中文摘要：

在无常下面的 Project scheduling 是吸引了增加的注意的研究的一个挑战性的领域。当大多数存在研究仅仅在无常下面考虑单个模式的 project scheduling 问题时，这篇论文试图应付打电话给随机的多模式资源的一个更现实主义的模特儿有打折的现金流动(S-MRCPSPDCF ) 的抑制 project scheduling 问题。在模型，活动持续时间和费用被随机的变量给。目的是发现一张最佳的基线时间表以便在场的期望的网络现金流动的价值(NPV ) 被最大化。解决这个问题，一个蚂蚁殖民地系统(交流) 基于途径被设计。算法派遣一组蚂蚁用 pheromones 和期望的打折的费用(EDC ) 反复地造基线时间表启发式。因为由于随机的变量的存在直接评估期望的 NPV 是不可能的，算法采用蒙特卡罗(MC ) 模拟技术。当 ACS 算法仅仅使用 best-so-far 答案更新 pheromone 价值，有随机的情形的一个小数字的不平的模拟为评估是足够的，这被发现。因此，计算费用被减少。33 个例子上的试验性的结果表明建议模型和 ACS 途径的有效性。

英文摘要：

Project scheduling under uncertainty is a challenging field of research that has attracted increasing attention. While most existing studies only consider the single-mode project scheduling problem under uncertainty, this paper aims to deal with a more realistic model called the stochastic multi-mode resource constrained project scheduling problem with discounted cash flows （S-MRCPSPDCF）. In the model, activity durations and costs are given by random variables. The objective is to find an optimal baseline schedule so that the expected net present value （NPV） of cash flows is maximized. To solve the problem, an ant colony system （ACS） based approach is designed. The algorithm dispatches a group of ants to build baseline schedules iteratively using pheromones and an expected discounted cost （EDC） heuristic. Since it is impossible to evaluate the expected NPV directly due to the presence of random variables, the algorithm adopts the Monte Carlo （MC） simulation technique. As the ACS algorithm only uses the best-so-far solution to update pheromone values, it is found that a rough simulation with a small number of random scenarios is enough for evaluation. Thus the computational cost is reduced. Experimental results on 33 instances demonstrate the effectiveness of the proposed model and the ACS approach.