摘要
数据包络分析是一种用来度量多投入多产出决策单元相对效率的“面向数据”的新方法。由于它很少需要各种假设或其他前提条件,经济学、会计学、信息管理、运作管理等不同领域的研究者们都利用DEA方法来度量企业的技术、管理和规模效率。近年来DEA方法广泛应用于医院、大学、法院、商业农场等不同行业以及不同地区和国家的效率度量。
本文关注DEA领域的几个热点问题,在已有研究的基础上进行了拓展。本文的主要创新在于:(1)提出投入导向和产出导向的改进超效率模型,从而彻底解决了已有超效率研究仍存在不可行解的情形,并对数据稳定性进行了灵敏度分析;(2)提出最小调整幅度的效率改进模型,考虑在现有投入产出水平基础上,如何进行最小幅度的调整,将无效单元投影到有效前沿面上;(3)提出基于偏好产出的资源配置模型,将额外投入配置到多个单元中,最大限度的提高偏好产出水平;(4)提出两阶段合作效率模型,调整投入在不同阶段的配置,使得两阶段系统的效率最优;(5)提出基于公共权重和标杆集的两种集成DEA排序方法。文章的组织结构如下:
首先综述了数据包络分析在模型方面的发展和当前研究的进展,概括了本文的研究内容和框架结构。
其次,为了克服传统超效率模型存在不可行解的情形,本文提出了VRS假设下的改进超效率模型。当传统模型无可行解时,该模型仍然可行,且得到有效DMUs的超效率;当传统模型有可行解时,该模型得到的结果与传统模型的结果相一致。本文的研究在一定程度上拓展了MalmquiSt productivity index和DEA benchmarking模型的应用范围。
接着研究如何改变现有的投入产出水平,使得无效单元变为有效。提出了效率改进的一般DEA模型,研究如何通过投入产出的变动来帮助决策者进行效率改进,试图寻找最小调整幅度的投影路径来改善无效决策单元的技术效率,从而使得无效单元投影到有效前沿面,变为有效。
然后研究额外投入既定的情形下,如何合理的配置资源,最大限度的提高产出水平。考虑产出中包含决策者偏好和不偏好两类产出的情形,提出一种改进的集中式资源配置模型,以期获得更多的偏好产出,同时限制不偏好产出的水平。文中还提出了基于期望效率改进的集中式资源配置准则,以此来评价不同资源配置模式之间的优劣。
本文还研究了复杂生产中投入的不同配置方式对整个生产的效率以及每个阶段效率的影响。分析了投入可在不同阶段自由配置的两阶段生产过程,提出了几何平均最优意义下的两阶段合作效率模型。分别讨论了非合作环境下不同阶段占据不同地位的情形,构建了基于CCR和BCC模型的两类几何平均合作效率模型,对多阶段生产过程的技术和规模效率都进行了合理的度量。
进一步提出一种基于公共权重的集成DEA模型。同时考虑所有决策单元,希望找到一组权重系数,使得所有单元的总体无效程度最小,达到系统效率最优。由于这组权重是希望所有单元的无效程度最小,即使得系统的无效程度最小,因此可以尽可能消除不同单元对权重的不同偏好,从而最大程度的被所有单元接受。另一方面,还提出了考虑决策者偏好的基于标杆集的排序方法。
最后对论文全文作了总结,说明了论文的几点创新,指出了论文研究的不足之处,并对论文研究的主题在今后可能的研究方向作了展望。
Data Envelopment Analysis is a relatively new "data oriented" approach for evaluating the performance of a set of peer entities called Decision Making Units which convert multiple inputs into multiple outputs. Because it requires very few assumptions, DEA has also opened up possibilities for use by researchers of various academic areas, such as economics, accounting, information management and operation management, etc. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc.
On the basis of the previous researches, this dissertation innovate in several aspects: (1) investigate sensitivity analysis using alternative super efficiency model, which deals with the infeasibility of current super efficiency models; (2) project the inefficient DMUs onto efficient production frontier with minimum amelioration; (3) allocate the additional inputs according to the central decision makers in order to maximize desirable outputs, as well as to restrict undesirable outputs; (4) regulate the allocative factor of the inputs freely among different sub-processes to optimize overall efficiency of the whole process; (5) how various weights influence the efficiency of the DMUs. This dissertation is organized as follows:
Firstly, review models and methodologies development within the context of DEA, lay emphasis on current researches of data variation or uncertainty, and generalize the main ideas and innovations of this dissertation.
Secondly, investigate super efficiency model for sensitivity analysis. The section develops a modified super-efficiency DEA model to overcome the infeasibility issue under the assumption of VRS. The newly developed approach yields (i) an optimal solution and a super-efficiency score for efficient DMUs for which feasible solutions do not exist under the original super-efficiency model; and (ii) super-efficiency scores that are equivalent to those from the original super-efficiency model when feasible solutions do exist. To some extent, the DEA Malmquist productivity index, and the DEA benchmarking models.
Thirdly, study the approach to convert inefficient DMUs into efficient by altering current inputs and outputs. A modified model is proposed to re-allocate the inputs and outputs of inefficient DMUs with minimum amelioration by considering the preference of decision makers and other factors which impact the learning process. A heuristic algorithm is proposed to solve the simplified model based upon the modified one.
Next, explore how to allocate the additional resources in order to maximize the outputs. A centralized resource allocation problem is studied focusing on the desirable outputs according to the overall goals of multi-unit organizations. We proposes modified models to reallocate the additional resources based upon the realized production level. Our problem is to find which units are worth reallocating more resources to maximize desirable outputs, as well as to restrict undesirable outputs, of the overall system. An algorithm is proposed to solve the allocation problem. Further, an criterion to evaluate various resource allocation plans by calculating the average expected system efficiency of each plan is provided.
