Capacity Planning in Stable Matching

• 成果类型: Article; Early Access
• 署名作者: Bobbio, Federico; Carvalho, Margarida; Lodi, Andrea; Ricos, Ignacio; Torrico, Alfredo
• 署名单位: Universite de Montreal; Universite de Montreal; Technion Israel Institute of Technology; University of Texas System; University of Texas Dallas; Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0386
• 发表日期: 2025
• 关键词: integer programming approach; school choice; college admissions; boston mechanism; DESIGN; allocation; STABILITY; tools; TIES

摘要

Motivated by the shortage of seats that the Chilean school choice system is facing, we introduce the problem of jointly increasing school capacities and finding a studentoptimal assignment in the expanded market. Because of the theoretical and practical complexity of the problem, we provide a comprehensive set of tools to solve the problem, including different mathematical programming formulations, a cutting-plane algorithm, and two heuristics that allow obtaining near-optimal solutions quickly. On the theoretical side, we show the correctness of our formulations, different properties of the objective and feasible region that facilitate computation, and also several properties of the underlying mechanism to find a student-optimal matching under capacity expansions. On the computational side, we use data from the Chilean school choice system to demonstrate the impact of our framework and derive insights that could help alleviate the problem. Our results show that each additional seat can benefit multiple students and that we can effectively target the assignment of previously unassigned students or improve the assignment of several students through improvement chains. Nevertheless, our results show that the marginal effect of each additional seat is decreasing and that simply adding seats is insufficient to ensure that every student gets assigned to some school. Finally, we discuss several extensions of our framework, showcasing its flexibility to accommodate different needs.