Efficiency evaluation of an interactive system by data envelopment analysis approach

•We develop a new approach to measure the efficiency of the interactive systems.•A parallel system with two interactive components are studied.•A centralized model and two non-cooperative models were built.•A heuristic method is proposed for solving the non-linear centralized model.•Chinese “985 Project” universities was used to illustrate our approach.

Many different network data envelopment analysis (DEA) models have been built to investigate the internal structure of a system which used to be considered as a “black box” in traditional DEA models. However, few of these previous works have taken into account the interactive relationship between system components, that is, one component's output (input) may be the input (output) of another component. The interactive network becomes more and more common in a system because of complex competition circumstances, it is therefore necessary to develop a new method to measure the efficiency of these systems. In this paper, a centralized model and two leader-follower game models were built to measure the efficiency of a parallel system with two components that have an interactive relationship in a centralized mode and non-centralized mode, respectively. Besides, since the centralized model is non-linear, a heuristic method is proposed for solving it. Finally, our approach is applied to analyze Chinese “985 Project” universities' performance.