中文摘要：

多模式的资源受限项目调度问题（MRCPSP）是生产实践中的一类常见的重要问题，它具有NP-完全性质，难以在多项式时间内准确求解。现金流是项目财务管理及风险评估的重要指标，实现现金流优化对项目管理具有重要的意义。考虑了现金流优化与项目调度相结合的带折现流的多模式资源受限项目调度模型（MRCPSPDCF），首先对该模型建模，然后给出运用遗传算法求解的具体方案，考虑了里程碑事件和相等时间间隔两种支付方式，在仿真实验中比较了这两种支付方式的实验结果，并证明了遗传算法的有效性。

英文摘要：

The multi-mode resource constrained project scheduling problem （MRCPSP） is common and important in manufacturing applications. It is a well-known NP-complete problem which cannot be accurately figured out by a polynomial-time method. Cash flow is the crucial criterion for project financial management and risk evaluation. So it is of great significance to optimize the cash flows of a project. The cash flow criterion is incorporated into the project scheduling problem to consider the model of multi-mode resource constrained project scheduling problem with discounted cash flows （MRCPSPDCF）. The model is formulated, and then a genetic algorithm （GA） approach is proposed. Two different payment models are taken into account in the model, which are the payments at event occurrences （PEO） and the equal time intervals （ETI） model. Numerical experiments are implemented to compare the performance of these two payment models as well as to demonstrate the effectiveness of the GA approach.