We also discuss various allocations of inputs among two sub-processes and the overall efficiency as well as the efficiencies of different sub stages. We analysis complex production process with two sub-processes connected serially. Cooperative and non-cooperative game theory was steered to manage the relationship among sub-DMUs, and cooperative efficiency was proceeded to match the actual instance well. Several new models are presented to calculate the efficiency of the sub-DMUs in a non-cooperative manner, whereby the upper and lower bounds of the efficiencies are explicitly determined. A geometric average cooperative DEA model is proposed to evaluate the efficiency of the DMUs, and a heuristic parametric linear programming is suggested to solve the cooperative model. Various situations as constant return to scale and various return scale are discussed separately to evaluate technical and scale efficiency.
Further, we investigate how various weights selection influences the efficiency of the DMUs. an integrated DEA model, which aims at minimizing the total inefficient score of all DMUs and correspondingly optimizing the relative system efficiency based upon the common weights. With such common weights, the efficiency of each DMU is evaluated equitably and effectively, as well as the contribution of each DMU to system, and as a result, a complete ranking order is proposed from it. Also, another ranking approach is proposed, considering the preference of decision makers and management practice. Our problem is to find common weights, putting the best practice and preferable information of decision makers into consideration, as well as concerning about the efficiencies of other DMUs, which is more convincible and feasible and can easily be accepted by all DMUs than that derived from traditional DEA models. We expect the common weights resulted from the proposed integrated DEA models could guarantee those DMUs in BS DEA efficient.
Finally, the concluding section of the full dissertation summarizes some of the breakthroughs made in this dissertation, as well as the shortcomings of this paper and the direction of further researches.
引文
冯俊文.1994.C2R和C2GS2的DEA有效性问题,系统工程与电子技术7,42-51.
顾荣忠.1995.全局DEA评价模型,河海大学学报5:50-56.
郭京福,杨德礼.1998.生产前沿参数方法与非参数方法的比较研究,系统工程理论与实践11,31-35.
李树根.1989.Banach空间的DEA模型.东北运筹与应用数学[M].大连理工大学出版社,大连.
盛昭瀚,朱乔,吴广谋.1996.DEA理论、方法与应用[M].科学出版社,北京.
王应明,傅国伟.1993.一种用于工业经济效益综合评价的模型与方法,系统工程与电子技术3,18-21.
王宗军.1998.综合评价的方法、问题及其研究趋势,管理科学学报1,74-79.
魏权龄,李宏余.1991.决策单元的变更对DEA有效性的影响,北京航空航天大学学报1:85-97.
魏权龄,卢刚,岳明.1989.关于综合DEA模型中的DEA有效决策单元集合的几个恒等式,系统科学与数学3:282-288.
吴文江.1993.“混合的”数据包络分析模型,系统工程理论方法应用1:23-30.
吴文江.1995.只改变输出使决策单元变为DEA有效,系统工程2:17-20.
吴育华,李从东.1995.DEA方法与生产函数法的比较,系统工程13(3):15-19.
杨印生,张德俊.1993.熵-DEA有效性,吉林工业大学学报23(1):22-27.
张俊容,郭耀煌.2002.Pareto有效性在DEA模型中的应用,系统工程理论方法应用11(2):165-168.
赵勇.1995.数据包络分析中有效单元的进一步分析,系统工程学报4:95-100.
周泽昆1986.评价管理效率的一种新方法[J].系统工程4:42-49.
朱乔,盛昭翰,吴广谋.1994.DEA模型中的有效性问题.东南大学学报
Ali,A.I.,Cook,W.D.and Seiford,L.M.1991.Strict vs.weak ordinal relations for multipliers in data envelopment analysis,Management Science 39/10,1261-1264.
Allen,R.,Athanassopoulos,A.,Dyson,R.G.and Thanassoulis,E.1997.Weights restrictions and value judgments in data envelopment analysis:Evolution,development and future directions,Annals of Operations Research 73,13-34.
Andersen,P.and Petersen,N.1993.A procedure for ranking efficient units in data envelopment analysis, Management Science 39/10,1261-1264.
Andersen, P., Hollinsgsworth, K. and Inman, L. 2002. The fixed weighting nature of a cross-evaluation model, Journal of Productivity Analysis 17/3,249-255.
Banker, R., Charnes, A. and Cooper, W.W. 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30,1078-1092.
Banker, R.D. 1980. A game theoretic approach to measuring efficiency, European Journal of Operational Research 5(4): 262-266.
Banker, R.D. 1984. Estimating most productive scale size using Data Envelopment Analysis, European Journal of Operational Research 17,35-44.
Banker, R.D. and Maindiratta, A. 1986. Piecewise loglinear estimation of efficient production surfaces, Management Science 32(1):126-135.
Banker, R.D. Vandana M. Gadh and Wilpen L. Gorr. 1993. A Monte Carlo comparison of two production frontier estimation methods: Corrected ordinary least squares and data envelopment analysis, European Journal of Operational Research 67(3): 332-343.
Banker, R.D., Chang, H., Cooper, W.W., 1996. Simulation studies of efficiency, returns to scale and misspecification with nonlinear functions in DEA. Annals of Operations Research 66, 233-253.
Banker, R.D., Charnes, A., Cooper, W.W. and Clarke, R. 1989. Constrained game formulations and interpretations for data envelopment analysis, European Journal of Operational Research 40(3), 299-308.
