资源不确定条件下项目调度多目标优化研究
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摘要
经典的资源受限项目调度问题（Resource-constrained Project SchedulingProblem, RCPSP）假设在满足项目确定的任务工期和资源约束及一定的逻辑约束条件下，为项目中的各项任务分配资源并确定各项任务的实际开始时间，以实现项目总工期最小化的目标。但是，经典RCPSP模型的假设在实际应用中具有太多的限制，特别是在实际项目调度中，完成一项任务所需要的时间和资源往往是模糊不确定的，项目调度的目标除了要考虑工期最小化之外，还要在工期最小化和资源使用效率最大化之间进行权衡。因此，研究资源不确定条件下项目调度多目标优化问题，不仅具有重要的理论意义，而且具有重要的实践应用价值。
本文将经典RCPSP问题中确定的工期和资源拓展为模糊不确定的，将工期最小化拓展为工期-资源均衡的多目标，重点研究了资源不确定条件下项目调度多目标优化中一系列问题的建模和求解方法，主要研究内容和创新性工作如下：
首先，针对任务工期模糊的情况，提出了一种模糊关键路径法，该方法采用改进的模糊取最大运算和模糊减运算以确定模糊时间参数，从而既解决了现有研究中忽视了在任务工期模糊的情况下关键路径可能会发生变化的问题，又有效避免了在传统的逆向递推计算中可能出现负的或者不可行解的情况。
其次，针对任务工期和资源均是模糊的情况，提出了一种改进的模糊数排序法，该方法基于模糊数的左右占优和决策者的乐观态度对模糊数进行排序。建立了该问题的模型，并提出了适用于求解该问题的一种基于模糊平行调度的遗传算法，通过实例分析验证了模型的合理性和模糊平行遗传算法的有效性。
再次，针对如何提高资源的利用效率并直接度量资源波动的问题，提出了一个创新的资源均衡度量指标：资源波动成本。该指标在出现不利的资源波动情况下，考虑分别采取允许资源闲置和允许解雇后再雇用两种不同的资源使用策略，从而可以直接度量并最小化资源波动对项目施工生产力和成本造成的负面影响。结合问题的实际特点，设计求解该模型的遗传算法，改进了算法的编码方式。通过一个实例说明了模型的合理性和算法的有效性。
最后，针对任务工期和资源都是模糊的情况下，研究了项目调度的工期-资源波动成本权衡多目标优化问题。建立了模糊资源受限项目调度多目标优化问题的模型，并针对问题的特点，设计了改进的非支配排序遗传算法，通过一个实例验证了模型的合理性和算法的有效性。
The classical Resource-constrained Project Scheduling Problem (RCPSP) aimsto achieve the objective of minimizing the project makespan by determining the realstart time of each activity and allocate resources to each activity, under the constraintsof certain activity duration and resource demand as well as the temporal constraintsbetween some activities. However, the assumption of the classical RCPSP model hasmany restrictions in practical applications. Especially, when the duration and theresource demand to accomplish an activity used to be fuzzy, there is a lot more thanthe minimization of project makespan to take into consideration, such as the trade-offbetween the makespan minimization and the efficiency of resource utilizationmaximization. Hence, there is not only theoretical significance, but also crucialpractical application value in researches on the project scheduling multi-objectiveoptimization under uncertain resource constraints.
This paper expands the assumption of the duration and resources of the classicalRCPSP from the certain to the fuzzy uncertain, and extends the goal from themakespan minimization into the time-resource trade-off. It studies the modeling andsolving methods of a series of problems in project scheduling multi-objectiveoptimization under uncertain resource constraints. The main contents and innovativework include:
Firstly, an improved fuzzy maximum operator and the fuzzy subtraction operatorare proposed for determining the fuzzy time parameters in fuzzy network under thecondition of fuzzy activity time. The improved methods thereby on the one hand,overcome the problem in the existing work which did not consider the fact that thecritical path may change in case of fuzzy activity time; on the other hand, theysuccessfully avoid generating negative and infeasible solution in the traditionalbackward recursive calculation.
Secondly, it is advanced to use an improved fuzzy numbers ranking method todeal with the fuzzy uncertain condition of both the activity time and resource demand.This improved method ranks the fuzzy numbers based on the left and right dominanceand the decision maker’s optimistic attitude. In order to solve this problem, a model ofthis problem is built, and a fuzzy parallel scheduling-based genetic algorithm isproposed. Besides, an example is put forward to demonstrate the rationality of themodel and the effectiveness of the proposed fuzzy parallel genetic algorithm.
Thirdly, an innovative resource leveling metric of resource fluctuation cost is presented on ways to improve the efficiency of the resource utilization and to measurethe resource fluctuation. The new metric can directly measure and minimize thenegative effect of resource fluctuation on the project construction productivity andcost by either allowing resource idle or adopting the fire-and-rehire resourceutilization strategy under the circumstance of unfavorable resource fluctuation. Afterconsidering the actual characteristics of the resource leveling problem, an improvedgenetic algorithm is presented to solve this model, and the encoding code of thisalgorithm is improved, meanwhile an actual project example is illustrated todemonstrate the rationality of the model and the effectiveness of the proposedalgorithm.
