In order to improve the accuracy of efficiency evaluation, based on the self-evaluation and peer-evaluation nature of cross-efficiency method and by referring to the idea of cross efficiency of interval DEA, the evaluation method of the three parameters interval cross efficiency is proposed by using data envelopment analysis. The paper, at first,explains the possibility and reasonability of CCR efficiency value as the upper limit of cross efficiency; then, constructs a model based on the same weight space and on maximizing the deviation for the weighting strategy to make sure the lower limit of cross-efficiency value; moreover,fully considers the relationship of competition and cooperation between decision-making units and establisbed the competitive and comperative cross-efficiency model and determines the optimist weights which maximize the total cross efficiency of cooperative companions and minimize it the competitive counterparts so as to gain the most possible value of interval cross-efficiency value based on different groups according to aforementioned relationship; finally, utilizes the triangular fuzzy number expectation value ranking method to sort - DOI:10.3969/j.issn.1000-1565.2018.04.001改进的三参数区间DEA交叉效率评价方法郭子雪1,2,王增超2(1.北京工商大学 首都流通业研究基地, 北京 100048;2.河北大学 管理学院,河北 保定 071002)摘 要:为了提高效率评价的有效性,基于交叉效率方法的自互评本质,借鉴区间DEA交叉效率思想,提出了三参数区间交叉效率DEA评价方法.首先,阐述了传统CCR效率值作为区间交叉效率值上限的可能性和合理性;其次,基于相同的权重空间,以最大化偏移量为赋权策略构建模型,确定区间交叉效率值的下限;然后,充分考虑决策单元之间同时存在竞争与合作的关系,基于不同关系对各个决策单元进行分组,通过建立并求解竞合交叉效率模型,使得到的最优偏好权重既可以最大化合作者的总效率,又可以最小化竞争者的总效率,进而确定区间交叉效率值的重心值;最后,利用三角模糊数期望值排序方法对决策单元进行排序.文末的算例验证了方法有效性和优越性.关键词:交叉效率;三参数区间DEA交叉效率;竞合关系;三角模糊数中图分类号:C934 文献标志码:A 文章编号:1000-1565(2018)04-0337-09Evaluation method of DEA cross efficiency basedon improved three-parameter intervalGUO Zixue1,2, WANG Zengchao2(1.Research Center for Capital Commercial Industry, Beijing Technology and Business University,Beijing 100048, China;2.College of Management, Hebei University, Baoding 071002, China)Abstract: In order to improve the accuracy of efficiency evaluation, based on the self-evaluation and peer-evaluation nature of cross-efficiency method and by referring to the idea of cross efficiency of interval DEA, the evaluation method of the three parameters interval cross efficiency is proposed by using data envelopment analysis. The paper, at first,explains the possibility and reasonability of CCR efficiency value as the upper limit of cross efficiency; then, constructs a model based on the same weight space and on maximizing the deviation for the weighting strategy to make sure the lower limit of cross-efficiency value; moreover,fully considers the relationship of competition and cooperation between decision-making units and establisbed the competitive and comperative cross-efficiency model and determines the optimist weights which maximize the total cross efficiency of cooperative companions and minimize it the competitive counterparts so as to gain the most possible value of interval cross-efficiency value based on different groups according to aforementioned relationship; finally, utilizes the triangular fuzzy number expectation value ranking method to sort - 收稿日期:2018-02-07 基金项目:国家社科基金资助项目(11BGL089);河北省教育厅人文社会科学研究重大课题攻关项目(ZD201439);北京工商大学首都流通业研究基地开放课题研究基金资助项目(JD-KFKT-YB-2017-03) 第一作者:郭子雪(1964—),男,河北清河人,北京工商大学特聘研究员,河北大学教授,博士生导师,主要从事决策理论与方法、物流与供应链管理方向研究.E-mail:guo_zx@163.com第4期郭子雪等:改进的三参数区间DEA交叉效率评价方法decision making units. The final example verifies the effectiveness and superiority of the method.
GUO Zixue
,
WANG Zengchao
. Evaluation method of DEA cross efficiency based on improved three-parameter interval[J]. Journal of Hebei University(Natural Science Edition), 2018
, 38(4)
: 337
-345
.
