Efficient demand management for the on-time arrival problem: A convexified multi-objective approach assuming macroscopic traffic dynamics

This work proposes a novel solution approach to address the On-Time Arrival (OTA) problem, considering macroscopic traffic dynamics. In this context, all drivers who intend to use the road infrastructure are required to communicate their origin-destination pair and desired arrival time to a central scheduler prior to starting their trip. In response, the scheduler assigns a departure time and a multi-regional route to each driver to make possible their on-time arrival at the destination. The OTA problem is formulated as a nonconvex, nonlinear, multi-objective optimization problem considering two objective criteria. The first criterion aims at minimizing the travel time of all drivers in the network to prevent congestion, while the second criterion seeks to minimize the discrepancy between the desired and actual arrival time. The proposed formulation is solved efficiently through an approximated convex solution that leverages the Normal Boundary Intersection (NBI) method to efficiently generate a representative sample of the Pareto Front. Additionally, two solution methodologies based on "knee"solution and the Nash Bargaining Game is proposed which can be used to select a unique solution across all the Pareto points, that offers a reasonable trade-off between the two objective criteria. Finally, simulation results demonstrate that the proposed solution can significantly reduce congestion while ensuring that most drivers will arrive at their destination on their desired time.