Can’t Get Into Classes? Sounds Like a Perfect Matching Problem.
For many students at Cornell, pre-enrollment and add/drop periods can be very stressful, especially if the demand for the classes you want to get into is high and the number of seats in them are low. In her article, Yao talks about how, throughout her three years at Cornell, she has been shut out of classes she needed for her major during each pre-enrollment period. She also mentions how scary it is to be unsure of what your classes are for the semester but to not worry too much because typically things work out by add/drop.
The problem is that classes have already started during add/drop periods and honestly, not knowing what classes you’re going to take– while taking classes– isn’t very ideal. What if students could be guaranteed to get into a set of five classes? Of course, you should be able to drop them and add classes you want to take, but I believe it could give students peace of mind to know that they’re always guaranteed to get into some five classes each semester.
What if we could treat the pre-enrollment period as a perfect matching problem? By assigning valuations to students based on their major, grade, classes they’ve already taken, and other factors we can set up a bipartite graph with class seats on one side as the items and the students as buyers. We can then go through the methodology to set prices for the items until we reach market clearing prices. Since market clearing prices always exist, this should result in everyone getting a seat in at least one class. We can then repeat this process four more times, removing the seats and valuations that students have already gotten. Of course, however, an assumption I have made is that there are enough seats for every student there are at least five seats. Another potential problem is that some students may be assigned to seats that they have a valuation of zero for and removing these could potentially mess up the process. However, I do believe that implementing perfect matching during pre-enrollment could really expedite the process and alleviate some student stress.
Reference:
YAO | The Best Way to Pre-Enroll is Waiting Until Add/Drop