摘要
效率的评价方法有参数和非参数之分。参数的方法(计量经济学模型)需要在评价前确定生产函数的形式；数据包络分析(Data Envelopment Analysis,简称DEA)无需假设生产函数的具体形式,而通过生产可能集来刻画出生产技术。通常情况下,计量经济学的方法是估计生产技术的平均水平,而DEA方法刻画的是一种“极端”的关系。两种方法各有利弊,在效率评价理论和应用中都不可缺少。
目前,DEA应用的领域在不断地扩大。从传统的广泛应用于历史的运营结果的评价用途(事后评价),如研究多家医院或学校之间的相对有效性,强调DEA的诊断功能,扩展应用于计划功能(事前评价),例如计划与目标设定,强调预测功能。本论文的主要研究DEA方法在资源分配上的应用,从而发展其事前评价的功能。
本论文共分六章,主要内容如下：
第一章对效率评价的基本概念进行阐述,然后总结数据包络分析的相关理论的研究现状。最后结合DEA方法中资源分配和目标设定中的研究现状,提出本文的研究意义和论文的结构。
第二章针对一类并联生产系统的生产可能集,在规模收益可变假设下无法由其内部各子生产单元的生产可能集凸包直接刻画出来的问题,系统地研究了并联生产系统在规模收益可变情况下的效率评价方法、性质以及资源配置含义。提出了并联系统中两类不同的技术效率：DMU内部技术效率及DMU技术效率,并以两者之比来反映DMU内部的资源配置状况。最后,以一个仿真实验来进一步分析所构建模型的特性。
第三章研究并联生产系统的FDH模型及其性质,并将提出的模型应用到传统的分配问题中。提出的方法首先拓展了DEA方法的理论和应用范围；其次,扩大了传统分配问题的内涵,即从传统的单一成本或利润指标扩展到多投入多产出的情形；最后,探讨在分配工作任务的同时考虑资源约束下的产出目标制订问题。
第四章提出多目标规划模型来辅助决策者进行资源分配和目标设定工作。提出了五个准则：效率性、效果性、公平性和最小变动特性准则,并将其引入到模型中来产生资源分配和目标设定的方案。因本章的模型是基于网络DEA理论,这使得模型能够同时处理组织中单元之间,以及单元内部各子单元间的资源最优配置问题。另外,提出的模型使得决策者可以在统一的框架下分析效果、效率、公平和分配成本之间替代关系。最后,使用虚拟的10个集中决策管理的银行数据演示提出的方法。
第五章针对存在并联的子决策单元的系统,建立了DEA效率评价模型。提出的DEA模型考虑了保证域和资源配置的优化约束问题,既保证了模型解的合理性,又可以向决策者提供每个系统内部子单元的资源分配信息。最后,通过对最近一届冬夏奥运会参赛国综合效率评价和资源配置的应用分析,说明了新模型的可行性和优越性。
第六章总结和展望。对本文的主要研究内容进行总结,指出研究存在的不足之处和进一步研究的方向。
Efficiency evaluation methodology can be classified as parametric and nonparametric. The parametric methods require explicit specification of production function before evaluation, while the DEA (Data envelopment analysis), as nonparametric method, doesn't need any a priori information such as production function. It takes advantage of production possibility set. In general, the econometric models estimate the mean efficiency, while the DEA characterize the extremal relation. Therefore, both mothods deserve merits, and are important in the application and theory of efficiency evaluation.
At present, the application field of DEA grows larger and larger. It has been extended from the traditional fuction as an ex post evaluation of the past performance to ex ante function as a planning tool. The former function is diagnostical, and the latter function is predictive. In the current thesis, DEA is studied from the perspective of ex ante function aiming at extending its predictive ability. In particular, it mainly studies the application of DEA for resource allocation purpose.
The thesis consists of six chapters, the topics of which are illustrated as follows:
Chapter1firstly reviews the basics in the field of efficiency evaluation. Then, it summarizes the main topics under research to date in the DEA literatue. In the end, associated with the application of DEA to the resource allocation and target setting topic, the significance of the thesis is highlighted. The chapter concludes with the structure of the thesis.
