Research On Cross Efficiency In Network DEA And Its Application

In the data envelopment analysis(DEA),the DEA basic model belongs to the self-evaluation mode,simplifies the decision making unit(DMU)as a "black box",and calculates the efficiency of DMU in each period separately.Some scholars have put forward cross efficiency,network DEA and multi-period DEA respectively to solve these three deficiencies,but these models all pay attention to one and lose the other,and fail to solve the three deficiencies of the basic DEA model at the same time;In recent years,some scholars began to improve two of the three deficiencies at the same time,and proposed network DEA cross efficiency and multi-period network DEA.However,existing network DEA cross efficiency still has shortcomings and few scholars proposed multi-period DEA cross efficiency;In addition,no scholars have improved the above three deficiencies at the same time.Based on the above background,this paper conducts the following research:(1)In order to make the efficiency evaluation results have credibility and comparability,and to judge the weak sub-stages that affect the overall efficiency,this paper proposes a network DEA game cross-efficiency model and algorithm.In order to demonstrate the applicability of the model to a variety of network structures,this paper applies the model to basic two-stage network structure and two-stage network structure with shared inputs,and verifies the feasibility of the model through numerical examples.(2)In order to make the efficiency evaluation results not only have credibility and comparability,but also can judge the efficiency variation trend of DMU in each period,this paper proposes a multi-period DEA game cross-efficiency model,and verifies the feasibility of the model through an example;Further,in view of the feasibility of both the proposed network DEA game cross-efficiency model and multi-period DEA game cross-efficiency model,this paper proposes a multi-period DEA game cross-efficiency model in view of the above three deficiencies of the basic model of DEA,and verifies the rationality of the model through an example.(3)In the empirical aspect,the industrial environmental system was decomposed into production stage and waste disposal stage by referring to previous literatures,and the proposed multi-period network DEA game cross-efficiency model was applied to evaluate the industrial environmental efficiency of various regions in China from2012 to 2015.Through the evaluation results,the causes were analyzed,and suggestions were put forward to improve the industrial environmental efficiency.