Finally, the resource constrained time-resource fluctuation cost multipleoptimization tradeoff project scheduling problem with fuzzy time and fuzzy resourceis studied. In this way, the model of fuzzy resource constrained project schedulingmulti-objective optimization problem is built, an improved non-dominated sortinggenetic algorithm is designed to address this problem, and later an actual example isillustrated to demonstrate the rationality of the model and the effectiveness of theproposed algorithm.
本文将经典RCPSP问题中确定的工期和资源拓展为模糊不确定的，将工期最小化拓展为工期-资源均衡的多目标，重点研究了资源不确定条件下项目调度多目标优化中一系列问题的建模和求解方法，主要研究内容和创新性工作如下：
首先，针对任务工期模糊的情况，提出了一种模糊关键路径法，该方法采用改进的模糊取最大运算和模糊减运算以确定模糊时间参数，从而既解决了现有研究中忽视了在任务工期模糊的情况下关键路径可能会发生变化的问题，又有效避免了在传统的逆向递推计算中可能出现负的或者不可行解的情况。
其次，针对任务工期和资源均是模糊的情况，提出了一种改进的模糊数排序法，该方法基于模糊数的左右占优和决策者的乐观态度对模糊数进行排序。建立了该问题的模型，并提出了适用于求解该问题的一种基于模糊平行调度的遗传算法，通过实例分析验证了模型的合理性和模糊平行遗传算法的有效性。
再次，针对如何提高资源的利用效率并直接度量资源波动的问题，提出了一个创新的资源均衡度量指标：资源波动成本。该指标在出现不利的资源波动情况下，考虑分别采取允许资源闲置和允许解雇后再雇用两种不同的资源使用策略，从而可以直接度量并最小化资源波动对项目施工生产力和成本造成的负面影响。结合问题的实际特点，设计求解该模型的遗传算法，改进了算法的编码方式。通过一个实例说明了模型的合理性和算法的有效性。
最后，针对任务工期和资源都是模糊的情况下，研究了项目调度的工期-资源波动成本权衡多目标优化问题。建立了模糊资源受限项目调度多目标优化问题的模型，并针对问题的特点，设计了改进的非支配排序遗传算法，通过一个实例验证了模型的合理性和算法的有效性。
The classical Resource-constrained Project Scheduling Problem (RCPSP) aimsto achieve the objective of minimizing the project makespan by determining the realstart time of each activity and allocate resources to each activity, under the constraintsof certain activity duration and resource demand as well as the temporal constraintsbetween some activities. However, the assumption of the classical RCPSP model hasmany restrictions in practical applications. Especially, when the duration and theresource demand to accomplish an activity used to be fuzzy, there is a lot more thanthe minimization of project makespan to take into consideration, such as the trade-offbetween the makespan minimization and the efficiency of resource utilizationmaximization. Hence, there is not only theoretical significance, but also crucialpractical application value in researches on the project scheduling multi-objectiveoptimization under uncertain resource constraints.
This paper expands the assumption of the duration and resources of the classicalRCPSP from the certain to the fuzzy uncertain, and extends the goal from themakespan minimization into the time-resource trade-off. It studies the modeling andsolving methods of a series of problems in project scheduling multi-objectiveoptimization under uncertain resource constraints. The main contents and innovativework include:
Firstly, an improved fuzzy maximum operator and the fuzzy subtraction operatorare proposed for determining the fuzzy time parameters in fuzzy network under thecondition of fuzzy activity time. The improved methods thereby on the one hand,overcome the problem in the existing work which did not consider the fact that thecritical path may change in case of fuzzy activity time; on the other hand, theysuccessfully avoid generating negative and infeasible solution in the traditionalbackward recursive calculation.
Secondly, it is advanced to use an improved fuzzy numbers ranking method todeal with the fuzzy uncertain condition of both the activity time and resource demand.This improved method ranks the fuzzy numbers based on the left and right dominanceand the decision maker’s optimistic attitude. In order to solve this problem, a model ofthis problem is built, and a fuzzy parallel scheduling-based genetic algorithm isproposed. Besides, an example is put forward to demonstrate the rationality of themodel and the effectiveness of the proposed fuzzy parallel genetic algorithm.
Thirdly, an innovative resource leveling metric of resource fluctuation cost is presented on ways to improve the efficiency of the resource utilization and to measurethe resource fluctuation. The new metric can directly measure and minimize thenegative effect of resource fluctuation on the project construction productivity andcost by either allowing resource idle or adopting the fire-and-rehire resourceutilization strategy under the circumstance of unfavorable resource fluctuation. Afterconsidering the actual characteristics of the resource leveling problem, an improvedgenetic algorithm is presented to solve this model, and the encoding code of thisalgorithm is improved, meanwhile an actual project example is illustrated todemonstrate the rationality of the model and the effectiveness of the proposedalgorithm.
Finally, the resource constrained time-resource fluctuation cost multipleoptimization tradeoff project scheduling problem with fuzzy time and fuzzy resourceis studied. In this way, the model of fuzzy resource constrained project schedulingmulti-objective optimization problem is built, an improved non-dominated sortinggenetic algorithm is designed to address this problem, and later an actual example isillustrated to demonstrate the rationality of the model and the effectiveness of theproposed algorithm.
引文
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