A Zero Sum Gains Slacks-based Measure Efficiency Decision-making Method and Its Application

doi:10.12005/orms.2020.0045

Operations Research and Management Science ›› 2020, Vol. 29 ›› Issue (2): 144-149.DOI: 10.12005/orms.2020.0045

• Application Research • Previous Articles Next Articles

A Zero Sum Gains Slacks-based Measure Efficiency Decision-making Method and Its Application

GUO Wen^1,2, SUN Tao², ZHU Jian-jun²

1. College of Accounting, Nanjing University of Finance & Economics, Nanjing 210046, China;
2. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2017-10-11 Online:2020-02-25

基于“零和收益”的SBM效率分配方法及应用

郭文^1,2, 孙涛², 朱建军²

1. 南京财经大学会计学院,江苏南京 210046;
2. 南京航空航天大学经济与管理学院,江苏南京211106摘要:在松弛变量度量slacks-based measure,SBM效率评价方法的基础上,首先明确投入产出要素固定的生产系统中,投入产出要素在各决策单元间的竞争性关系;然后采用比例分配策略对SBM无效决策单元的投入产出松弛进行效率分配,以构建一个基于零和收益的SBMzero sum gains SBM,ZSG-SBM效率分配方法;再通过分析ZSG-SBM模型与SBM模型效率评价结果的关系,给出了比例分配策略ZSG-SBM模型的求解方法;最后应用实例研究验证了本文模型在要素存在竞争性的复杂生产系统效率评价和资源分配中的优势。关键词:零和收益;SBM效率决策;比例分配策略中图分类号:O224 文章标识码:A 文章编号:1007-3221202001-0144

作者简介:郭文(1987-), 男, 江西新余人, 副教授, 博士, 主要从事系统效率评价研究。
基金资助:
国家自然科学基金面上项目(71571099,71671080);国家自然科学青年基金(71602083);教育部人文社科基金青年项目(18YJC630042);江苏省社会科学基金青年项目(19GLC007);全国统计科学研究重点项目(2016LZ36);江苏高校哲学社会科学研究基金(2017SJB0243);南京财经大学校级高等教育研究及改革发展专项课题(GJ201821)

Abstract

Abstract: On the basis of slacks-based measure(SBM)efficiency decision-making method, we clear the competitiveness relationship among all of the decision-making units(DMU)in the production system which has fixed input(output)elements. Then, we allocate input(output)slacks of SBM inefficiency DMU through using proportional allocation strategy, and establish a zero sum gains SBM(ZSG-SBM) efficiency decision-making method. And then we provide solution method of ZSG-SBM model through analyzing the relationship between the ZSG-SBM model and traditional SBM model. Finally, we verify the advantage of ZSG-SBM model in solving efficiency evaluation and resource allocation decision-making problems by an example.

Key words: zero sum gains, SBM efficiency decision-making, proportional allocation strategy

摘要： 在松弛变量度量(slacks-based measure,SBM)效率评价方法的基础上,首先明确投入(产出)要素固定的生产系统中,投入(产出)要素在各决策单元间的竞争性关系;然后采用比例分配策略对SBM无效决策单元的投入(产出)松弛进行效率分配,以构建一个基于零和收益的SBM(zero sum gains SBM,ZSG-SBM)效率分配方法;再通过分析ZSG-SBM模型与SBM模型效率评价结果的关系,给出了比例分配策略ZSG-SBM模型的求解方法;最后应用实例研究验证了本文模型在要素存在竞争性的复杂生产系统效率评价和资源分配中的优势。

关键词: 零和收益, SBM效率决策, 比例分配策略

CLC Number:

O224

GUO Wen, SUN Tao, ZHU Jian-jun. A Zero Sum Gains Slacks-based Measure Efficiency Decision-making Method and Its Application[J]. Operations Research and Management Science, 2020, 29(2): 144-149.

郭文, 孙涛, 朱建军. 基于“零和收益”的SBM效率分配方法及应用[J]. 运筹与管理, 2020, 29(2): 144-149.

