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Patient transportation systems are instrumental in lowering access barriersin primary care by taking patients to their GPs. As part of this setting, eachtransportation request of a chronic or walk-in patient consists of an outboundtrip to the GP and an inbound trip back home. The economic sustainability ofpatient transportation systems mainly depends on their utilization and how welltransportation requests can be bundled through ride sharing. To ease thelatter, we consider a flexible scheduling of chronic patients in which only acertain range for an appointment is fixed a priori while the exact time isdetermined by the scheduling of the outbound trip. This leads to a novelextension of the dial-a-ride problem that we call the dial-a-ride problem withcombined requests and flexible scheduling (DARPCF). In this paper, we introducetwo heuristics for the DARPCF that exploit this increased flexibility. Bothapproaches initially compute so-called mini-clusters of outbound requests.Then, the mini-clusters are linked by (i) solving a traveling salesman problemand creating routes of outbound rides with a splitting procedure or by (ii)using a rolling horizon approach and solving bipartite matching problems forthe vehicle assignment. Our computational study shows that by using thepresented algorithms with the flexible scheduling of chronic appointments, theaverage number of served requests can be increased by 16% compared to anon-flexible setting.

The Dial-a-Ride Problem in Primary Care with Flexible Scheduling