For solving problems from the domain of vehicle routing with time windows, we often need to connect vehicle plans into sequences spanning a longer time horizon or, in other words, we need to perform a plan chaining. Recently, a network-based solution has been proposed to solve the fleet-sizing problem. The method, however, does not consider the time flexibility of the plans, an essential property of all vehicle routing problems with time windows. Instead, plans have fixed times and cannot be delayed. This work presents a new problem formulation that considers delays in line with the given time windows and a method that can be used to solve it. Moreover, we prove that the method is optimal, and we analyze its complexity. Finally, we list some practical applications and perform a demonstration for one of them: the method for solving the static Dial-a-ride problem. The demonstration results show that for a significant number of instances, the proposed method provides a better solution than the other two heuristic baseline methods we have evaluated, while not having the largest computational time requirements.

翻译：在求解带时间窗的车辆路径问题时，我们常常需要将车辆计划连接成跨越更长时域的任务序列，即执行计划链接操作。近期，一种基于网络的方法被提出用于解决车队规模问题，但该方法未考虑计划的时间灵活性——这是所有带时间窗的车辆路径问题的核心属性。在原有方法中，计划具有固定时间且无法延迟。本研究提出了一种新的问题建模方法，该方法可根据给定时间窗考虑延迟，并给出相应的求解算法。此外，我们证明了该算法的最优性并分析其复杂度。最后，我们列举了若干实际应用场景，并针对静态Dial-a-ride问题进行了方法验证。实验结果表明：在大量测试实例中，相较于另外两种启发式基准方法，本方法在计算时间未显著增加的前提下，能够获得更优的解。