, Yao, 2016. "Modeling leakage in two-stage DEA models: An application to US mutual fund families," Omega, Elsevier, vol. 61(C), pages 62-77.
    5. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    6. Mohammad Amirkhan & Hosein Didehkhani & Kaveh Khalili-Damghani & Ashkan Hafezalkotob, 2018. "Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1429-1467, September.
    7. Li, Wanghong & Li, Zhepeng & Liang, Liang & Cook, Wade D., 2017. "Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China," Socio-Economic Planning Sciences, Elsevier, vol. 60(C), pages 77-86.
    8. Huang, Chin-wei, 2018. "Assessing the performance of tourism supply chains by using the hybrid network data envelopment analysis model," Tourism Management, Elsevier, vol. 65(C), pages 303-316.
    9. AGRELL, Per & HATAMI-MARBINI, Adel, 2011. "Frontier-based performance analysis models for supply chain management; state of the art and research directions," LIDAM Discussion Papers CORE 2011069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Ang, Sheng & Liu, Pei & Yang, Feng, 2020. "Intra-Organizational and inter-organizational resource allocation in two-stage network systems," Omega, Elsevier, vol. 91(C).
    11. Khoveyni, Mohammad & Fukuyama, Hirofumi & Eslami, Robabeh & Yang, Guo-liang, 2019. "Variations effect of intermediate products on the second stage in two-stage processes," Omega, Elsevier, vol. 85(C), pages 35-48.
    12. Huang, Chin-wei & Ho, Foo Nin & Chiu, Yung-ho, 2014. "Measurement of tourist hotels׳ productive efficiency, occupancy, and catering service effectiveness using a modified two-stage DEA model in Taiwan," Omega, Elsevier, vol. 48(C), pages 49-59.
    13. Wade D. Cook & Chuanyin Guo & Wanghong Li & Zhepeng Li & Liang Liang & Joe Zhu, 2017. "Efficiency Measurement of Multistage Processes: Context Dependent Numbers of Stages," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-18, December.
    14. Pournader, Mehrdokht & Kach, Andrew & Fahimnia, Behnam & Sarkis, Joseph, 2019. "Outsourcing performance quality assessment using data envelopment analytics," International Journal of Production Economics, Elsevier, vol. 207(C), pages 173-182.
    15. Suvvari Anandarao & S. Raja Sethu Durai & Phanindra Goyari, 2019. "Efficiency Decomposition in two-stage Data Envelopment Analysis: An application to Life Insurance companies in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(2), pages 271-285, June.
    16. Halkos, George & Argyropoulou, Georgia, 2024. "Use of indexes in evaluating environmental and health efficiency," MPRA Paper 119800, University Library of Munich, Germany.
    17. An, Qingxian & Chen, Haoxun & Xiong, Beibei & Wu, Jie & Liang, Liang, 2017. "Target intermediate products setting in a two-stage system with fairness concern," Omega, Elsevier, vol. 73(C), pages 49-59.
    18. Liu, Hui-hui & Yang, Guo-liang & Liu, Xiao-xiao & Song, Yao-yao, 2020. "R&D performance assessment of industrial enterprises in China: A two-stage DEA approach," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    19. Guo, Chuanyin & Abbasi Shureshjani, Roohollah & Foroughi, Ali Asghar & Zhu, Joe, 2017. "Decomposition weights and overall efficiency in two-stage additive network DEA," European Journal of Operational Research, Elsevier, vol. 257(3), pages 896-906.
    20. Koronakos, Gregory & Sotiros, Dimitris & Despotis, Dimitris K., 2019. "Reformulation of Network Data Envelopment Analysis models using a common modelling framework," European Journal of Operational Research, Elsevier, vol. 278(2), pages 472-480.

    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:77:y:2018:i:c:p:180-188. 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.