Cross-efficiency Network Models For Processing Negative Data

Data envelopment analysis(DEA)is an evaluation method developed on the idea of “relative efficiency evaluation”.Traditional DEA not only ignores the internal production process of decision making unit(DMU),but also fails to deal with negative data.Meanwhile,DEA excessively relies on self-evaluation and ignores peer evaluation.Network cross efficiency evaluation methods take the internal production process of DMUs and peer evaluation into account.However,the existing methods are unable to process negative data,and they are established based on the CRS,so the methods under the series structure cannot be extended to the VRS.At the same time,the cross efficiency of DMU cannot be evaluated from both inputs and outputs.Based on the DDF model that can evaluate efficiency from both inputs and outputs,this paper proposes the VRS DDF models under the basic series and parallel structures.The system efficiency under the two structures is decomposed into the weighted average of the stage efficiency.In combination with the idea of cross efficiency,the cross efficiency evolution methods under two structures are proposed.These methods solve the problems that the existing network cross efficiency evaluation methods can not measure the efficiency of inputs and outputs simultaneously and can not deal with negative data.Numerical examples are used to verify the practicability of the methods.Then this paper proposes a general series DDF model based on the basic series structure DDF model.The proposed model can accept external inputs and export external outputs in each stage,and then the cross efficiency approach under the general series structure is proposed based on the idea of cross efficiency evaluation.The numerical example analysis shows that the model has strong discriminative power.Finally,through empirical analysis,this paper uses the proposed general series model to analyze the efficiency of 34 chinese banks.We find that compared with the existing models,the proposed general series method can handle negative data well.This can help us analyze the performance of domestic banks in each period well.This paper extends the black box DDF model to network structures,and proposes the corresponding cross efficiency evaluation methods.This broadens the application scope of the DDF DEA model and solves the problems that the existing network corss efficiency evalution method cannot handle negative data.Therefore,the proposed network cross efficiency evalution methods are very good at solving complex practical problems and has a strong application prospect.