The Improvement And Application Of DEA Model Based On Convex Hull Algorithm

Efficiency evaluation and improvement is one of the most important research in management science.Data envelopment analysis(DEA)is the most commonly used model in efficiency evaluation and improvement.This study discusses and proposes some methods based on some convex hull algorithms to improve the rationality,fairness and availability of radial and non-radial DEA.As an efficiency evaluation method,the fairness and rationality of data envelopment analysis are particularly important.For radial DEA model,the goal of optimization is to maximize the ratio of the value of total outputs and the value of total inputs.The result is that each decision making unit(DMU)will choose a set of best weights for themselves.Such extreme weights do not guarantee compliance with real conditions and preferences of decision makers.Because the weights are different from each other,the efficiency cannot be used for ranking.This study proposes a full weight space efficiency analysis model combining probability and statistical theory under the framework of radial data envelope analysis to deal with the issues.Full weight space efficiency model can provide more useful information to decision makers than traditional radial DEA models such as CCR.At the same time,the proposed model can give not only inefficiency DMU but also efficiency DMU improvement target.Some non-radial data envelope analysis models require large amounts of computation to get reasonable reference set and efficiency score.This reduces the usability of some non-radial data envelope analysis models such as SBM.For Non-radial DEA models such as SBM,these models always maximize the slacks and get a minimal efficiency.This leads to a small efficiency and far improvement projection target.Tone proposes a feasible method to solve this issue, but Tone's method needs huge amount of calculation when the data size is large.This study improves the calculation efficiency of Tone's method by applying a convex hull algorithm called CDD.This improvement will extend the SBM model to more extensive applications.Then,this study extends this improved method to leader-follower two-stage SBM model.This study also applies the leader-follower two-stage SBM model to a real data set of several commercial banks in China.