Chapter2studies FDH model for parallel production system, and the related properties. The proposed model is then applied to the research of traditional assignment problem in operational research by modeling it as a parallel production system. In doing so, this paper firstly extends the DEA methodologies both in theory and application; secondly, the paper broadens the application of the traditional assignment problem in operational research, i.e., this paper extends the traditional assignment problem to cases with multiple inputs and outputs from a single criterion such as cost or profit. Finally, the proposed model is able to aid decision makers in assigning jobs with resource constraints together with target setting.
Chapter3aims at the problem with a particular parallel production system that the variable returns to scale production possibility set (PPS) of decision maki" (DMUs) can not be directly characterized by the convex hull of PPS's of Sub-DMUs (SDMUs). This chapter studies the efficiency assessment models, the relevant properties, and its resource configuration implication for parallel production system. Then it proposes two different definitions of technical efficiencies:the first is termed as DMU internal technical efficiency and the other is DMU technical efficiency. The ratio of the two indicators is used to reflect the performance of the internal resource allocation of DMU. Finally, a simulation experiment is used to study the proposed models deeply.
Chapter4presents a multi-objective programming to aid the decision makers in resource allocation and targets setting. Five criteria, namely feasibility criterion, effectiveness criterion, efficiency criterion, equality criterion, and minimal variation criterion are proposed and incorporated into the formation of resource allocation and target setting scheme. The proposed approach is based on network Data Envelopment Analysis (NDEA). Hence it can be used to generate the optimal distribution of resources among the internal components of each DMU. In this way, it enables decision makers to link the resource allocation and target setting scheme at a DMU level to that at an organization level. In addition, the proposed methodology offers decision makers an approach to exploring the tradeoffs among effectiveness, efficiency, equity, and allocation cost in a consistent way. Finally, simulated data of10banks under the administration of a centralized office are used to illustrate the approach.
Chapter5proposes a new DEA model to study efficiency of parallel system. In addition, it takes into account the AR restrictions and resource allocation of the parallel system. Not only can this method obtain reasonable solutions to the proposed DEA model, but also provide the managers with inner-information relative to resource allocation among the sub-systems within each DMU, and this really aids them in allocating resources efficiently in the real producing processes. Finally, to illustrate the advantages of the new DEA model, the paper presented an example of application to all countries that had participated in the last Summer and Winter Olympic Games.
Chapter6summarizes all the work of this thesis and presents some useful directions for future researches.
引文
Allen R, Athanassopoulos A, Dyson R.G., Thanassoulis E.1997. Weights restrictions and value judgements in Data Envelopment Analysis:Evolution, development and future directions[J]. Annals of Operations Research,73:13-34.
Andersen P, Petersen NC.1993. A procedure for ranking efficient units in data envelopment analysis [J]. Management Science,39:1261-1264.
Anderson TR, Hollingsworth KB, Inman LB.2002. The fixed weighting nature of a cross-evaluation model[J]. Journal of Productivity Analysis,18 (1),249-255.
Athanassopoulos A D, Lambroukos N, Seiford L.1999. Data envelopment scenario analysis for setting targets to electricity generating plants [J]. European Journal of Operational Research, 115:413-428.
Athanassopoulos A D.1998. Decision Support for Target-Based Resource Allocation of Public Services in Multiunit and Multilevel Systems [J]. Management Science,44 (2),173-187.
Athanassopoulos A D.1995. 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,87:535-550.
Avkiran NK. Opening the black box of efficiency analysis:An illustration with UAE banks[J]. Omega,37(2009):930-941.
Banker R, Charnes A, Cooper W.1984. Some models for the estimation of technical and scale inefficiencies in data envelopment analysis [J]. Management Science,30:1078-1092.
Banker R, Cooper W, Seiford L, Thrall R, Zhu J.2004. Returns to scale in different DEA models [J]. European Journal of Operations Research,154:345-362.
Banker RD, Thrall RM.1992. Estimation of returns-to-scale using Data Envelopment Analysis [J]. European Journal of Operational Research,62:74-84.
Banker RD.1993. Maximum Likelihood, Consistency and Data Envelopment Analysis:A Statistical Foundation[J]. Management Science,39(10):1265-1273.
Banker RD.1996. Hypothesis Tests Using Data Envelopment Analysis[J]. The Journal of Productivity Analysis,7:139-159.
