网络计划中构建对偶网络模型的理论和方法

苏志雄; 李星梅; 乞建勋

网络计划中构建对偶网络模型的理论和方法

华北电力大学经济与管理学院, 北京 102206

基金项目: 国家自然科学基金资助项目(70671040); 华北电力大学博士研究生创新基金资助项目

详细信息

中图分类号: TB 114.1
计量
- 文章访问数: 2556
- HTML全文浏览量: 112
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- 被引次数: 0
出版历程
- 收稿日期: 2010-11-19
- 网络出版日期: 2012-02-29

Theory and method of creating dual network model in network planning

School of Business Administration, North China Electric Power University, Beijing 102206, China

摘要

摘要: 针对现有的网络计划模型重点体现的不是其核心机动时间和路差,而是具体的时间和路长,进而使得该模型在运用时往往会遇到阻碍的问题,利用对偶原理,构建网络计划模型的对偶模型.首先,通过分析机动时间和路长之间的关系,推导出路差定理;其次,在路差定理的基础上,利用对偶原理构建对偶网络模型,并分析其性质;然后利用该模型揭示网络计划的对偶等价性;最后,通过例子进行验证和说明.该对偶网络模型重点体现了机动时间和路差,使得网络计划更具针对性和有效性.
- 运筹学 /
- 对偶理论 /
- 网络计划 /
- 时差
Abstract: Aiming at problem that existing network planning model incarnates specific time and path length prominently instead of its core float and path length difference, which makes obstacles common exist when using the model in practice, dual model of network planning model was founded by using dual theory. Firstly, path length theorem was deduced by analyzing relation between float and path length; Secondly, based on path length theorem, dual network model was founded by using dual theory, and its properties were analyzed; Thirdly, dual equivalence property of network planning was revealed by using the model; Finally, the model was validated and illuminated by illustration. The dual network model incarnates float and path length difference prominently, which makes network planning have more prominent pertinence and validity.
- operational research /
- dual theory /
- network planning /
- float

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参考文献(20)

[1]	Demeulemeester E L,Herrlelen W S.Project scheduling[M].Boston:Kluwer Academic Publishers,2002:17-48
[2]	Michael D J,Kamburowski J,Stallman M.On minimum dummy arc problem[J].Operations Research,1993,27(2):153-168
[3]	Elmaghraby S E,Kamburowski J.On project representationand activity floats [J].Arabian Journal of Science and Engineering,1990,15:627-637
[4]	Elmaghraby S E.Activity nets:a guided tour through some recent developments[J].European Journal of Operational Research,1995,82:383-408
[5]	王强,李星梅,乞建勋.双代号网络图中虚工序对时差计算公式的影响与修正[J].系统工程理论与实践,2008(6):106-114 Wang Qiang,Li Xingmei,Qi Jianxun.A research on the influence of dummy activity on float in an AOA networkand its amendments[J].Systems Engineering-Theory & Practice,2008(6):106-114(in Chinese)
[6]	乞建勋,张立辉,李星梅.网络计划管理中的机动时间特性及其应用[M].北京:科学出版社,2009:22-45 Qi Jianxun,Zhang Lihui,Li Xingmei.Property and application of float in network planning management[M].Beijing:Science Publisher,2009:22-45(in Chinese)
[7]	王佳,李星梅,乞建勋.基于机动时间的平行序链顺序优化算法设计[J].系统工程学报,2008,23(4):455-461 Wang Jia,Li Xingmei,Qi Jianxun.Sequencing optimalarithmetic design of parallel procedure chains basedon activity float[J].Journal of Systems Engineering,2008,23(4):455-461(in Chinese)
[8]	Yakhchali S H,Ghodsypour S H.Computing latest starting times of activities in interval-valued networks with minimal time lags[J].European Journal of Operational Research,2010,200(3):874-880
[9]	Sirakoulis K K.The effectiveness of resource leveling tools for resource constraint project scheduling problem[J].International Journal of Project Management,2009,27(5):493-500
[10]	Karaca Z,Onargan T.The application of critical path method (CPM) in workflow schema of marble processing plants[J].Materials and Manufacturing Processes,2007,22(1):37-44
[11]	Rodder W.A generalized saddlepoint theory:its application to duality theory for linear vector optimum problems[J].European Journal of Operational Researh,1977,1(1):55-59
[12]	Ivanov E H,Nehse R.Some results on dual vector optimization problems[J].Optimization,1985,16(4):505-517
[13]	乞建勋,李星梅,王强.等效子网络的理论与方法[J].管理科学学报,2010,13(1):40-44 Qi Jianxun,Li Xingmei,Wang Qiang.Theories and methods of creating equivalent sub-network[J].Journal of Management Sciences in China,2010,13(1):40-44(in Chinese)
[14]	李星梅,乞建勋,苏志雄.自由时差定理与k阶次关键路线的求法[J].管理科学学报,2009,12(2):98-104 Li Xingmei,Qi Jianxun,Su Zhixiong.Free float theorem and algorithm of seeking the k-th order critical path[J].Journal of Management Sciences in China,2009,12(2):98-104(in Chinese)
[15]	李星梅,乞建勋,苏志雄.双代号网络计划中工序机动时间蔓延性研究[J].系统工程学报,2009,24(1):39-45 Li Xingmei,Qi Jianxun,Su Zhixiong.Study of activity float spread property in activity-on-arc network planning[J].Journal of Systems Engineering,2009,24(1):39-45(in Chinese)
[16]	王众托,张军.网络计划技术[M].沈阳:辽宁出版社,1984 Wang Zhongtuo,Zhang Jun.Network planning technology[M].Shenyang:Liaoning Publisher,1984(in Chinese)
[17]	张连营,王亮,吕文学.网络计划的模糊分析[J].天津大学学报,2004,37(2):175-178 Zhang Lianying,Wang Liang,Lü Wenxue.Calculation and analysis of project network based on fuzzy set[J].Journal of Tianjin University,2004,37(2):175-178(in Chinese)
[18]	Elmaghraby S E,Kamburowski J.The analysis of activity networks under generalized precedence relations (GPRs)[J].Management Science,1992,38(9):1245-1263
[19]	杨冰.网络计划计算模型的统一[J].系统工程理论与实践,2002(3):51-55 Yang Bing.Unifying calculating models for the network Planning[J].Systems Engineering-Theory & Practice,2002(3):51-55(in Chinese)
[20]	苏志雄,李星梅,乞建勋.基于CPM原理和Dijkstra算法的SPM网络计划模型及性质[J].运筹与管理,2008,17(1):148-153 Su Zhixiong,Li Xingmei,Qi Jianxun.SPM network planning model and its characteristics based on CPM theory and Dijkstra algorithm[J].Operations Research and Management Science,2008,17(1):148-153(in Chinese)