Problem Model

The problem we faced was developing an optimal student-course allocation based on the following criteria:

1. Total Utility - The best solution should maximize the total sum of utilities across all students. Individual student utility is found by summing the utility of each of a student’s individual classes and individual class utility is determined by subtracting the students ranking for a class from a fixed constant. This presents a function where students receive correspondingly higher utility if placed in their preferred classes.

2. Fairness – A good allocation should be equitable. To optimize “fairness,” we will seek to minimize the variance in student utility. If the variance of student utilities is low then the distribution is relative fair.

3. Stability – A good solution should be stable. This means that no two students would both be willing to swap classes to improve their utility. This is used to measure Pareto efficiency, which means no student can be made better off without making another student worse off.

4. Class Diversity – A good course allocation should be good for both students and teachers. For our model, we will assume that teachers prefer a diverse classroom to maximize learning and perspective. We will measure class diversity by examining variance in student-year, where a higher variance represents greater levels of diversity and a better solution.

5. Feasibility – Ultimately a good solution must be feasible. To evaluate this criterion, we will use our professional judgement and examine concerns such as the time cost to students and university administration.

Outputs

These inputs will be used to generate a variety of student schedules and student-course allocations. By this we mean, each student will select or be assigned a number of classes (used to calculate student utility, fairness, and stability). Each of these schedules will then be aggregated to fill c_i class times with m students.