On the Edge of Feasiblity

The last full season played, the 2018-2019 season was 171 game days(i.e. the season minus the all star break). Therefore teams played on 47.9% of game days. I was able to squish my season down to 170 game days, resulting in teams playing on 48.2% of game days.

Playing on over 50% of potential game days creates a situation in which a season with no back to backs is impossible, like Major League Baseball's 162 game season. MLB Baseball teams must play consecutive days to complete their season on time. On the other hand, NBA Basketball teams do not necessarily have to play on consecutive days.

This type of modeling could also be useful for the NHL or other leagues in which teams play on between 40 to 50 percent of potential game days.

Linear Programming Model Feasibility

This project features two linear programming models. One for each conference, the content below details how tight of a squeeze this model is.

15 teams must play 26 away games in the same conference, totaling 390 games. With 15 teams, the maximum amount of games in a day is 7 games. (15/2, no remainder). This model has 56 game days. With a maximum of 392 game/day spots (56*7) and a requirement of 390 games. I could make one model for the full season, including cross conference play. This model would have more flexibility and could potentially be made even shorter.

If the model is condensed to 55 game days, the Linear Programming software package called Open Solver quickly recognizes the problem as infeasible.