A Constraint Programming Approach to Fair High School Course Scheduling
Mitsuka Kiyohara, Masakazu Ishihata
TL;DR
The paper addresses inequity in high school course scheduling by extending the standard HSSP with a fairness-aware formulation (FHSSP) that incorporates student preferences via degree of interest and priority. It develops an IP-based solution with binary encodings for lectures, enrollments, and unit assignments, plus envy-based fairness constraints, and demonstrates two objective modes: maximizing allocations for HSSP and minimizing envy for FHSSP. Experiments on a real California dataset show feasible, envy-free schedules for FHSSP and high feasibility for HSSP, with runtimes indicating scalability challenges but potential for parallelization. The work highlights that fairness can be effectively integrated into constraint-based scheduling, with implications for broader real-world applications and the inclusion of human emotions in mathematical models.
Abstract
Issues of inequity in U.S. high schools' course scheduling did not previously exist. However, in recent years, with the increase in student population and course variety, students perceive that the course scheduling method is unfair. Current integer programming (IP) methods to the high school scheduling problem (HSSP) fall short in addressing these fairness concerns. The purpose of this research is to develop a solution methodology that generates feasible and fair course schedules using student preferences. Utilizing principles of fairness, which have been well studied in market design, we define the fair high school scheduling problem (FHSSP), a novel extension to the HSSP, and devise a corresponding algorithm based on integer programming to solve the FHSSP. We test our approach on a real course request dataset from a high school in California, USA. Results show that our algorithm can generate schedules that are both feasible and fair. In this paper, we demonstrate that our IP algorithm not only solves the HSSP and FHSSP in the United States but has the potential to be applied to various real-world scheduling problems. Additionally, we show the feasibility of integrating human emotions into mathematical modeling.