考虑“时间-资源”的大型客机协同研制GERT网络优化
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摘要
研究大型客机协同研制过程中项目活动时间和投入资源具有不确定性的图示评审技术(GERT)网络优化问题.采用GERT网络表征复杂项目研制过程,给出基于GERT的项目完成费用计算方法,提出项目时间与资源投入数量影响下的完工实现概率表征方式;为实现对复杂产品研制项目中时间-费用-资源优化调整,针对项目各活动和整体完工时间的不确定性,建立总完工时间、资源、实现概率受限情况下的时间规划与资源调度优化模型,并给出问题求解的差分进化启发式算法;考虑到大型客机全面试制过程是衡量能否按期完工的关键,以此过程为例进行案例分析,从而表明所提出方法的可行性和有效性.
The paper studies a graphic evaluation and review techuique(GERT) network optimization problem with uncertain project activity time and resources invested in the collaborative development process of airliners. Firstly, the development process of the complex product is characterized by a GERT network which is considered as a basis of calculating the project completion cost, then a form denoting the completion probability is proposed considering the influence of project duration and resources involved in the project. Then, to adjust and optimize the time-cost-resources involved in the project when each activity time and the total project completion time are uncertain, a time planning and resource scheduling optimization model is proposed under the limitation of the total completion time, resources and implementation probability, and a difference evolutionary heuristic algorithm is developed to solve the model. Finally, as the comprehensive trial-manufacture process of airliners is the key to measure whether the project is completed on schedule, this paper considers it as the background of the case study to verify the feasibility and effectiveness of the proposed method.
The paper studies a graphic evaluation and review techuique(GERT) network optimization problem with uncertain project activity time and resources invested in the collaborative development process of airliners. Firstly, the development process of the complex product is characterized by a GERT network which is considered as a basis of calculating the project completion cost, then a form denoting the completion probability is proposed considering the influence of project duration and resources involved in the project. Then, to adjust and optimize the time-cost-resources involved in the project when each activity time and the total project completion time are uncertain, a time planning and resource scheduling optimization model is proposed under the limitation of the total completion time, resources and implementation probability, and a difference evolutionary heuristic algorithm is developed to solve the model. Finally, as the comprehensive trial-manufacture process of airliners is the key to measure whether the project is completed on schedule, this paper considers it as the background of the case study to verify the feasibility and effectiveness of the proposed method.
引文
[1]马国丰,顾凌赟,艾琪.项目多资源均衡--投资成本最小的混合整数线性规划[J].系统管理学报,2015,24(6):842-846.(Ma G F,Gu L Y,Ai Q.Multiple resource leveling in a project:A mix-integer linear programming for minimizing the investment cost[J].J of Systems&Management,2015,24(6):842-846.)
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[9]崔南方,梁洋洋.基于资源流网络与时间缓冲集成优化的鲁棒性项目调度[J].系统工程理论与实践,201838(1):102-112.(Cui N F,Liang Y Y.Robust project scheduling based on the integrated optimization between resource flow network and time buffers[J].Systems Engineering-Theory&Practice,2018,38(1):102-112.)
[10]杨保华,方志耕,刘思峰,等.基于GERT网络的应急抢险过程资源优化配置模型研究[J].管理学报,20118(12):1879-1883.(Yang B H,Fang Z G,Liu S F,et al.Optimal resources allocation model for emergency rescue process based on the GERT network[J].Chinese J of Management,20118(12):1879-1883.)
[11]Zhou L,Xie J P,Gu X Y,et al.Forecasting return of used products for remanufacturing using graphical Evaluation and review technique(GERT)[J].Int J of Production Economics,2016,181(4):315-324.
[12]耿瑞,朱建军.结果输出受控下的灰色GERT网络时间和概率的联合优化模型[J].系统工程,2015,34(4)112-119.(Geng R,Zhu J J.Optimization model for the joint of time and probability under the controlled result of the GERTnetwork[J].Systems Engineering,2015,34(4):112-119.)
