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

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 non-linear 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. (C) 2017 Elsevier B.V. All rights reserved.