IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v32y3i2020p641-660.html
   My bibliography  Save this article

Optimization-based Mechanisms for the Course Allocation Problem

Author

Listed:
  • Hoda Atef Yekta

    (Department of Management, Youngstown State University, Youngstown, Ohio 44555)

  • Robert Day

    (Department of Operations and Information Management, University of Connecticut, Storrs, Connecticut 06269)

Abstract

In recent years, several universities have adopted an algorithmic approach to the allocation of seats in courses, for which students place bids (typically by ordering or scoring desirable courses), and then seats are awarded according to a predetermined procedure or mechanism. Designing the appropriate mechanism for translating bids into student schedules has received attention in the literature, but there is currently no consensus on the best mechanism in practice. In this paper, we introduce five new algorithms for this course-allocation problem , using various combinations of matching algorithms, second-price concepts, and optimization, and compare our new methods with the natural benchmarks from the literature: the (proxy) draft mechanism and the (greedy) bidding-point mechanism. Using simulation, we compare the algorithms on metrics of fairness, efficiency, and incentive compatibility, measuring their ability to encourage truth telling among boundedly rational agents. We find good results for all of our methods and that a two-stage, full-market optimization performs best in measures of fairness and efficiency but with slightly worse incentives to act strategically compared with the best of the mechanisms. We also find generally negative results for the bidding-point mechanism, which performs poorly in all categories. These results can help guide the decision of selecting a mechanism for course allocation or for similar assignment problems, such as project team assignments or sports drafts, for example, in which efficiency and fairness are of utmost importance but incentives must also be considered. Additional robustness checks and comparisons are provided in the online supplement.

Suggested Citation

  • Hoda Atef Yekta & Robert Day, 2020. "Optimization-based Mechanisms for the Course Allocation Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 641-660, July.
    • Handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:641-660
    DOI: 10.1287/ijoc.2018.0849
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0849
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2018.0849?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    3. repec:bla:jpbect:v:3:y:2001:i:3:p:257-71 is not listed on IDEAS
    4. Aradhna Krishna & M. Utku Ünver, 2008. "Research Note—Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies," Marketing Science, INFORMS, vol. 27(2), pages 262-282, 03-04.
    5. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    6. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    7. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    8. Thanh Nguyen & Ahmad Peivandi & Rakesh Vohra, 2014. "One-Sided Matching with Limited Complementarities," PIER Working Paper Archive 14-030, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Franz Diebold & Haris Aziz & Martin Bichler & Florian Matthes & Alexander Schneider, 2014. "Course Allocation via Stable Matching," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 6(2), pages 97-110, April.
    10. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ciamac C. Moallemi & Utkarsh Patange, 2024. "Hybrid Scheduling with Mixed-Integer Programming at Columbia Business School," Interfaces, INFORMS, vol. 54(3), pages 222-240, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    2. Eric Budish & Judd B. Kessler, 2022. "Can Market Participants Report Their Preferences Accurately (Enough)?," Management Science, INFORMS, vol. 68(2), pages 1107-1130, February.
    3. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    4. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    5. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    6. Franz Diebold & Haris Aziz & Martin Bichler & Florian Matthes & Alexander Schneider, 2014. "Course Allocation via Stable Matching," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 6(2), pages 97-110, April.
    7. 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.
    8. Gian Caspari, 2023. "A market design solution to a multi-category housing allocation problem," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 75-96, December.
    9. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    10. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    11. Romero-Medina, Antonio & Triossi, Matteo, 2024. "Strategic priority-based course allocation," Journal of Economic Behavior & Organization, Elsevier, vol. 226(C).
    12. Eric Budish & Judd B. Kessler, 2016. "Can Market Participants Report their Preferences Accurately (Enough)?," NBER Working Papers 22448, National Bureau of Economic Research, Inc.
    13. Yan Chen & Peter Cramton & John A. List & Axel Ockenfels, 2021. "Market Design, Human Behavior, and Management," Management Science, INFORMS, vol. 67(9), pages 5317-5348, September.
    14. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    15. Caspari, Gian, 2020. "Booster draft mechanism for multi-object assignment," ZEW Discussion Papers 20-074, ZEW - Leibniz Centre for European Economic Research.
    16. Echenique, Federico & Goel, Sumit & Lee, SangMok, 2024. "Stable allocations in discrete exchange economies," Journal of Economic Theory, Elsevier, vol. 222(C).
    17. 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.
    18. Daniel Kornbluth & Alexey Kushnir, 2024. "Undergraduate Course Allocation through Competitive Markets," Papers 2412.05691, arXiv.org.
    19. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202103100800001123, Iowa State University, Department of Economics.
    20. Parag A. Pathak & Alex Rees-Jones & Tayfun Sönmez, 2025. "Immigration Lottery Design: Engineered and Coincidental Consequences of H-1B Reforms," The Review of Economics and Statistics, MIT Press, vol. 107(1), pages 1-13, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:32:y:3:i:2020:p:641-660. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.