Banker, R.D., et al. 1987. A comparison of data envelopment analysis and translog estimates of production frontiers using simulated observations from a known technology. In: Dogramaci A. And Fare R. eds. Applications of modern production theory inefficiency and productivity. Kluwer Academic Publishers.
Banker, R.D. and Morey, R., 1986a. Efficiency analysis for exogenously fixed inputs and outputs. Operations Research 34(4), 513-521.
Banker, R.D. and Morey, R., 1986b. The use of categorical variables in data envelopment analysis. Management Science 32(12), 1613-1627.
Beasley, J., 1995. Determining teaching and research efficiencies. Journal of the Operational Research Society 46,441-452.
Beasley, J., 1990. Comparing university departments, Omega: the international Journal of Management Science 18/2,171-183.
Boussofiane, A., Dyson, R.G. and Thanassoulis, E. 1991. Applied data envelopment analysis, European Journal of Operational Research 52/1,1-15.
Bouyssou, D. 1999. Using DEA as a tool for MCDM: some remarks, Journal of the Operational Research Society 50:974-978.
Chang, Y., Sueyoshi, T., 1991. An interactive application of DEA in microcomputers. Computer Science in Economics and Management, 4(1), 51-64.
Charnes, A. 1985. Sensitivity and Stability Analysis in DEA. Annals of Operations Research 2:139-156.
Charnes, A. and Cooper, W.W. 1968. Structural sensitivity analysis in linear programming and an exact product form left inverse, Naval Research Logistics Quarterly 15,517-522.
Charnes, A. and Neralic, L. 1992. Sensitivity analysis of the proportionate change of inputs (or outputs) in data envelopment analysis, Glasnik Matematicki 27,393-405.
Charnes, A., Clarke, C, Cooper, W.W., Golany, B., 1985. A development study of DEA in measuring the effect of maintenance units in the U.S. Air Force. Annuls of Operations Research 2, 95-112.
Charnes, A., Cooper, W.W. and Wei, Q.L. 1987. A two-person zero-sum semi-infinite game model and data envelopment analysis with infinitely many decision making units, Center for Cybernetic Stuides Report CCS 572.
Charnes, A., Cooper, W.W., Huang, Z.M., Sun, D.B. Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks, Journal of Econometries. 46(1990), 73-91.
Charnes, A., Cooper, W.W., Rhodes E. Measuring the Efficiency of Decision Making Units. European Journal of Operational Research. 6(2), 1978:429-444.
Charnes, A., Cooper, W.W., Wei, Q.L. A Semi-infinite Multicriteria Programming Approach to Data Envelopment Analysis with Infinitely Many Deeision Making Units[R]. The University of Texas at Austin, Center for Cybernetic Studies Report CCS 551,1986.
Charnes, A., et al. 1988. Compositive data envelopment analysis and multi-objective programming, The university of Texas at Austin Center for Cybernetic Studies Report, CCS.
Charnes, A., Haag, S., Jaska, P., Semple, J. 1992. Sensitivity of efficiency classifications in the additive model of data envelopment analysis, International Journal of Systems Science 23, 789-798.
Cook, W.D., Chai, D., Doyle, J., Green, R.H., 1998. Hierarchies and groups in DEA. Journal of Productivity Analysis 10,177-198.
Cook, W.D., Green, R., Zhu, J., 2006. Dual role factors in DEA. HE Transactions 38,1-11.
Cook, W.D., Green, R.H., 2005. Evaluating power plant efficiency: A hierarchical model. Computers and Operations Research 32,813-823.
Cook, W.D., Hababou, M., Tuenter, H., 2000. Multi-component efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches. Journal of Productivity Analysis 14,209-224.
Cook, W.D., Kazakov, A. and Roll, Y. 1994. On the measurement and monitoring of relative efficiency of Highway maintenance patrols. In Data Envelopment Analysis, Theory, Methodology and Applications, Charnes, A., Cooper, W.W., Lewin, A.Y. and Seiford, L.M. eds, Kluwer Academic Publishers, 195-210.
Cook, W.D., Kazakov, A., Roll, Y. and Seiford, L.M. 1991. A data envelopment analysis approach to measuring efficiency: Case analysis of highway maintenance patrols, The Journal of Socio-Economics 20/1,83-103.
Cook, W.D., Kress, M. and Seiford, L.M. 1992. Prioritization models for frontier decision making units in DEA, European Journal of Operational Research 59(2), 319-323.
Cook, W.D., Kress, M., Seiford, L.M., 1993. On the use of ordinal data in data envelopment analysis. Journal of the Operational Research Society 44,133-140.
Cook, W.D., Kress, M., Seiford, L.M., 1996. Data envelopment analysis in the presence of both quantitative and qualitative factors. Journal of the Operational Research Society 47, 945-953.
Cook, W.D., Roll, Y., Kazakov, A., 1990. A DEA model for measuring the relative efficiency of highway maintenance patrols. INFOR 28,113-124.
Cook, W.D., Zhu, J., 2006. Rank order data in DEA: A general framework. European Journal of Operational Research 174,1021-1038.
Cook, W.D., Zhu, J., 2007. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research 180(2), 692-699.
Cook, W.D. and Seiford, L.M. 2007. Data Envelopment Analysis (DEA) - Thirty years on. European Journal of Operational Research. Forthcoming.
Cooper, W.W,. Seiford L.M., Tone, K., 2006. Introduction to Data Envelopment Analysis and its Uses, Springer Science, 351.
Cooper, W.W. and Tone, K. 1997. Measures of inefficiency in data envelopment analysis and stochastic frontier estimation, European Journal of Operational Research 99(1): 72-88.
Cooper, W.W., Huang, Z., Li, S., 1996. Satisficing DEA models under chance constraints. Annals of Operations Research 66,279-295.
