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The dial-a-ride problem with time windows is studied in this article. First, a new efficient mixed integer programming formulation is proposed by merging some of drop-off nodes into paired pick-up nodes when a size of the order forbids ridesharing, so a vehicle must visit the paired drop-off nodes directly after the pick-up, thus reducing the number of decision variables by 40% on benchmark instances. Secondly, three different constraint programming formulations are proposed for the first time, generating efficient schedules within a few seconds. Thirdly, a real-time rescheduling perspective is further studied, since the ridesharing becomes dynamic when a schedule must be provided instantly. In particular, the warm-start search method, in which a precalculated schedule is continuously revised as new orders come in, is proposed.

Dial-a-ride problem: mixed integer programming revisited and constraint programming proposed