额外资源按需分配方法研究
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摘要
文献Wei Quanling等~([1])的最后一段提出了这样一类额外资源分配问题:假设有一些额外的投入资源将要分配给全部或者部分决策单元,如果我们希望分配结果对于整个系统(该系统由全部决策单元组成)来说是最有益的,那么应当如何分配这些额外的投入资源?他们同时还指出系统中哪些决策单元能够获得额外的投入资源,这不仅取决于决策单元的效率,还需要考虑规模报酬。针对此类问题,本文提出一种额外资源按需分配方法:首先,综合决策单元的技术效率与其投影点的规模弹性构建发展曲线,并由决策单元的发展曲线获知其投入变动与产出变动的对应关系;然后,把额外资源分成若干等份,依次分配每一个等份的额外资源,每次分配使系统的总产出增加实现最大,直至分配完全部的额外资源,或者分配某一份额外资源不再带来任何的产出增加,分配就会停止;最后,把决策单元在每一次分配过程中获得的额外资源进行累加,得到这个决策单元最终的分配结果。全文的最后分别在"一个投入一个产出"和"两个投入一个产出"情况下给出两个具体的分配算例。分配结果表明,这种按需分配方法不会缩减任意一个决策单元当前占有的投入资源数量,并且还可以有效地在辨识出某种额外资源在规模上和结构上存在的冗余,从而有效地避免不必要的分配。
The last paragraph of literature Wei Quanling et al.~([1])raises an extra resource allocation problem:suppose there are some extra resources which can be given to all or only apart of DMUs,and if we want the allocation to be most beneficial to the whole system,how should the extra resources be distributed.They also point out that the extra resource allocation problem and the selection of DUMs should depend on not only DMUs' efficiency,but also the returns to scale.An on-demand allocation method is proposed to deal with such problem.Firstly,on the basis of technical efficiency and scale elasticity,DMUs' development curves are established.Development curves are used to reveal the corresponding relationships between input change and output change.Secondly,extra resources are divided into several equal parts,and the allocation goal of each part is to achieve the maximum output increase.The allocation will stop once all extra resources are allocated or a part of extra resources does not result in any output increase.Finally,the extra resources obtained by DMU in each allocation process are accumulated to obtain the final allocation results.At the end of this paper,two examples are given to illustrate our method,in the case of‘one input and one output'and ‘two inputs,one output'respectively.The allocation results show that the method proposed in this paper do not reduce the amount of input resources currently occupied by any DMU.Moreover,it can identify the redundancy of extra resources in scale or in structure,so as to timely avoid unnecessary distribution.
The last paragraph of literature Wei Quanling et al.~([1])raises an extra resource allocation problem:suppose there are some extra resources which can be given to all or only apart of DMUs,and if we want the allocation to be most beneficial to the whole system,how should the extra resources be distributed.They also point out that the extra resource allocation problem and the selection of DUMs should depend on not only DMUs' efficiency,but also the returns to scale.An on-demand allocation method is proposed to deal with such problem.Firstly,on the basis of technical efficiency and scale elasticity,DMUs' development curves are established.Development curves are used to reveal the corresponding relationships between input change and output change.Secondly,extra resources are divided into several equal parts,and the allocation goal of each part is to achieve the maximum output increase.The allocation will stop once all extra resources are allocated or a part of extra resources does not result in any output increase.Finally,the extra resources obtained by DMU in each allocation process are accumulated to obtain the final allocation results.At the end of this paper,two examples are given to illustrate our method,in the case of‘one input and one output'and ‘two inputs,one output'respectively.The allocation results show that the method proposed in this paper do not reduce the amount of input resources currently occupied by any DMU.Moreover,it can identify the redundancy of extra resources in scale or in structure,so as to timely avoid unnecessary distribution.
引文
[1]Wei Quanling,Zhang Jianzhong,Zhang Xiangsun.An inverse DEA model for inputs/outputs estimate[J].European Journal of Operational Research,2000,121(1):151-163.
[2]魏权龄.数据包络分析(DEA)[M].北京:科学出版社,2004.
[3]Emrouznejad A,Yang Guoliang.A survey and analysis of the first 40years of scholarly literature in DEA:1978-2016[J].Socio-Economic Planning Sciences,2018,61:4-8.
[4]Golany B,Tamir E.Evaluating efficiency-effectiveness equality trade-offs:A data envelopment analysis approach[J].Management Science,1995,41(7):1172-1184.
[5]Athanassopoulos A D.Goal programming&data envelopment analysis(GoDEA)for target-based multi-level planning:Allocating central grants to the Greek local authorities[J].European Journal of Operational Research,1995,87(3):535-550.
[6]Fare R,Grabowski R,Grosskopf S,et al.Efficiency of a fixed but allocatable input:A non-parametric approach[J].Economics Letters,2004,56(2):187-193.
[7]Yan Hong,Wei Quanling,Hao Gang.DEA models for resource reallocation and production input/output estimation[J].European Journal of Operational Research,2002,136(1):19-31.
[8]Beasley J E.Allocating fixed costs and resources via data envelopment analysis[J].European Journal of Operational Research,2003,147(1):198-216.
[9]Korhonen P,Syrjanen M.Resource allocation based on efficiency analysis[J].Management Science,2004,50(8):1134-1144.
[10]Asmild M,Paradi J C,Pastor J T.Centralized resource allocation BCC models[J].Omega,2009,37(1):40-49.
[11]Bi Gongbing,Ding Jingjing,Luo Yan,et al.Resource allocation and target setting for parallel production system based on DEA[J].Applied Mathematical Modelling,2011,35(9):4270-4280.
[12]Nasrabadi N,Dehnokhalaji A,Kiani N A,et al.Resource allocation for performance improvement[J].Annals of Operations Research,2012,196(1):459-468.
[13]Cherchye L,Rock B D,Dierynck B,et al.Opening the“Black Box”of efficiency measurement:Input allocation in multioutput settings[J].Operations Research,2013,61(5):1148-1165.
[14]Fang Lei.Centralized resource allocation based on efficiency analysis for step-by-step improvement paths[J].Omega,2015,51:24-28.
[15]Mandell M B.Modeling effectiveness-equity tradeoffs in public service delivery systems[J].Management Science 1991;37(4):467-482.
[16]Golany B,Tamir E.Evaluating efficiency-effectiveness-equality trade-offs:A data envelopment analysis approach[J].Management Science,1995,41(7):1172-1184.
[17]Athanassopoulos A D.Decision support for targetbased resource allocation of public services in multiunit and multilevel systems[J].Management Science,1998,44(2):173-187.
[18]Karsu O,Morton A.Incorporating balance concerns in resource allocation decisions:A bi-criteria modelling approach[J].OMEGA,2014,44:70-82.
[19]李晓亚,崔晋川.基于DEA方法的额外资源分配算法[J].系统工程学报,2007,22(1):57-61.
[20]Du Juan,Cook W D,Liang Liang,et al.Fixed cost and resource allocation based on DEA cross-efficiency[J].European Journal of Operational Research,2014,235(1):206-214.
[21]崔玉泉,张宪,芦希,等.随机加权交叉效率下的资源分配问题研究[J].中国管理科学,2015,23(1):121-127.
[22]Zhang Meng,Wang Lili,Cui Jinchuan.Extra resource allocation:A DEA approach in the view of efficiencies[J].Journal of the Operations Research Society of China,2018(1):1-22.
[23]Cook W D,Kress M.Characterizing an equitable allocation of shared costs:A DEA approach[J].European Journal of Operational Research,1999,119(3):652-661.
[24]Cook W D,Zhu Joe.Allocation of shared costs among decision making units:A DEA approach[J].Computers and Operations Research,2005,32(8):2171-2178.
[25]Lin Ruiyue.Allocating fixed costs or resources and setting targets via data envelopment analysis[J].Applied Mathematics&Computation,2011,217(13):6349-6358.
[26]Li Yongjun,Yang Feng,Liang Liang,et al.Allocatingthe fixed cost as a complement of other cost inputs:A DEA approach[J].European Journal of Operational Research,2009,197(1):389-401.
[27]雷西洋,戴前智,李勇军,等.考虑系统内部平行结构的DEA资源分摊方法[J].中国管理科学,2015,23(1):50-55.
[28]张冉,冉伦,杜涛,等.考虑满意度的两阶段DEA固定成本分摊方法[J].中国管理科学,2019,27(2):138-149.
[29]佘冰玲,崔晋川.基于DEA和弹性的额外资源分配算法[J].运筹与管理,录用.
[30]Banker R,Charnes A,Cooper W W.Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis[J].Management Science,1984,30(9):1078-1092.
[31]Asmild M,Paradi J C,Reese D N.Theoretical perspectives of trade-off analysis using DEA[J].Omega,2006,34:337-343.
[32]Khoshandam L,KazemiMatin R,Amirteimoori A.Marginal rates of substitution in data envelopment analysis with undesirable outputs:A directional approach[J].Measurement,2015,68:49-57.
[2]魏权龄.数据包络分析(DEA)[M].北京:科学出版社,2004.
[3]Emrouznejad A,Yang Guoliang.A survey and analysis of the first 40years of scholarly literature in DEA:1978-2016[J].Socio-Economic Planning Sciences,2018,61:4-8.
[4]Golany B,Tamir E.Evaluating efficiency-effectiveness equality trade-offs:A data envelopment analysis approach[J].Management Science,1995,41(7):1172-1184.
