Maximising the number of participants in a ride-sharing scheme: MIP versus CP formulations

Ride sharing schemes aim to reduce the number of cars in congested cities, while providing the participants with a cheaper alternative to solo driving. To ensure a ride-sharing scheme thrives, it is important to maintain a high participation rate. This requires an adequate balance between drivers and riders. And thus ride matches should be proposed which maximize the number of participants. Different variants of the ride sharing problem have been solved using mixed integer programming. In this paper, we introduce a constraint programming formulation for the problem that uses cumulative constraints with dependencies between trip times. In experiments based on collected trip schedules from four different regions, the constraint model outperforms the MIP model. However, when we change the problem by assuming all drivers have flexible roles, the MIP model allows faster solution times than the CP model