A Successive Convexification-Based Approach for Efficient School Scheduling in Multi-Region Urban Networks

In urban traffic networks, morning commuters exhibit diverse travel patterns, with some needing to make intermediate stops, such as dropping off children at school, before reaching their destination. When schools have synchronized start times, this induces high peak demand, exacerbating congestion. To address this challenge, we consider the problem of regulating the start times of schools in a multi-region urban network characterized by well-defined Macroscopic Fundamental Diagrams in different regions. We formulate the problem as a bi-objective mixed-integer nonlinear program aiming to jointly minimize (i) the total time spent by all vehicles, and (ii) the overall deviation from current school start times. The problem is challenging due to its large-scale and combinatorial nature, as well as the nonconvexity present in the traffic dynamics across multiple interconnected urban regions. To address these challenges, we introduce a successive convexification algorithm that iteratively tightens traffic density bounds and convexifies constraints, enabling the acquisition of feasible and efficient solutions concerning the optimization problem. Numerical experiments demonstrate that our approach yields near-optimal results, significantly mitigating congestion and improving overall traffic efficiency.