Sparked by suspected, and later confirmed, scheduling disadvantages affecting the Buffalo Bills, UB researchers developed a mathematical approach to help the NFL address this complex challenge. They modeled a large-scale mixed integer linear programming (MILP) problem with more than 10,000 variables and constraints, which grows more complex as the scheduling process evolves and new conditions are added.
The NFL starts by affixing 40 to 50 key games into set time slots based on network and stadium requirements, which gives the MILP software a starting point to fill in the rest of the schedule around them. Over 100 programmed computers strategically seed games in thousands of trials, which run eight to 12 hours overnight for months testing infinite solutions to create schedules that reduced the number of NFL fairness penalty points by 20 percent in the first year alone.