摘要
随着经济全球化和市场竞争日趋激烈,项目环境也日趋复杂,企业对项目管理要求越来越高。为应对复杂环境中出现的各种不确定因素而形成鲁棒性项目调度问题已成为国内外关注的热点。其中,关键链法和资源流网络法的研究最为广泛,此两种方法已在理论和实践中被证明是有效的具有鲁棒性的管理方法。关键链法提出输入缓冲,项目缓冲,资源缓冲及接力赛策略。其中,接力赛策略要求项目各任务节点尽早开工以达到尽快完成项目的目的。与接力赛策略相对应的时刻表策略则要求项目各任务节点不能早于计划时刻开工,此策略通过延长工期来增强项目的鲁棒性。本文将采用关键链法和资源流网络法研究多模式资源受限项目调度问题。在随机DTRTP环境下,按照时刻表策略和接力赛策略模拟仿真执行项目,对项目这两种调度策略进行比较研究,并对模拟仿真得到的数据构建合适的多层次混合模型,采用SAS软件进行影响分析。
首先,提出一个识别关键链的启发式算法,通过数值计算说明算法的可行性和有效性。其次,在关键链项目计划中插入缓冲区后,分析可能出现资源冲突和紧前关系冲突,提出基于分支定界法的局部性重排算法和基于分支定界法的全局性重排算法来解决冲突问题。通过模拟仿真,从三个不同层次分析项目任务的不确定性对项目即时完工率和项目惩罚成本的影响,并比较基于分支定界法的局部性重排算法和基于分支定界法的全局性重排算法的优越性。再次,关键链法应用到多模式的随机DTRTP项目调度问题中,从输入缓冲区设置(输入缓冲区设置大小影响)、优先级别(关键链法产生的优先级与其他优先级的影响)和不同层次的可用资源量(可用资源量的影响)三个不同角度,分别按照接力赛策略和时刻表策略进行模拟仿真,对接力赛策略与时刻表策略进行比较分析。最后,资源流网络法应用到多模式的随机DTRTP项目调度问题中,保留较好优先级以及适合随机DTRTP问题的缓冲区大小的关键链法,通过对小规模问题和大规模问题进行模拟仿真来分析优先级及资源流网络各自对接力赛策略和时刻表策略的影响。针对模拟仿真数据,构建符合试验数据的多层次混合模型,采用SAS软件从统计的角度来分析它们的相互影响。
With rapid development of economic and market, the environment of project becomes more and more complicate, resulting in high level of project management. In order to deal with various uncertainty in the complicated project environment, robust project scheduling has become one of the most hot and popular topic in the filed of project scheduling probelm. Especially, the Critical Chain Scheduling and Buffer Management (CC/BM) methodology and resource flow network have attack much attention to the world and have been proved to be good methodology to deal with robust project scheduling problem. CC/BM introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early on the one side. On the other side, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. This dissertation applied the CC/BM and resource flow network to the multiple resource constrained project scheduling problem. Railway scheduling and roadrunner scheduling is compared in a stochastic DTRTP environment, a multi-level mixed model is built to fit the data of computational results through SAS, and the impact of resource flow network and priority list on the roadrunner scheduling and railway scheduling is analyzed.
Firstly, a heuristic algorithm is proposed to identify the critical chain; some numerical results proved that this algorithm is feasible and effective. Secondly, some resource conflicts or precedence conflicts that might be occure after inserting the feeding buffer are shown and global/local branch and bound rescheduling algorithms are proposed to deal with these conflicts. Some simulations are designed to estimate the three different levels of activity uncertainty on the project completion rate and stability cost. Global branch and bound rescheduling algorithms was proved to be better than the local branch and bound rescheduling algorithms. Thirdly, CC/BM is applied to a stochastic DTRTP problem, three different experiments are designed to compare of roadrunner scheduling and railway scheduling from three different angles:the impact of feeding buffer, the impact of priority lists (critical chain priority list and other priority lists), and the impact of different level of availability. Finally, resource flow network is applied to a stochastic DTRTP environment. Retaining some good priority lists and critical chian priority list with good feeding buffer, computational experiments are simulated on the small-scale and larger-scale instances sets. A multi-level mixed model is designed to fit the data of computational results and some analysis are made for the impact of resource flow network/priority list on the roadrunner scheduling and railway scheduling by using SAS software.
