考虑非期望因素的决策单元排序:两阶段综合效率法

doi:10.12005/orms.2021.0314

运筹与管理 ›› 2021, Vol. 30 ›› Issue (10): 57-63.DOI: 10.12005/orms.2021.0314

考虑非期望因素的决策单元排序:两阶段综合效率法

张琳彦^1,3, 陈鸣², 徐倩^1,4, 张健^1,3,4

1.北京信息科技大学经济管理学院,北京 100192;
2.北京理工大学管理与经济学院,北京 100081;
3.北京知识管理研究基地,北京 100192;
4.绿色发展大数据决策北京市重点实验室,北京 100192

收稿日期:2019-08-23 出版日期:2021-10-25
作者简介:张琳彦(1985-),女,安徽阜阳人,副教授,硕士生导师,经济学博士,研究方向: 绩效评价与经济计量;陈鸣 (1992-),男,天津人,博士研究生,研究方向:数量经济、能源经济;徐倩(1993-),女,山东济宁人,硕士研究生,研究方向:全要素生产率;张健(1974-),男, 山东泰安人,教授,博士生导师,管理学博士,研究方向:循环经济仿真、知识管理、信息系统与智能决策。
基金资助:
国家自然科学基金资助项目(71901032);教育部人文社会科学基金资助项目(19C11232004);北京市自然科学基金资助项目(9212005);北京市社会科学基金资助项目(19GLC073,19JDGLB021);北京市教委科研计划一般项目(SM202011232003,SM202011232004);北京信息科技大学‘勤信人才'培育计划;北京信息科技大学促进高校内涵发展-科研重点研究培育项目(2020KYNH215)

The Ranking of Decision Making Units with Undesirable Factors: Two-stage Comprehensive Efficiency Approach

ZHANG Lin-yan^1,3, CHEN Ming², XU Qian^1,4, ZHANG Jian^1,3,4

1. School of Economics and Management, Beijing Information Science & Technology University, Beijing 100192, China;
2. School of Management & Economics, Beijing Institute of Technology, Beijing 100081, China;
3. Research Center for Knowledge Management, Beijing 100192, China;
4. Beijing Key Lab of Green Development Decision Based on Big Data, Beijing 100192, China

Received:2019-08-23 Online:2021-10-25

摘要/Abstract

摘要： 对所有平行级别上的同等类型的决策单元(DMUs)在绩效表现上的排序一直是管理决策领域研究的重要课题之一。基于数据包络分析的超效率理论和SBM模型,探讨考虑非期望因素的DMUs排序问题。首先构建新的考虑非期望因素的超效率SBM模型,此模型不仅能对有效DMUs排序,而且能够转化成线性规划问题求解,具有有界性、单调性等良好性质。然后将新模型与Tone的SBM模型结合提出了考虑非期望因素的SBM综合排序法,同时给出了相对应的多项式时间算法。该方法以SBM模型作为第一阶段完成非有效DMUs排序,以新模型作为第二阶段完成有效DMUs排序,两阶段综合即完成所有DMUs排序。研究结果表明,综合排序法能够完成对考虑非期望因素的DMUs的排序,为绩效评价的管理实践提供了重要的理论依据。选取中国2010年的30个省份为实证研究对象,应用所提出的综合效率排序法对其环境效率进行排序。分析结果与中国的现实情况的相吻合,表明该排序方法是合理的,能够完成对这些地区的环境效率进行排序,可以为决策者评价环境的绩效表现提供有效的决策支持。

关键词: 效率排序, 非期望因素, SBM模型, 超效率, 综合效率

Abstract: The rankings of the same type of decision making units with the parallel level on performance is always one of the important issues in the management decisions field. Based on the super-efficiency and slack-based measure model in data envelopment analysis, this paper focuses on the ranking problem of DMUs with undesirable factors. This paper firstly proposes a new super-efficiency SBM model with undesirable factors. This model can not only complete rankings of the efficient DMUs, but be transformed into linear model. It also has some good properties, such as boundedness and monotonic property. This paper then proposes a comprehensive efficiency SBM ranking method with undesirable factors and a polynomial-time algorithm based on new model and Tone's SBM model. The method takes the SBM model as the first stage to rank the non-efficient DMUs and takes the new model as the second stage to rank efficient DMUs. The two stages are combined to complete the rankings of all DMUs. The results show that the comprehensive ranking method can complete rankings of DMUs with undesirable factors and provides an important theoretical basis for the practice of performance evaluation. We apply the proposed method to rank the environmental efficiencies of China's 30 provinces in 2010. The results of empirical analyses are consistent with the realities in China. It indicates that the method is reasonable. The method can complete the rankings of all regional environmental efficiencies and provide policy makers with decision support for evaluating environmental performance.

