A project by a mathematics class will be used in 2022 to schedule sports for the Minnesota Intercollegiate Athletic Conference (MIAC).
Always on the lookout for projects his students can work on, Dr. Nathan Axvig, associate professor of mathematics and computer science, just happened to mention to Rachel Bergeson, Concordia’s athletic director, that his students could work on something like sports scheduling.
“I like giving my students a chance at cutting their teeth with a real-world problem that an actual person will care about and might use,” Axvig said.
At the same time Dan McKane, commissioner for the MIAC, was looking for a fresh start with scheduling, Bergeson mentioned Axvig’s class to him.
“The timing was perfect, so thanks to Rachel for bringing us together,” McKane said. “We were changing our membership up with St. Thomas leaving the MIAC and St. Scholastica coming in, and it really allowed us a chance to say ‘how can we reinvent this.’”
McKane sent Axvig three Excel spreadsheets: one with men’s teams, one with women’s teams, and one with dates for games. Axvig then divided the 16 students* in his Introduction to Operations Management/Research class into five groups with each taking a sport: men’s and women’s basketball, volleyball, men’s and women’s soccer, men’s and women’s hockey, and baseball and softball.
Next, students had to model a lengthy list of complex constraints. For example, basketball teams play each other twice a year, each men’s team has two bye weeks, Concordia plays all games as doubleheaders, and longer trips need to be on weekends. There were other variables to include like some teams not wanting to play several teams in a row that were just coming off a bye week. Basketball was the most complicated. When a women’s team plays St. Kate’s, the men’s team has a bye week because St. Kate’s doesn’t have men’s teams.
“The students had to do information gathering to see which pegs fit into which holes and what are the rules of how to do that and how do we make that happen,” Axvig said. “Then you can model all those things using mathematical inequalities and equalities, and that was the type of math that I was teaching in the class.”
Students were then tasked with taking the problem and writing a system of equations and a system of inequalities that corresponds to a viable schedule for the MIAC. They formatted the data in an Excel spreadsheet anyone can read and then translated it into mathematics so the computer could read it.
The computer programs read the Excel files – one of the commands is actually <read_excel>. By reading the men’s teams, the women’s teams, and the dates they are going to play, the program builds a model. The modeling process includes identifying unnecessary and important data. Everything not written into math gets ignored.
For example, to model just the first half of the season’s schedule for basketball, students wrote 1,937 lines of code with 2,365 variables.
“I don’t want to trivialize my students’ work,” Axvig said. “It’s not that they got a program to read the Excel files; that’s the easy part. They read in the Excel files and wrote code that processed that – build the model, solve the model, and interpret it – which took half a semester to do resulting in a workable schedule for the MIAC.”
For more than 20 years, McKane has used a matrix of schedules that basically alternate every year, meaning there isn’t much variety in the schedules. It’s complicated and took many hours of time.
“It was pretty much us just plugging stuff into an Excel or Word doc and writing it out,” he said. “I’ve tried over the years to figure out a better solution, but it’s really complex and it’s expensive if you purchase it.”
McKane said the Concordia students really put their heart and soul into the project and tried to understand the many intricacies of all the sports because everyone wants something different.
The class’s algorithm starts each year fresh. Each team will have everything they want and play everybody the same number of home and away games, but it won’t look the same as it has in the past. It’ll take a bit of a learning curve for coaches, but from now on each year will have a fresh look to it.
“For a lot of the students, this was the first class where they’ve been expected to write something serious – the baseline requirement for getting a passing grade on the project is it has to work,” Axvig said. “You can’t put Concordia in two places on the same day at the same time.”
Axvig noted that people can hamstring themselves by not using computer programs for tedious things they’re spending many hours of time trying to do by hand. The MIAC schedule now takes approximately three to four minutes to solve once you get the three Excel spreadsheets.
“Working with the class was so great,” McKane said. “And I think it’s who we are. We’re about athletics and education, so if we can give real-world experience to students in the MIAC this really falls in line with that. That’s a really cool process.”
*Students in the class:
Joseph Addy ’21
Abby Auran ’21
Laura Bieberdorf ’21
Britney Freund ’22
Tony Froland ’21
Andrew Jennissen ’21
Anders Johnson ’21
Jacob LePard ’21
Jake Peters ’21
Rachel Saxen ’22
Nicholas Smith ’21
Sudip Subedi ’21
Jamie Van Overschelde ’21
Abigail Voronyak ’21
Qian Yang ’21