Combining common-weights DEA window with the Malmquist index: A case of China's iron and steel industry

In the conventional data envelopment analysis (DEA) window analysis, a decision-making unit (DMU) in each window is treated as different units in each period so that the evaluation for one unit is performed on different scales over time. This paper proposes a novel window analysis based on common weight across time (CWAT), which evaluates each unit in each window by its common scale independent of time. The model for obtaining common weights is described as linear programming. And the paper suggests the Malmquist productivity index (MPI) on CWAT, CWAT MPI, to analyze productivity change by inheriting the result of window analysis. The numerical experiments are illustrated to examine the validity of CWAT and MPI, and the result shows that the proposed method provides a new evaluation scale compared to previous studies. The proposed model is applied to evaluate the performance of China 45 iron and steel enterprises during 2009-2017. The energy and environmental efficiency are calculated using CWAT, and CWAT MPI analyzes the productivity change.