Scale efficiency in two-stage network DEA

Network data envelopment analysis (DEA) considers internal structures of decision-making units. Unlike the standard DEA, network DEA imposes hurdles for measuring scale efficiency due to the fact that (i) overall efficiency aggregated by the stage or divisional technical efficiencies is highly non-linear and only solvable in a heuristic manner, or (ii) the overall efficiency which concerns exclusively inputs and outputs of a system is difficult to be decomposed into divisional efficiencies. In this paper, we establish a mathematical transformation to convert the corresponding non-linear programming problem into second order cone programming programme. The transformation is shown to be versatile in dealing with both constant returns to scale and variable returns to scale models under the two-stage network DEA. Meanwhile, our numerical results reveal that overall scale efficiency in two-stage network DEA is consistent with scale efficiency in conventional DEA.