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The study develops exact and heuristic methods that make this theoretically complex problem tractable in practice. Using rich administrative data from the Chilean school choice system, the framework demonstrates how adding a limited number of seats can trigger improvement chains benefiting multiple students, also revealing diminishing marginal returns to capacity expansion. Beyond the Chilean context, the framework provides a versatile toolkit that can be adapted to other constrained allocation problems, offering a rigorous foundation for data-driven policy design in education and beyond.<\/jats:p>","DOI":"10.1287\/opre.2023.0386","type":"journal-article","created":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:45:56Z","timestamp":1760103956000},"page":"1562-1580","source":"Crossref","is-referenced-by-count":1,"title":["Capacity Planning in Stable Matching"],"prefix":"10.1287","volume":"74","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1524-4740","authenticated-orcid":false,"given":"Federico","family":"Bobbio","sequence":"first","affiliation":[{"name":"Centre Interuniversitaire de Recherche sur les Reseaux d\u2019Entreprise, la Logistique et le Transport and D\u00e9partement d\u2019Informatique et de Recherche Op\u00e9rationnelle, Universit\u00e9 de Montr\u00e9al, Montreal, Quebec H3T 1J4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2344-0960","authenticated-orcid":false,"given":"Margarida","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Centre Interuniversitaire de Recherche sur les Reseaux d\u2019Entreprise, la Logistique et le Transport and D\u00e9partement d\u2019Informatique et de Recherche Op\u00e9rationnelle, Universit\u00e9 de Montr\u00e9al, Montreal, Quebec H3T 1J4, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9269-633X","authenticated-orcid":false,"given":"Andrea","family":"Lodi","sequence":"additional","affiliation":[{"name":"Jacobs Technion-Cornell Institute, Cornell Tech, New York, New York 10044"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8526-9353","authenticated-orcid":false,"given":"Ignacio","family":"Rios","sequence":"additional","affiliation":[{"name":"School of Management, The University of Texas at Dallas, Richardson, Texas 75080"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9695-9018","authenticated-orcid":false,"given":"Alfredo","family":"Torrico","sequence":"additional","affiliation":[{"name":"Center for Data Science for Enterprise and Society, Cornell University, Ithaca, New York 14853"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1257\/000282803322157061"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1257\/aer.101.1.399"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1257\/aer.99.5.1954"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1257\/000282805774669637"},{"key":"B5","doi-asserted-by":"crossref","unstructured":"Abe K, Komiyama J, Iwasaki A (2022) Anytime capacity expansion in medical residency match by Monte Carlo tree search: Data-driven robust optimization. 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