基于基尼系数-交叉效率的多属性决策方法
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摘要
在数据包络分析(DEA)方法的基础上,提出一种基于基尼系数-交叉效率的多属性决策方法,用于解决具有多个投入、产出指标的多属性决策问题.首先,借鉴基尼系数的优化准则构建基尼系数-交叉评价策略模型,从而得到相对唯一的DEA交叉效率矩阵;然后,应用基尼准则计算各个效率值所包含的信息纯度,并借之实现交叉效率矩阵的集结;最后,根据集结结果对决策单元进行排序和择优.所提决策方法不仅能够克服传统DEA交叉效率方法的交叉评价策略选择难的问题,而且能够保证决策过程的客观性和公平性.同时,所提方法还对交叉评价所得的决策信息进行提纯,为科学合理地进行决策提供更多的有效信息.通过对中国各地区的医疗资源配置效率进行实证,验证了所提出方法的有效性和实用性.
Based on the data envelopment analysis(DEA) method, the multi-attribute decision-making method based on Gini coefficient and cross efficiency is proposed for solving the multi-attribute decision-making problem with multiple inputs and outputs. Firstly, the method introduces the optimization criterion of Gini coefficient to construct the Gini coefficient and cross efficiency strategy model, which can be used to gain a relative unique DEA cross efficiency matrix.Then, the Gini criterion is used to calculate the information purity of each efficiency value for cross efficiency matrix aggregation. Finally, according to the results of aggregation, the decision-making units(DMUs) are ranked. The decisionmaking method not only overcomes the problem that the cross evaluation strategy is difficult to choose in the traditional DEA cross efficiency method, but also ensures the objectivity and fairness in the decision-making process. In addition,the method also can purify the information obtained by cross evaluation, so that more effective information is provided to make scientific and reasonable decisions. An empirical study on the allocation efficiency of medical resources in China is provided to illustrate the effectiveness and practicability of the proposed method.
Based on the data envelopment analysis(DEA) method, the multi-attribute decision-making method based on Gini coefficient and cross efficiency is proposed for solving the multi-attribute decision-making problem with multiple inputs and outputs. Firstly, the method introduces the optimization criterion of Gini coefficient to construct the Gini coefficient and cross efficiency strategy model, which can be used to gain a relative unique DEA cross efficiency matrix.Then, the Gini criterion is used to calculate the information purity of each efficiency value for cross efficiency matrix aggregation. Finally, according to the results of aggregation, the decision-making units(DMUs) are ranked. The decisionmaking method not only overcomes the problem that the cross evaluation strategy is difficult to choose in the traditional DEA cross efficiency method, but also ensures the objectivity and fairness in the decision-making process. In addition,the method also can purify the information obtained by cross evaluation, so that more effective information is provided to make scientific and reasonable decisions. An empirical study on the allocation efficiency of medical resources in China is provided to illustrate the effectiveness and practicability of the proposed method.
引文
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[10]胡祖光.基尼系数理论最佳值及其简易计算公式研究[J].经济研究,2004,39(9):60-69.(Hu Z G.A study of the best theoretical value of Gini coefficient and its concise calculation formula[J].Economic Research J,2004,39(9):60-69.)
[11]王海燕,于荣,郑继媛,等.DEA-Gini准则在城市公共交通企业绩效评价中的应用[J].系统工程理论与实践,2012,32(5):1083-1090.(Wang H Y,Yu R,Zheng J Y,et al.Evaluating the efficiency of urban public transit enterprises:An application of DEA-Gini approach[J].Systems Engineering—Theory&Practice,2012,32(5):1083-1090.)
[12]Wang Y M,Luo Y.DEA efficiency assessment using ideal and anti-ideal decision making units[J].Applied Mathematics&Computation,2006,173(2):902-915.
[13]李春好,苏航,佟轶杰,等.基于理想决策单元参照求解策略的DEA交叉效率评价模型[J].中国管理科学,2015,23(2):116-122.(Li C H,Su H,Tong Y J,et al.DEA cross-efficiency evaluation model by the solution strategy referring to the ideal DMU[J].Chinese J of Management Science,2015,23(2):116-122.)
