Evaluating operation and coordination efficiencies of parallel-series two-stage system: A data envelopment analysis approach

- A parallel-series two-stage DEA approach for efficiency assessment is proposed.
- The proposed approach is based on the additive and multiplicative DEA methods.
- The notion of coordination efficiency of network system is introduced.
- Coordination efficiency is the ratio of optimal efficiency over maximal efficiency.

Our motivation of this study is to provide a data envelopment analysis (DEA) approach for evaluating and decomposing the operation efficiency, moreover, computing the coordination efficiency of systems with complex internal structure. We consider a two-stage system composed of three sub-systems, where the first stage is comprised of two independent sub-systems in parallel and then linked to the second stage or the third sub-system in series. Additive and multiplicative DEA efficiency measures are proposed to be jointly applied to illustrate the efficiency formation mechanism of the parallel-series system. The definition of coordination efficiency is inspired by the “gap” between accomplished optimal efficiency and idealized maximal efficiency of relevant systems. This study contributes in creating novel means to consider the different structural characteristics in the efficiency assessment of complex network systems, and to measure the externalities in terms of efficiency within their interior. The proposed models are demonstrated by revisiting the case of Taiwanese non-life insurance companies studied by Kao and Hwang. Corresponding implications of the empirical application are also discussed.