Cooper, W.W., Huang, Z., Li, S., 2004. Chance constraint DEA. In W.W. Cooper, L.M. Seiford and J. Zhu, eds., Handbook on Data Envelopment Analysis, Norwell, Mass., Kluwer Academic Publishers.
Cooper, W.W., Li, S., Seiford, L.M., Tone, K., Thrall, R.M., Zhu, J., 2001. Sensitivity and stability analysis in DEA: Some recent developments. 15, 217-246.
Cooper, W.W., Park, K., Pastor, J.T., 1999. RAM: Range adjusted measure of inefficiency for use with additive models and relations to other models and measures in DEA. Journal of Productivity Analysis 11 (1), 5-42.
Cooper, W.W., Seiford, L.M. and Tone, K. 2000. Data Envelopment Analysis: A Comprehensive Text with Models, Application, References and DEA-Solver Software, Kluwer Academic Publishers, Boston.
Cooper, W.W., Seiford, L.M. and Zhu, J. 2004. Handbook on Data Envelopment Analysis [M]. Kluwer Academic Publishers. Boston.
Dyson, R.G. and Thanassoulis, E. 1988. Reducing weight flexibility in data envelopment analysis, Journal of the Operational Research Society. 39(6), 563-576.
Fare, R., and S. Grosskopf. 1996. Intertemporal Production Frontiers: With Dynamic DEA. Kluwer Academic Publishers, Boston.
Fare, R., Grosskopf, S. and Lovell, C.A.K. 1994. Production Frontiers, Cambridge University Press.
Fare, R., Grosskopf, S., 2004. Modelling undesirable factors in efficiency evaluation: Comment. European Journal of Operational Research 157,242-245.
Fare, R.S., Lovell, C.A.K., 1978. Measuring the technical efficiency of production. Journal of Economic Theory 19, 150-162.
Golany, B. and Roll, Y. 1989. An application procedure for DEA, Omega: the international Journal of Management Science 17/3,237-250.
Gonzalez E, Alvarez A. 2001. From efficiency measurement to efficiency improvement: the
??choice of a relevant benchmark, European Journal of Operational Research 133,512-520.
Green, R., Doyle, J., Cook, W.D. 1996. Efficiency bounds in data envelopment analysis. European Journal of Operational Research 89,482-490.
Green, R.H., Doyle, J., and Cook, W.D. 1996. Preference voting and project ranking using DEA and corss-evaluation, European Journal of Operational Research 90,461-472.
Hao, G., Wei, Q.L. and Yan, H. 2000a. A game theoretical model for DEA efficiency, Journal of the Operational Research Society 51,1319-1329.
Hao, G., Wei, Q.L. and Yan, H. 2000b. The generalized DEA model and the convex cone constrained game, European Journal of Operational Research 126(3), 515-525.
Hua, Z., Bin, Y., 2007. Chapter 6 in Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. J. Zhu and W.D. Cook, editors, Springer Jahanshahloo, G.R., Afzalinejad, M. 2006. A Ranking Method Based on a Full-inefficient Frontier, Applied Mathematical Modeling 30:248-260.
Jahanshahloo, G.R., Hosseinzadeh, F., Shoja, N., Sanei b, M., Tohidi, G. 2005. Sensitivity and stability analysis in DEA, Applied Mathematics and Computation 169,897-904.
Kamakura, W.A., 1988. A note on the use of categorical variables in data envelopment analysis. Management Science 34(10), 1273-1276.
Land, K.C., Lovell, C.A.K., Thore, S., 1992. Productive efficiency under capitalism and state socialism: The chance constrained programming approach. Public Finance in a World of Transition 47,109-121.
Land, K.C., Lovell, C.A.K., Thore, S., 1994. Production efficiency under capitalism and state socialism: an empirical inquiry using chance-constrained data envelopment analysis. Technological Forecasting and Social Change 46,139-152.
Li, X.B. and Reeves, G.R. 1999. A multiple criteria approach to data envelopment analysis, European Journal of Operational Research 115/3, 507-517.
Liang, L.F., Yang, F., Cook, W.D., Zhu, J., 2006. DEA models for supply chain efficiency evaluation. Annals of Operations Research 145(1), 35-49.
Meza, L.A. and Lins, M.P.E. 2002. Review of methods for increasing discrimination in data envelopment analysis, Annals of Operational Research 116,1-4,225-242.
Muniz, M., Paradi, J., Ruggiero, J.,Yang, Z.J., 2006. Evaluating alternative DEA models used to control for non-discretionary inputs. Computers & Operations Research 33,1173-1183.
Neralic, L., 1997. Sensitivity in data envelopment analysis for arbitrary perturbations of data. Glasnik Matematicki 32,315-335.
Neralic, L., 2004. Preservation of efficiency and inefficiency classification in data envelopment analysis. Mathematical Communications 9,51-62.
Olesen, O.B. and Petersen, N.C. 2002. The use of data envelopment analysis with probabilistic assurance regions for measuring hospital efficiency, Journal of Productivity Analysis 17, 83-109.
Pastor, J.T., Ruiz, J.L., Sirvent, I., 1999. An enhanced DEA Russell graph efficiency measure. European Journal of Operational Research 115, 596-607.
Podinovski, V.V. 1999. Side effects of absolute weight bounds in DEA models, European Journal of Operational Research 115/3,583-595.
Podinovski, V.V. 2001. DEA models for the explicit maximization of relative efficiency, European Journal of Operational Research 131,572-586.
Podinovski, V.V. and Athanassopoulos, A.D. 1998. Assessing the relative efficiency of decision making units sing DEA models with weights restrictions, Journal of the Operational Research Society 49/5,500-508.