Banker, R. D., Morey, R.C.1986. Efficiency Analysis for Exogenously Fixed Inputs and Outputs, Operations Research,32 (4):513-521.
Beasley J E.2003. Allocating fixed costs and resources via data envelopment analysis[J]. European Journal of Operational Research,147:198-216.
Bessent A, Bessent W, Elam J, Clark T.1988. Efficiency frontier determination by constrained facet analysis [J]. Operations Research,36(5):785-796.
Castelli L, Pesenti R, Ukovich W.2008. A classification of DEA models when the internal structure of the Decision Making Units is considered[J]. Ann Oper Res, DOI 10.1007/s10479-008-0414-2.
Charnes A, Cooper W W, Rhodes E.1978. Measuring the efficiency of decision making units [J]. European Journal of Operational Research,2:429-444
Charnes A, Cooper WW, Golany B, Seiford LM, Stutz J.1985. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions[J]. Journal of Econometrics,30:91-107.
Charnes A, Cooper WW, Huang ZM, Sun DB.1990. Polyhedral Cone-Ratio DEA Models With an Illustrative Application to Large Industrial Banks [J]. Journal of Econometrics,46:73-91.
Charnes A, Wei QL, Huang ZM.1986. Cone-ratio data envelopment analysis and multi-objective programming[J]. International Journal of Systems Science,20:1099-1118.
Chen C-M.2009. A network-DEA model with newe efficiency measures to incorporate the dynamic effect in production networks[J]. European Journal of Operational Research, 194:687-699.
Cook W D, Liang L, Zhu J.2009. Measuring performance of two-stage network structures by DEA:A review and future perspective[J]. Omega, doi:10.1016/j.omega.2009.12.001
Cook WD, Kress M, Seiford L.1993. On the use of ordinal data in Data Envelopment Analysis[J]. Journal of the Operational Research Society,44(2):33-140.
Cook WD, Kress M, Seiford L.1996. Data Envelopment Analysis in the presence of both quantitative and qualitative factors[J]. Journal of the Operational Research Society,47, 945-953.
Cook WD, Kress M.1991. A multiple criteria decision model with ordinal preference data[J]. European Journal of Operational Research,54(2):191-198.
Cook WD, Kress M.1994. A multiple criteria composite index model for quantitative and qualitative data[J]. European Journal of Operational Research,78(3):367-379.
Cook WD, Seiford LM.2009. Data envelopment analysis (DEA)-Thirty years on[J]. European Journal of Operational Research,192(1):1-17.
Cooper WW, Huang ZM, Lelas V, Li SX, Olesen OB.1998. Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA[J]. Journal of Productivity Analysis,9,53-79.
Cooper WW, Park KS, Yu G.1999. IDEA and AR-IDEA:Models for dealing with imprecise data in DEA[J]. Management Science,45(4),597-607.
Cooper WW, Park KS, Yu G.2001. IDEA (Imprecise Data Envelopment Analysis) with CMDs (column maximum decision making units) [J], Journal of the Operational Research Society,52: 176-181.
Debreu G.1951. The Coefficient of Resource Utilization[J]. Econometrica,19(3):273-92.
Deprins DL, Simar H. Tulkens.1984. Measuring labor efficiency in post offices, In M. Marchand, P. Pestieau, and H. Tulkens (eds.), The performance of public enterprises:concepts and measurement [M]. Amsterdam:North-Holland.
Doyle J, Green R.1994. Efficiency and cross efficiency in DEA:Derivations, meanings and the uses[J]. Journal of the Operational Research Society,45 (5),567-578.
Fare R, Grabowski R, Grosskopf S, Kraft S.1997. Efficiency of a fixed but allocable input:A non-parametric approach[J]. Economics Letters,56:187-193.
Fare R, Grosskopf S, Lovell C.1985. The Measurement of Efficiency of Production[M]. Kluwer Nijhoff.
Fare R, Grosskopf S, Lovell CAK.1985. The measurement of efficiency of production [M]. Boston:Kluwer Academic Publishers.
Fare R, Grosskopf S.2000. Network DEA[J]. Socio-Economic Planning Sciences, 34(2000):35-49.
Fare R, Grosskopf S.2000. Slacks and congestion:A comment[J]. Socio-economic Planning Sciences,34:27-33.
