Abstract: In an uncertain environment, a schedule with high robustness can ensure the smooth execution of the project. Considering that resources may have multiple skills in reality, which can affect the development of a robust schedule, this paper studies the proactive project scheduling problem with flexible resource constraints. Firstly, the research problem is defined. Then, from the perspective of robustness maximization, the optimization model is constructed. Based on the analysis of the model, it is decomposed into two sub-models: one is classical robust optimization model and the other is skill allocation model for resources. Subsequently, a heuristic algorithm based on the peak clipping algorithm is designed to solve the problem. Finally, a practical case is introduced to verify the effectiveness of the algorithm and the influence of key parameters on the schedule robustness is analyzed. The following conclusions are drawn: with the extension of the project deadline, and the increase of the resource availability or resource flexibility, the schedule robustness increases.

Key words: proactive project scheduling, optimization model, heuristic algorithm, flexible resource, stochastic activity duration

摘要： 在不确定环境中,一个具有较高鲁棒性的进度计划可以保证项目的稳定实施。考虑到现实中资源可能具有多种技能,会对制定鲁棒性较高进度计划的过程产生影响,因此本文研究了柔性资源约束下前摄性项目调度优化问题。首先界定研究问题;然后从鲁棒性最大化的视角出发,构建了研究问题的优化模型,在对模型进行分析的基础上将其分解为经典鲁棒优化和资源技能分配两个子模型;随后设计了求解问题的基于削峰算法的启发式算法;最后用一个实际案例验证了算法有效性,并分析了关键参数对进度计划鲁棒性的影响,得到如下结论:项目进度计划鲁棒性随着项目工期的延长、资源可用量的增加或资源柔性的提高而增大。

关键词: 前摄性项目调度, 优化模型, 启发式算法, 柔性资源, 随机工期