Portela, M., Thanassoulis, E., 2007. Developing a decomposable measure of profit efficiency using DEA. Journal of the Operational Research Society 58(4), 481-490.
Portela, M.C.A.S and Thanassoulis, E. 2002. Profit efficiency in DEA, Aston Business School Research Paper RP 0206, ISBN 1 85449 502 X, University of Aston, Aston Triangle, Birmingham B4 7ET, UK.
Ray, S.C., Seiford, L.M. and Zhu, J. 1998. Market entity behavior of Chinese state-owned enterprises, Omega: the international Journal of Management Science 26/2,263-278.
Roll, Y. and Golany, B. 1993. Alternate methods of treating factor weights in DEA, Omega: the international Journal of Management Science 21/1,99-109.
Roll, Y., Cook, W.D. and Golany, B. 1991. Controlling factor weights in data envelopment analysis, IIE Transactions 23/1,2-9.
Rousseau, J.J. and J.H. Semple. 1995. Two-person ratio efficiency games. Management Science, 41,435-441.
Rousseau, J.J., Semple, J.H., 1993. Categorical outputs in data envelopment analysis. Management Science 39(3), 384-386.
Ruggiero, J., 1996. On the measurement of technical efficiency in the public sector. European Journal of Operational Research 90,553-565.
Ruggiero, J., 1998. Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research 111,461-469.
Ruggiero, J., 2007. Non-discretionary inputs. Chapter 5 in Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. J. Zhu and W.D. Cook, editors, Springer Science Series.
Sahoo, B.K., Mohapatra, Pratap K. J.; Trivedi, M. L. 1999. A comparative application of data envelopment analysis and frontier translog production function for estimating returns to scale and efficiencies, International Journal of Systems Science 30(4): 379-394.
Sarkis, J. 2000. Comparative analysis of DEA as a discrete alternative multiple criteria decision tool, European Journal of Operational Research 123:543-557.
Schaffnit, C, Rosen, D. and Paradi, J.C. 1997. Best practice analysis of bank branches: An application of DEA in a large Canadian bank, European Journal of Operational Research 98, 269-289.
Scheel, H., 2001. Undesirable outputs in efficiency valuations. European Journal of Operational Research 132,400-410.
Seiford, L.M. and Zhu, J., 1997. An investigation of returns to scale in data envelopment analysis. OMEGA 27,1-11.
Seiford, L.M. and Zhu, J. 1998a. Sensitivity analysis of DEA models for simultaneous changes in all of the data, Journal of the Operational Research Society 49,1060-1071.
Seiford, L.M. and Zhu, J. 1998b. Stability regions for maintaining efficiency in data envelopment analysis, European Journal of Operational Research 108(1), 127-139.
Seiford, L.M. and Zhu, J., 1999. Profitability and marketability of the top 55 US commercial banks. Management Science 45(9), 1270-1288.
Seiford, L.M. and Zhu, J., 2002a. Modelling undesirable factors in efficiency evaluation. European Journal of Operational Research 142,16-20.
Seiford, L.M. and Zhu, J. 2002b. Value judgment versus allocative efficiency: a case of Tenesse county jails, The Journal of Management Sciences &Regional Development 4, 89-98.
Semple, J. 1997. Constrained games for evaluating organizational performance, European Journal of Operational Research 96(1), 103-112.
Sengupta, J.K. 1987. Data envelopment analysis for efficiency measurement in the stochastic case, Computers and Operations Research 14(2):117-129.
Sengupta, J.K. 1996. Dynamic data envelopment analysis, International Journal of Systems Science 27(3):277-284.
Sexton, T.R., Silkman, R.H. and Hogan, R.H. 1986. Measuring efficiency: An assessment of data envelopment analysis, new directions for program evaluations, in R.H. Silkman, ed., Measuring efficiency: An assessment of Data Envelopment Analysis. Publication No. 32 in the series New Directions for Program Evaluations. A publication of the American Evaluation Association (San Francisco: Jossy Bass).
Stewart, T.J. 1996. Relationships between data envelopment analysis and multicriteria decision analysis, Journal of the Operational Research Society 47:654-665.
Sueyoshi, T. 1990. A special algorithm for the additive model in DEA. Journal of the Operational Research Society 41 (3), 249-257.
Sueyoshi, T. 1991. Estimation of stochastic frontier cost function using data envelopment analysis: an application to the AT&T divestiture, Journal of the Operational Research Society 42(6): 463-477.
Sueyoshi, T. 1992. Comparisons and analyses of managerial efficiency and returns to scale of telecommunication enterprises by using DEA/WINDOW. Communications of the Operations Research Society of Japan 37,210-219.
Sueyoshi, T. 1994. Stochastic frontier production analysis: Measuring performance of public telecommunications in 24 OECD countries, European Journal of Operational Research 74(3), 466-478.
Sueyoshi, T. 1999. DEA-discriminant analysis in the view of goal programming, European Journal of Operational Research 115(3), 564-582.
Syrjanen, M.J. 2004. Non-discretionary and discretionary factors and scale in data envelopment analysis. European Journal of Operational Research 158,20-33.
Thanassoulis, E. and Dyson, R.G. 1992. Estimating preferred input-output levels using data envelopment analysis, European Journal of Operational Research 56, 80-97.
Thanassoulis, E., Boussofiane, A. and Dyson, R.G. 1995. Exploring output quality targets in the provision of perinatal care in England using data envelopment analysis, European Journal of Operational Research 80,588-607.
Xiao-Bai Li and Gary R. Reeves. 1999. A multiple criteria approach to data envelopment analysis, European Journal of Operational Research 115(3), 507-517.
