The Optimization And Practical Study On DEA Cross-efficiency Model

To measure the efficiency of DMUs is the major concern on the subject of management.It concerns the resource usage efficiency.Data envelopment analysis(DEA)is an effective way to measure the efficency of DMUS.It is a non-parametric method for efficiency evaluation of a group of homogenous decision-making units(DMUS).It uses input output ratio to measure the efficiency.Compared with other related efficiency evaluation methods,it has a good ability to identify the production frontier and it does not determine the concrete form of production frontier in advance and it can deal with the DMUS with multiple inputs and oututs.However,it has a significant drawback that it can not further rank efficient DMUS.To solve this problem,some sholars extended DEA taditional models and proposed some methods such as DEA superefficiency model,DEA common weight model and DEA cross-efficiency model and so on.Among them,DEA cross-efficiency model was widely used.However,before the use of DEA cross-efficiency model,we need to solve two problems that are non-uniqueness of corssefficiency and cross-efficincy aggregation.This paper carries out study on two theoretical problems.Sustainable development is consensus of human.When implementing sustainable development,it needs to carry out sustainable development evaluation.We utilized the theoretical research achievements on sustainable development evaluation taking sustainable development evaluation of China regional areas as an example.To solve the non-uniqueness of cross-efficiency,we proposed the revised neutral DEA cross-efficency model and DEA cross-efficency models considering the original efficiency of DMUS.While constructing the revised neutral DEA cross-efficency model,we choose relative importance levels of each output as the weights of each output efficeny of DMU under evaluation.Then the weighted comprehensive output efficiency value of DMU under evaluation will be determined.The revised neutral DEA cross-efficiency model maximizes the weighted comprehensive output efficiency value of DMU under evaluation while choosing the unique set of inputs and outputs weights among multiple sets of weights.Moreover,we illustrate CCR model from original efficency of DMUS and then we construct aggressive and benevolent and neutral DEA cross-efficiency models condidering the original efficiency values of DMUS.The aggressive model minimizes average original efficency value of other DMUs.Benevolent model adopts adverse choice strategy.The neutral model maximizes its own original efficiency value of DMU under evaluation.In order to aggregate cross-efficiency values,we propose the use of expert scoring method and principal component analysis.While using expert scoring method for cross-efficiency aggregation,the target DMUS in cross-efficiency matrix are viewed as external experts.In that case,the cross-efficiency matrix will be viewed as expert scores matrix to DMUS and we use Euclidean distance matrix to measure the difference levels among experts.From the difference level of one given expert to other ones,we can gain his expert scores weight.After achieving the weights,the final aggregation results will be determined.While using the principal component analysis for cross-efficiency aggregation,the efficiency value determines by a given unique set of weights for each DMU will be viewed as its one given attribute value.Then the cross-efficiency matrix will be transformed to be the attributes values matix of DMUS.In that case,we can use principal component analysis to aggregate cross-efficiencies.Finally,this paper uses the theoretical research achievements to measure the sustainable development level of China regional areas.Based on sustainable development concept,indicator choice considers not only economical indicators but also environmental indicators.Concretely,the input indicators choose labor and capital inputs and output indicators are GDP,carbon dioxide emissions,oxynitride emissions and dust emissions.This paper measures the sustainable development levels of China regional areas from comprehensive perspective,economical perspective and environmental perspective respectively.At the same time,it provides learning benchmark and further improvement direction for regions which perform unsatisfactorily.The main conclusions of this paper are as follows:(1)We propose the revised neutral DEA cross-efficiency model and DEA cross-efficiency models considering the original efficiency values of DMUS to solve the non-uniqueness of cross-efficiency.The revised neutral DEA cross-efficiency model is more logical than the related methods.The DEA cross-efficiency models considering the original efficiency values of DMUS concern the importance of original efficiency values of DMUS that is the drawback of existing DEA cross-efficiency models.At the same time,they choose the set of weights that includes fewer numbers of zero weights than the corresponding models who only consider the standard efficiency value of DMUS.(2)We illustrate CCR model from the original efficiency value.If it exists one set of weights that can ensure the efficency value of one given DMU is maximal,it will be DEA efficient from original efficiency value perspective.(3)We propose the use of experts scoring method and principal component analysis for cross-efficiency aggregation.They all consider the relative importance of cross-efficiencies and the final aggregation results using them have relationship with weights.The aggregation results determined by them are unique and it does not need to measure the optimal level of DM(decision maker)while using them.At same time,they provide the concrete reason why we need to aggregate cross-efficiencies with different weights.Moreover,the aggregation result determined by principal component analysis is more logical than that by expert scoring method.(4)This paper measures the sustainable development level of China regional areas from comprehensive,economical and environmental perspectives respectively.Meanwhile,it gives the learnng benchmark and further improvement direction for regions which perform unsatisfactorily.The theoretical research of this paper furter enrichs DEA cross-efficiency model and the practical research can further improve sustainable development level of China.