只有输出的广义样本区间DEA模型
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摘要
在应用多个绩效指标综合评价决策单元有效性时,决策者常常把这些决策单元与另外预先指定的标准(样本单元)进行比较。由于客观事物的复杂性和不确定性导致样本单元和决策单元的指标信息有时必须用区间数的形式给出。针对区间数指标信息的综合评价问题,本文通过分解的方法讨论样本单元和决策单元指标信息为区间数时用广义DEA模型评价决策单元有效性的方法,并相应地构建了只有输出的广义区间DEA模型。同时,对模型的含义、求解以及性质等进行了分析。之后,探讨了该方法在决策单元有效性分类和排序中的应用。最后,通过实例表明该方法的可行性和有效性。
When multiple performance measures are used to evaluate the effectiveness of the decision-making units,the decision makers often compare these decision units with the pre-specified criteria(sample units).Because of the complexity and uncertainty of the objective things,the index information of sample units and decision unit must be given in the form of interval numbers.According to the three cases of the interval number of the evaluation index value of the sample unit or the decision unit,or the evaluation index values of both of them,it is established respectively that the generalized interval DEA model with only output(IS-DEA model,S-IDEA model and IS-IDEA model)based on the sample unit to evaluate the effectiveness of the decision making unit,and three types of generalized interval DEA models with output are further given according to the index types-benefit,cost and hybrid.At the same time,the meaning of the model,the solving methods,the related properties,the effectiveness classification and sequencing of decision making units of these models are discussed.Finally,an example of comprehensive performance evaluation of commercial banks is given to verify its feasibility and effectiveness.The method proposed in this paper extends the relative efficiency of the traditional DEA method,which is based on the effective decision unit,to evaluate the relative efficiency of the decision making unit,which is based on the arbitrary reference set,and extends the index value to the interval value.These models have their own advantages and application fields and can be chosen according to practical problems.
When multiple performance measures are used to evaluate the effectiveness of the decision-making units,the decision makers often compare these decision units with the pre-specified criteria(sample units).Because of the complexity and uncertainty of the objective things,the index information of sample units and decision unit must be given in the form of interval numbers.According to the three cases of the interval number of the evaluation index value of the sample unit or the decision unit,or the evaluation index values of both of them,it is established respectively that the generalized interval DEA model with only output(IS-DEA model,S-IDEA model and IS-IDEA model)based on the sample unit to evaluate the effectiveness of the decision making unit,and three types of generalized interval DEA models with output are further given according to the index types-benefit,cost and hybrid.At the same time,the meaning of the model,the solving methods,the related properties,the effectiveness classification and sequencing of decision making units of these models are discussed.Finally,an example of comprehensive performance evaluation of commercial banks is given to verify its feasibility and effectiveness.The method proposed in this paper extends the relative efficiency of the traditional DEA method,which is based on the effective decision unit,to evaluate the relative efficiency of the decision making unit,which is based on the arbitrary reference set,and extends the index value to the interval value.These models have their own advantages and application fields and can be chosen according to practical problems.
引文
[1]Charnes A,Cooper W W,Rohodes E.Measuring the efficiency of decision making units[J].European Journal of Operational Research,1978,2(6):429-444.
[2]Charnes A,Cooper W W,Golany B,et al.Foundations of data envelopment analysis for pareto-koopmansefficient empirical production functions[J].Journal of Econometrics,1985,30(1):91-107.
[3]Banker R D,Charnes A,Cooper W W.Some models for estimating technical and scale inefficiencies data envelopment analysis[J].Management Science,1984,30(9):1078-1092.
[4]Cooper W W,Park K S,Yu Gang.IDEA and AR-IDEA:Models for dealing with imprecise data in DEA[J].Management Science,1999,45(4):597-607.
[5]Despotis D K,Smirlis Y G.Data envelopment analysis with imprecise data[J].European Journal of Operational Research,2002,140(1):24-36.
[6]马占新.广义数据包络分析方法[M].北京:科学出版社,2012.
[7]杨国梁,刘文斌,郑海军.数据包络分析方法(DEA)综述[J].系统工程学报,2013,28(6):841-860.
[8]冯晨鹏,王慧玲,毕功兵.存在多种非期望产出的非径向零和收益DEA模型我国区域环境效率实证研究[J].中国管理科学,2017,25(10):42-50.