Zhu, J. 1996a. Data Envelopment Analysis with preference structure, Journal of the Operational Research Society 47,136-150.
Zhu, J. 1996b. Robustness of the efficient DMUs in data envelopment analysis. European Journal of Operational Research 90,451-460.
Zhu, J. 2001. Super-efficiency and EA sensitivity analysis, European Journal of Operational Research 129, No. 2,443-460.
Zhu, J. 2003. Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research 144,513-529.
Zhu, J. and Z. Shen, H., 1995. A discussion of testing DMUs' returns to scale. European Journal of Operational Research 81,590-596.
Andersen,P.,N.C.Petersen.1993.A procedure for ranking efficient units in data envelopment analysis.Management Science,39,1261-1264.
Banker, R.D, A. Charnes, W.W. Cooper. 1984. Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science, 30,1078-1092.
Charnes, A, W.W. Cooper, E. Rhodes. 1978. Measuring the efficiency of decision making units. European Journal of Operational Research, 2,429-444.
Charnes, A., S. Hang, P. Jaska and J. Semple, "Sensitivity of efficiency classifications in the additive model of data envelopment analysis," International Journal of Systems Science. 23(1992), 789-798.
Chen, Y. 2004 "Ranking Efficient Units in DEA", OMEGA, 32,213-219.
Chen, Y. 2005. "Measuring Super-efficiency in DEA in the Presence of Infeasibility", European Journal of Operational Research, 161,545-551.
Cook, W.D., Seiford, L.M. and J. Zhu. 2004. Models for performance benchmarking: Measuring the effect of e-commerce activities on banking performance, OMEGA, 32(4), 313-322.
Dula, J.H. and B.L. Hickman. 1997. Effects of excluding the column being scored from the DEA envelopment LP technology matrix". Journal of the Operational Research Society, 48, 1001-1012.
Fare, R. and Grosskopf, S.1992. Malmquist indexes and Fisher ideal indexes, The Economic Journal, 102,158-160.
Fare, R., S. Grosskopf and C. A. K. Lovell, Production Frontiers, Cambridge University Press, 1994.
Lovell, C.A.K. and A.P.B. Rouse, 2003. Equivalent standard DEA models to provide super-efficiency scores, Journal of the Operational Research Society, 54(1), 101-108.
Rousseau, J.J. and J.H. Semple. 1995. Two-person ratio efficiency games. Management Science, 41,435-441.
Seiford, L.M. and Zhu, J. 1998a. An acceptance system decision rule with data envelopment analysis. Computers and Operations Research, 25,329-332
Seiford, L.M. and Zhu, J. 1998b. Sensitivity analysis of DEA models for simultaneous changes in all the data. Journal of the Operational Research Society, 49,1060-1071.
Seiford, L.M. and Zhu, J. 1999. Infeasibility of super-efficiency data envelopment analysis models. INFOR, 37 (May), 174-187.
Zhu, J. 1996. Robustness of the efficient DMUs in data envelopment analysis. European Journal of Operational Research, 90,451-460.
Banker R.D.1984.Chames A,Cooper W W.Some models for estimating technical and scale inefficiencies in data envelopment analysis.Management Science,30(9),1078-1092.
Bogetoft P,Hougaard J.L.1999.Efficiency evaluations based on potential non-proportional improvements. Journal of Productivity Analysis, 12,233-247.
Bogetoft P. 1994. Incentive efficient production frontiers: An agency perspective on DEA. Management Science, 40(8), 959-968.
Brockett P L, Charnes W W, Huang Z M and Sun D B. 1997. Data transformations in DEA cone ratio envelopment approaches for monitoring bank performances, European Journal of Operational Research, 98(2), 250-268.
Charnes A, Cooper W W, Rhodes E. 1978. Measuring the efficiency of decision making units. European Journal of Operational Research, 2,429-444.
Coelli T.J. 1998. A multi-stage methodology for the solution of orientated DEA models. Operations Research Letters, 23(3-5), 143-149.
Cooper W W, Seiford L M and Zhu J. 2000. A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA. Socio-Economic Planning Sciences, 34(1),1-25.
Dervaus B, Kerstens K, Vanden E.P. 1998. Radial and nonradial static efficiency decompositions: A focus on congestion measurement. Transportation Research B, 32(5), 299-312.
Edvardsen D.F. 2003. Forsund F R. International benchmarking of electricity distribution utilities. Resource and Energy Economics, 25,353-371.
Fare R and Grosskopf S. 2000. Theory and application of directional distance functions, Journal of Productivity Analysis, 13,93-102.
Farrell M.J. 1957. The measurement of production efficiency. Journal of the Royal Statistics Society A, 120,253-281.
Frei F.X, Harker P.T. 1999. Projections onto efficient frontiers: Theoretical and computational extensions to DEA. Journal of Production Analysis, 11,275-300.
Gonzalez E and Carcaba A. 2004. Efficiency improvement through learning. International Journal of Technology Management, 27(6-7), 628-638.
Gonzalez E, Alvarez A. 2001. From efficiency measurement to efficiency improvement: the choice of a relevant benchmark. European Journal of Operational Research, 133,512-520.
Guan Jiancheng, Ma Ning. 2003. A multi-objective DEA projection model and its applications. Chinese Journal of Management Science, 11(1), 66-70(in Chinese)
Leibenstein H. 1966. Allocative efficiency versue X-efficiency. American Economic Review, 56,392-415.
Peng Yu. 1997. The gradient of DEA efficiency. System Engineering Theory & Practice.11, 51-55(in Chinese)
Schaffnit C, Rosen D, Paradi J C. 1997. Best practice analysis of bank branches: an application of DEA in a large Canadian bank. European Journal of Operational Research, 98, 269-289.
