1 optimization problems
A local amateur league, a university tournament, a regional sports league, or a professional clubs league with 8–20 teams faces a season-start fixture problem. The decision: which team plays which team on which week, home or away, at what time, in which venue. Constraints to honor in parallel: in a double round-robin, every team plays every other team twice (one home, one away); no team should play home or away in consecutive weeks (minimize breaks); travel distance should be fair; broadcast-selected matches must align with broadcaster slots and venue capacity; international break weeks must stay empty; rival-derby matches should be distributed across the season; pedagogical soft preferences (e.g. avoid pairing two derby matches in the same week) apply. Manual preparation for an 8-team league takes 1–2 days; for a 16–20 team double round-robin in a non-professional environment, weeks of negotiation are routine.