引文
[1]Alcaraz, J., Maroto, C., Ruiz, R. (2003). Solving the multi-mode resource constrained project scheduling problem with genetic algorithms [J]. Journal of the Operational Research Society,54(6),614-626
[2]Al-Fawzan, M.A, Haouari, M. (2005). A bi-objective model for robust resource-constrained project scheduling [J]. Int. J. Production Economics, (96): 175-187.
[3]Artigues, C., Michelon, P., Reusser, S. (2003). Insertion techniques for static and dynamic resourceconstrained project scheduling [J]. European Journal of Operational Research,149(2),249-267.
[4]Billaut, J.C. Moukrim, A and Rinnooy Kan, A.H.G. (2008). Flexibility and robustness in scheduling [M], Hoboken:John Wiley & sons.
[5]Best, W. D. (2006). Critical Chain Project Management Flies [J]. Industrial Engineer,38(11):46.
[6]Boctor, F.F. (1993). Heuristics for scheduling projects with resource restrictions and several resource-duration modes [J]. International Journal of Production Research,31(11),2547-2558.
[7]Boctor, F.F. (1996a). Resource-constrained project scheduling by simulated annealing [J]. International Journal of Production Research,34,2335-2352.
[8]Boctor, F.F. (1996b). A new and efficient heuristic for scheduling projects with resource restrictions and multiple execution modes [J]. European Journal of Operational Research,90(2),349-361.
[9]Bouleimen, K., Lecocq, H. (2003). A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode versions [J]. European Journal of Operational Research,149(2),268-281.
[10]Chtourou, H., Haouari, M. (2008). A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling [J]. Computers and Industrial Engineering,2008,55(1):183-194.
[11]Cui N F, Tian W D, Bie L. (2010). Rescheduling after inserting the buffer in the critical chain scheduling [J].2010 International Conference on Logistics Systems and Intelligent Management,1105-1110.
[12]Davenport, A. and Beck, J. A survey of techniques for scheduling with uncertainty. 2002, Unpublished manuscript.
[13]Daniels, R. L., Kouvelis, P. (1995). Robust scheduling to hedge against processing time uncertainty in single stage production [J]. Management Science,41(2): 363-376.
[14]De, P., Dunne, E.J., Gosh, J.B., Wells, C.E. (1997). Complexity of the discrete time/cost problem for project networks [J]. Operation Research,45,302-306.
[15]De Reyck, B., Demeulemeester, E., Herroelen, W. (1998). Local search methods for the discrete time/resource trade-off problem in project networks [J], Naval Research Logistics Quarterly,45,553-578.
[16]De Reyck, B. (1998). Scheduling project with generalized precedence Relations: Exact and heuristic approach, Ph.D. Thesis, Department of Applied Economics, Katholieke Universiteit Leuven, Leuven, Belgium.
[17]Demeulemeester, E., Herroelen, W. (1992). A branch-and-bound procedure for the multiple resource constrained project scheduling problem [J]. Management Science, 38(12),1803-1818.
[18]Demeulemeester, E., De Reyck, B., Herroelen, W. (2000). The discrete time/resource trade-off problem in project networks:A branch and bound approach [J], IIE Transactions,32,1059-1069.
[19]Demeulemeester, E., Herroelen, W. (2002). Project Scheduling:A research handbook (pp.473-530). Kluwer Academic Publishers
[20]Drexl, A., Grunewald, J. (1993). Non-preemptive multi-mode resource-constrained project scheduling [J]. IIE Transactions,25,74-81.
[21]Deblaere, F., Demeulemeester, E., Herroelen, W., Van de Vonder, S. (2007). Robust resource allocation decisions in resource-constrained projects [J]. Decision sciences, 38(1),5-37.
[22]Deblaere F, Demeulemeester E, Herroelen W. (2011). Reactive scheduling in the multi-mode RCPSP [J]. Computers and Operations Research.38(1):63-74.
[23]Elmaghraby, S.E. (2005). On the fallacy of averages in project risk management [J]. European Journal of Operational Research,165(2),307-313.
[24]Fiindeling, C.U., Trautmann, N. (2010). A priority-rule method for project scheduling with work-content constraints [J]. European Journal of Operational Research,203(3),568-574.
[25]Goldratt, E.M. (1997). Critical Chain [M]. New York:North River Press.