Shephard R.W. 1953. Cost and Production Functions, Princeton University Press, Princeton. Wang Xinyu, Wang Hongxin. 2000. A general algorithm to calculate the gradient of DEA efficiency for inefficient DMUs. Operations Research and Management Science, 9(2), 12-17(in Chinese)
Wu Jianjiang. 2004. A method on minimizing the sum of deviations to transform decision making unit into DEA efficient. Mathematics in Practice and Theory, 34(10), 69-73(in Chinese)
Zheng Jinghai, Liu Xiaxuan and Bigsten A. 2000. Efficiency, technical progress and best practice in Chinese Stage Enterprises. Working papers in Economics no 30.
Asmild,M.,Paradi,J.C.,Pastor,J.T.2006.Centralized resource allocation BCC models.Omega doi:10.1016/j.omega.2006.07.006.
Athanassopoulos,A.D.1995.Goal programming & data envelopment analysis(GoDEA)for target-based multi-level planning:Allocating central grants to the Greek local authorities.European Journal of Operational Research 87(3),535-550.
Athanassopoulos,A.D.1998.Decision support for target-based resource allocation of public services in multiunit and multilevel systems.Management Science 44(2),173-187.
Banker,R.D.,Chames,A.,Cooper,W.1984.Some models for estimating technical and scale inefficiencies in data envelopment analysis.Management Science 30(9),1078-1092.
Blake,J.T.,Carter,M.W.2002.A goal programming approach to strategic resource allocation in acute care hospitals.European Journal of Operational Research 140(2002),541-561.
Bouyssou,D.1999.Using DEA as a tool for MCDM:some remarks,Journal of the Operational Research Society 50:974-978.
Cook,W.D.,Chai,D.,Doyle,J.,Green,R.1998.Hierarchies and groups in DEA.The Journal of Productivity Analysis 10(2),177-198.
Fare,R.and Grosskopf,S.2000.Network DEA.Socio-Economic Planning Sciences 34,35-49.
Golany, B. 1988. An interactive MOLP procedure for the extension of DEA to effectiveness analysis. Journal of the Operational Research Society 39(8), 725-734.
Golany, B., Phillips, F. Y., Rousseau, J.J. 1993. Models for improved efficiencies based on DEA efficiency results. IIE Transactions 25(6), 2-10.
Golany, B., Tamir, E. 1995. Evaluating efficiency-effectiveness equality trade-offs: A data envelopment analysis approach. Management Science 41(7), 1172-1184.
Green, R.H., Doyle, J.R., Cook, W.D. 1996. Preference voting and project ranking using DEA and cross-evaluation. European Journal of Operational Research 90(1996), 461-472.
Hussein, M.L., Abo-Sinna, M.A. 1995, A fuzzy dynamic approach to the multicriterion resource allocation problem. Fuzzy Sets and Systems, 69(1995), 115-124.
Jahanshahloo, G.R., Lotfi, F.H., Shoja, N., Tohidi, G., Razavyan, S. 2005. Undesirable inputs and outputs in DEA models. Applied Mathematics and Computation 169(1), 917-925.
Korhonen, P., Syrjanen, M. 2004. Resource Allocation Based on Efficiency Analysis. Management Science 50(8), 1134-1144.
Lai, K. K., Li, Lushu. 1999. A dynamic approach to multiple-objective resource allocation problem. European Journal of Operational Research, 117(1999), 293-309.
Lozano, S., Villa, G. 2004. Centralized resource allocation using data envelopment analysis. Journal of Productivity Analysis 22,143-161.
Lozano, S., Villa, G., Adenso-Diaz, B. 2004. Centralized target setting for regional recycling operations using DEA. OMEGA 32,101-110.
Lu, Y.D. 2005. Solving a Dynamic Resource Allocation Problem Through Continuous Optimization. IEEE Transactions on Automatic Control, 50(2005), 890-894.
Osman, M.S., Abo-Sinna, M.A., Mousa, A.A. 2005. An effective genetic algorithm approach to multiobjective resource allocation problems (MORAPs). Applied Mathematics and Computation, 163(2005), 755-768.
Ramanathan, R., Ganesh, L. S. 1995. Using AHP for resource allocation problems. European Journal of Operational Research, 80,410-417.
Scheel H. 2001. Undesirable outputs in efficiency valuations. European Journal of Operational Research 132,400-410.
Stewart, T.J. 1996. Relationships between DEA and MCDM. Journal of the Operational Research Society 47(5), 654-665.
Thanassoulis, E. and Dyson, R.G. 1992. Estimating preferred input-output levels using data envelopment analysis, European Journal of Operational Research 56,80-97.
Yan, H., Wei, Q.L., Hao, G. 2002. DEA models for resource reallocation and production input/output estimation. European Journal of Operational Research 136(2001), 19-31.
Zha, Y., Liang, L., Gou, Q. L. 2007. Centralized Resource Allocation with desirable outputs, working paper.
Amirteimoori,A.and Kordorstami,S.2005.DEA-like models for multi-component performance measurement.Applied Mathematics and Computation,163:735-743.
Castelli C,Pesenti,R.and Ukovich,W.2001.DEA-like models for efficiency evaluations of specialized and interdependent units.European Journal of Operational Research,132:274-86.
Castelli,L,Pesenti,R.and Ukovich,W.2004.DEA-like models for the efficiency evaluation of hierarchically structured units.European Journal of Operational Research,154(2):465-476.
Charnes,A.,Cooper,W.W.and Rhodes,E.1978.Measuring the efficiency of decision making units.European Journal of Operational Research,2,429-444.
