Optimizing Orientation Trips

Last fall, Chenchen Zhao ’18 took Linear Optimization, a mathematics course with Professor Sally Cockburn. “Since there are only a finite amount of resources, people want to find a way to maximize profit while minimizing the usage of resources. We study optimization to find more efficient solutions to problems,” said Zhao. Though optimization is applicable to a number of other areas, including economics and computer science, Zhao did not get the chance to explore these other functions during the semester.

Then, this spring, Professor Cockburn mentioned a project which would allow Zhao to apply both optimization and coding toward completing a computer program for use in the Hamilton community. Using her knowledge of optimization and of programming, Zhao and Cockburn are designing an integer linear program that places incoming students into Orientation groups, with as many as possible getting their top choices. “I have always been interested in the ways mathematics can be used to solve real-world problems,” she said.

The basic idea of optimization is to find the best possible solution that satisfies a set of constraints for a problem. Since limited resources and limited time are universal, optimization can be applied to a vast range of quandaries, from mapping airline routes to designing the LSAT test.                                                                                                 

First, Zhao met with the members of residential life who are responsible for assigning incoming students to orientation trips in order to learn more about the preexisting system. She then stated the problem mathematically and decided which constraints were going to be used in the program. After developing the linear program, Zhao encoded it, and solved it using Gurobi, a math program solver software.

Software programs can save a lot of time on solving optimization problems and show a more accurate result. It takes several days to complete orientation trip assignments manually, but it takes less than a minute (about 30 to 60 seconds) for the computer to find a solution that satisfies the constraints.

At this point, Zhao and Cockburn have built a program that can generate a solution for the assignments. They will soon set up meetings with residential life to discuss the feasibility of their solution, taking note of ways they can make their model easier for use. At the end of the summer, Zhao will write a paper outlining the model she created, and the work required to construct it.