Ride-Sharing in Medical Transportations: Dealing with Temporal Requirements

The ride-sharing problem aims at optimizing the path from one starting point to one destination point. The problem can be enriched by intermediate stops, spatio-temporal constraints, and external constraints (e.g. traffic congestion), adding uncertainty and increasing the overall complexity. Spatio-temporal networks can properly describe the problem by graphs, helping to identify the optimal or sub-optimal solution. We face here the specific issue, where a driver picks up several patients from their respective pick-up locations and drops them off at one care center. Ride-sharing of patients has specific requirements due to the particular health state of every patient. Indeed, every patient has his/her own constraints, which could be related to the maximum sustainable duration of the trip, according to the patient’s conditions, the maximum waiting time, and the time when the visit or treatment is scheduled. In our approach, we first consider the spatial facets, and then we superimpose the temporal facets, to recommend the best paths and schedules, allowing some kind of temporal uncertainty in the specification of different possible constraints.