Chen,Y.,Liang,L.,Yang,F.and Zhu,J.2004.Evaluation of information technology investment:a data envelopment analysis approach.Computers & Operations Research,33(5):1368-1379.
Fare,R.and Grosskopf,S.2000.Network DEA.Socio-Economic Planning Sciences 34,35-49.
Fare,R.,and Grosskopf,S.1996.Intertemporal Production Frontiers:With Dynamic DEA.Kluwer Academic Publishers,Boston.
Fare,R.,Primont,D.1984.Efficiency measures for multiplant firms.Operations Research Letters,3,257-260.
Fare, R., Whittaker, G. 1995. An intermediate input model of dairy production using complex survey data. Journal of Agricultural Economics 46 (2), 201-213.
Fare, R., Grosskopf, S. and Li, S. 1992. Linear programming models for .rm and industry performance. The Scandinavian Journal of Economics 94,599-608.
Lewis H.F. and Sexton, T. R. 2004. Network DEA: efficiency analysis fo organizations with complex internal structure. Computers & Operations Research, 31,1365-1410.
Liang, L., Yang, F., Cook, W.D. and Zhu, J. 2006. DEA models for supply chain efficiency evaluation. Annals of Operations Research, 145(1), 35-49.
Lothgren, M. and Tambour, M. 1999. Productivity and costumer satisfaction in Swedish Pharmacies' performance: A DEA network model. European Journal of Operational Research 115, 449-458.
Sexton, T.R. and Lewis, H.F. 2003. Two-stage DEA: an application to major league baseball. Journal of Productivity Analysis, 19(2/3): 227-49.
Wu, D.S., Yang, Z.J. and Liang, L. 2006. Using DEA-neural network approach to evaluate branch efficiency of a large Canadian bank. Expert Systems with Applications, 31,108-115.
刘英平,林志贵,沈祖诒.2006.有效区分决策单元的数据包络方法.系统工程理论与实践.3,112-116.
Adler,N.,Friedman,L.and Sinuany-Stern,Z.2002.Review of ranking methods in the data envelopment analysis context.European Journal of Operational Research,140,249-265.
Ammons David N.2000.Benchmarking as a performance management tool:experiences among municipalities in North Carolina.J Pub Budg Account Financ Manag,12(1),106-24.
Andersen,P.,Petersen,N.C.1993.A procedure for ranking efficient units in data envelopment analysis.Management Science,39(10),1261-1294.
Banker,R.,Chames,A.and Cooper,W.W.1984.Some models for estimating technical and scale inefficiencies in data envelopment analysis,Management Science 30,1078-1092.
Bardhan,I.,Bowlin,W.F.,Cooper,W.W.,Sueyoshi,T.,1996.Models for efficiency dominance in data envelopment analysis.Part Ⅰ:Additive models and MED measures.Journal of the Operations Research Society of Japan 39,322-332.
Charnes,A.et al.1985.A Developmental Study of Data Envelopment Analysis in Measuring the Efficiency of Maintenance Units in the US Air Forces[J],Annals of Operations Research,2:95-112.
Charnes,A.,Cooper,W.W.,Rhodes E.1978.Measuring the Efficiency of Decision Making Units.European Journal of Operational Research.6(2),429-444.
Cook,W.D.,Kress,M.1990.A Data Envelopment Model for Aggregating Preference Rankings[J],Management Science,36(11):1302-1310.
Donthu,N.,Hershberger,E.K.and Osmonbekov,T.2005.Benchmarking marketing productivity using data envelopment analysis.Journal of Business Research,58,1474-1482.
Doyle,J.R.,Green,R.1994.Efficiency and cross-efficiency in data envelopment analysis:Derivatives,meanings and uses.Journal of the Operational Research Society,45(5),567-578.
Ertay,T.,Ruan,D.and Tuzkaya,U.R.2006.Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems.Information Sciences,176,237-262.
Golany, B., Roll, Y.A. 1994. Incorporating Standards via Data Envelopment Analysis, In: Charnes, A. et al (Eds.), Data Envelopment Analysis: Theory, Methodology and Applications [M]. Kluwer Academic Publishers, Norwell.
Grupp H. 1990. Technometrics as a missing link in science and technology indicators. In: Sigurdson J, editor. Measuring the dynamics of technological change. London: Pinter, p. 57-76.
Jahanshahloo, G.R., Afzalinejad, M. 2006. A Ranking Method Based on a Full-inefficient Frontier [J], Applied Mathematical Modelling, 30:248-260.
L. Friedman and Z. Sinuany-Stern. 1997. Scaling units via the canonical correlation analysis in the DEA context. European Journal of Operational Research, 100(3): 629-637.
Sarkis, J. 2000. A comparative analysis of DEA as a discrete alternative multiple criteria decision tool. European Journal of Operational Research, 3, 543-557.
Sexton, T.R., Siklman, R.H., Hogan, A.J. 1986. Data Envelopment Analysis: Critique and Extensions, in: R.H. Silkman(Ed.), Measuring Efficiency: An Assessment of Data Envelopment Analysis, Jossey-Bass, San Francisco, CA, 73-105.
Sinuany-Stern, Z. et al,. 1994. Academic Departments Efficiency via Data Envelopment Analysis [J], Computers and Operations Research, 21 (5):543-556.
Sinuany-Stern, Z., Friedman, L. 1998. Data Envelopment Analysis and the Discriminant Analysis of Ratios for Ranking Units [J], European Journal of Operational Research, 111:470-478.
Tata Jasmine. 2000. Benchmarking quality management practices: US versus Costa Rica. Multinatl Bus Rev, 8(2), 37-51.