{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:57:53Z","timestamp":1760234273781,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,4,25]],"date-time":"2021-04-25T00:00:00Z","timestamp":1619308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>During the pandemic, school districts have adopted hybrid schedules to continue the education of the students while maintaining social distance. In a hybrid schedule, students in the same classroom are usually divided into two groups and students only in the same group can physically attend class together two days a week. School districts do not take preferences of the students\/parents over the days they would like to come to school into account during this procedure. In this paper, we propose a solution that divides students into groups based on their preferences. Our solution respects the number of classrooms initially reserved for each grade and enables possible efficiency gains by swapping classrooms across grades. Moreover, when there are two alternative schedules provided for students, our solution is immune to preference manipulations.<\/jats:p>","DOI":"10.3390\/g12020037","type":"journal-article","created":{"date-parts":[[2021,4,26]],"date-time":"2021-04-26T22:21:57Z","timestamp":1619475717000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["School Choice with Hybrid Schedules"],"prefix":"10.3390","volume":"12","author":[{"given":"Mustafa O\u011fuz","family":"Afacan","sequence":"first","affiliation":[{"name":"Faculty of Arts and Social Sciences, Sabanci University, Istanbul 34956, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0553-8382","authenticated-orcid":false,"given":"Umut","family":"Dur","sequence":"additional","affiliation":[{"name":"Department of Economics, North Carolina State University, Raleigh, NC 27695, USA"}]},{"given":"William","family":"Harris","sequence":"additional","affiliation":[{"name":"Department of Economics, North Carolina State University, Raleigh, NC 27695, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,25]]},"reference":[{"key":"ref_1","unstructured":"Darrough, M. (Port City Daily, 2020). Feds kick in nearly $22 million to bring high-speed internet to rural Pender, Port City Daily."},{"key":"ref_2","unstructured":"Lavigne, L. (2020, November 22). Durham Public Housing Properties Will Soon Receive Stable Internet Connection. Available online: https:\/\/www.wral.com\/durham-public-housing-properties-will-soon-receive-stable-internet-connection\/19259576\/."},{"key":"ref_3","unstructured":"Hicks, T. (2020, November 22). \u2018It\u2019s a Challenge to Maintain Our Empathy: Parents Struggle with Online Learning at Home. Available online: https:\/\/www.ktvu.com\/news\/parents-struggle-with-home-schooling-and-online-learning."},{"key":"ref_4","unstructured":"Kantor, J. (New York Times, 2014). Working Anything but 9 to 5, New York Times."},{"key":"ref_5","unstructured":"Bateman, N. (2020). Working Parents Are Key to COVID-19 Recovery, The Brookings Institution. Tech. Rep."},{"key":"ref_6","unstructured":"North, A. (2020, November 22). America\u2019s Child Care Problem is an Economic Problem. Available online: https:\/\/www.vox.com\/2020\/7\/16\/21324192\/covid-schools-reopening-daycare-child-care-coronavirus."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/00029890.1962.11989827","article-title":"College Admissions and the Stability of Marriage","volume":"69","author":"Gale","year":"1962","journal-title":"Am. Math. Mon."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1006\/jeth.1998.2469","article-title":"A Tale of Two Mechanisms: Student Placement","volume":"84","author":"Balinski","year":"1999","journal-title":"J. Econ. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1257\/000282803322157061","article-title":"School Choice: A Mechanism Design Approach","volume":"93","year":"2003","journal-title":"Am. Econ. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1257\/aer.98.3.669","article-title":"What\u2019s the matter with tie-breaking? Improving efficiency in school choice","volume":"98","author":"Erdil","year":"2008","journal-title":"Am. Econ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1257\/aer.99.5.1954","article-title":"Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match","volume":"99","author":"Pathak","year":"2009","journal-title":"Am. Econ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1297","DOI":"10.1162\/qjec.2010.125.3.1297","article-title":"School Choice with Consent","volume":"125","author":"Kesten","year":"2010","journal-title":"Q. J. Econ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1257\/aer.103.1.80","article-title":"School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation","volume":"103","author":"Pathak","year":"2013","journal-title":"Am. Econ. Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.jet.2014.03.004","article-title":"School Choice with Controlled Choice Constraints: Hard Bounds versus Soft Bounds","volume":"153","author":"Ehlers","year":"2014","journal-title":"J. Econ. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2457","DOI":"10.1086\/699974","article-title":"Reserve Design: Unintended Consequences and the Demise of Boston\u2019s Walk Zones","volume":"126","author":"Dur","year":"2018","journal-title":"J. Political Econ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1146\/annurev-economics-061109-080213","article-title":"The Mechanism Design Approach to Student Assignment","volume":"3","author":"Pathak","year":"2011","journal-title":"Annu. Rev. Econ."},{"key":"ref_17","unstructured":"Samuelson, L. (2016). What Really Matters in Designing School Choice Mechanisms. Advances in Economics and Econometrics, 11th World Congress of the Econometric Society, Cambridge University Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1257\/0002828054825466","article-title":"Matching with Contracts","volume":"95","author":"Hatfield","year":"2005","journal-title":"Am. Econ. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1257\/aer.98.3.1189","article-title":"Matching with Contracts: Comment","volume":"98","author":"Hatfield","year":"2008","journal-title":"Am. Econ. Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1016\/j.jet.2010.01.007","article-title":"Substitutes and stability for matching with contracts","volume":"145","author":"Hatfield","year":"2010","journal-title":"J. Econ. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"451","DOI":"10.3982\/ECTA10570","article-title":"Matching with (Branch-of-Choice) Contracts at the United States Military Academy","volume":"81","author":"Switzer","year":"2013","journal-title":"Econometrica"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Hafalir, I.E., Kojima, F., and Yenmez, M.B. (2018). Interdistrict School Choice: A Theory of Student Assignment, Boston College Department of Economics. Boston College Working Papers in Economics 970.","DOI":"10.2139\/ssrn.3307731"},{"key":"ref_23","unstructured":"Dur, U., Morrill, T., and Phan, W. (2020). Family Ties: School Assignment with Siblings, Mimeo."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s10479-018-2848-5","article-title":"Solving shift scheduling problem with days-off preference for power station workers using binary integer goal programming model","volume":"272","author":"Shuib","year":"2019","journal-title":"Ann. Oper. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1257\/aer.103.5.2050","article-title":"Matching with Contracts: Comment","volume":"103","year":"2013","journal-title":"Am. Econ. Rev."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/12\/2\/37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:52:36Z","timestamp":1760161956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/12\/2\/37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,25]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["g12020037"],"URL":"https:\/\/doi.org\/10.3390\/g12020037","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2021,4,25]]}}}