Common Weights Method Based On Cross-weights For Two-stage Data Envelopment Analysis

Data Envelopment Analysis(DEA)has been widely used in the single-stage DEA model since its development,but it is rare in the two-stage DEA model.Based on the theoretical background of the common weight method in the single-stage DEA model,this paper attempts to introduce the common weight method into the two-stage DEA model,and provides a more reasonable efficiency assessment method for the actual production system with two-stage characteristics.Therefore,this study has strong theoretical significance and practical application value.Based on the existing two-stage DEA model,this paper points out the shortcomings of the main two-stage DEA model.And based on the product model,the problem of the instability optimal weight,the zero elements in optimal weight and the comparison among decision unit(DMU)in the two-stage DEA model are studied.To solve the problem of the instability optimal weight,the optimal weight stability model and its extended model are proposed,then,the two-stage DEA common weight model is constructed on the foundation of the above study.By applying the case of the bank and make a comparison among all results,showing that the optimal weight stability model can solve the shortcomings of the traditional two-stage DEA model,and ensure the stability of the optimal weight of all DMUs,and does not appear zero element.The two-stage DEA common weight model can find a set of common weight that is close to all optimal weights for all DMUs,that is to say,the evaluation process and the final results by two-stage DEA common weight model are more reliable than similar models.The common weight model is used to find the common weight as the uniform criterion for all DMUs,so it is different from the addition model based on the sub-stage weighting factor to make a stage prevail over the other stage.Therefore,the two-stage DEA common weight model is more fair,reasonable and reliable than the previous two-stage DEA model in efficiency evaluation and sorting comparison.