What We Do
There is no magic formula when it comes to scheduling, because every schedule is different and therefore each schedule needs to be approached in a different way. We at the Center for Athletic Scheduling use a technique known as Mixed Integer Linear Programming to solve these varied problems.
This technique involves translating the real world constraints into a mathematical model, called a linear program, which is then solved, and interpreted. Linear programs are very versatile and can be used to solve any number of problems from maximizing a companies profit to, in our case, finding an optimal athletic schedule.
About the simplest constraint we would use is that two teams must play one another on a given date. The mathematical model keeps track of all the possible games that could be played, and then ensures that the given game is played on that date. For example, if Team B must play Team A at home for Game 1 then the mathematical model we construct forces that game to be played (FIGURE 1). Other constraints will make sure that neither Team A or Team B plays another game on that date.
When the rest of the constraints are defined in the mathematical model, the model can be submitted to a solver, and a solution can be found. Some of these additional constraints may include, but are in no way limited to:
- Schedule format (i.e. double round robin)
- limiting the number of consecutive home or away games
- bye game specifications
- travel restrictions
- minimum number of games between repeated match ups
- black-out dates
- playing one home game and one away game in the last two games of the season