IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v205y2010i2p332-338.html
   My bibliography  Save this article

Two-stage cooperation model with input freely distributed among the stages

Author

Listed:
  • Zha, Yong
  • Liang, Liang

Abstract

Shared flow has been widely used in production scenarios where inputs and outputs are shared among various activities. In DEA literature, shared flow represents situations that DMUs are divided into different components that require common resources or produce goods or services obtained through collaboration among them. The objective of this paper is to offer an approach for studying shared flow in a two-stage production process in series, where shared inputs can be freely allocated among different stages. A product-form cooperative efficiency model is proposed to illustrate the overall efficiency of the DMU, and the relationship between the stages. First, we use a game-theory framework to decide the upper and lower bounds of the efficiencies of the stages in a non-cooperative context. A heuristic is suggested to transform the non-linear model into a parametric linear one, which is then used to solve the cooperative model. The model is justified by a numerical evaluation of bank performances.

Suggested Citation

  • Zha, Yong & Liang, Liang, 2010. "Two-stage cooperation model with input freely distributed among the stages," European Journal of Operational Research, Elsevier, vol. 205(2), pages 332-338, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:2:p:332-338
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00018-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Castelli, Lorenzo & Pesenti, Raffaele & Ukovich, Walter, 2004. "DEA-like models for the efficiency evaluation of hierarchically structured units," European Journal of Operational Research, Elsevier, vol. 154(2), pages 465-476, April.
    2. Yu, Ming-Miin & Lin, Erwin T.J., 2008. "Efficiency and effectiveness in railway performance using a multi-activity network DEA model," Omega, Elsevier, vol. 36(6), pages 1005-1017, December.
    3. Amor Diez-Ticio & Maria-Jesus Mancebon, 2002. "The efficiency of the Spanish police service: an application of the multiactivity DEA model," Applied Economics, Taylor & Francis Journals, vol. 34(3), pages 351-362.
    4. 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.
    5. 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.
    6. Cook, Wade D. & Hababou, Moez, 2001. "Sales performance measurement in bank branches," Omega, Elsevier, vol. 29(4), pages 299-307, August.
    7. Tsai, P. F. & Mar Molinero, C., 2002. "A variable returns to scale data envelopment analysis model for the joint determination of efficiencies with an example of the UK health service," European Journal of Operational Research, Elsevier, vol. 141(1), pages 21-38, August.
    8. Wade Cook & Moez Hababou & Hans Tuenter, 2000. "Multicomponent Efficiency Measurement and Shared Inputs in Data Envelopment Analysis: An Application to Sales and Service Performance in Bank Branches," Journal of Productivity Analysis, Springer, vol. 14(3), pages 209-224, November.
    9. 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.
    10. Cook, Wade D. & Green, Rodney H., 2004. "Multicomponent efficiency measurement and core business identification in multiplant firms: A DEA model," European Journal of Operational Research, Elsevier, vol. 157(3), pages 540-551, September.
    Full references (including those not matched with items on IDEAS)

    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. Kao, Chiang, 2014. "Network data envelopment analysis: A review," European Journal of Operational Research, Elsevier, vol. 239(1), pages 1-16.
    2. Lorenzo Castelli & Raffaele Pesenti & Walter Ukovich, 2010. "A classification of DEA models when the internal structure of the Decision Making Units is considered," Annals of Operations Research, Springer, vol. 173(1), pages 207-235, January.
    3. 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.
    4. 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).
    5. Kao, Chiang, 2016. "Efficiency decomposition and aggregation in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 255(3), pages 778-786.
    6. Xiyang Lei & Yongjun Li & Alec Morton, 2022. "Dominance and ranking interval in DEA parallel production systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 649-675, June.
    7. Yande Gong & Joe Zhu & Ya Chen & Wade D. Cook, 2018. "DEA as a tool for auditing: application to Chinese manufacturing industry with parallel network structures," Annals of Operations Research, Springer, vol. 263(1), pages 247-269, April.
    8. Kao, Chiang, 2017. "Efficiency measurement and frontier projection identification for general two-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 261(2), pages 679-689.
    9. Chen, Xiafei & Liu, Zhiying & Zhu, Qingyuan, 2020. "Reprint of "Performance evaluation of China's high-tech innovation process :Analysis based on the innovation value chain"," Technovation, Elsevier, vol. 94.
    10. Chen, Xiafei & Liu, Zhiying & Zhu, Qingyuan, 2018. "Performance evaluation of China's high-tech innovation process: Analysis based on the innovation value chain," Technovation, Elsevier, vol. 74, pages 42-53.
    11. Xiyang Lei & Yongjun Li & Qiwei Xie & Liang Liang, 2015. "Measuring Olympics achievements based on a parallel DEA approach," Annals of Operations Research, Springer, vol. 226(1), pages 379-396, March.
    12. Entezam, Hasan Farmani & Sobhani, Farzad Movahedi & Najafi, Seyed Esmaeil & Roshdi, Israfil, 2020. "A multi-component enhanced Russell measure of efficiency: With application to water supply plans," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    13. 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.
    14. Sanjeet Singh & Prabhat Ranjan, 2018. "Efficiency analysis of non-homogeneous parallel sub-unit systems for the performance measurement of higher education," Annals of Operations Research, Springer, vol. 269(1), pages 641-666, October.
    15. Jie Wu & Beibei Xiong & Qingxian An & Jiasen Sun & Huaqing Wu, 2017. "Total-factor energy efficiency evaluation of Chinese industry by using two-stage DEA model with shared inputs," Annals of Operations Research, Springer, vol. 255(1), pages 257-276, August.
    16. Xiao Shi & Ali Emrouznejad & Minyue Jin & Feng Yang, 2020. "A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 311-332, September.
    17. 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.
    18. 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.
    19. Kao, Chiang, 2019. "Inefficiency identification for closed series production systems," European Journal of Operational Research, Elsevier, vol. 275(2), pages 599-607.
    20. Laurens Cherchye & Bram De Rock & Bart Dierynck & Filip Roodhooft & Jeroen Sabbe, 2013. "Opening the “Black Box” of Efficiency Measurement: Input Allocation in Multioutput Settings," Operations Research, INFORMS, vol. 61(5), pages 1148-1165, October.

    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:205:y:2010:i:2:p:332-338. 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.