Fare R, Lovell CAK., Zieschang K.1983. Measuring the technical efficiency of multiple outputs technologies[M]. In:Eichhorn, W., Henn, R., Neumann, K., Shephard, R.W. (Eds.), Quantitative Studies on Production and Prices. Physica-Verlag, Vienna.
Farrell MJ.1957. The Measurement of Productive Efficiency [J]. Journal of the Royal Statistical Society, Series A,120(3) 253-82.
Fried O H, Lovell CAK, Schmidt SS.2008. The Measurement of Productive Efficiency and Productivity Growth [M]. New York:Oxford University Press.
Fuss M, McFadden D.1975. Production economics [M], Volume Ⅰ. North-Holland Publishing Company.
Golany B, Roll Y.1993. Some extensions of techniques to handle non-discretionary factors in Data Envelopment Analysis[J]. Journal of Productivity Analysis,4:419-432.
Golany B, Tamir E.1995. Evaluating Efficiency-Effectiveness-Equality trade-offs:a data envelopment analysis approach[J]. Management Science,41(7):1172-1184.
Golany B.1988. An Interactive MOLP Procedure for the Extension of DEA to Effectiveness Analysis[J]. Journal of Operational Research Society,39(8):725-734.
Gongbing Bi, Jingjing Ding, Yan Luo, Liang Liang.2011. A new Malmquist productivity index based on semi-discretionary variables with an application to commercial banks of China[J]. International Journal of Information Technology & Decision Making,10(4):713-730.
Green R, Doyle J, Cook WD.1996. Preference voting and project ranking using DEA and cross-evaluation[J]. European Journal of Operational Research,90,461-472.
Green RH, Doyle JR, Cook WD.1996. Efficiency Bounds in Data Envelopment Analysis[J]. European Journal of Operational Research,89:482-490.
Green RH, Doyle JR, Cook WD.1996. Efficiency bounds in data envelopment analysis[J]. European Journal of Operational Research,89:482-490.
Grosskopf S.1996. Statistical Inference and Nonparametric Efficiency:A Selective Survey[J]. The Journal of Productivity Analysis,7:161-176.
Hsieh L-F, Lin L-H.2009. A performance evaluation model for international tourist hotels in Taiwan-An application of the relational network DEA [J]. International Journal of Hospitality Management,29:14-24.
Kao C, Hwang SN.2008. Efficiency decomposition in two-stage data envelopment analysis:An application to non-life insurance companies in Taiwan[J]. European Journal of Operational Research 185:418-429.
Kao C.2009. Efficiency decomposition in network data envelopment analysis:A relational model[J]. European Journal of Operational Research,192:949-962.
Koopmans TC.1951. An Analysis of Production as an Efficient Combination of Activities, in T. C. Koopmans, ed., Activity Analysis of Production and Allocation[M]. Cowles Commission for Research in Economics Monograph No.13. New York:John Wiley and Sons.
Korhonen P, Syrjanen M.2004. Resource allocation based on efficiency analysis[J]. Management Science,50(8):1134-1144.
Land KC, Lovell CAK, Thore S.1993. Chance-Constrained Data Envelopment Analysis[J]. Managerial and Decision Economics,14(6):541-554.
Lang P, Yolalan OR, Kettani O.1995. Controlled Envelopment by Face Extension in DEA[J]. Journal of Operational Research Society,46(4):473-491.
Lewisa HF, Sexton TR.2004. Network DEA:efficiency analysis of organizations with complex internal structure[J]. Computers & Operations Research,31:1365-1410.
Liang L, Wu J, Cook W D, Zhu J.2008. The DEA game cross-efficiency model and its Nash equilibrium[J]. Operations research 56, (5):1278-1288.
Lovell CAK, Pastor JT.1995. Units invariant and translation invariant DEA models [J]. Operations research letters,18:147-151.
Mas-Colell, Whinston MD, Green J R.1995. Microeconomics Theory [M]. New York:Oxford University Press.
Olesen OB, Petersen NC.1995. Chance Constrained Efficiency Evaluation[J]. Management Science,41 (3):442-457.
