Efficiency evaluation in hybrid two-stage network DEA with non-discretionary inputs and shared discretionary inputs

In the network DEA models, it is assumed that all inputs are varied according to decisions of manager. However, in many cases, there are non-discretionary inputs that are beyond the control of a sub-DMUs and DMUs management in the efficiency evaluation, and this problem has not been discussed considerably in network DEA so far. This study proposed a multiplier model to treat a two-stage network system comprised of three sub-DMUs in hybrid form with non-discretionary inputs and shared discretionary inputs, while this issue is not sufficiently rich in the network systems, here, it is being analysed seriously in this study. The proposed model simulate precisely the parallel-series internal structure of network system with non-discretionary inputs and shared discretionary inputs between sub-DMUs, and also uses synthetically additive and multiplicative DEA approaches for evaluating the efficiency of two-stage network system. Finally, a practical example demonstrates the feasibility of the proposed model.