We consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on which one physical vehicle can serve a customer. This is the main reason why different time windows for different vehicles are of high practical relevance. To ensure that the appointment windows are adhered to as much as possible, we introduce a new objective function that penalizes delays. Our novel approach allows us to find solutions that are robust with respect to uncertainties in travel and service times limited by a budget polytope. We present a set-partitioning model, the solution of which is based on column generation and employs a labeling algorithm that integrates robustness into the calculations and is adapted to our problem-specific constraints. In a Monte-Carlo simulation on real-life data, we evaluate this method in terms of runtime and solution quality. Our solutions show very good performance, even if the data is more uncertain than assumed for the optimization, incurring only marginal extra travel time compared to a naive deterministic planning scheme.

我们考虑具有异构时间窗的车辆路径问题（RVRP-HTW）的鲁棒变体，重点关注抗延迟解决方案。在这里，客户对每辆车都有不同的可用时间窗口，并且必须为计划的服务提供最好的紧凑预约窗口。不同的车辆可以模拟不同的日子，让一辆实体车辆可以为客户提供服务。这就是为什么不同车辆的不同时间窗具有较高实际相关性的主要原因。为了确保尽可能遵守预约窗口，我们引入了一个新的目标函数来惩罚延迟。我们的新颖方法使我们能够找到针对受预算多面体限制的旅行和服务时间的不确定性而稳健的解决方案。我们提出了一个集合划分模型，其解决方案基于列生成，并采用将鲁棒性集成到计算中并适应我们特定问题的约束的标记算法。在对现实数据的蒙特卡罗模拟中，我们从运行时间和解决方案质量方面评估了该方法。我们的解决方案显示出非常好的性能，即使数据比优化假设的更加不确定，与朴素的确定性规划方案相比，仅产生边际的额外行程时间。