Education
2 optimization problems
Which Course at Which Hour, in Which Room?
Every term, a private school with 15–50 teachers, 8–30 classes, and 5–20 rooms, a 30–100-teacher learning center, or a 50–200-course university faculty must produce the weekly course timetable. The decision: which course is taught by which teacher, on which day, at which time, in which room. Constraints to honor in parallel: teacher availability (most teachers have certain hours when they can't teach), room capacity and type (lab, music room, gym), student-group non-overlap, limits on consecutive periods, lunch breaks, and pedagogical preferences (e.g. no academic class right after PE). Manual preparation for 50–100 courses takes 2–5 days of labor; above that, weeks of negotiation, teacher complaints, and last-minute revisions become routine.
Which Student to Which Stop, and Which Bus in Which Order?
For a private school transporting 200-1,500 students with 10-50 buses, running twice a day in the morning and afternoon. At the start of every term four nested decisions must be made: where to place stops, which student goes to which stop, which bus visits which stops and in what order, and how the same fleet is shared between a 7:30 primary and an 8:30 high school. Mistakes are costly: a 90-minute one-way ride for a 7-year-old loses parents, a half-empty bus burns fuel, and a late bus erases an hour of class. Routes drawn in a spreadsheet have to be reworked from scratch each time a new enrolment arrives.