[26]Graves, S. C. (1981). A review of production scheduling [J]. Operations Research, 29(4):646-675.
[27]Hartmann, S., Sprecher, A. (1996). A note on "hierarchical models for multi-project planning and scheduling" [J]. European Journal of Operational Research,94(2): 377-383.
[28]Hartmann, S., Drexl, A. (1998). Project scheduling with multiple modes:A comparison of exact algorithms [J]. Networks,32,283-297.
[29]Hartmann, S. (2001). Project scheduling with multiple modes:A genetic algorithm [J]. Annals of Operations Research,102,111-135.
[30]Hartmann, S. Briskorn, D. (2010). A survey of variants and extensions of the resource-constrained project scheduling problem [J]. European Journal of Operational Research,207(1):1-14.
[31]Herroelen, W., De Reyck, B., Demeulemeester, E. (1998).Resourse-constrained project scheduling:a survey of recent developments [J]. Computers Operations Reseach,25(4):279-302.
[32]Herroelen, W., Demeulemeester, E., De Reyck, B. (1999). A classification scheme for project scheduling. In Jan Weglarz (Ed.), project scheduling:recent models, algorithm, and applications (pp.1-26). Kluwer Academic Publishers.
[33]Herroelen, W., Demeulemeester, E., De Reyck, B. (2000). On the paper "Resource-constrained project scheduling:Notation, classification, models, and methods" by Brucker et al. [J], European Journal of Operational Research,128(3): 221-230.
[34]Herroelen, W., Leus, R. (2001). On the Merits and Pitfalls of Critical Chain Scheduling [J]. Journal of Operational Management,19(5):559-577.
[35]Herroelen W.S., Leus R. (2004a). The construction of stable project baseline schedules [J]. European Journal of Operational Research.156 (3):550-565.
[36]Herroelen W.S., Leus R. (2004b). Stability and resource allocation in project planning [J]. HE Transactions,2004b,36 (7):667-682.
[37]Herroelen, W., Leus, R. (2004c). Robust and reactive project scheduling:a review and classification of procedures [J]. International Journal of Production Research, 42(8):1599-1620.
[38]Herroelen, W. (2007). "Generating robust baseline schedules", INFORMS Tutorials in Operations Research 2007 (ed. T. Klastorin), pp.124-144, Hanover:INFORMS.
[39]Hoel, K., Taylor, S. (1999).Quantifying buffers for project schedules [J]. Production and Inventory Management Journal,40(2):43-47.
[40]Jarboui, B., Damak, N., Siarry, P., Rebai, A. (2008). A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems [J]. Applied Mathematics and Computation,195(1):299-308.
[41]Jozefowska, J., Mika, M., Rozycki, R., Waligora, G, Weglarz, J. (2001). Simulated annealing for multi-mode resource-constrained project scheduling [J]. Annals of Operations Research,102,137-155.
[42]Knotts, G., Dror, M., Hartman, B. (2000). Agent-based project scheduling [J]. HE Transactions,32(5),387-401.
[43]Kolisch, R., Sprecher, A. (1996). PSPLIB—A project scheduling problem library [J]. European Journal of Operational Research,96(1):205-216.
[44]Kolisch, R., Drexl, A. (1997). Local search for nonpreemptive multi-mode resource constrained project scheduling [J]. IIE Transactions,29(11):987-999.
[45]Lambrechts, O., Demeulemeester, E. and Herroelen, W. (2007). Exact and suboptimal reactive strategies for resource-constrained project scheduling with uncertain resource availabilities. Research Report KBI 0702, Department of Decision Sciences and Information Management, Katholieke Universiteit Leuven, Belgium.
[46]Lambrechts, O., Demeulemeester, E., Herroelen, W. (2008a). A tabu search procedure for developing robust predictive project schedules [J]. International Journal of Production Economics,111,493-508.
[47]Lambrechts, O., Demeulemeester, E., Herroelen, W. (2008b). Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities [J]. Journal of Scheduling.11(2):121-136.
[48]Lambrechts, O., Demeulemeester, E., Herroelen, W. (2010).Time slack-based techniques for robust project scheduling subject to resource uncertainty [J]. Annals of Operations Research. DOI 10.1007/s10479-010-0777-z.
[49]Leach, L.P. (1999). Critical Chain Project Management Improves Project Performance [J]. Project Management Journal,30(2),39-51.
