Efficiency measurement in multi-period network DEA model with feedback

Decision-making unit (DMU) internal structure simulation is the basis for network Data Envelopment Analysis (DEA) to open "black box" and evaluate system efficiency with complex internal structure. Based upon summarizing and analyzing the existing model assumptions in network DEA, this paper proposes a hybrid multiperiod DEA model with feedback to open the internal structure of the DMU system, as well as to provide horizontal comparison of the efficiency change of a same DMU at different time periods. In the model construction, the global production frontier is used for multi-period evaluation, Chebyshev distance is used to construct an unbiased two-stage model. Under the cooperation hypothesis, it is considered that the two stages are equally important, which solves the defect that the current two-stage method is not unique in its optimal solution and has two-stage contribution bias. A binary heuristic algorithm is proposed to reduce the time complexity of model solving while maintaining relatively high accuracy. The correctness and feasibility of the algorithm are demonstrated through the investigation of the relevant properties. Finally, the 5-year ecological data of China is used for illustrative application, providing suggestions for future environmental governance. Several comparative experiments are conducted to demonstrate the advantages of our proposed model.