The time/cost trade-off problem is a well-known project scheduling problem that has been extensively studied. In recent years, many researchers have begun to focus on project scheduling problems under uncertainty to cope with uncertain factors, such as resource idleness, high inventory, and missing deadlines. To reduce the disturbance from uncertain factors, the aim of robust scheduling is to generate schedules with time buffers or resource buffers, which are capped by project makespan and project cost. This paper addresses a time-cost-robustness trade-off project scheduling problem with multiple activity execution modes under uncertainty. A multiobjective optimization model with three objectives (makespan minimization, cost minimization, and robustness maximization) is constructed and three propositions are proposed. An epsilon-constraint method-based genetic algorithm along with three improvement measures is designed to solve this NP-hard problem and to develop Pareto schedule sets, and a large-scale computational experiment on a randomly generated dataset is performed to validate the effectiveness of the proposed algorithm and the improvement measures. The final sensitivity analysis of three key parameters shows their distinctive influences on the three objectives, according to which several suggestions are given to project managers on the effective measures to improve the three objectives.

时间/成本的权衡问题是众所周知的项目调度问题，已经得到了广泛的研究。近年来，许多研究人员已开始关注不确定性下的项目进度问题，以应对不确定性因素，例如资源闲置，高库存和缺少截止日期。为了减少不确定因素的干扰，稳健的调度的目的是生成带有时间缓冲区或资源缓冲区的进度表，这些进度表受项目工期和项目成本的限制。本文解决了不确定性下具有多种活动执行模式的时间成本鲁棒性折衷的项目调度问题。构造了具有三个目标（最小制造距离，最小成本和最大鲁棒性）的多目标优化模型，并提出了三个命题。设计了一种基于ε约束方法的遗传算法以及三种改进措施来解决该NP难问题并开发帕累托进度表集，并对随机生成的数据集进行大规模计算实验以验证该算法的有效性。提出的算法及改进措施。对三个关键参数的最终敏感性分析显示了它们对三个目标的独特影响，据此，向项目经理提供了有关改善三个目标的有效措施的一些建议。对随机生成的数据集进行了大规模的计算实验，验证了所提算法的有效性和改进措施。对三个关键参数的最终敏感性分析显示了它们对三个目标的独特影响，据此，向项目经理提供了有关改善三个目标的有效措施的一些建议。对随机生成的数据集进行了大规模的计算实验，验证了所提算法的有效性和改进措施。对三个关键参数的最终敏感性分析显示了它们对三个目标的独特影响，据此，向项目经理提供了有关改善三个目标的有效措施的一些建议。