[50]Leach, L.P. (2000). Critical Chain Project Management [M]. Artech House.
[51]Leach, L.P. (2006). Critical Chain Project Management [M]. Second edition, Artech House.
[52]Long, L., Ohsato, A. (2008). Fuzzy critical chain method for project scheduling under resource constraints and uncertainty [J]. International Journal of Project Management,26,688-698.
[53]Leus, R. (2003). The generation of stable project plans. PhD Thesis, Department of Applied Economics, Belgium:Katholieke Universiteit Leuven.
[54]Leus, R., Herroelen, W. (2004). Stability and resource allocation in project planning [J]. HE Transactions,36(7),667-682.
[55]Lechler, T.G., Ronen B., Stohr E. A. (2005). Critical Chain:A new project management paradigm or old wine in new bottles? [J]. Engineering Management Journal,17(4):45-58.
[56]Lee, B., Miller, J. (2004). Multi-project management in software engineering using simulation modeling [J]. Software Quality Journal,12(1):59-60
[57]Lova, A., Tormos, P., Barber, F. (2006). Multi-mode resource constrained project scheduling:Scheduling schemes, priority rules and mode selection rules [J]. Inteligencia Artificial,30,69-86.
[58]Lova, A., Tormos, P., Cervantes, M., Barber, F. (2009). An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes [J]. International Journal of Production Economics,117(2),302-316.
[59]Maroto, C., Tormos, P. (1994). Project management:An evaluation of software quality [J]. International Transactions in Operational Research,1(2),209-221.
[60]Mori, M., Tseng, C. (1997). A genetic algorithm for multi-mode resource constrained project scheduling problem [J]. European Journal of Operational Research,100(1),134-141.
[61]Newbold, R.C. (1998). Project management in the fast lane:Applying the theory of constraints [M]. St. Lucie Press.
[62]Nonobe, K., Ibaraki, T. (2001). Formulation and Tabu Search Algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). Technical Report, Kyoto University.
[63]Ozdamar, L., Ulusoy, G (1994). A local constraint based analysis approach to project scheduling under general resource constraints [J]. European Journal of Operational Research,79(2):287-298.
[64]Ozdamar, L., (1999). A genetic algorithm approach to a general category project scheduling problem. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions,29(1),44-59.
[65]Patterson, J., Slowinski, R., Talbot, F., Weglarz, J. (1989). An algorithm for a general class of precedence and resource constrained scheduling problem. In Slowinski, R.and Weglarz (Ed.), Advances in Project Scheduling (pp.3-28). Amsterdam:Elsevier.
[66]Patrick, S. F. (1998). Critical Chain Scheduling and Buffer Management, getting out from between Parkinson's Rock and Murphy's Hard Place. http://www.focusedperformance.com
[67]Policella, N., Oddi, A., Smith, S., Cesta, A. (2004). Generating robust partial order schedules.10th International Conference on the Principles and Practice of Constraint Programming—CP 2004 Proceedings, Toronto, Canada:Springer,3258, 496-511.
[68]Policella, N. (2005). Scheduling with uncertainty—A proactive approach using partial order schedules. PhD Thesis, Italy:Universita degli Studi di Roma "La Sapienza."
[69]Rabbani, M., Ghomi, S.M.T., Jolai, F., Lahiji, N.S.(2007) A New Heuristic for Resource-Constrained Project Scheduling in Stochastic Networks using Critical Chain Concept [J]. European Journal of Operational Research,176(2):794-808.
[70]Rasconi, R. Cesta, A and Policella. (2010).Validating scheduling approaches against executional uncertainty [J]. Journal of Intelligent Manufacturing.21,49-64.
[71]Ranjbar, M., Kianfar, F. (2007) Solving the discrete time/resource trade-off problem with genetic algorithm [J]. Applied Mathematics and Computation,191(2): 451-456.
[72]Ranjbar, M., De Reyck, B., Kianfar, F. (2009). A hybrid scatter search for discrete time/resource trade-off problem in project scheduling [J]. European Journal of Operational Research,193(1):35-48.
[73]Rand, G. K. (2002) Critical chain:the theory of constraints applied to project management [J]. International Journal of Project Management,18(3):173-177.
