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On second order cone programming approach to two-stage network data envelopment analysis

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  • Roshdi, Israfil
  • Mahdiloo, Mahdi
  • Arjomandi, Amir
  • Margaritis, Dimitris

Abstract

In two recent papers, [Guo, C., Wei, F., & Chen, Y. (2017). A note on second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 263(2), 733–735; and Chen, K., & Zhu, J. (2017). Second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 262(1), 231238] converted the general multiplicative two-stage DEA (data envelopment analysis) network model into a parametric/single second order conic programming (SOCP) problem. In this paper, we (i) note that the proposed transformation cannot result in an equivalent mathematical program in view of the fact that the general multiplicative two-stage DEA model is basically a nonconvex optimisation problem, possibly with several local and global optimums, whereas a single SOCP is a convex optimisation; (ii) demonstrate that there is a subtle technical error contained in the main transformation process proposed in both papers; (iii) illustrate, by providing a numerical counterexample, that the optimal solution obtained from the resulting single SOCP problem might be substantially different from the original model’s optimum; and (iv) offer some computational remark for solving the multiplicative/additive two-stage DEA model.

Suggested Citation

  • Roshdi, Israfil & Mahdiloo, Mahdi & Arjomandi, Amir & Margaritis, Dimitris, 2023. "On second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 309(2), pages 953-956.
    • Handle: RePEc:eee:ejores:v:309:y:2023:i:2:p:953-956
    DOI: 10.1016/j.ejor.2023.02.022
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    References listed on IDEAS

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    1. Rolf Färe & Shawna Grosskopf & Gerald Whittaker, 2014. "Network DEA II," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 307-327, Springer.
    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. 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.
    4. Hasannasab, Maryam & Margaritis, Dimitris & Roshdi, Israfil & Rouse, Paul, 2019. "Hyperbolic efficiency measurement: A conic programming approach," European Journal of Operational Research, Elsevier, vol. 278(2), pages 401-409.
    5. 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.
    6. Fukuyama, Hirofumi & Mirdehghan, S.M., 2012. "Identifying the efficiency status in network DEA," European Journal of Operational Research, Elsevier, vol. 220(1), pages 85-92.
    7. Dimitris Despotis & Gregory Koronakos & Dimitris Sotiros, 2016. "Composition versus decomposition in two-stage network DEA: a reverse approach," Journal of Productivity Analysis, Springer, vol. 45(1), pages 71-87, February.
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    Cited by:

    1. Guo, Chuanyin & Song, Qiwei & Yu, Ming-Miin & Zhang, Jian, 2024. "A digital economy development index based on an improved hierarchical data envelopment analysis approach," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1146-1157.
    2. Wen, Yao & An, Qingxian & Gong, Yeming & Wu, Pengkun, 2024. "Structural rearrangement of the network system from an efficiency perspective: A silver lining of profit improvement," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1001-1011.

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