Dial-a-Ride systems involve dispatching a vehicle to satisfy demands from a set of customers who call a vehicle operating agency requesting that an item be picked up from a specific location and delivered to a specific destination. Dial-a-ride problems differ from other routing and scheduling problems in that they typically involve service related constraints. It is common to have maximum wait time constraints and maximum ride time constraints. In the presence of maximum wait time and maximum ride time restrictions, it is not clear how to efficiently determine, given a sequence of pickups and deliveries, whether a feasible schedule exists. We demonstrate that this, in fact, can be done in linear time.
Brady Hunsaker, Martin W. P. Savelsbergh