IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v20y2023i1d10.1007_s10287-023-00477-9.html
   My bibliography  Save this article

On efficiency and the Jain’s fairness index in integer assignment problems

Author

Listed:
  • Nahid Rezaeinia

    (NHH Norwegian School of Economics)

  • Julio C. Góez

    (NHH Norwegian School of Economics)

  • Mario Guajardo

    (NHH Norwegian School of Economics)

Abstract

Given two sets of objects, the integer assignment problem consists of assigning objects of one set to objects in the other set. