基于未来效率的兼顾公平与效率的资源分配DEA模型研究——以各省碳排放额分配为例
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摘要
根据需要实现的目标,评估各生产决策单元的投入产出效率及改进潜力,可以为资源分配提供重要参考。构建一个基于未来效率的兼顾公平与效率的资源分配DEA模型可以有效、灵活地解决该问题。该DEA模型首先根据历史数据计算每个生产决策单元过去各期的技术增长率,并预测各DMU未来的技术增长率,从而获得未来的生产前沿面。以此为基础,在九个硬性目标约束下,分三个步骤分别解决三个追求的软性目标:最大化期望总产出、最小化非期望总产出、最小化可变要素总投入。管理者不仅可以改变九个硬性目标的参数值,以及调整三个软性目标的优先顺序和软性目标参数值,进而形成各种兼顾效率与公平的资源分配方案。最后,运用该DEA模型评估了我国各省碳排放削减潜力,并形成了能够实现管理者期望目标的各省碳排放削减责任分配方案。
It can provide a reference for formulating reasonable resource allocation scheme that assesses Input-Output efficiency and improving potential according to the manager's expected objectives.As a nonparametric approach,DEA-type approaches have several most obvious advantages relative to traditional parametric approaches—no specification of a specific parametric functional form is required,nor is specification of error structures,thus avoiding possible specification error.Another advantage is the ease with which technologies with multiple outputs and inputs.Furthermore,these technologies can be estimated even in the absence of prices or costs,which proves useful when we wish to model joint production with undesirable outputs and useful for analysis in environmental and natural resource applications.The existing literature has achieved fruitful results in the research of DEA model.However,shortcomings exist.Firstly,Most of the existing DEA models evaluate the efficiency of each Decision-Making Unit(DMU)and allocate resources according to the previous data.However,the optimal efficiency in the past does not represent the optimal efficiency in the future.According to the economic principle,the optimal resource allocation in the future period can only be realized according to the optimal efficiency of each DMU in the future period.According to the historical data,each DMU’s technical growth rate of every period is calculated,and then each DMU technical growth rate of future is forecasted so that acquires the prospective efficient frontier.Secondly,each DMU’s input-output efficiency is measured in DEA models by moving the actual input-output point of each DMU to a point on the production frontier;path improvement is merely movement of different points of the production frontier.However,in actual economic management,such assessment of the potential for efficiency improvement and resource allocation is limited;in the real economy,management often achieves some of the desired goals.Managers want to assess how much DMU's actual input-output space must be improved to meet the managers'expectations,as a basis for allocating resources.Goals pursued by managers are often complex and multi-purposed,not merely consisting of the pursuit of economic and technological optimization,but also considering social goals,such as social equity.On the basis of the DEA model proposed by Adler&Volta(2016),a DEA model of resource allocation is constructed based on future efficiency with consideration of fairness and efficiency.With nine rigid objectives constraints the proposed approach has three phases,which correspond to three soft objectives that are pursued lexicographically.The nine rigid objectives constraints are as following:constraints■require per-capita stand-ard input,per-capita desirable output,per-capita undesirable output of each DMU controlled■ within theexpected fair range,respectively;constraintsrequire target standard input,target desir-able output,target undesirable output of each DMU controlled within the expected range,respectively;constraints■require total target standard input,to-tal target desirable output,total target undesirable output of all DMU controlled within the expected range,respectively.The three soft objectives are maximizing aggregated desirable production described as■,minimizing undesirable total emissions described as■,minimizing the con-sumption of input resources described as■The regulator not only can alter the parametervalues of the six rigid objectives and define the relative priority of these objectives,but also can set reasonable desired objectives according to the potential of energy saving and emission reduction assessed in every phase,thus forming various objective-oriented allocation scheme which considers to Efficiency and Equity.At last,the DEA model for empirical analysis is applied to allocate Carbon Emission Rights in each China’s Province.Each province is regarded as a DMU.Each DMU’s inputs and outputs are that inputs are labor,energy,fixed capital;desirable output are Gross Domestic Product(GDP);undesirable outputs are solid waste emissions,waste water and carbon emissions.Because some data are unavailable and the statistical caliber is nont consistent,29provinces are included in this study;the Tibet Autonomous Region,Hong Kong Special Administrative Region,Macao Special Administrative Region,and Taiwan Province are not included in the analysis,and the Sichuan Province and Chongqing City are merged into one province(Sichuan)before administrative division.In the empirical analysis,the proposed DEA method solves the problem of potential assessment and responsibility allocation of carbon emission reduction in China's provinces.On the one hand,the total amount of carbon emissions are reduced by 8%than the current emissions,on the other hand,the gap between per capita carbon emissions and reasonable per capita carbon emissions has narrowed,thus both the equity and efficiency are realized.In general,the DEA model of this paper has four characteristics.(1)the DEA model allocates resources in the future period based on the future efficiency.(2)the DEA model sets targets on the basis of potential evaluation,which makes the resource allocation scheme more feasible.(3)the DEA model assesses the efficiency and allocates the resource according to the expected goals,which include nine rigid objectives and three soft objectives.(4)additional important feature of the DEA model is its flexibility,i.e.,a different relative weight u_k、ν_sandμ_ican be given to desirable output k,desirable output s and input i,soas to form new target formula■.
It can provide a reference for formulating reasonable resource allocation scheme that assesses Input-Output efficiency and improving potential according to the manager's expected objectives.As a nonparametric approach,DEA-type approaches have several most obvious advantages relative to traditional parametric approaches—no specification of a specific parametric functional form is required,nor is specification of error structures,thus avoiding possible specification error.Another advantage is the ease with which technologies with multiple outputs and inputs.Furthermore,these technologies can be estimated even in the absence of prices or costs,which proves useful when we wish to model joint production with undesirable outputs and useful for analysis in environmental and natural resource applications.The existing literature has achieved fruitful results in the research of DEA model.However,shortcomings exist.Firstly,Most of the existing DEA models evaluate the efficiency of each Decision-Making Unit(DMU)and allocate resources according to the previous data.However,the optimal efficiency in the past does not represent the optimal efficiency in the future.According to the economic principle,the optimal resource allocation in the future period can only be realized according to the optimal efficiency of each DMU in the future period.According to the historical data,each DMU’s technical growth rate of every period is calculated,and then each DMU technical growth rate of future is forecasted so that acquires the prospective efficient frontier.Secondly,each DMU’s input-output efficiency is measured in DEA models by moving the actual input-output point of each DMU to a point on the production frontier;path improvement is merely movement of different points of the production frontier.However,in actual economic management,such assessment of the potential for efficiency improvement and resource allocation is limited;in the real economy,management often achieves some of the desired goals.Managers want to assess how much DMU's actual input-output space must be improved to meet the managers'expectations,as a basis for allocating resources.Goals pursued by managers are often complex and multi-purposed,not merely consisting of the pursuit of economic and technological optimization,but also considering social goals,such as social equity.On the basis of the DEA model proposed by Adler&Volta(2016),a DEA model of resource allocation is constructed based on future efficiency with consideration of fairness and efficiency.With nine rigid objectives constraints the proposed approach has three phases,which correspond to three soft objectives that are pursued lexicographically.The nine rigid objectives constraints are as following:constraints■require per-capita stand-ard input,per-capita desirable output,per-capita undesirable output of each DMU controlled■ within theexpected fair range,respectively;constraintsrequire target standard input,target desir-able output,target undesirable output of each DMU controlled within the expected range,respectively;constraints■require total target standard input,to-tal target desirable output,total target undesirable output of all DMU controlled within the expected range,respectively.The three soft objectives are maximizing aggregated desirable production described as■,minimizing undesirable total emissions described as■,minimizing the con-sumption of input resources described as■The regulator not only can alter the parametervalues of the six rigid objectives and define the relative priority of these objectives,but also can set reasonable desired objectives according to the potential of energy saving and emission reduction assessed in every phase,thus forming various objective-oriented allocation scheme which considers to Efficiency and Equity.At last,the DEA model for empirical analysis is applied to allocate Carbon Emission Rights in each China’s Province.Each province is regarded as a DMU.Each DMU’s inputs and outputs are that inputs are labor,energy,fixed capital;desirable output are Gross Domestic Product(GDP);undesirable outputs are solid waste emissions,waste water and carbon emissions.Because some data are unavailable and the statistical caliber is nont consistent,29provinces are included in this study;the Tibet Autonomous Region,Hong Kong Special Administrative Region,Macao Special Administrative Region,and Taiwan Province are not included in the analysis,and the Sichuan Province and Chongqing City are merged into one province(Sichuan)before administrative division.In the empirical analysis,the proposed DEA method solves the problem of potential assessment and responsibility allocation of carbon emission reduction in China's provinces.On the one hand,the total amount of carbon emissions are reduced by 8%than the current emissions,on the other hand,the gap between per capita carbon emissions and reasonable per capita carbon emissions has narrowed,thus both the equity and efficiency are realized.In general,the DEA model of this paper has four characteristics.(1)the DEA model allocates resources in the future period based on the future efficiency.(2)the DEA model sets targets on the basis of potential evaluation,which makes the resource allocation scheme more feasible.(3)the DEA model assesses the efficiency and allocates the resource according to the expected goals,which include nine rigid objectives and three soft objectives.(4)additional important feature of the DEA model is its flexibility,i.e.,a different relative weight u_k、ν_sandμ_ican be given to desirable output k,desirable output s and input i,soas to form new target formula■.
引文
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[2]Charnes A,Cooper W W,Rhodes E.Measuring the efficiency of decision making units[J].European Journal of Operational Research,1978,2(6):429-444.
[3]Banker R D,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.
[4]Adler N,Volta N.Accounting for externalities and disposability:A directional economic environmental distance function[J].European Journal of Operational Research,2016,250(1):314-327.
[5]Fre R,Grosskopf S,Pasurka C,et al.On nonparametric estimation:With a focus on agriculture[J].Annual Review of Resource Economics,2013,5(1):93-110.
[6]卞亦文.基于DEA的污染物排放配额分配方法研究[J].运筹学学报,2010,14(4):75-82.
[7]Chung Y H,Fre R,Grosskopf S.Productivity and undesirable outputs:A directional distance function approach[J].Microeconomics,1995,51(3):229-240.
[8]Lozano S,Villa G,Brnnlund R.Centralised reallocation of emission permits using DEA[J].European Journal of Operational Research,2009,193(3):752-760.
[9]范建平,肖慧,樊晓宏.考虑非期望产出的改进EBM-DEA三阶段模型---基于中国省际物流业效率的实证分析[J].中国管理科学,2017,25(8):166-174.
[10]Tone K.Dealing with undesirable outputs in DEA:Aslacks-based measure(SBM)approach[J].The Operations Research Society of Japan,2004:44-45.
[11]Scheel H.Undesirable outputs in efficiency valuations[J].European Journal of Operational Research,2001,132(2):400-410.
[12]韩松,魏权龄.资源配置的非参数DEA模型[J].系统工程理论与实践,2002,22(7):59-64.
[13]Cook W D,Zhu J.Allocation of shared costs among decision making units:A DEA approach[J].Computers and Operations Research,2005,32(2):2171-2178.
[14]Beasley J E.Allocating fixed costs and resources via data envelopment analysis[J].European Journal of Operational Research,2003,147(1):198-216.
[15]Lotfi F H,Hatami-Marbini A,Agrell P J,et al.Allocating fixed resources and setting targets using a common-weights DEA approach[J].Computers&Industrial Engineering,2013,64(2):631-640.
[16]Lozano S,Villa G,Brnnlund R.Centralised reallocation of emission permits using DEA[J].European Journal of Operational Research,2009,193(3):752-760.
[17]林坦,宁俊飞.基于零和DEA模型的欧盟国家碳排放权分配效率研究[J].数量经济技术经济研究,2011(3):36-50.
[18]Avellar J V G,Milioni A Z,Rabello T N.Modelos DEA com variáveis limitadas ou soma constante[J].Pesquisa Operacional,2005,25(1):135-150.
[19]Avellar J V G,Milioni A Z,Rabello T N.Spherical frontier DEA model based on a constant sum of inputs[J].Journal of the Operational Research Society,2007,58(3):1246-1251.
[20]Silva R C,Milioni A Z.The adjusted spherical frontier model with weight restrictions[J].European Journal of Operational Research,2012,220(3):729-735.
[21]Milioni A Z,De Avellar J V G,Gomes E G,et al.An ellipsoidal frontier model:Allocating input via parametric DEA[J].European Journal of Operational Research,2011,209(2):113-121.
[22]Mehdiloozad M,Zhu J,Sahoo B K.Identification of congestion in data envelopment analysis under the occurrence of multiple projections:A reliable method capable of dealing with negative data[J].European Journal of Operational Research,2018,265(2):644-654.
[23]Kuosmanen T K.Measurement and analysis of ecoefficiency:An economist's perspective[J].Journal of Industrial Ecology,2005,9(4):15-18.
[24]Fare R,Grosskopf S.Productivity growth,technical progress,and efficiency change in industrialized countries[J].American Economic Review,1994,84(1):66-83.