Olesen OB, Petersen NC.1996. Indicators of Ill-Conditioned Data Sets and Model Misspecication in Data Envelopment Analysis:An Extended Facet Approach[J]. Management Science,42(2):205-219.
Oral M, Kettani O, Lang P.1991. A methodology for collective evaluation and selection of industrial R&D projects[J]. Management Science,37 (7),871-883.
Pachkova EV.2009. Restricted reallocation of resources[J]. European Journal of Operational Research,196:1049-1057.
Pastor JT, Ruiz JL, Sirvent I. An enhanced DEA Russell graph efficiency measure[J]. European Journal of Operational Research,115:596-607.
Prieto AM, Zofio JL.2007. Network DEA efficiency in input-output models:With an application to OECD countries[J]. European Journal of Operational Research,178:292-304.
Ruggiero J.1996. On the measurement of technical efficiency in the public sector [J]. European Journal of Operational Research,90:553-565.
Seiford L M, Thrall R M.1990. Recent development in DEA:the mathematical programming approach to frontier analysis [J]. Journal of Econometrics,46:7-38.
Sexton TR, Silkman RH, Hogan AJ.1986. Data envelopment analysis:Critique and extensions. In:Silkman, R.H. (Ed.), Measuring Efficiency:An Assessment of Data Envelopment Analysis, vol.32. Jossey-Bass, San Francisco, pp.73-105.
Shephard RW.1970. The Theory of Cost and Production Functions [M]. Princeton University Press.
Simar L, Wilson P.2000. Statistical Inference in Nonparametric Frontier Models:The State of the Art[J]. Journal of Productivity Analysis,13(1),49-78.
Thanassoulis E.1996. A Data Envelopment Analysis Approach to Clustering Operating Units for Resource Allocation Purposes[J]. International Journal of Management Science,24(4): 463-476.
Thompson RG, Singleton JFD, Thrall RM, Smith BA.1986. Comparative Site Evaluations for Locating a High-energy Physics Lab in Texas [J]. Interfaces, (16):35-49.
Tone K, Tsutsui M.2009. Network DEA:A slacks-based measure approachfJ]. European Journal of Operational Research,197:243-252.
Tone K.2001. A slacks-based measure of efficiency in data envelopment analysis [J]. European Journal of Operational Research,130:498-509.
Tulkens H.1993. On FDH efficiency Analysis:Some methodological issues and applications to retail banking, courts [J]. The Journal of Productivity Analysis, and urban transit,4:183-210.
Yu M-M, Fan C-K.2009. Measuring the performance of multimode bus transit:A mixed structure network DEA model[J]. Transportation Research Part E,45:501-515.
Yu M-M, Lin ETJ.2008. Efficiency and effectiveness in railway performance using a multi-activity network DEA model[J]. Omega,36:1005-1017.
毕功兵,梁梁,杨锋.2008一类基于属性变量的DEA模型[J].运筹与管理,17(2)：53-56.
毕功兵,梁梁,杨锋.2009.资源约束型两阶段生产系统的DEA效率评价模型[J].中国管理科学,17(2)：71-75.
黄祎,葛虹,冯英浚.2009.基于链形系统的关联网络DEA模型：以我国14家商业银行为例[J].系统工程理论与实践,29：106-114.
魏权龄.1988.评价相对有效性的DEA方法——运筹学的新领域[M].北京：中国人民大学出版社.
魏权龄.2000.数据包络分析(DEA)[J].科学通报,45(17)：1793-1808.
Athanassopoulos AD, Lambroukos N, Seiford L.1999. Data envelopment scenario analysis for setting targets to electricity generating plants [J]. European Journal of Operational Research, 115:413-428.
Banker R, Charnes A, Cooper W.1984. Some models for the estimation of technical and scale inefficiencies in Data Envelopment Analysis [J]. Management Science,30:1078-1092.
Banker RD, Maindiratta A.1986. Piecewise log-linear estimation of efficient production surfaces[J]. Management Science,32:126-135.
Castelli L, Pesenti R, Ukovich W.2004. DEA-like models for the efficiency evaluation of hierarchically structured units [J]. European Journal of Operational Research,154:465-476.
Charnes A, Cooper WW, Rhodes E.1978. Measuring the efficiency of decision making units [J]. European Journal of Operational Research,2:429-444.
