×

School choice with hybrid schedules. (English) Zbl 1479.91232

Summary: 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.

MSC:

91B68 Matching models

References:

[1] Darrough, M.; Feds kick in nearly \(22 million to bring high-speed internet to rural Pender; Port City Daily: 2020; \)
[2] Lavigne, L.; Durham Public Housing Properties Will Soon Receive Stable Internet Connection; ; .
[3] Hicks, T.; ‘It’s a Challenge to Maintain Our Empathy: Parents Struggle with Online Learning at Home; ; .
[4] Kantor, J.; Working Anything but 9 to 5; New York Times: 2014; .
[5] Bateman, N.; ; Working Parents Are Key to COVID-19 Recovery: Washington, DC, USA 2020; .
[6] North, A.; America’s Child Care Problem is an Economic Problem; ; .
[7] Gale, D.; Shapley, L.S.; College Admissions and the Stability of Marriage; Am. Math. Mon.: 1962; Volume 69 ,9-15. · Zbl 0109.24403
[8] Balinski, M.; Sönmez, T.; A Tale of Two Mechanisms: Student Placement; J. Econ. Theory: 1999; Volume 84 ,73-94. · Zbl 0916.90008
[9] Abdulkadiroğlu, A.; Sönmez, T.; School Choice: A Mechanism Design Approach; Am. Econ. Rev.: 2003; Volume 93 ,729-747.
[10] Erdil, A.; Ergin, H.; What’s the matter with tie-breaking? Improving efficiency in school choice; Am. Econ.: 2008; Volume 98 ,669-689.
[11] Abdulkadiroğlu, A.; Pathak, P.A.; Roth, A.E.; Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match; Am. Econ.: 2009; Volume 99 ,1954-1978.
[12] Kesten, O.; School Choice with Consent; Q. J. Econ.: 2010; Volume 125 ,1297-1348. · Zbl 1197.91153
[13] Pathak, P.A.; Sönmez, T.; School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation; Am. Econ. Rev.: 2013; Volume 103 ,80-106.
[14] Ehlers, L.; Hafalir, I.E.; Yenmez, M.B.; Yildirim, M.A.; School Choice with Controlled Choice Constraints: Hard Bounds versus Soft Bounds; J. Econ. Theory: 2014; Volume 153 ,648-683. · Zbl 1309.91102
[15] Dur, U.; Kominers, S.D.; Pathak, P.A.; Sönmez, T.; Reserve Design: Unintended Consequences and the Demise of Boston’s Walk Zones; J. Political Econ.: 2018; Volume 126 ,2457-2479.
[16] Pathak, P.A.; The Mechanism Design Approach to Student Assignment; Annu. Rev. Econ.: 2011; Volume 3 ,513-536.
[17] Pathak, P.A.; What Really Matters in Designing School Choice Mechanisms; Advances in Economics and Econometrics, 11th World Congress of the Econometric Society: Cambridge, UK 2016; .
[18] Hatfield, J.; Milgrom, P.; Matching with Contracts; Am. Econ. Rev.: 2005; Volume 95 ,913-935.
[19] Hatfield, J.W.; Kojima, F.; Matching with Contracts: Comment; Am. Econ. Rev.: 2008; Volume 98 ,1189-1194.
[20] Hatfield, J.W.; Kojima, F.; Substitutes and stability for matching with contracts; J. Econ. Theory: 2010; Volume 145 ,1704-1723. · Zbl 1245.91068
[21] Sönmez, T.; Switzer, T.B.; Matching with (Branch-of-Choice) Contracts at the United States Military Academy; Econometrica: 2013; Volume 81 ,451-488. · Zbl 1274.91334
[22] Hafalir, I.E.; Kojima, F.; Yenmez, M.B.; ; Interdistrict School Choice: A Theory of Student Assignment: Boston, MA, USA 2018; .
[23] Dur, U.; Morrill, T.; Phan, W.; ; Family Ties: School Assignment with Siblings: Memphis, TN, USA 2020; .
[24] Shuib, A.; Kamarudin, F.I.; Solving shift scheduling problem with days-off preference for power station workers using binary integer goal programming model; Ann. Oper. Res.: 2019; Volume 272 ,355-372. · Zbl 1434.90069
[25] Aygün, O.; Sönmez, T.; Matching with Contracts: Comment; Am. Econ. Rev.: 2013; Volume 103 ,2050-2051.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.