  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.
