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Matching with indifferences: A comparison of algorithms in the context of course allocation

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  • Diebold, Franz
  • Bichler, Martin

Abstract

We evaluate six one- and eight two-sided matching mechanisms with preferences based on a collection of 28 field data sets. Although important properties of matching mechanisms such as strategy-proofness or Pareto efficiency can be shown by formal proofs, the size, the average rank, and the popularity of matchings ask for an empirical evaluation. We introduce different metrics to compare the results. The study shows trade-offs between various design desiderata, which are relevant in the field. The results provide guidelines for the selection of matching mechanisms.

Suggested Citation

  • Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:1:p:268-282
    DOI: 10.1016/j.ejor.2016.12.011
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    2. Karaenke, Paul & Bichler, Martin & Merting, Soeren & Minner, Stefan, 2020. "Non-monetary coordination mechanisms for time slot allocation in warehouse delivery," European Journal of Operational Research, Elsevier, vol. 286(3), pages 897-907.
    3. Kondratev, Aleksei Y. & Nesterov, Alexander S., 2022. "Minimal envy and popular matchings," European Journal of Operational Research, Elsevier, vol. 296(3), pages 776-787.
    4. Delorme, Maxence & García, Sergio & Gondzio, Jacek & Kalcsics, Jörg & Manlove, David & Pettersson, William, 2019. "Mathematical models for stable matching problems with ties and incomplete lists," European Journal of Operational Research, Elsevier, vol. 277(2), pages 426-441.
    5. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    6. Li, Mengling, 2020. "Ties matter: Improving efficiency in course allocation by allowing ties," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 354-384.
    7. Martin Bichler & Alexander Hammerl & Thayer Morrill & Stefan Waldherr, 2021. "How to Assign Scarce Resources Without Money: Designing Information Systems that are Efficient, Truthful, and (Pretty) Fair," Information Systems Research, INFORMS, vol. 32(2), pages 335-355, June.
    8. Erdil, Aytek & Ergin, Haluk, 2017. "Two-sided matching with indifferences," Journal of Economic Theory, Elsevier, vol. 171(C), pages 268-292.
    9. Hoang Huu Viet & Nguyen Thi Uyen & SeungGwan Lee & TaeChoong Chung & Le Hong Trang, 2021. "A max-conflicts based heuristic search for the stable marriage problem with ties and incomplete lists," Journal of Heuristics, Springer, vol. 27(3), pages 439-458, June.
    10. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.
    11. Christian Haas, 2021. "Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1115-1148, April.
    12. Martin Bichler & Soeren Merting, 2021. "Randomized Scheduling Mechanisms: Assigning Course Seats in a Fair and Efficient Way," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3540-3559, October.
    13. Gartner, Daniel & Kolisch, Rainer, 2021. "Mathematical programming for nominating exchange students for international universities: The impact of stakeholders’ objectives and fairness constraints on allocations," Socio-Economic Planning Sciences, Elsevier, vol. 76(C).
    14. Suresh P. Sethi & Sushil Gupta & Vipin K. Agrawal & Vijay K. Agrawal, 2022. "Nobel laureates’ contributions to and impacts on operations management," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4283-4303, December.

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