不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化
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摘要
项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。
Time and cost are two important indicators in project scheduling,and the robustness of the schedule is the key issue for ensuring the smooth execution of the project under uncertainty. This paper involves the multiobjective project scheduling optimization problem under uncertainty,arranging the start time of activities in order to optimize time,cost and robustness simultaneously. Based on this purpose,we construct the multi-objective optimization model for the problem,analyze the trade-off relationships among the objectives through dividing the model into three sub-models,design non-dominated sorting genetic algorithm to solve the problem,apply the elitism strategy and the trade-off relationships optimization strategy among sub-models to optimize the algorithm,and perform algorithm testing and sensitivity analysis of instance parameters. Finally,the proposed model and algorithm are illustrated through a practical case,with the non-dominated set founded,and the sensitivity analysis of this case further validates the trade-off relationships in the sub-models. An effective utilization strategy of resources is presented in the end. The research of this paper can provide quantitative decision support for multi-objective project scheduling.
Time and cost are two important indicators in project scheduling,and the robustness of the schedule is the key issue for ensuring the smooth execution of the project under uncertainty. This paper involves the multiobjective project scheduling optimization problem under uncertainty,arranging the start time of activities in order to optimize time,cost and robustness simultaneously. Based on this purpose,we construct the multi-objective optimization model for the problem,analyze the trade-off relationships among the objectives through dividing the model into three sub-models,design non-dominated sorting genetic algorithm to solve the problem,apply the elitism strategy and the trade-off relationships optimization strategy among sub-models to optimize the algorithm,and perform algorithm testing and sensitivity analysis of instance parameters. Finally,the proposed model and algorithm are illustrated through a practical case,with the non-dominated set founded,and the sensitivity analysis of this case further validates the trade-off relationships in the sub-models. An effective utilization strategy of resources is presented in the end. The research of this paper can provide quantitative decision support for multi-objective project scheduling.
引文
[1]方晨,王凌.资源约束项目调度研究综述[J].控制与决策,2010,25(5):641-650,656.
[2]彭武良,王成恩.产品开发项目的离散时间/成本/质量平衡问题研究[J].控制与决策,2009,24(3):423-428.
[3] Al-Fawzan M A,Haouari M. A bi-objective model for robust resource-constrained project scheduling[J]. International Journal of Production Economics,2005,96(2):175-187.
[4] Demeulemeester E,Vanhoucke M. New computational results on the discrete time/cost trade-off problem in project networks[J]. Journal of the Operational Research Society,1998,49(11):1153-1163.
[5] Deckro R F,Hebert J E,Verdini W A,Grimsrud P H,Venkateshwar S. Nonlinear time/cost tradeoff models in project management[J]. Computers&Industrial Engineering,1995,28(2):219-229.
[6] Erenguc S,Ahn T,Conway D G. The resource constrained project scheduling problem with multiple crashable modes:an exact solution method[J]. Naval Research Logistics,2001,48(2):107-127.
[7] HazlrO,Haouari M,Erel E. Discrete time/cost trade-off problem:a decomposition-based solution algorithm for the budget version[J]. Computers&Operations Research,2010,37(4):649-655.
[8] Van De Vonder S,Demeulemeester E,Herroelen W,Leus R. The trade-off between stability and makespan in resource-constrained project scheduling[J]. International Journal of Production Research,2006,44(2):215-236.
[9]李洪波,徐哲.鲁棒项目调度研究综述[J].系统工程,2014(2):123-131.
[10] Ke H,Ma W,Ni Y. Optimization models and a GAbased algorithm for stochastic time-cost trade-off problem[J]. Applied Mathematics&Computation,2009,215(1):308-313.
[11]何正文,刘人境,徐渝.基于随机活动工期的资源约束项目鲁棒性调度优化[J].系统工程理论与实践,2013,33(3):650-659.
[12]庞南生,孟俊姣.多目标资源受限项目鲁棒调度研究[J].运筹与管理,2012,21(3):27-32.
[13]寿涌毅,王伟.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,2009,23(4):148-152.
[14]何立华,孔云霄.基于活动延期风险加权时差的资源受限项目调度鲁棒性度量[J].运筹与管理,2015,24(5):167-174.