[13]郭本海,方志耕,俞斌,等.基于能效视角的主导产业选择多参量GERT网络模型[J].系统工程理论与实践,2011,31(5):944-953.(Guo B H,Fang Z G,Yu B,et al.Multi-parameter GERTnetwork model of leading industry choice based on energy efficiency perspective[J].Systems Engineering-Theory&Practice,2011,31(5):944-953.)
[14]Xu R T,Fang Z G,Sun J Y.A grey STA-GERTquality evaluation model for complex products based on manufacture-service dual-network[J].Grey Systems:Theory and Application,2014,4(2):195-206.
[15]Tao L,Wu D,Liu S,et al.Schedule risk analysis for new-product development:The GERT method extended by a characteristic function[J].Reliability Engineering&System Safety,2017,167(6):464-473.
[16]Nelson R G,Azaron A,Aref S.The use of a GERTbased method to model concurrent product development processes[J].European J of Operational Research,2015,250(2):566-578.
[17]陶良彦,刘思峰,方志耕,等.以特征函数为传递参数的CF-GERT及其矩阵法求解[J].系统工程理论与实践,2018,38(2):509-521.(Tao L Y,Liu S F,Fang Z G,et al.CF-GERTmodel conveying characteristic function and its matrix solution[J].Systems Engineering-Theory&Practice,2018,38(2):509-521.)
[18]Pich M T,Loch C H,Meyer A D.On uncertainty,ambiguity,and complexity in project management[J].Management Science,2002,48(8):1008-1023.
[19]Leon H C M,Farris J A,Letens G,et al.An analytical management framework for new product development processes featuring uncertain iterations[J].J of Engineering and Technology Management,2013,30(1):45-71.
[20]王海燕,赵燕伟,王万良,等.两级差分进化算法求解多资源作业车间批量调度问题[J].控制与决策,2010,25(11):1635-1644.(Wang H Y,Zhao Y W,Wang W L,et al.New parallel algorithm based on DE for batch splitting job shop scheduling under multiple-resource constraints[J].Control and Decision,2010,25(11):1635-1644.)
[21]胡蓉,钱斌.一种求解随机有限缓冲区流水线调度的混合差分进化算法[J].自动化学报,2009,35(12):1580-1586.(Hu R,Qian B.A hybrid differential evolution algorithm for stochastic flow shop scheduling with limited buffers[J].Acta Automatica Sinica,2009,35(12):1580-1586.)
[2]Schutt A,Feydy T,Stuckey P J,et al.Solving RCPSP/max by lazy clause generation[J].J of Scheduling,2013,16(3):273-289.
[3]Ballestín F.When it is worthwhile to work with the stochastic RCPSP?[J].J of Scheduling,2007,10(3):153-166.
[4]Damay J,Quilliot A,Sanlaville E.Linear programming based algorithms for preemptive and non-preemptive RCPSP[J].European J of Operational Research,2007182(3):1012-1022.
[5]谢芳,徐哲,于静.柔性资源约束下的项目调度问题双目标优化[J].系统工程理论与实践,2016,36(3)674-683.(Xie F,Xu Z,Yu J.Bi-objective optimization for the project scheduling problem with variable resource availability[J].Systems Engineering-Theory&Practice,2016,36(3):674-683.)
[6]于静,徐哲,谢芳.活动重叠模式与资源约束下的项目调度优化[J].管理科学学报,2017,26(9):36-45.(Yu J,Xu Z,Xie F.Project scheduling optimization with overlapping modes and resource con-straints[J].Jof Management Sciences in China,2017,26(9):36-45.)
[7]王海鑫,王祖和,温国锋,等.自适应粒子群算法求解资源受限多项目调度问题[J].管理工程学报,201731(4):220-225.(Wang H X,Wang Z H,Wen G F,et al.Resource constrained multi-project scheduling based on adaptive particle swarm optimization algorithm[J].J of Industria Engineering/Engineering Management,2017,31(4)220-225.)
