How a Math Student Found a More Efficient Way to Groom Campus Ski Trails

In 2023, Onno Oerlemans, the Elizabeth J. McCormack Professor of Literature and member of the trail system grooming team, approached Sally Cockburn, the Samuel F. Pratt Professor of Mathematics & Statistics, with a project to mathematically determine a trail route that would minimize the amount of fuel and time needed for grooming. Cockburn saw the potential to use linear optimization to solve the problem—with the help of computer programming. Grisha Hatavets ’25, a  mathematics and computer science double major in Cockburn’s linear optimization class, had both the mathematical knowledge and computer science background to find the solution. He spent three to four weeks of his 2023 summer working on this project.

Grisha Hatavets ’25

Hometown: Minsk, Belarus
High School: Shattuck St. Mary's (Faribault, MN)
Major: Computer Science

“A lot of the ideas you learn in the classroom are really cool, but it’s hard to find real world applications,” Hatavets said. “But this specific problem was applying math that I had learned in my course and finding a real solution. I thought it was pretty exciting to get my hands on something like that.”

Linear optimization takes a problem that a human could find a feasible solution to and finds the optimal solution, Hatavets said. It requires an objective function, which in this case was to minimize the value of the trail distance. Constraints were then applied to the objective function—the starting and ending position must be at the point closest to the equipment storage, the route cannot include U-turns, and certain wider sections must be groomed additional times—to formulate a mathematical model. Exact distances of the trail were found with an ATV-connected odometer and applied to the model.

After meeting and discussing the project with the trail grooming team, Hatavets adapted some techniques that he had learned during his final presentation in the linear optimization course, and he wrote a Python program to determine the optimal grooming path. These results were given to Oerlemans for future use in grooming the course. Todd Rayne, retired Joel W. Johnson Family Professor of Environmental Science Emeritus and member of the trail system grooming team, recently used the optimal path to groom the trails. Since different snow conditions (i.e. density and snowpack density) can heavily impact the speed of grooming and the number of trails groomed, it is difficult to directly compare the effectiveness of Hatavets’ route to previous routes. Rayne, however, did find that the route was easy to use and appeared to be faster than previous routes. He expects that using the new route will continue to improve their grooming experience as they become more familiar with it.

“Using my knowledge to give something back to my community was a really fulfilling experience,” Hatavets said.