A Constraint Programming Approach to Fair High School Course Scheduling

TL;DR

This paper introduces a novel integer programming method to generate fair and feasible high school course schedules based on student preferences, addressing fairness issues in modern school scheduling.

Contribution

It extends the high school scheduling problem by incorporating fairness principles and develops an IP-based algorithm to produce equitable schedules.

Findings

The algorithm successfully generates fair and feasible schedules.

The approach can be applied to real-world scheduling problems.

It demonstrates the integration of human emotions into 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.