Atlantic Coast Conference 1997-98 basketball schedule built by integer programming

The Atlantic Coast Conference's nine schools play a nine-week, 18-slot double round robin each January and February, and basketball was the league's biggest earner: in 1995 the conference and its universities drew over $30 million from the sport, nearly all of it TV and radio rights plus gate receipts. Until 1996-97 the schedule was drawn up by hand in the conference office. After a ninth team (Florida State) joined in 1991-92 and television requests multiplied, a constraint-programming attempt for 1996-97 still delivered a schedule with poor separation of repeat meetings and unmet TV needs.

For 1997-98 the ACC turned to George Nemhauser and Michael Trick. Their system enumerated every legal season pattern - 8 homes, 8 aways, 2 byes over 18 slots, at most two consecutive homes or aways - keeping 38 of 2,304 candidates. An integer program assembled nine-pattern sets (17 sets, under a minute each), and a second IP of about 300 variables generated all 826 feasible timetables in under ten minutes, all on a Sun SPARCstation 20 with CPLEX 4.0. A final 24-hour enumeration of team-to-pattern assignments - roughly 300 million options - left 17 feasible schedules.

Those were pruned to three and submitted; the ACC, consulting ESPN and Raycom, adopted one as the official men's schedule, and an accepted women's schedule came from the same system. The hardest requirements surfaced only in dialogue - ESPN wanted Duke-North Carolina in slot 10 and in the finale, which rules out a fully mirrored schedule, and Raycom had elaborate February preferences. Nemhauser and Trick credit the system's one-day turnaround: the conference could look at real schedules and keep refining what it actually needed.

Enumerate home/away patterns, then integer-pick the season

Splitting the season into an H/A/B pattern first separates what a team's year looks like from which opponent it meets, turning one enormous problem into three small ones.

Enumeration was cheap at this size — 2,304 candidate patterns of which 38 were legal — while combinatorial design theory could characterize only a few hand-derived timetables.

Deferring the assignment of real teams to patterns until the end let the timetable stage ignore school-specific preferences, keeping the integer programs small and fast.

The binding constraint was not algorithmic elegance but turnaround speed: the ACC kept adding late requirements, and only a day-fast system could absorb them.

When stakeholders can't state their requirements up front, fast candidate schedules teach them what they actually need. Enumeration plus off-the-shelf optimization beats waiting for elegant methods.

The pattern-timetable-assign framework became the standard template for round-robin sports scheduling in the OR literature. The episode stayed a live benchmark: a 2001 Operations Research follow-up re-solved the same 1997-98 instance with finite-domain constraint programming and reported a dramatic speedup over enumeration plus integer programming. The deeper lesson - that fast schedule generation is a negotiation tool among schedulers, conferences and broadcasters - has shaped league scheduling projects since.