[15] Herroelen W,Leus R. The construction of stable project baseline schedules[J]. European Journal of Operational Research,2004,156(3):550-565.
[16]王杜娟,刘锋,王建军,王延章.加工时间可控单机加权总完工时间Pareto优化研究[J].运筹与管理,2016,25(1):35-45.
[17]刘士新,宋健海.模糊多目标资源受限项目调度问题的优化方法[J].系统工程学报,2008,23(6):744-750.
[18] Yamashita D S,Armentano V A,Laguna M. Robust optimization models for project scheduling with resource availability cost[J]. Journal of Scheduling,2007,10(1):67-76.
[19] De P,Dunne E J,Ghosh J B,Wells C E. The discrete time-cost tradeoff problem revisited[J]. European Journal of Operational Research, 1995, 81(2):225-238.
[20] Kolisch R,Sprecher A. PSPLIB——a project scheduling problem library[J]. European Journal of Operational Research,1996,96(1):205-216.
[2]彭武良,王成恩.产品开发项目的离散时间/成本/质量平衡问题研究[J].控制与决策,2009,24(3):423-428.
[3] Al-Fawzan M A,Haouari M. A bi-objective model for robust resource-constrained project scheduling[J]. International Journal of Production Economics,2005,96(2):175-187.
[4] Demeulemeester E,Vanhoucke M. New computational results on the discrete time/cost trade-off problem in project networks[J]. Journal of the Operational Research Society,1998,49(11):1153-1163.
[5] Deckro R F,Hebert J E,Verdini W A,Grimsrud P H,Venkateshwar S. Nonlinear time/cost tradeoff models in project management[J]. Computers&Industrial Engineering,1995,28(2):219-229.
[6] Erenguc S,Ahn T,Conway D G. The resource constrained project scheduling problem with multiple crashable modes:an exact solution method[J]. Naval Research Logistics,2001,48(2):107-127.
[7] HazlrO,Haouari M,Erel E. Discrete time/cost trade-off problem:a decomposition-based solution algorithm for the budget version[J]. Computers&Operations Research,2010,37(4):649-655.
[8] Van De Vonder S,Demeulemeester E,Herroelen W,Leus R. The trade-off between stability and makespan in resource-constrained project scheduling[J]. International Journal of Production Research,2006,44(2):215-236.
[9]李洪波,徐哲.鲁棒项目调度研究综述[J].系统工程,2014(2):123-131.
[10] Ke H,Ma W,Ni Y. Optimization models and a GAbased algorithm for stochastic time-cost trade-off problem[J]. Applied Mathematics&Computation,2009,215(1):308-313.
[11]何正文,刘人境,徐渝.基于随机活动工期的资源约束项目鲁棒性调度优化[J].系统工程理论与实践,2013,33(3):650-659.
[12]庞南生,孟俊姣.多目标资源受限项目鲁棒调度研究[J].运筹与管理,2012,21(3):27-32.
[13]寿涌毅,王伟.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,2009,23(4):148-152.
[14]何立华,孔云霄.基于活动延期风险加权时差的资源受限项目调度鲁棒性度量[J].运筹与管理,2015,24(5):167-174.
[15] Herroelen W,Leus R. The construction of stable project baseline schedules[J]. European Journal of Operational Research,2004,156(3):550-565.
[16]王杜娟,刘锋,王建军,王延章.加工时间可控单机加权总完工时间Pareto优化研究[J].运筹与管理,2016,25(1):35-45.
[17]刘士新,宋健海.模糊多目标资源受限项目调度问题的优化方法[J].系统工程学报,2008,23(6):744-750.
[18] Yamashita D S,Armentano V A,Laguna M. Robust optimization models for project scheduling with resource availability cost[J]. Journal of Scheduling,2007,10(1):67-76.
[19] De P,Dunne E J,Ghosh J B,Wells C E. The discrete time-cost tradeoff problem revisited[J]. European Journal of Operational Research, 1995, 81(2):225-238.
[20] Kolisch R,Sprecher A. PSPLIB——a project scheduling problem library[J]. European Journal of Operational Research,1996,96(1):205-216.
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