[14]王中华,李湘君.补偿机制转化与公立医院产出效率驱动[J].系统工程,2015,33(8):95-104.(Wang Z H,Li X J.Compensation mechanism reform and public hospital output efficiency[J].Systems Engineering,2015,33(8):95-104.)
[15]Hu H H,Qi Q,Yang C H.Analysis of hospital technical efficiency in China:Effect of health insurance reform[J].China Economic Review,2012,23(4):865-877.
[2]Wu J,Chu J,Sun J,et al.DEA cross-efficiency evaluation based on Pareto improvement[J].European J of Operational Research,2016,248(2):571-579.
[3]Sexton T R,Silkman R H,Hogan A J.Data envelopment analysis:Critique and extensions[M].Silkman R H ed.Measuring Efficiency:An Assessment of Data Envelopment Analysis.San Francisco:Jossey-Bass,1986.
[4]龚本刚,张孝琪,郭丹丹.基于证据理论-DEA交叉效率的混合型多属性决策方法[J].控制与决策,2016,31(5):943-948.(Gong B G,Zhang X Q,Guo D D.Method for hybrid multiple attribute decision-making based on Dempster-Shafer theory and cross efficiency of DEA[J].Control and Decision,2016,31(5):943-948.)
[5]陈磊,王应明.基于环境绩效视角的交叉效率评价方法[J].系统工程学报,2016,31(5):700-709.(Chen L,Wang Y M.Cross efficiency evaluation method based on environmental performance[J].J of Systems Engineering,2016,31(5):700-709.)
[6]Doyle J,Green R.Efficiency and cross-efficiency in DEA:Derivations,meanings and uses[J].J of the Operational Research Society,1994,45(5):567-578.
[7]Wu J,Chu J,Sun J,et al.Extended secondary goal models for weights selection in DEA cross-efficiency evaluation[J].Computers&Industrial Engineering,2016,93:143-151.
[8]Fabrizi E,Trivisano C.Small area estimation of the Gini concentration coefficient[J].Computational Statistics&Data Analysis,2016,99:223-234.
[9]Chandra B,Varghese P P.Fuzzifying Gini index based decision trees[J].Expert Systems with Applications,2009,36(4):8549-8559.
[10]胡祖光.基尼系数理论最佳值及其简易计算公式研究[J].经济研究,2004,39(9):60-69.(Hu Z G.A study of the best theoretical value of Gini coefficient and its concise calculation formula[J].Economic Research J,2004,39(9):60-69.)
[11]王海燕,于荣,郑继媛,等.DEA-Gini准则在城市公共交通企业绩效评价中的应用[J].系统工程理论与实践,2012,32(5):1083-1090.(Wang H Y,Yu R,Zheng J Y,et al.Evaluating the efficiency of urban public transit enterprises:An application of DEA-Gini approach[J].Systems Engineering—Theory&Practice,2012,32(5):1083-1090.)
[12]Wang Y M,Luo Y.DEA efficiency assessment using ideal and anti-ideal decision making units[J].Applied Mathematics&Computation,2006,173(2):902-915.
[13]李春好,苏航,佟轶杰,等.基于理想决策单元参照求解策略的DEA交叉效率评价模型[J].中国管理科学,2015,23(2):116-122.(Li C H,Su H,Tong Y J,et al.DEA cross-efficiency evaluation model by the solution strategy referring to the ideal DMU[J].Chinese J of Management Science,2015,23(2):116-122.)
[14]王中华,李湘君.补偿机制转化与公立医院产出效率驱动[J].系统工程,2015,33(8):95-104.(Wang Z H,Li X J.Compensation mechanism reform and public hospital output efficiency[J].Systems Engineering,2015,33(8):95-104.)
[15]Hu H H,Qi Q,Yang C H.Analysis of hospital technical efficiency in China:Effect of health insurance reform[J].China Economic Review,2012,23(4):865-877.