The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). In the RCPSP, the goal is to determine a minimal makespan schedule subject to precedence and resource constraints. The generalization introduced in the RCPSP-PS is that, instead of executing all activities, only a subset of all activities has to be executed. We present a model that is based on two graphs: one representing precedence relations and one representing the activity selection structure. The latter defines which subset of activities has to be executed. Additionally, we present theoretical properties of this model and give an exact solution method that makes use of these properties by generating cutting planes and setting bounds on variables. Furthermore, three problem properties are introduced to classify problems in the literature. We compare our model to a model from literature on instances that possess a subset of these three problem properties and find a reduction in computing time. Furthermore, by comparing results on instances that possess all problem properties, it is shown that the computing times are decreased and better lower bounds are found by the cutting planes and variable bounds presented in this paper.

中文翻译：

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具有灵活项目结构的资源受限项目调度问题的精确求解方法


具有灵活项目结构的资源约束项目调度问题 （RCPSP-PS） 是资源约束项目调度问题 （RCPSP） 的推广。在 RCPSP 中，目标是根据优先级和资源限制确定最小 makespan 计划。RCPSP-PS 中引入的泛化是，只需执行所有活动的子集，而不是执行所有活动。我们提出了一个基于两个图形的模型：一个表示优先关系，另一个表示活动选择结构。后者定义必须执行的活动子集。此外，我们还介绍了该模型的理论属性，并给出了一种精确的求解方法，该方法通过生成切割平面和设置变量边界来利用这些属性。此外，还介绍了三个问题属性来对文献中的问题进行分类。我们将我们的模型与具有这三个问题属性子集的实例的文献中的模型进行了比较，发现计算时间减少了。此外，通过比较具有所有问题属性的实例的结果，表明计算时间缩短了，并且通过本文中提出的切割平面和变量边界找到了更好的下界。