[25]张军,吴桂英,张吉鹏.中国省际物质资本存量估算:1952-2000[J].经济研究,2004,(10):35-44.
[26]Cook W D,Du J,Zhu J.Units invariant DEA when weight restrictions are present:Ecological performance of US electricity industry[J].Annals of Operations Research,2017,255(1-2):323-346.
[2]Charnes A,Cooper W W,Rhodes E.Measuring the efficiency of decision making units[J].European Journal of Operational Research,1978,2(6):429-444.
[3]Banker R D,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.
[4]Adler N,Volta N.Accounting for externalities and disposability:A directional economic environmental distance function[J].European Journal of Operational Research,2016,250(1):314-327.
[5]Fre R,Grosskopf S,Pasurka C,et al.On nonparametric estimation:With a focus on agriculture[J].Annual Review of Resource Economics,2013,5(1):93-110.
[6]卞亦文.基于DEA的污染物排放配额分配方法研究[J].运筹学学报,2010,14(4):75-82.
[7]Chung Y H,Fre R,Grosskopf S.Productivity and undesirable outputs:A directional distance function approach[J].Microeconomics,1995,51(3):229-240.
[8]Lozano S,Villa G,Brnnlund R.Centralised reallocation of emission permits using DEA[J].European Journal of Operational Research,2009,193(3):752-760.
[9]范建平,肖慧,樊晓宏.考虑非期望产出的改进EBM-DEA三阶段模型---基于中国省际物流业效率的实证分析[J].中国管理科学,2017,25(8):166-174.
[10]Tone K.Dealing with undesirable outputs in DEA:Aslacks-based measure(SBM)approach[J].The Operations Research Society of Japan,2004:44-45.
[11]Scheel H.Undesirable outputs in efficiency valuations[J].European Journal of Operational Research,2001,132(2):400-410.
[12]韩松,魏权龄.资源配置的非参数DEA模型[J].系统工程理论与实践,2002,22(7):59-64.
[13]Cook W D,Zhu J.Allocation of shared costs among decision making units:A DEA approach[J].Computers and Operations Research,2005,32(2):2171-2178.
[14]Beasley J E.Allocating fixed costs and resources via data envelopment analysis[J].European Journal of Operational Research,2003,147(1):198-216.
[15]Lotfi F H,Hatami-Marbini A,Agrell P J,et al.Allocating fixed resources and setting targets using a common-weights DEA approach[J].Computers&Industrial Engineering,2013,64(2):631-640.
[16]Lozano S,Villa G,Brnnlund R.Centralised reallocation of emission permits using DEA[J].European Journal of Operational Research,2009,193(3):752-760.
[17]林坦,宁俊飞.基于零和DEA模型的欧盟国家碳排放权分配效率研究[J].数量经济技术经济研究,2011(3):36-50.
[18]Avellar J V G,Milioni A Z,Rabello T N.Modelos DEA com variáveis limitadas ou soma constante[J].Pesquisa Operacional,2005,25(1):135-150.
[19]Avellar J V G,Milioni A Z,Rabello T N.Spherical frontier DEA model based on a constant sum of inputs[J].Journal of the Operational Research Society,2007,58(3):1246-1251.
[20]Silva R C,Milioni A Z.The adjusted spherical frontier model with weight restrictions[J].European Journal of Operational Research,2012,220(3):729-735.
[21]Milioni A Z,De Avellar J V G,Gomes E G,et al.An ellipsoidal frontier model:Allocating input via parametric DEA[J].European Journal of Operational Research,2011,209(2):113-121.
[22]Mehdiloozad M,Zhu J,Sahoo B K.Identification of congestion in data envelopment analysis under the occurrence of multiple projections:A reliable method capable of dealing with negative data[J].European Journal of Operational Research,2018,265(2):644-654.
[23]Kuosmanen T K.Measurement and analysis of ecoefficiency:An economist's perspective[J].Journal of Industrial Ecology,2005,9(4):15-18.
[24]Fare R,Grosskopf S.Productivity growth,technical progress,and efficiency change in industrialized countries[J].American Economic Review,1994,84(1):66-83.
[25]张军,吴桂英,张吉鹏.中国省际物质资本存量估算:1952-2000[J].经济研究,2004,(10):35-44.
[26]Cook W D,Du J,Zhu J.Units invariant DEA when weight restrictions are present:Ecological performance of US electricity industry[J].Annals of Operations Research,2017,255(1-2):323-346.
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