School start time optimization for the morning commute problem in four-region urban networks

During the morning rush hour, some commuters head directly to their destination, whereas a different portion of commuters make an intermediate stop to drop off their children at school before heading to their destination. When schools start simultaneously, commuters compete for space, leading to a peak demand, resulting in congestion. To remedy this shortcoming, we propose a novel MFD-based approach that regulates the start time of schools for a four-region architecture. The related problem is formulated as a bi-objective mixed-integer nonlinear program whose target is to jointly minimize i) the total time spent by all vehicles and ii) the overall deviation of the school start times. We develop a solution approach where the nonlinear constraints are approximated with a set of linear constraints. We demonstrate through extensive simulation experiments that our approach yields results close to the optimal solution obtained through an exhaustive search approach, leading to significant congestion mitigation.