Combining mathematical optimization and stochastic simulation for a robust integrated vehicle and crew scheduling in public transport

作为研究单元“公共交通综合规划”的一部分，该子项目涉及公共交通中强大的综合车辆和机组人员调度的数学优化和随机模拟相结合。我们在子项目中区分两种目标。从问题的角度来看，我们希望在公共交通中生成强大的车辆和机组人员时间表。从一个有条不紊的角度来看，我们要开发一个综合的车辆和机组人员调度问题，在公共交通，考虑运营中的干扰模型和解决方案。为此，我们专注于开发一种迭代方法，结合数学优化与模拟，以实现强大的时间表。离散事件仿真允许对具有几乎无限复杂性（包括随机过程）的物流系统进行非常接近现实的建模。然而，找到最佳的系统配置是非常困难和耗时的，因为有许多替代方案，必须进行评估和比较。相比之下，离散数学优化能够为物流问题的（接近）最佳解决方案做出非常复杂的决策。由于它们的复杂性，真实的世界物流系统只能在不具有随机行为的较不精确和详细的水平上建模和求解。该研究项目不仅旨在通过缩小现有的科学和方法差距，为组合模拟和优化方法领域贡献有价值的成果。此外，我们想证明我们的新方法在公共交通的综合规划问题的具体实际效益。数学优化和离散事件模拟的结合利用了它们的互补优势，最终导致了比单独使用两种方法更好的结果。与研究单位内的其他子项目的合作，特别是在公共交通的相邻规划步骤，算法设计（分解），以及鲁棒性的分析和测量领域。

As a part of the research unit "lntegrated planning in public transport" this subproject deals with the combination of mathematical optimization and stochastic simulation for a robust integrated vehicle and crew scheduling in public transport. We differentiate between two kinds of goals within the subproject. From a problem point of view, we want to generate robust vehicle and crew schedules in public transport. From a methodical point of view, we want to develop models and solution approaches for an integrated vehicle and crew scheduling problem in public transport that considers disturbances in operation. For this purpose, we focus on the development of an iterative approach that combines mathematical optimization with simulation in order to achieve robust schedules. The discrete-event Simulation allows the modeling of logistics systems with almost unlimited complexity (including stochastic processes) very close to reality. However, finding the best system configuration is very difficult and time-consuming since there are many alternative scenarios that have to be evaluated and compared. ln contrast, discrete mathematical optimization has the ability to make very complex decisions for (near) optimal solutions of logistical problems. Due to their complexity, real world logistic systems can only be modeled and solved on a less accurate and detailed Ievel without stochastic behavior. This research project does not only aim at contributing valuable results to the field of combined Simulation and optimization approaches by closing existing scientific and methodological gaps. Furthermore, we want to prove the concrete practical benefit of our new approach for an integrated planning problem in public transport. By making use of their complementary advantages, the combination of the two methods mathematical optimization and discrete-event Simulation eventually Ieads to better results than one of both methods could achieve alone.The collaboration with other subprojects within the research unit especially takes place in the fields of adjacent planning steps in public transport, algorithm design (decomposition), and the analysis and measurement of robustness.