[9]王美强,李勇军.具有双重角色和非期望要素的供应商评价两阶段DEA模型[J].中国管理科学,2016,24(12):91-97.
[10]范建平,肖慧,樊晓宏.考虑非期望产出的改进EBMDEA三阶段模型[J].中国管理科学,2017,25(8):166-174.
[11]刘文丽,王应明,吕书龙.基于交叉效率和合作博弈的决策单元排序方法[J].中国管理科学,2018,26(4):163-170.
[12]成达建,薛声家.基于交叉效率新计算方法的区间效率值排序[J].中国管理科学,2017,25(7):191-196.
[13]周忠宝,金倩颖,曾喜梅,等.存在基数约束的投资组合效率评价方法[J].中国管理科学,2017,25(2):174-179.
[14]陶杰,卢超.整数DEA问题的求解方法与改进[J].中国管理科学,2016,24(11):103-108.
[15]马占新.一种基于样本前沿面的综合评价方法[J].内蒙古大学学报,2002,33(6):606-610.
[16]马占新.样本数据包络面的研究与应用[J].系统工程理论与实践,2003,23(12):32-37.
[17]马占新,吕喜明.带有偏好锥的样本数据包络分析方法研究[J].系统工程与电子技术,2007,29(8):1275-1282.
[18]马占新,马生昀.基于C2 W模型的广义数据包络分析方法研究[J].系统工程与电子技术,2009,31(2):366-372.
[19]马占新,马生昀.基于C2 WY模型的广义数据包络分析方法研究[J].系统工程学报,2011,26(2):251-261.
[20]木仁,马占新,文宗川.数据包络分析方法中决策单元偏序关系的建立[J].中国管理科学,2016,24(11):103-108.
[21]孙娜,马占新,马生昀.广义超效率区间DEA模型及其有效性研究[J].数学的实践与认识,2014,44(3):175-180.
[22]孙娜,马生昀,马占新.广义模糊DEA模型及其有效性研究[J].数学的实践与认识,2015,45(3):181-186.
[23]马占新,伊茹.基于经验数据评价的非参数系统分析方法[J].控制与决策,2012,27(2):199-204.
[24]魏权龄.数据包络分析[M].北京:科学出版社,2004.
[25]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004.
[26]Aiche F,Abbas M,Dubois D.Chance-constrained programming with fuzzy stochastic coefficients[J].Fuzzy Optimization and Decision Making,2013,12(2):125-152.
[27]何静.只有输出(入)的数据包络分析及其应用[J].系统工程学报,1995,10(2):48-55.
[28]Cook W D,Kress M.A data envelopment model for aggregating preference rankings[J].Management Science,1990,36(11):1302-1310.
[29]Green R H,Doyle J R,Cook W D.Preference voting and project ranking using DEA and cross evaluation[J].European Journal of Operational Research,1996,90(3):461-472.
[30]曾祥云,吴育华.L-R型区间DEA模型及其变换[J].管理工程学报,2001,18(1):60-65.
[31]马生昀,马占新,孙娜.广义与传统BC2模型效率评价差异及其几何刻画[J].数学的实践与认识,2014,44(9):11-18.
[32]Jahanshahloo G R,Lotfi F H,Malkhalifeh M R,et al.A generalized model for data envelopment analysis with interval data[J].Applied Mathematical Modelling,2009,33(7):3237-3244.
[33]Kundu S.Min-transitivity of fuzzy leftness relationship and its application to decision making[J].Fuzzy Sets and Systems,1997,86(3):357-367.
[34]Hu Baoqing,Wang Song.A novel approach in uncertain programming part I:New arithmetic and order relationfor interval numbers[J].Journal of Industrial&Management Optimization,2006,2(4):351-371.
[2]Charnes A,Cooper W W,Golany B,et al.Foundations of data envelopment analysis for pareto-koopmansefficient empirical production functions[J].Journal of Econometrics,1985,30(1):91-107.
[3]Banker R D,Charnes A,Cooper W W.Some models for estimating technical and scale inefficiencies data envelopment analysis[J].Management Science,1984,30(9):1078-1092.
[4]Cooper W W,Park K S,Yu Gang.IDEA and AR-IDEA:Models for dealing with imprecise data in DEA[J].Management Science,1999,45(4):597-607.
