For solving problems from the domain of Mobility-on-Demand (MoD), we often need to connect vehicle plans into plans spanning longer time, a process we call plan chaining. As we show in this work, chaining of the plans can be used to reduce the size of MoD providers' fleet (fleet-sizing problem) but also to reduce the total driven distance by providing high-quality vehicle dispatching solutions in MoD systems. Recently, a solution that uses this principle has been proposed to solve the fleet-sizing problem. The method does not consider the time flexibility of the plans. Instead, plans are fixed in time and cannot be delayed. However, time flexibility is an essential property of all vehicle problems with time windows. This work presents a new plan chaining formulation that considers delays as allowed by the time windows and a solution method for solving it. Moreover, we prove that the proposed plan chaining method is optimal, and we analyze its complexity. Finally, we list some practical applications and perform a demonstration for one of them: a new heuristic vehicle dispatching method for solving the static dial-a-ride problem. The demonstration results show that our proposed method provides a better solution than the two heuristic baselines for the majority of instances that cannot be solved optimally. At the same time, our method does not have the largest computational time requirements compared to the baselines. Therefore, we conclude that the proposed optimal chaining method provides not only theoretically sound results but is also practically applicable.

翻译：在解决移动出行即服务（MoD）领域问题时，常需将车辆计划连接成覆盖更长时间的扩展计划，这一过程称为计划链式连接。本研究证明，计划链式连接可用于缩减MoD服务商的车辆规模（车队规模优化问题），亦可通过提供高质量车辆调度方案降低MoD系统的总行驶里程。近期已有基于该原理的解决方案被提出用于解决车队规模优化问题，但该方法未考虑计划的时间灵活性——计划的时间节点固定且不可延迟。然而时间灵活性是所有带时间窗车辆问题的关键属性。本文提出一种新的计划链式连接形式化方法，在时间窗允许范围内考虑延迟可能性，并给出相应求解方案。进一步地，我们证明了所提计划链式连接方法的最优性并分析了其复杂度。最后列举若干实际应用场景，并针对其中之一——静态拨召问题的启发式车辆调度方法——进行实验验证。结果表明，在多数无法求得最优解的实例中，本方法相较于两种启发式基准算法能提供更优解，且计算耗时并非最大。因此我们得出结论：所提出的最优链式连接方法不仅具有理论严谨性，亦具备实际应用价值。