The studied problem arises in the context of non-emergency transportation of patients. We consider a hospital (the depot) and a set of patients with a medical appointment. Patients require either to go from home to hospital (inbound request) or from hospital to home (outbound request). The problem can be addressed either as a Pickup and Delivery Problem or as a special Multi-Trip Vehicle Routing Problem because for any request the depot is either the pickup or the delivery node. The problem is called Multi-Trip Vehicle Routing Problem with Mixed Pickup and Delivery, and Release and Due dates (MTMPD-RD).

Seen as a multi-trip VRP, the problem raises a complex time and vehicle capacity management but we adopt this standpoint and prove that the multi-trip model outperforms the Pickup and Delivery model.