[5]Despotis D K,Smirlis Y G.Data envelopment analysis with imprecise data[J].European Journal of Operational Research,2002,140(1):24-36.
[6]马占新.广义数据包络分析方法[M].北京:科学出版社,2012.
[7]杨国梁,刘文斌,郑海军.数据包络分析方法(DEA)综述[J].系统工程学报,2013,28(6):841-860.
[8]冯晨鹏,王慧玲,毕功兵.存在多种非期望产出的非径向零和收益DEA模型我国区域环境效率实证研究[J].中国管理科学,2017,25(10):42-50.
[9]王美强,李勇军.具有双重角色和非期望要素的供应商评价两阶段DEA模型[J].中国管理科学,2016,24(12):91-97.
[10]范建平,肖慧,樊晓宏.考虑非期望产出的改进EBMDEA三阶段模型[J].中国管理科学,2017,25(8):166-174.
[11]刘文丽,王应明,吕书龙.基于交叉效率和合作博弈的决策单元排序方法[J].中国管理科学,2018,26(4):163-170.
[12]成达建,薛声家.基于交叉效率新计算方法的区间效率值排序[J].中国管理科学,2017,25(7):191-196.
[13]周忠宝,金倩颖,曾喜梅,等.存在基数约束的投资组合效率评价方法[J].中国管理科学,2017,25(2):174-179.
[14]陶杰,卢超.整数DEA问题的求解方法与改进[J].中国管理科学,2016,24(11):103-108.
[15]马占新.一种基于样本前沿面的综合评价方法[J].内蒙古大学学报,2002,33(6):606-610.
[16]马占新.样本数据包络面的研究与应用[J].系统工程理论与实践,2003,23(12):32-37.
[17]马占新,吕喜明.带有偏好锥的样本数据包络分析方法研究[J].系统工程与电子技术,2007,29(8):1275-1282.
[18]马占新,马生昀.基于C2 W模型的广义数据包络分析方法研究[J].系统工程与电子技术,2009,31(2):366-372.
[19]马占新,马生昀.基于C2 WY模型的广义数据包络分析方法研究[J].系统工程学报,2011,26(2):251-261.
[20]木仁,马占新,文宗川.数据包络分析方法中决策单元偏序关系的建立[J].中国管理科学,2016,24(11):103-108.
[21]孙娜,马占新,马生昀.广义超效率区间DEA模型及其有效性研究[J].数学的实践与认识,2014,44(3):175-180.
[22]孙娜,马生昀,马占新.广义模糊DEA模型及其有效性研究[J].数学的实践与认识,2015,45(3):181-186.
[23]马占新,伊茹.基于经验数据评价的非参数系统分析方法[J].控制与决策,2012,27(2):199-204.
[24]魏权龄.数据包络分析[M].北京:科学出版社,2004.
[25]徐泽水.不确定多属性决策方法及应用[M].北京:清华大学出版社,2004.
[26]Aiche F,Abbas M,Dubois D.Chance-constrained programming with fuzzy stochastic coefficients[J].Fuzzy Optimization and Decision Making,2013,12(2):125-152.
[27]何静.只有输出(入)的数据包络分析及其应用[J].系统工程学报,1995,10(2):48-55.
[28]Cook W D,Kress M.A data envelopment model for aggregating preference rankings[J].Management Science,1990,36(11):1302-1310.
[29]Green R H,Doyle J R,Cook W D.Preference voting and project ranking using DEA and cross evaluation[J].European Journal of Operational Research,1996,90(3):461-472.
[30]曾祥云,吴育华.L-R型区间DEA模型及其变换[J].管理工程学报,2001,18(1):60-65.
[31]马生昀,马占新,孙娜.广义与传统BC2模型效率评价差异及其几何刻画[J].数学的实践与认识,2014,44(9):11-18.
[32]Jahanshahloo G R,Lotfi F H,Malkhalifeh M R,et al.A generalized model for data envelopment analysis with interval data[J].Applied Mathematical Modelling,2009,33(7):3237-3244.
[33]Kundu S.Min-transitivity of fuzzy leftness relationship and its application to decision making[J].Fuzzy Sets and Systems,1997,86(3):357-367.
[34]Hu Baoqing,Wang Song.A novel approach in uncertain programming part I:New arithmetic and order relationfor interval numbers[J].Journal of Industrial&Management Optimization,2006,2(4):351-371.