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

作为“公共交通综合规划”研究单元的一部分，该子项目将数学优化和随机模拟相结合，研究公共交通车辆和乘务人员的综合调度问题。我们区分了子项目中的两种目标。从问题的角度来看，我们希望在公共交通中产生稳健的车辆和乘务时间表。从系统的角度出发，我们希望建立一个考虑运营扰动的公交车辆和乘务综合调度问题的模型和求解方法。为此，我们专注于开发一种迭代方法，将数学优化与模拟相结合，以实现稳健的调度。离散事件仿真使物流系统的建模具有几乎无限的复杂性(包括随机过程)，非常接近实际。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需要评估和比较。相比之下，离散数学优化有能力对物流问题的(接近)最优解做出非常复杂的决定。由于物流系统的复杂性，只有在没有随机行为的情况下，才能在较不精确和详细的水平上对其进行建模和求解。这一研究项目不仅旨在通过弥合现有的科学和方法差距，为综合模拟和优化方法领域贡献有价值的成果。此外，我们想要证明我们的新方法在解决公共交通综合规划问题方面的具体实际好处。利用两种方法的互补优势，数学优化和离散事件仿真的结合最终取得了比两种方法单独使用更好的结果，特别是在公共交通的相邻规划步骤、算法设计(分解)以及稳健性分析和测量等领域与研究单位内的其他子项目进行了合作。

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.