DOI: 10.3969/j.issn.1000-1565.2018.04.001
[1] SEXTON T R, SILKM R H, HOGAN A J. Data envelopment analysis: Critique and extensions[J].New Directions for Program Evolution, 1986(32):73-105. DOI:10.1002/ev.1441.
[2] DOYLE J R, GREEN R H. Efficiency and cross-efficiency in DEA: derivations, meanings and uses[J]. Journal of the Operations Research Society, 1994, 45(5): 567-578. DOI:10.1057/jors.1994.84.
[3] LIANG L,WU J,WADE D C. Alternative secondary goals in DEA cross-efficiency evaluation[J]. International Journal of Production Economics, 2008, 113(2):1025-1030. DOI:10.1016/j.ijpe.2007.12.006.
[4] WANG Y M, CHIN K S. Some alternative models for DEA cross-efficiency evaluation[J].International Journal of Production Economics,2010,128(1):332-338. DOI:10.1016/j.ijpe.2010.07.032.
[5] LIANG L,WU J,WADE D C,et al. The DEA game cross-efficiency model and its nash equilibrium[J].Operations Research,2008, 56(5):1278-1288. DOI:10.1287/opre.1070.0487.
[6] 杨锋,夏琼,梁樑. 同时考虑决策单元竞争与合作关系的DEA交叉效率评价方法[J]. 系统工程理论与实践,2011, 31(1):92-98. YANG F,XIA Q,LIANG L.DEA cross efficiency evaluation method for competitive and cooperative decision making units[J].Systems Engineering-Theory&Practice,2011,31(1):92-98.
[7] 马立杰,赵益军,邓伟.区间DEA模型下的决策单元排序[J]. 山东大学学报,2006, 41(6):61-64. DOI:10.3969/j.issn.1671-9352.2006.06.014.
[8] 吴杰,梁樑. 一种考虑所有权重信息的区间交叉效率排序方法[J]. 系统工程与电子技术,2008, 30(10):1980-1984. DOI:10.3321/j.issn:1001-506X.2008.10.019.
[9] 王美强,梁樑. CCR模型中决策单元的区间交叉效率值及其排序[J]. 系统工程,2008, 26(4):109-114. WANG M Q, LIANG L. Interval cross efficiency values of decision units in CCR Model and their ranking. [J]. Systems Engineering,2008, 26(4):109-114.
[10] 王科,魏法杰. 三参数区间交叉效率DEA评价方法[J].工业工程,2010,13(2):19-23.DOI:10.3969/j.issn.1007-7375.2010.02.005. WANG K, WEI F J. Three-parameter interval cross-efficiency DEA evaluation method[J].Industrial Engineering,2010, 13(2):19-23.DOI:10.3969/j.issn.1007-7375.2010.02.005.
[11] LI X B, GARY R R. A multiple criteria approach to data envelopment analysis[J]. European Journal of Operational Research,1999,115(3):507-517. DOI:10.1016/S0377-2217(98)00130-1.
[12] 吴华清,梁樑,吴杰,等. DEA博弈模型的分析与发展[J]. 中国管理科学,2010,18(5):184-192. WU H Q, LIANG L, WU J,et al. Analysis and development of DEA game model[J].China Management Science,2010,18(5):184-192.
[13] 姜艳萍, 樊治平. 一种三角模糊数互补判断矩阵的排序方法[J]. 系统工程与电子技术, 2002, 24(7):34-36. JIANG Y P, FAN Z P.A ranking method for triangular fuzzy number complementary judgment matrix[J]. Systems Engineering and Electronics, 2002, 24(7):34-36. DOI:10.3321/j.issn:1001-506X.2002.07.011.
[14] 郭子雪,郑玉蒙,李双双.基于模糊几何加权的区间多目标规划问题[J].河北大学学报(自然科学版),2015,35(3):230-235. DOI:10.3969/j.issn.1000-3565.2015.03.002. GUO Z X,ZHENG Y M,LI S S.Interval multi-objective programming problem based on fuzzy gemetrin weighting method[J].Journal of Hebei University(Natural Science Edition),2015,35(3):230-235.DOI:10.3969/j.issn.1000-3565.2015.03.002.
[15] WANG Y M, CHIN K S. The use of OWA operator weights for cross-efficiency aggregation[J]. Omega, 2011, 39(5): 493-503. DOI:10.1016/j.omega.2010.10.007.