Cook WD, Hababou M, Tuenter HJH.2000. Multi-component Efficiency Measurement and Shared Inputs in Data Envelopment Analysis:An Application to Sales and Service Performance in Bank Branches [J]. Journal of Productivity Analysis,14:209-224.
Cook WD, Liang L, Zhu J.2010. Measuring performance of two-stage network structures by DEA:A review and future perspective [J]. Omega,38:423-430.
Debreu G.1951. The Coefficient of Resource Utilization [J]. Econometrica,19(3):273-92.
Fare R, Grosskopf S.1996. Productivity and intermediate products:A frontier approach[J]. Economics Letters,50(1):65-70.
Fare R, Grosskopf S.2000. Network DEA [J]. Socio-Economic Planning Sciences,34:35-49.
Fare R, Whittaker G.1995, An intermediate input model of dairy production using complex survey data [J]. Journal of Agricultural Economics,46(2):201-213.
Farrell MJ.1957. The Measurement of Productive Efficiency [J]. Journal of the Royal Statistical Society, Series A,120(3):253-82.
Kao C.2009. Efficiency measurement for parallel production systems [J]. European Journal of Operational Research,196:1107-1112.
Koopmans TC.1951. An Analysis of Production as an Efficient Combination of Activities, in T. C. Koopmans, ed., Activity Analysis of Production and Allocation [M]. Cowles Commission for Research in Economics Monograph No.13. New York:John Wiley and Sons.
Tone T, Tsutsui M.2009. Network DEA:A slacks-based measure approach [J]. European Journal of Operational Research,197:243-252.
Yinsheng Yang, Benjiang Ma, Masayuki Koike.2000. Efficiency-measuring DEA Model for Production System with k Independent Subsystems [J]. Journal of Operational Research of Japan,43(3):343-354.
魏权龄.1988.评价相对有效性的DEA方法——运筹学的新领域[M].北京：中国人民大学出版社.
Bogetoft P, Tama JM, Tind J.2000. Convex input and output projections of Non-convex production possibility sets[J]. Management Science,46:858-869.
Castelli L, Pesenti R, Ukovich W.2004. DEA-like models for the efficiency evaluation of hierarchically structured units [J]. European Journal of Operational Research,154:465-476.
Charnes A, Cooper WW, Rhodes E.1978. Measuring the efficiency of decision making units [J]. European Journal of Operational Research,2:429-444.
Chen L-H, Lu H-W.2007. An extended assignment problem considering multiple inputs and outputs [J]. Applied Mathematical Modelling,31:2239-2248.
Cook WD, Liang L, Zhu J.2010. Measuring performance of two-stage network structures by DEA:A review and future perspective [J]. Omega,38:423-430.
Deprins D, Simar L, Tulkens H.1984. Measuring labor efficiency in post offices, In M. Marchand, P. Pestieau, and H. Tulkens(eds.), The performance of public enterprises:concepts and measurement [M]. Amsterdam:North-Holland, pp.243-267.
Fare R, Grosskopf S.1996. Productivity and intermediate products:A frontier approach [J]. Economics Letters,50(1):65-70.
Fare R, Grosskopf S.2000. Network DEA [J]. Socio-Economic Planning Sciences,34:35-49.
Fare R, Whittaker G.1995. An intermediate input model of dairy production using complex survey data [J]. Journal of Agricultural Economics,46 (2):201-213.
Hillier FS, Lieberman G J.2001. Introduction to Operations Research (Seventh edition). The McGraw-Hill Higher Education. New York.
Kao C.2009. Efficiency measurement for parallel production systems [J]. European Journal of Operational Research,196:1107-1112.
Lewis HF, Sexton TR.2004. Network DEA:efficiency analysis of organizations with complex internal structure [J]. Computers & Operations Research,31:1365-1410.
Tone T, Tsutsui M.2009. Network DEA:A slacks-based measure approach[J]. European Journal of Operational Research,197:243-252.
Tulkens H.1993. On FDH efficiency Analysis:Some methodological issues and applications to retail banking, courts and urban transit [J]. The Journal of Productivity Analysis,4:183-210.
Yinsheng Yang, Benjiang Ma, Masayuki Koike.2000. Efficiency-measuring DEA Model for Production System with k Independent Subsystems [J]. Journal of Operational Research of Japan,43(3):343-354.