[5]Athanassopoulos A D.Goal programming&data envelopment analysis(GoDEA)for target-based multi-level planning:Allocating central grants to the Greek local authorities[J].European Journal of Operational Research,1995,87(3):535-550.
[6]Fare R,Grabowski R,Grosskopf S,et al.Efficiency of a fixed but allocatable input:A non-parametric approach[J].Economics Letters,2004,56(2):187-193.
[7]Yan Hong,Wei Quanling,Hao Gang.DEA models for resource reallocation and production input/output estimation[J].European Journal of Operational Research,2002,136(1):19-31.
[8]Beasley J E.Allocating fixed costs and resources via data envelopment analysis[J].European Journal of Operational Research,2003,147(1):198-216.
[9]Korhonen P,Syrjanen M.Resource allocation based on efficiency analysis[J].Management Science,2004,50(8):1134-1144.
[10]Asmild M,Paradi J C,Pastor J T.Centralized resource allocation BCC models[J].Omega,2009,37(1):40-49.
[11]Bi Gongbing,Ding Jingjing,Luo Yan,et al.Resource allocation and target setting for parallel production system based on DEA[J].Applied Mathematical Modelling,2011,35(9):4270-4280.
[12]Nasrabadi N,Dehnokhalaji A,Kiani N A,et al.Resource allocation for performance improvement[J].Annals of Operations Research,2012,196(1):459-468.
[13]Cherchye L,Rock B D,Dierynck B,et al.Opening the“Black Box”of efficiency measurement:Input allocation in multioutput settings[J].Operations Research,2013,61(5):1148-1165.
[14]Fang Lei.Centralized resource allocation based on efficiency analysis for step-by-step improvement paths[J].Omega,2015,51:24-28.
[15]Mandell M B.Modeling effectiveness-equity tradeoffs in public service delivery systems[J].Management Science 1991;37(4):467-482.
[16]Golany B,Tamir E.Evaluating efficiency-effectiveness-equality trade-offs:A data envelopment analysis approach[J].Management Science,1995,41(7):1172-1184.
[17]Athanassopoulos A D.Decision support for targetbased resource allocation of public services in multiunit and multilevel systems[J].Management Science,1998,44(2):173-187.
[18]Karsu O,Morton A.Incorporating balance concerns in resource allocation decisions:A bi-criteria modelling approach[J].OMEGA,2014,44:70-82.
[19]李晓亚,崔晋川.基于DEA方法的额外资源分配算法[J].系统工程学报,2007,22(1):57-61.
[20]Du Juan,Cook W D,Liang Liang,et al.Fixed cost and resource allocation based on DEA cross-efficiency[J].European Journal of Operational Research,2014,235(1):206-214.
[21]崔玉泉,张宪,芦希,等.随机加权交叉效率下的资源分配问题研究[J].中国管理科学,2015,23(1):121-127.
[22]Zhang Meng,Wang Lili,Cui Jinchuan.Extra resource allocation:A DEA approach in the view of efficiencies[J].Journal of the Operations Research Society of China,2018(1):1-22.
[23]Cook W D,Kress M.Characterizing an equitable allocation of shared costs:A DEA approach[J].European Journal of Operational Research,1999,119(3):652-661.
[24]Cook W D,Zhu Joe.Allocation of shared costs among decision making units:A DEA approach[J].Computers and Operations Research,2005,32(8):2171-2178.
[25]Lin Ruiyue.Allocating fixed costs or resources and setting targets via data envelopment analysis[J].Applied Mathematics&Computation,2011,217(13):6349-6358.
[26]Li Yongjun,Yang Feng,Liang Liang,et al.Allocatingthe fixed cost as a complement of other cost inputs:A DEA approach[J].European Journal of Operational Research,2009,197(1):389-401.
[27]雷西洋,戴前智,李勇军,等.考虑系统内部平行结构的DEA资源分摊方法[J].中国管理科学,2015,23(1):50-55.
[28]张冉,冉伦,杜涛,等.考虑满意度的两阶段DEA固定成本分摊方法[J].中国管理科学,2019,27(2):138-149.
[29]佘冰玲,崔晋川.基于DEA和弹性的额外资源分配算法[J].运筹与管理,录用.
[30]Banker R,Charnes A,Cooper W W.Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis[J].Management Science,1984,30(9):1078-1092.
[31]Asmild M,Paradi J C,Reese D N.Theoretical perspectives of trade-off analysis using DEA[J].Omega,2006,34:337-343.
[32]Khoshandam L,KazemiMatin R,Amirteimoori A.Marginal rates of substitution in data envelopment analysis with undesirable outputs:A directional approach[J].Measurement,2015,68:49-57.