[74]Slowinski, R. (1980). Two approaches to problems of resource allocation among project activities—A comparative study [J]. Journal of Operational Research Society,31(8),711-723.
[75]Slowinski, R., Soniewicki, B., Weglarz, J. (1994). DSS for multi objective project scheduling [J]. European Journal of Operational Research,79(2),220-229.
[76]Speranza, M., Vercellis, C. (1993). Hierarchical models for multi-project planning and scheduling [J]. European Journal of Operational Research,64,312-325.
[77]Sprecher, A. (1994). Resource-constrained project scheduling:Exact methods for the multi-mode case. Lecture Notes in Economics and Mathematical Systems, vol. 409, Berlin:Springer.
[78]Sprecher, A., Hartmann, S., Drexl, A. (1997). An exact algorithm for the project scheduling with multiple modes. OR Spektrum 19,195-203.
[79]Sprecher, A., Drexl, A. (1998). Multi-mode resource-constrained project scheduling problems by a simple, general and powerful sequencing algorithm [J]. European Journal of Operational Research,107(2),431-450.
[80]Spoede, C.W., Jacob D.B. (2002) Policing, firefighting, or managing? [J]. Strategic Finance,4(6):31.
[81]Shou, Y.Y., Yeo, K. T. (2000). Estimation of Project Buffers in Critical Chain Project Management. Proceedings of the IEEE international conference on management of innovation and technology,1(1):162-167.
[82]Sung, C.S., Lim, S.K. (1997). A scheduling procedure for a general class of resource constrained projects [J]. Computers and Industrial Engineering,32,9-17.
[83]Talbot, F. (1982). Resource-constrained project scheduling with time/resource tradeoffs:The nonpreemptive case [J]. Management Science,28(10),1197-1210.
[84]Turner, R. (1999). The Handbook of Project-Based Management [M], McGraw Hill.
[85]Tukel, O.I., Rom, W.O. (1997). Ensuring quality in resource constrained project scheduling [J], European Journal of Operational Research,103,483-496.
[86]Tukel, O.I., Rom, W. O., Eksioglu, S.D. (2006). An Investigation of Buffer Sizing Techniques in Critical Chain Scheduling [J]. European Journal of Operational Research,172(2),401-416.
[87]TOMASSUBRT, PAVLINA LANGROVA CUA, SLOVAKIA (2002). Mathematical programming model of the critical chain method [J]. http://www.fhi.sk/files/katedry/kove/ssov.
[88]Umble, M., Umble, E. (2000). Manage your Projects for Success:An Application of the Theory of Constraints [J]. Production and Inventory Management Journal,41(2), 27.
[89]Van de Vonder, S., Demeulemeester, E., Herroelen, W., Leus,R. (2005). The use of buffers in project management:The trade-off between stability and makespan [J]. International Journal of Production Economics.97,227-240.
[90]Van de Vonder, S., Demeulemeester,E. and Herroelen,W. (2007a). A classification of predictive-reactive project scheduling procedures [J]. Journal of Scheduling.10, 195-207.
[91]Van de Vonder, S., Ballest, F., Demeulemeester, E., Herroelen, W. (2007b). Heuristic procedures for reactive project scheduling [J]. Computers & Industrial Engineering,52,11-28.
[92]Van de Vonder, S., Demeulemeester, E., Herroelen, W. (2008). Proactive heuristic procedures for robust project scheduling:an experiment analysis [J]. European Journal of Operational Research,189,723-733.
[93]Vanhoucke, M., Debels, D. (2008). The impact of various activity assumptions on the lead time and resource utilization of resource-constrained projects [J]. Computers and Industrial Engineering,54(1),140-154.
[94]Van Peteghem, V, Vanhoucke, M. (2010). A genetic algorithm for the preemptive and non-preemptive Multi-mode resource constrained project scheduling problem. European Journal of Operational Research,201(2),409-418.
[95]Wang, J. (2004). A fuzzy robust schedu ling app roach for product development projects [J]. European Journal of Operational Research,152(1):180-194.
[96]Wang, J. (2005). Constraint-based schedule repair for product development projects with time-limited constraints [J]. International Journal of Production Economics,95, 399-414.
[97]Worley, T. L. F. (2005) Using Constraint Management to Optimize Motion Picture Production Management [J]. Project Management Journal,36(4):44.
