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

Keywords Data envelopment analysis; Network production process; Two-stage efficiency measurement; Second order conic programming; Nonconvex optimisation 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. Author Affiliation: (a) Department of Basic Sciences, Semnan Branch, Islamic Azad University, Semnan, Iran (b) School of Business, Faculty of Business and Law, University of Wollongong, Wollongong, Australia (c) Department of Accounting and Finance, The University of Auckland, Auckland, New Zealand * Corresponding author. Article History: Received 31 January 2023; Accepted 16 February 2023 Byline: Israfil Roshdi [i.roshdi@semnaniau.ac.ir] (a,*), Mahdi Mahdiloo (b), Amir Arjomandi (b), Dimitris Margaritis (c)