Key words: efficiency ranking, undesirable factors, slacks-based measure (SBM), super-efficiency, comprehensive efficiency

中图分类号:

C934

张琳彦, 陈鸣, 徐倩, 张健. 考虑非期望因素的决策单元排序:两阶段综合效率法[J]. 运筹与管理, 2021, 30(10): 57-63.

ZHANG Lin-yan, CHEN Ming, XU Qian, ZHANG Jian. The Ranking of Decision Making Units with Undesirable Factors: Two-stage Comprehensive Efficiency Approach[J]. Operations Research and Management Science, 2021, 30(10): 57-63.

参考文献

[1] Liu J S, Lu L Y Y, Lu W M, Lin B J Y. A survey of DEA applications[J]. Omega-The International Journal of Management Science, 2013, 41(5): 893-902.
[2] Liu J S, Lu L Y Y, Lu W M, Lin B J Y. Data envelopment analysis 1978~2010: a citation-based literature survey[J]. Omega-The International Journal of Management Science, 2013, 41(1): 3-15.
[3] Charnes A, Cooper W W, Huang Z M, and Sun D B. Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks[J]. Journal of Econometrics, 1990, 46(1-2): 73-91.
[4] Bogetoft P, Otto L. Benchmarking with DEA, SFA, and R, International series in operations research and management science[M]. Dordrecht: Springer Verlag, 2011.81-113.
[5] 卞亦文.非合作博弈两阶段生产系统的环境效率评价[J].管理科学学报,2012,15(7):11-19.
[6] Lozano S. Slacks-based inefficiency approach for general networks with bad outputs: an application to the banking sector[J]. Omega-International Journal of Management Science, 2015, in press.
[7] 杜娟,霍佳震,梁樑.基于数据包络分析松弛变量的排序方法[J].系统工程,2014,32(4):96-104.
[8] Adler N, Friedman L, Sinuany-Stern Z. Review of ranking methods in the data envelopment analysis context[J]. European Journal of Operational Research, 2002, 140(2): 249-265.
[9] Andersen P, Petersen N C. A procedure for ranking efficient units in data envelopment analysis[J]. Management Science, 1993, 39(10): 1261-1264.
[10] Zhu J. Robustness of the efficient decision-making units in data envelopment analysis[J]. European Journal of Operational Research, 1996, 90(3): 451-460.
[11] Thrall R M. Duality, classification and slacks in data envelopment analysis[J]. The Annals of Operations Research, 1996, 66(2): 109-138.
[12] Tone K. A slacks-based measure of super-efficiency in data envelopment analysis[J]. European Journal of Operational Research, 2002, 143(1): 32-41.
[13] Fang H H, Lee H S, Hwang S N, Chung C C. A slacks-based measure of super-efficiency in data envelopment analysis: an alternative approach[J]. Omega-The International Journal of Management Science, 2013, 41(4): 731-734.
[14] Li H, Fang K, Yang W, Wang D, Hong X X. Regional environmental efficiency evaluation in China: analysis based on the Super-SBM model with undesirable outputs[J]. Mathematical & Computer Modelling, 2013, 58(5-6): 1018-1031.
[15] Cooper W W, Seiford L M, Tone K. Undesirable outputs models. data envelopment analysis: a comprehensive text with models, applications, references and DEA-Solver software[M]. Dordrecht: Springer Verlag, 2007.367-379.
[16] Färe R, Lovell C A K. Measuring the technical efficiency of production[J]. Journal of Economic Theory, 1978, 19(1): 150-62.
[17] Liu J S, Lu L Y, Lu W M. Research fronts in data envelopment analysis[J]. Omega-The International Journal of Management Science, 2016, 58: 33-45.
[18] Banker R D, Chang H. The super-efficiency procedure for outlier identification, not for ranking efficient units[J]. European Journal of Operational Research, 2006, 175(2): 1311-1320.

考虑非期望因素的决策单元排序:两阶段综合效率法

The Ranking of Decision Making Units with Undesirable Factors: Two-stage Comprehensive Efficiency Approach

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

编辑推荐

Metrics

[1]	李根忠, 朱洪亮. 长江经济带产业结构升级与绿色全要素生产率研究[J]. 运筹与管理, 2021, 30(5): 227-231.
[2]	刘炳胜, 王敏, 李灵, 王然, 孟俊娜. 中国建筑产业链两阶段综合效率、纯技术效率、规模效率及其影响因素[J]. 运筹与管理, 2019, 28(2): 174-183.
[3]	董锋, 树琳, 李靖云, 乔均. 产学研协同创新效率及提升路径研究[J]. 运筹与管理, 2018, 27(10): 185-192.
[4]	陈晓红, 易国栋, 刘翔. 基于三阶段SBM-DEA模型的中国区域碳排放效率研究[J]. 运筹与管理, 2017, 26(3): 115-122.
[5]	何明珂, 程红晶. 快递企业航空货运网络的构建[J]. 运筹与管理, 2013, 22(6): 232-242.