In this research, we present several extensions for the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). First of all, we investigate more complex variants of the alternative project structure. More precisely, we consider nested alterative subgraphs, linked alternative branches, multiple selection, caused and closed choices, and split choices. Secondly, we introduce non-renewable resources in the RCPSP-AS in order to implicitly avoid certain combinations of alternatives given a limited availability of this resource over the complete project horizon. We formulate both the basic RCPSP-AS and its extensions as an ILP model and solve it using Gurobi. The computational experiments are conducted on a large set of artificial project instances as well as three case studies. The results show the impact of the different extensions on the project makespan and the computational complexity. We observe that combinations of the proposed extensions might imply complex alternative project structures, resulting in an increasing computational complexity or even infeasible solutions. The analysis of the three case studies shows that it is hard to find feasible solutions with a small time limit or optimal solutions with a larger time limit for projects with a realistic size in terms of the number of activities or alternatives.

在这项研究中，我们提出了具有替代子图（RCPSP-AS）的资源受限项目调度问题的几个扩展。首先，我们研究替代项目结构的更复杂的变体。更准确地说，我们考虑嵌套的替代子图、链接的替代分支、多重选择、导致和封闭的选择以及拆分选择。其次，我们在 RCPSP-AS 中引入了不可再生资源，以隐含地避免某些替代方案的组合，因为该资源在整个项目范围内的可用性有限。我们将基本的 RCPSP-AS 及其扩展都制定为 ILP 模型，并使用 Gurobi 解决它。计算实验是在大量人工项目实例以及三个案例研究上进行的。结果显示了不同扩展对项目制造周期和计算复杂性的影响。我们观察到，提议的扩展组合可能意味着复杂的替代项目结构，导致计算复杂性增加，甚至不可行的解决方案。对三个案例研究的分析表明，对于具有现实规模的项目，在活动或备选方案的数量方面，很难找到具有较小时限的可行解决方案或具有较大时限的最佳解决方案。