Stability Representations of Many-to-One Matching Problems: An Integer Optimization Approach

References

• Abdulkadiroğlu A, Sönmez T (2003) School choice: A mechanism design approach. Amer. Econom. Rev. 93(3):729–747.Crossref, Google Scholar
• Abdulkadiroğlu A, Pathak P, Roth AE, Sönmez T (2006) Changing the Boston school choice mechanism. Technical report, National Bureau of Economic Research, Cambridge, MA.Google Scholar
• Ágoston KC, Biró P, McBride I (2016) Integer programming methods for special college admissions problems. J. Combin. Optim. 32(4):1371–1399.Crossref, Google Scholar
• Ahani N, Andersson T, Martinello A, Teytelboym A, Trapp AC (2021) Placement optimization in refugee resettlement. Oper. Res. 69(5):1468–1486.Link, Google Scholar
• Alcalde J, Barberà S (1994) Top dominance and the possibility of strategy-proof stable solutions to matching problems. Econom. Theory 4(3):417–435.Crossref, Google Scholar
• Baïou M, Balinski M (2000) The stable admissions polytope. Math. Programming 87(3):427–439.Crossref, Google Scholar
• Bertsimas D, King A, Mazumder R (2016) Best subset selection via a modern optimization lens. Ann. Statist. 44(2):813–852.Crossref, Google Scholar
• Delacrétaz D, Kominers SD, Teytelboym A (2019) Matching mechanisms for refugee resettlement. Technical report, University of Oxford, UK.Google Scholar
• Delorme M, García S, Gondzio J, Kalcsics J, Manlove D, Pettersson W (2019) Mathematical models for stable matching problems with ties and incomplete lists. Eur. J. Oper. Res. 277(2):426–441.Crossref, Google Scholar
• Gale D, Shapley LS (1962) College admissions and the stability of marriage. Amer. Math. Monthly 69(1):9–15.Crossref, Google Scholar
• Gurobi Optimization LLC (2020) Gurobi Optimizer Reference Manual, version 9.1. http://www.gurobi.com.Google Scholar
• Harris CR, Millman KJ, van der Walt SJ, Gommers R, Virtanen P, Cournapeau D, Wieser E, et al. (2020) Array programming with NumPy. Nature 585(7825):357–362.Crossref, Google Scholar
• Kojima F, Ünver MU (2014) The Boston school-choice mechanism: An axiomatic approach. Econom. Theory 55(3):515–544.Crossref, Google Scholar
• Kwanashie A, Manlove DF (2014) An integer programming approach to the hospitals/residents problem with ties. Oper. Res. Proc. 2013 (Springer), 263–269.Google Scholar
• Maass KL, Lo VMH, Weiss A, Daskin MS (2015) Maximizing diversity in the engineering global leadership cultural families. Interfaces 45(4):293–304.Link, Google Scholar
• Manlove DF, O’Malley G, Prosser P, Unsworth C (2007) A constraint programming approach to the hospitals/residents problem. Internat. Conf. Integration Artificial Intelligence (AI) Oper. Res. (OR) Techniques Constraint Programming (Springer), 155–170.Google Scholar
• Roth AE (1982) The economics of matching: Stability and incentives. Math. Oper. Res. 7(4):617–628.Link, Google Scholar
• Roth AE (1985) The college admissions problem is not equivalent to the marriage problem. J. Econom. Theory 36(2):277–288.Crossref, Google Scholar
• Roth AE (1986) On the allocation of residents to rural hospitals: A general property of two-sided matching markets. Econometrica 54(2):425–427.Crossref, Google Scholar
• Roth AE, Sotomayor M (1989) The college admissions problem revisited. Econometrica 57(3):559–570.Crossref, Google Scholar
• Roth AE, Sotomayor M (1992) Two-sided matching. Handbook of Game Theory with Economic Applications, vol. 1, 485–541.Crossref, Google Scholar
• Roth AE, Rothblum UG, Vande Vate JH (1993) Stable matchings, optimal assignments, and linear programming. Math. Oper. Res. 18(4):803–828.Link, Google Scholar
• Shapley L, Scarf H (1974) On cores and indivisibility. J. Math. Econom. 1(1):23–37.Crossref, Google Scholar
• Shimada N, Yamazaki N, Takano Y (2020) Multi-objective optimization models for many-to-one matching problems. J. Inform. Processing 28:406–412.Crossref, Google Scholar
• Vande Vate JH (1989) Linear programming brings marital bliss. Oper. Res. Lett. 8(3):147–153.Crossref, Google Scholar
• Wiratchotisatian P, Yekta HA, Trapp AC (2022) WPI data sets: A comparative study of stability representations for solving many-to-one matching problems with utility-weighted objectives, ties, and incomplete lists via integer optimization v2021.0058. https://github.com/INFORMSJoC/2021.0058.Google Scholar
• Wolsey LA (1998) Integer Programming (John Wiley & Sons, New York).Google Scholar