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DEA Models for Parallel Systems: Game-Theoretic Approaches

Author

Listed:
  • Juan Du

    (School of Economics and Management, Tongji University, Shanghai 200092, P. R. China)

  • Joe Zhu

    (International Center for Auditing and Evaluation, Nanjing Audit University, Nanjing 211815, P. R. China;
    Robert A. Foisie School of Business, Worcester Polytechnic Institute, Worcester, MA 01609, USA)

  • Wade D. Cook

    (Schulich School of Business, York University, Toronto, Ontario, Canada M3J 1P3, Canada)

  • Jiazhen Huo

    (School of Economics and Management, Tongji University, Shanghai 200092, P. R. China)

Abstract

In many settings, systems are composed of a group of independent sub-units. Each sub-unit produces the same set of outputs by consuming the same set of inputs. Conventional data envelopment analysis (DEA) views such a system as a "black-box", and uses the sum of the respective inputs and outputs of all relevant component units to calculate the system efficiency. Various DEA-based models have been developed for decomposing the overall efficiency. This paper further investigates this kind of structure by using the cooperative (or centralized) and non-cooperative (Stackelberg or leader–follower) game theory concepts. We show that the existing DEA approaches can be viewed as a centralized model that optimizes the efficiency scores of all sub-units jointly. The proposed leader–follower model will be useful when the priority sequence is available for sub-units. Consider, for example, the evaluation of relative efficiencies of a set of manufacturing facilities where multiple work shifts are operating. Management may wish to determine not only the overall plant efficiency, but as well, the performance of each shift in some priority sequence. The relationship between the system efficiency and component efficiencies is also explored. Our approaches are demonstrated with an example whose data set involves the national forests of Taiwan.

Suggested Citation

  • Juan Du & Joe Zhu & Wade D. Cook & Jiazhen Huo, 2015. "DEA Models for Parallel Systems: Game-Theoretic Approaches," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-22.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:02:n:s0217595915500086
    DOI: 10.1142/S0217595915500086
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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