关键链项目进度计划的鲁棒优化的研究

A Study on Robust Optimization of Critical Chain Project Scheduling

针对任务工期不确定程度较大的资源受限的关键链项目进度计划问题,提出了求解该问题的鲁棒优化数学模型。在传统关键链项目进度计划模型的基础上,针对该鲁棒优化模型设计了遗传算法。通过基于顺序表示的遗传基因编码方式,形成随机优先权列表,以保证初始种群的多样性。通过三角模糊数描述任务的持续时间,进而获得相应情景的任务工期向量和该情境下的发生概率。应用该模型对项目实例进行求解,分析表明,所求得的关键链进度计划能够有效应对任务工期不确定性导致的随机差异,具有较强的鲁棒性。另外,决策者通过调整模型中目标函数以及约束函数中的参数,可以有效平衡解的可行性和最优性,有助于决策者根据风险偏好选择合适的进度计划。

For the resource-constrained critical chain project scheduling problem, where the task durations are greatly uncertain, a new robust optimization approach is developed. Based on the traditional critical chain project scheduling model, a genetic algorithm is designed for solving this robust optimization model. By the genetic gene coding based on order, the list of random priority is formed to ensure the diversity of incipient species group. Through the durations of tasks described by Triangular Fuzzy Number, the corresponding vector of task durations and its probability are obtained. The model is applied to a real- world project. The analytical results show that the Critical Chain schedule obtained using the robust optimization model is not affected by the randomness resulting from the uncertainty of the task durations, in other words, it is robust. Furthermore, decision makers may balance the feasibility and optimality of the solution through adjusting the parameters of objective function and constraints in the model, which helps them to choose the appropriate schedule based on risk preference.