Efficiency measurement and decomposition in hybrid two-stage DEA with additional inputs

The simulation and analysis of structure within decision making unit (DMU) is the basis on which network data envelopment analysis (DEA) opens the “black box” and evaluates the efficiency of system with complex internal structure. The efficiency measurements of system with sub-DMU in series or with sub-DMUs in parallel are two common cases in the theory development and applications of two-stage DEA. However, the research on parallel-series hybrid system is not rich enough. The paper develops a set of DEA models to treat a two-stage system comprised of three sub-DMUs in hybrid form with additional inputs to the second stage. The proposed models simulate precisely the system's parallel-series internal structure, employ synthetically additive and multiplicative DEA approaches to estimate and decompose the efficiencies of system, and adopt a heuristic method to convert non linear program due to the additional inputs into a linear program. This approach gives more information about the sources of inefficiency by penetrating into the depth of system and modeling the efficiency formation mechanism. A model application is provided.