[8]李迁,张怀明,丁翔.基于计算实验的资源受限多项目调度策略优化[J].系统管理学报,2018,27(1):168-175.(Li Q,Zhang H M,Ding X.Resource-constrained multi-project scheduling optimization-based on a computational experiment analysis[J].J of Systems&Management,2018,27(1):168-175.)
[9]崔南方,梁洋洋.基于资源流网络与时间缓冲集成优化的鲁棒性项目调度[J].系统工程理论与实践,201838(1):102-112.(Cui N F,Liang Y Y.Robust project scheduling based on the integrated optimization between resource flow network and time buffers[J].Systems Engineering-Theory&Practice,2018,38(1):102-112.)
[10]杨保华,方志耕,刘思峰,等.基于GERT网络的应急抢险过程资源优化配置模型研究[J].管理学报,20118(12):1879-1883.(Yang B H,Fang Z G,Liu S F,et al.Optimal resources allocation model for emergency rescue process based on the GERT network[J].Chinese J of Management,20118(12):1879-1883.)
[11]Zhou L,Xie J P,Gu X Y,et al.Forecasting return of used products for remanufacturing using graphical Evaluation and review technique(GERT)[J].Int J of Production Economics,2016,181(4):315-324.
[12]耿瑞,朱建军.结果输出受控下的灰色GERT网络时间和概率的联合优化模型[J].系统工程,2015,34(4)112-119.(Geng R,Zhu J J.Optimization model for the joint of time and probability under the controlled result of the GERTnetwork[J].Systems Engineering,2015,34(4):112-119.)
[13]郭本海,方志耕,俞斌,等.基于能效视角的主导产业选择多参量GERT网络模型[J].系统工程理论与实践,2011,31(5):944-953.(Guo B H,Fang Z G,Yu B,et al.Multi-parameter GERTnetwork model of leading industry choice based on energy efficiency perspective[J].Systems Engineering-Theory&Practice,2011,31(5):944-953.)
[14]Xu R T,Fang Z G,Sun J Y.A grey STA-GERTquality evaluation model for complex products based on manufacture-service dual-network[J].Grey Systems:Theory and Application,2014,4(2):195-206.
[15]Tao L,Wu D,Liu S,et al.Schedule risk analysis for new-product development:The GERT method extended by a characteristic function[J].Reliability Engineering&System Safety,2017,167(6):464-473.
[16]Nelson R G,Azaron A,Aref S.The use of a GERTbased method to model concurrent product development processes[J].European J of Operational Research,2015,250(2):566-578.
[17]陶良彦,刘思峰,方志耕,等.以特征函数为传递参数的CF-GERT及其矩阵法求解[J].系统工程理论与实践,2018,38(2):509-521.(Tao L Y,Liu S F,Fang Z G,et al.CF-GERTmodel conveying characteristic function and its matrix solution[J].Systems Engineering-Theory&Practice,2018,38(2):509-521.)
[18]Pich M T,Loch C H,Meyer A D.On uncertainty,ambiguity,and complexity in project management[J].Management Science,2002,48(8):1008-1023.
[19]Leon H C M,Farris J A,Letens G,et al.An analytical management framework for new product development processes featuring uncertain iterations[J].J of Engineering and Technology Management,2013,30(1):45-71.
[20]王海燕,赵燕伟,王万良,等.两级差分进化算法求解多资源作业车间批量调度问题[J].控制与决策,2010,25(11):1635-1644.(Wang H Y,Zhao Y W,Wang W L,et al.New parallel algorithm based on DE for batch splitting job shop scheduling under multiple-resource constraints[J].Control and Decision,2010,25(11):1635-1644.)
[21]胡蓉,钱斌.一种求解随机有限缓冲区流水线调度的混合差分进化算法[J].自动化学报,2009,35(12):1580-1586.(Hu R,Qian B.A hybrid differential evolution algorithm for stochastic flow shop scheduling with limited buffers[J].Acta Automatica Sinica,2009,35(12):1580-1586.)