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

In two recent papers, [Guo, C., Wei, F., & Chen, Y. (2017). A note on second order cone programming ap-proach 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 gen-eral 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 transfor-mation cannot result in an equivalent mathematical program in view of the fact that the general multi-plicative 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) illus-trate, 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. & COPY; 2023 Elsevier B.V. All rights reserved.