School choice : a discrete optimization approach

Abstract

An equitable and flexible mechanism for assigning students to schools is a major concern for many school districts. The school a student attends dramatically impacts the quality of education, access to resources, family and neighborhood cohesion, and transportation costs. Facing this intricate optimization problem, school districts often utilize to stable-matching techniques which only produce stable matchings that do not incorporate these different objectives; this can be expensive and inequitable. We present a new optimization model for the Stable Matching (SM) school choice problem which relies on an algorithm we call Price-Costs-Flexibility-and- Fairness (PCF2). Our model leverages techniques to balance competing objectives using mixed-integer optimization methods. We explore the trade-offs between stability, costs, and preferences and show that, surprisingly, there are stable solutions that decrease transportation costs by 8-17% over the Gale-Shapley solution.