References

[1] Lozano S, Gutiérrez E. Slacks-based measure of efficiency of airports with airplanes delays as undesirable outputs[J]. Computers & Operations Research, 2011, 38(1): 131-139.
[2] Barros C P, Managi S, Matousek R. The technical efficiency of the japanese banks: non-radial directional performance measurement with undesirable output[J]. Omega, 2012, 40(1): 1-8.
[3] Li L B, Hu J L. Ecological total-factor energy efficiency of regions in China[J]. Energy Policy, 2012, 46(4): 216-224.
[4] Tone K, Tsutsui M. Network DEA: a slacks-based measure approach[J]. European Journal of Operational Research, 2009, 197(1): 243-252.
[5] Cook W D, Zhu J, Bi G, et al. Network DEA: additive efficiency decomposition[J]. European Journal of Operational Research, 2010, 207(2): 1122-1129.
[6] Fukuyama H, Weber W L. A slacks-based inefficiency measure for a two-stage system with bad outputs[J]. Omega, 2010, 38(5): 398-409.
[7] 陈磊,王应明.基于松弛变量方法的动态网络系统效率测度及分解[J].系统科学与数学,2015(3):361-370.
[8] Tone K, Tsutsui M. Dynamic DEA with network structure: a slacks-based measure approach[J]. Omega, 2014, 42(1): 124-131.
[9] Zhao C B. Does regulation on CO₂ emissions influence productivity growth? the empirical test based on DEA analysis[J]. Energy Procedia, 2012, 16: 667-672.
[10] Chung Y, Heshmati A. Measurement of environmentally sensitive productivity growth in korean industries[J]. Journal of Cleaner Production, 2014, 104: 380-391.
[11] Juo J C, Lin Y H, Chen T C. Productivity change of taiwanese farmers' credit unions: a nonparametric meta frontier malmquist-luenberger productivity indicator[J]. Central European Journal of Operations Research, 2015, 23(1): 125-147.
[12] Tone K, Tsutsui M. Network DEA: a slacks-based measure approach[J]. European Journal of Operational Research, 2009, 197(1): 243-252.
[13] 郭文,孙涛,朱建军.基于不可分离变量的非期望SBM效率评价方法[J].系统工程与电子技术,2015,37(6):1331-1337.
[14] Gomes E G, Lins M P E. Modelling undesirable outputs with zero sum gains data envelopment analysis models[J]. Journal of the Operational Research Society, 2008, 59(5): 616-623.
[15] Mello A B, Mello J C C B S, Gomes E G, et al. Uniformization of frontiers in non-radial ZSG-DEA models: an application to airport revenues[J]. Pesquisa Operacional, 2010, 30(1): 175-193.
[16] Chiu Y H, Lin J C, Hsu C C, et al. Carbon emission allowances of efficiency analysis: application of super SBM ZSG-DEA model[J]. Polish Journal of Environmental Studies, 2013, 22(3): 653-666.
[17] Lins M P E, Gomes E G, Joo Carlos C B. Soares de Mello, et al. Olympic ranking based on a zero sum gains DEA model[J]. European Journal of Operational Research, 2003, 148(2): 312-322.
[18] Tone K. Variations on the theme of slacks-based measure of efficiency in DEA[J]. European Journal of Operational Research, 2010, 200(3): 901-907.
[19] Zhou Y, Liang D, Xing X. Environmental efficiency of industrial sectors in China: an improved weighted SBM model[J]. Mathematical & Computer Modelling, 2013, 58(9): 990-999.
[20] 殷群,张娇.长三角地区科技企业孵化器运行效率研究——基于DEA的有效性分析[J].科学学研究,2010,129(01):86-94.
[21] 代碧波,孙东生.基于DEA方法的科技企业孵化器运行效率评价——以东北地区14家国家级企业孵化器为例[J].科技进步与对策,2012,293(01):142-146.

A Zero Sum Gains Slacks-based Measure Efficiency Decision-making Method and Its Application

基于“零和收益”的SBM效率分配方法及应用

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

[1]	ZHENG Fei-feng, SONG Qin-rui, XU Yin-feng, LIU Ming. A Study onOptimal Strategies for Parallel Machine Scheduling with Processing Rate Interference [J]. Operations Research and Management Science, 2021, 30(12): 1-5.
[2]	LIU Guo-shan, WANG Min, ZHANG Zhuan-xia. ABi-level Programming Problem Based on Time-window Delay for Resource-Constrained Project Scheduling [J]. Operations Research and Management Science, 2021, 30(12): 6-12.
[3]	WANG Hai-yu. Multi-objective Optimization Design of ARMA Control Chart Considering Efficiency and Cost [J]. Operations Research and Management Science, 2021, 30(10): 80-86.
[4]	ZHAO Ju, WANG Yan, LIU Long. Study on Profit Model and Pricing Strategy of Online Short-term Rental Platform [J]. Operations Research and Management Science, 2021, 30(9): 139-144.
[5]	YU Jiang-xia, ZHAO Yang, LUO Tai-bo, LI Hong-mei. The Study on New Facility Location Strategy under Minmax Regret Criterion [J]. Operations Research and Management Science, 2021, 30(5): 15-20.
[6]	LI Gang-gang, LU Xi-wen. An Approximation Algorithm for Two-machine scheduling Problem with Flexible Maintenance to Minimize Makespan [J]. Operations Research and Management Science, 2021, 30(5): 129-133.
[7]	LI Xue-yan, LI Xue-wei, LI Jing. Attribute Reduction of Multi Objective Rough Set Based on Chaotic Swarm Intelligent Optimization Algorithm [J]. Operations Research and Management Science, 2020, 29(12): 30-37.
[8]	MA Long, LU Cai-wu, GU Qing-hua. Production Scheduling Optimization Method for Metal Mine Enterprises [J]. Operations Research and Management Science, 2020, 29(9): 34-42.
[9]	CHEN Ping, DONGWen-zhe, YU Xin-yao. Studyon Routing Problemfor New Energy Mobile Charging Vehicles [J]. Operations Research and Management Science, 2020, 29(2): 12-18.
[10]	MA Bin, WU Ze-zhong. Research on Supply Chain Network Equilibrium Model Based on Improved Particle Swarm Optimization [J]. Operations Research and Management Science, 2020, 29(2): 122-136.
[11]	ZHANG ling, LAN yun. Emergency Resource Allocation Model Based on Demand Forecasting of Domino Effect [J]. Operations Research and Management Science, 2019, 28(11): 98-105.
[12]	SONG Yan, TENG Chen-mei. Facility Location under Existing Facilities: Responses to Terrorist Attacks [J]. Operations Research and Management Science, 2019, 28(10): 5-12.
[13]	HE Lan, MENG Xian-yun. Strategy of Imperfect Maintenance Replacement Based on Censored Shock Model [J]. Operations Research and Management Science, 2019, 28(8): 100-106.
[14]	PAN Shan-shan, ZHU Yu-nan, JIAN Jin-bao. A Semidefinite Convex Relaxation Method for Hydrothermal Coordination with Valve Point Effect [J]. Operations Research and Management Science, 2019, 28(4): 89-93.
[15]	SONG Yan, TENG Chen-mei, JIANG Jin-gui. A Decision Model of Reserve Coverage Selection for Multi-level Service Facilities Based on Improved NSGA-II Algorithm [J]. Operations Research and Management Science, 2019, 28(1): 71-78.