School Bus Routing

School Bus Routing Problem (SBRP) is the question a school or school chain (private chain, municipal transport office, cooperative) faces in deciding the bus-stop placement, student-to-stop assignment and bus route generation needed to move students to and from school every day. Distinguishing constraints versus generic VRP: maximum ride time per student (typically 45-75 minutes one-way, age- and regulation-dependent), maximum walking distance from home to stop, equitable distribution of walking distances across neighborhoods, bell-time coordination across schools, and door-to-door service for special-needs students. Park and Kim (2010) decompose the problem into five sub-problems: (i) data preparation, (ii) stop selection, (iii) student-to-stop assignment, (iv) route generation, (v) route-bell-time adjustment. Newton and Thomas (1969) pioneered the cluster-first-route-second heuristic. Solution approaches: clustering heuristics, capacitated VRP MIP, location-routing models, column generation and metaheuristics (genetic, tabu, large neighborhood search). Typical objectives: minimum fleet size, minimum average ride time, minimum walk-distance variance (equity), minimum weighted bell-time penalty.