Abstract: During the research on the robustness of project scheduling, each activity of the project has different weight of delay risk because of its different nature when it appears delay risk. The higher the weight is, the more likely the activity will affect the makespan of the project. In view of the resource-constrained project scheduling problem, a new robustness measure index based on activity delay risk weighted slack is put forward. When uncertain factors appear, this index not only considers influences of the weight of delay risk, but also takes the number of preceding activities into account to realize the share of slack among multiple activities. A robust optimization model for the resource-constrained project scheduling problem aimed at weighted slack maximization is developed. According to the feature of the model, a simulated annealing algorithm based on the tabu search is presented. Finally, the results of the numerical example validate the reasonableness and the effectiveness of the measurement and the algorithm. Also, the superiority of the newly proposed index over the old ones is proven by comparison results and it can meet the demands of quality robustness of the project scheduling better.

Key words: project scheduling, robustness, weight of delay risk, slack, simulated annealing

摘要： 在项目调度鲁棒性研究中,当活动出现延期风险时,由于各活动性质不同,其延期风险权重也不同,权重越大的活动越有可能影响项目的完工时间。针对资源受限项目调度问题,提出一个基于活动延期风险加权时差的鲁棒性度量新指标。在出现不确定因素干扰时,该指标不仅考虑了活动延期风险权重的影响,同时为实现时差在多个任务之间的共享,还考虑了紧前任务数量的影响。建立一个以加权时差最大化为目标的资源受限项目调度鲁棒优化模型,并针对模型特点,设计了基于禁忌搜索的模拟退火算法。最后,通过算例验证了该度量方式和算法的合理性和有效性,对比分析结果表明所提出的指标优于现有的度量指标,较好地满足了项目调度质量鲁棒性的要求。

关键词: 项目调度, 鲁棒性, 延期风险权重, 时差, 模拟退火