Athanassopoulos AD, Lambroukos N, Seiford L.1999. Data envelopment scenario analysis for setting targets to electricity generating plants[J]. European Journal of Operational Research, 115:413-428.
Athanassopoulos AD.1995. 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,87:535-550.
Athanassopoulos AD.1998. Decision Support for Target-Based Resource Allocation of Public Services in Multiunit and Multilevel Systems[J]. Management Science,44 (2):173-187.
Avkiran NK.2009. Opening the black box of efficiency analysis:An illustration with UAE banks[J]. Omega,37:930-941.
Banker RD, Charnes A, Cooper WW.1984. Some models for the estimation of technical and scale inefficiencies in data envelopment analysis[J]. Management Science,30:1078-1092.
Beasley JE.2003. Allocating fixed costs and resources via data envelopment analysis[J]. European Journal of Operational Research,147:198-216.
Berne R, Stiefel L.1984. The measurement of equity in school finance:conceptual, methodological, and empirical dimensions[M]. The Johns Hopkins University Press, Baltimore, MD.
Charnes A, Cooper WW, Rhodes E.1978. Measuring the efficiency of decision making units[J]. European Journal of Operations Research,2:429-444.
Charnes A, Cooper WW, Rousseau J, Semple J.1987. Data envelopment analysis and axiomatic notions of efficiency and reference sets[R]. Research Report CCS 558. Center for Cybernetic Studies. University of Texas, Austin, TX, USA.
Fare R, Grosskopf S, Li SK.1992. Linear programming models for firm and industry performance [J]. Scandinavian Journal of Economics,94:559-608.
Fare R, Grosskopf S.2000. Network DEA[J]. Socio-Economic Planning Sciences,34:25-49.
Golany B, Tamir E.1995. Evaluating Efficiency-Effectiveness-Equality trade-offs:a data envelopment analysis approach[J]. Management Science,41(7):1172-1184.
Golany B.1988. An Interactive MOLP Procedure for the Extension of DEA to Effectiveness Analysis[J]. Journal of Operational Research Society,39(8):725-734.
Lewis HF, Sexton TR.2004. Network DEA:efficiency analysis of organizations with complex internal structure[J]. Computers & Operations research,31:1365-1410.
Lovell CAK, Pastor JT.1995. Units invariant and translation invariant DEA models[J]. Operations research letters,18:147-151.
Mandell MB.1991. Modeling effectiveness-equity trade-offs in public service delivery systems. Management Science,37(4):467-482.
Pachkova EV.2009. Restricted reallocation of resources[J]. European Journal of Operational Research,196:1049-1057.
Tone K.2001. A slacks-based measure of efficiency in data envelopment analysis[J]. European Journal of Operational Research,130:498-509.
Bernard AB, Busse MR.2004. Who wins the Olympic Games:Economic resources and medal totals [J]. Review of Economics and Statistics,86(1):413-417.
Chiang K.2009. Efficiency measurement for parallel production systems[J]. European Journal of Operational Research,196:1107-1112.
Churilov L, Flitman A.2006. Towards fair ranking of Olympics achievements:the case of Sydney 2000 [J]. Computers & Operations Research,3:2057-2082.
Jie Wu, Liang Liang, Yao Chen.2009. DEA game cross-efficiency approach to Olympic rankings [J]. Omega,37:909-918.
Jie Wu,Liang Liang, Feng Yang.2009. Achievement and benchmarking of countries at the Summer Olympics using cross efficiency evaluation method [J]. European Journal of Operational Research,197:722-730.
Yinsheng Yang, Benjiang Ma, Masayuki Koike.2000. Efficiency-measuring DEA Model for Production System with k Independent Subsystems [J]. Journal of Operational Research of Japan,43(3):343-354.
Yongjun Li, Liang Liang, Yao Chen, Hiroshi Morita.2008. Models for measuring and benchmarking Olympics achievements [J]. Omega,36:933-940.
魏权龄.2004.DEA数据包络分析[M].北京：科学出版社,53-62.
杨锋,杨琛琛,梁樑,吴华清.2009.各国奥运会参赛效率评价与排序研究[J].中国软科学,3：166-173.