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Efficiency measurement and frontier projection identification for general two-stage systems in data envelopment analysis

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  • Kao, Chiang

Abstract

The multiplier and envelopment models in data envelopment analysis (DEA) have a primal-dual relationship, and produce the same efficiency measure for a decision making unit (DMU). In addition to measuring efficiency, the multiplier model is able to identify the production frontier facets defined by the DMUs being evaluated, and the envelopment model is able to identify the projection point, based on which the efficiencies are measured. For general two-stage systems where the whole operation of the system is divided into two smaller operations carried out by two divisions connected in series, the multiplier model is generally used to measure division efficiencies, and the envelopment model is used to identify the projection point. This paper shows that the projection point identified by the envelopment model is not the one used by the multiplier model to measure the division efficiencies for general two-stage systems. Based on the primal-dual relationship of the two models, the envelopment model is reformulated to be able to obtain the projection point and measure the division efficiencies at the same time. The input- and output-orientation of the two divisions lead to four forms of the model. A case of measuring the innovation efficiency of thirty-five countries is used to illustrate the characteristics of this model and its differences from the multiplier model.

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  • 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.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:679-689
    DOI: 10.1016/j.ejor.2017.03.016
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    2. K. Hafsal & Anandarao Suvvari & S. Raja Sethu Durai, 2020. "Efficiency of Indian banks with non-performing assets: evidence from two-stage network DEA," Future Business Journal, Springer, vol. 6(1), pages 1-9, December.
    3. LiHsien Chien & ShuYi Chi, 2019. "An integrated data envelopment approach for evaluating the meat companies efficiency," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 65(10), pages 470-480.
    4. Xiaohong Liu & Jiasen Sun & Feng Yang & Jie Wu, 2020. "How ownership structure affects bank deposits and loan efficiencies: an empirical analysis of Chinese commercial banks," Annals of Operations Research, Springer, vol. 290(1), pages 983-1008, July.
    5. Riju Chaudhary & H. D. Arora, 2022. "Efficiency evaluation of public and nationalized Indian banks using data envelopment analysis," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 469-478, February.
    6. Kao, Chiang, 2019. "Inefficiency identification for closed series production systems," European Journal of Operational Research, Elsevier, vol. 275(2), pages 599-607.
    7. Xiong, Xi & Yang, Guo-liang & Guan, Zhong-cheng, 2018. "Assessing R&D efficiency using a two-stage dynamic DEA model: A case study of research institutes in the Chinese Academy of Sciences," Journal of Informetrics, Elsevier, vol. 12(3), pages 784-805.
    8. Jiawei Yang, 2023. "Disentangling the sources of bank inefficiency: a two-stage network multi-directional efficiency analysis approach," Annals of Operations Research, Springer, vol. 326(1), pages 369-410, July.
    9. Dorgyles C.M. Kouakou, 2022. "Separating innovation short-run and long-run technical efficiencies: Evidence from the Economic Community of West African States (ECOWAS)," European Journal of Comparative Economics, Cattaneo University (LIUC), vol. 19(1), pages 103-141, June.
    10. Dorgyles C.M. Kouakou, 2022. "Separating innovation short-run and long-run technical efficiencies: Evidence from the Economic Community of West African States (ECOWAS)," European Journal of Comparative Economics, Cattaneo University (LIUC), vol. 19(1), pages 103-141, June.
    11. Zhang, Linyan & Chen, Kun, 2019. "Hierarchical network systems: An application to high-technology industry in China," Omega, Elsevier, vol. 82(C), pages 118-131.
    12. Meiqiang Wang & Yingwen Chen & Zhixiang Zhou, 2020. "A Novel Stochastic Two-Stage DEA Model for Evaluating Industrial Production and Waste Gas Treatment Systems," Sustainability, MDPI, vol. 12(6), pages 1-17, March.
    13. Jiawei Yang & Lei Fang, 2022. "Average lexicographic efficiency decomposition in two-stage data envelopment analysis: an application to China’s regional high-tech innovation systems," Annals of Operations Research, Springer, vol. 312(2), pages 1051-1093, May.
    14. Kao, Chiang, 2018. "Multiplicative aggregation of division efficiencies in network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 270(1), pages 328-336.
    15. Zhu, Qingyuan & Xu, Shuqi & Sun, Jiasen & Li, Xingchen & Zhou, Dequn, 2022. "Energy efficiency evaluation of power supply system: A data-driven approach based on shared resources," Applied Energy, Elsevier, vol. 312(C).
    16. Fang, Lei, 2020. "Stage efficiency evaluation in a two-stage network data envelopment analysis model with weight priority," Omega, Elsevier, vol. 97(C).

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