[98]Yeo, K.T., Ning, J.H. (2002) Integrating Supply Chain and Critical Chain Concepts in Engineer-Procure-Construct (EPC) projects [J]. International Journal of Project Management,20(4):253-262.
[99]Yang, J.B. (2007). How the critical chain scheduling method is working for construction [J]. Cost Engineering,49(4):25-32.
[100]Yu, G., Qi, X. (2004). Disruption Management-Framework, Models and Applications [M]. World Scientific, New Jersey.
[101]Zhang, H., Tam, C.M., Li, H. (2006). Multimode project scheduling based on particle swarm optimization [J]. Computer Aided Civil and Infrastructure Engineering,21(2),93-103.
[102]Zhu, G., Bard, J., Yu, G. (2005). Disruption management for resource constrained project scheduling [J]. Journal of the Operation Research Society,56,365-381.
[103]Zhu, G., Bard, J.F., Yu, G. (2006). A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem [J]. Journal on Computing,18(3), 377-390.
[104]高德拉特学院机构和高德拉特学院(2006). CCPM内部培训教程.内部资料.
[105]李宁,吴之明(2002).网络计划技术的新发展——项目关键链管理(CCPM)[J],公路,10,83-86.
[106]蔡晨,万伟(2003).基于PERT/CPM的关键链管理[J],中国管理科学,6,35-39.
[107]万伟,蔡晨,王长锋(2003).在单资源约束项目中的关键链管理[J],中国管理科学,2,70-75.
[108]唐建波,关昕,马力(2004).关键链技术研究与基于关键链的项目管理系统[J],计算机工程与设计,25(11):2077-2080.
[109]杨雪松,胡昊(2005).基于关键链方法的多项目管理[J],工业工程与管理,2,48-52.
[110]刘士新(2007).项目优化调度理论与方法[M].机械工业出版社,95-98.
[111]刘士新,宋健海,唐加福(2003).关键链——一种项目计划与调度新方法[J],控制与决策,18(05):513-518.
[112]刘士新,宋健海,唐加福(2006a).基于关键链的资源受限项目调度新方法[J],自动化学报,32(01):60-66.
[113]刘士新,宋健海,唐加福(2006b).资源受限项目调度中缓冲区的设定方法[J],系统工程学报,21(04):381-386.
[114]莫巨华(2005).基于关键链的项目调度模型与算法[D],沈阳东北大学.
[115]赵道致,廖华(2005).对关键链法的几个认识误区[J],工业工程,8(2):4-6.
[116]崔东红,孟娜(2006).基于TOC的项目进度控制[J],2006中国控制与决策学术年会论文集,719-724.
[117]蒋国萍,陈英武(2005).基于关键链的软件项目进度风险管理[J],计算机应用,25(1):56-57.
[118]马国丰,尤建新(2007),关键链项目群进度管理的定量分析[J],系统工程理论与实践,9,54-60.
[119]徐小琴,韩文民(2007),关键链汇入缓冲区的设置方法[J],工业工程与管理,12(5): 51-55.
[120]程婷婷,李伟波,程霞(2007).关键链新技术在项目管理中的研究和应用[J],微计算机应用,28(5):539-543.
[121]喻道远,罗方珍,何敏(2007).基于TOC的模具生产多项目管理研究[J],现代制造工程,3,18-21.
[122]周阳,丰景春(2008).基于排队论的关键链缓冲区研究[J],科技进步与对策,2,174-176.
[123]边志兴(2008).作业车间的模糊动态调度问题研究[J],中国管理科学,16,76-83.
[124]王勇胜,梁昌勇(2009).资源约束项目调度鲁棒性研究的现状与展望[J],中国科技论坛,8,95-99.
[125]寿涌毅,王伟(2009).基于鲁棒优化模型的项目调度策略遗传算法[J],管理工程学报,4:148-152.
[126]张宏国,徐晓飞,战德臣(2009).不确定资源约束下项目鲁棒性调度算法[J],计算机应用研究,26(6):2079-2089.
[127]田文迪,崔南方(2009).关键链项目管理中关键链与非关键链的识别[J],工业工程与管理,14(2):88-93.
[128]崔万安,王先甲(2010).资源约束项目计划内在稳健性度量方法[J],水电能源科学,28(8):123-125.
[129]付芳,周泓(2010).针对项目式生产调度的模拟退火算法[J],工业工程,5,75-79.