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 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.