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A note on second order cone programming approach to two-stage network data envelopment analysis

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  • Guo, Chuanyin
  • Wei, Fajie
  • Chen, Yao

Abstract

In network data envelopment analysis (DEA) literature, the general multiplicative two-stage network model, where the objective function is the product of the two stage efficiency ratios, is highly nonlinear and is impossible to be directly transformed into linear programming problems. Chen and Zhu (2017) discovered that this model corresponds to a cone-type structure and can be transformed into a second order cone programming (SOCP) problem with a parameter. The transformed parametric SOCP problem is solved by computing a series of SOCP models when the parameter is varied. We show that Chen and Zhu's (2017) model can be directly transformed into a single SOCP problem, without the need for solving parametric SOCP problems. This greatly reduces the computational burden.

Suggested Citation

  • Guo, Chuanyin & Wei, Fajie & Chen, Yao, 2017. "A note on second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 263(2), pages 733-735.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:2:p:733-735
    DOI: 10.1016/j.ejor.2017.06.011
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    References listed on IDEAS

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    1. 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.
    2. Chen, Kun & Zhu, Joe, 2017. "Second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 262(1), pages 231-238.
    3. 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.
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    Cited by:

    1. Yu, Anyu & Lee, Andy & Chen, Yao, 2021. "Carbon allocation targeting with abatement capability: A firm-level study," International Journal of Production Economics, Elsevier, vol. 235(C).
    2. Jianhui Xie & Qiwei Xie & Yongjun Li & Liang Liang, 2021. "Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique," Annals of Operations Research, Springer, vol. 304(1), pages 453-480, September.
    3. Phung, Manh-Trung & Cheng, Cheng-Ping & Guo, Chuanyin & Kao, Chen-Yu, 2020. "Mixed Network DEA with Shared Resources: A Case of Measuring Performance for Banking Industry," Operations Research Perspectives, Elsevier, vol. 7(C).
    4. N. Torabi Golsefid & M. Salahi, 2023. "An SOCP approach to a two-stage network DEA with feedbacks and shared resources," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1153-1178, September.
    5. Alireza Moradi & Saber Saati & Mehrzad Navabakhsh, 2023. "Genetic algorithms for optimizing two-stage DEA by considering unequal intermediate weights," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1202-1217, September.
    6. Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    7. Pham, Manh D. & Zelenyuk, Valentin, 2019. "Weak disposability in nonparametric production analysis: A new taxonomy of reference technology sets," European Journal of Operational Research, Elsevier, vol. 274(1), pages 186-198.
    8. Gerami, Javad & Mozaffari, Mohammad Reza & Wanke, Peter F. & Correa, Henrique L., 2022. "Improving information reliability of non-radial value efficiency analysis: An additive slacks based measure approach," European Journal of Operational Research, Elsevier, vol. 298(3), pages 967-978.
    9. Qu, Jingjing & Wang, Baohui & Liu, Xiaohong, 2022. "A modified super-efficiency network data envelopment analysis: Assessing regional sustainability performance in China," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    10. Zhang, Linyan & Chen, Kun, 2019. "Hierarchical network systems: An application to high-technology industry in China," Omega, Elsevier, vol. 82(C), pages 118-131.
    11. 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.
    12. Kremantzis, Marios Dominikos & Beullens, Patrick & Kyrgiakos, Leonidas Sotirios & Klein, Jonathan, 2022. "Measurement and evaluation of multi-function parallel network hierarchical DEA systems," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    13. Joe Zhu, 2022. "DEA under big data: data enabled analytics and network data envelopment analysis," Annals of Operations Research, Springer, vol. 309(2), pages 761-783, February.
    14. Chen, Kun & Zhu, Joe, 2020. "Additive slacks-based measure: Computational strategy and extension to network DEA," Omega, Elsevier, vol. 91(C).
    15. Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.

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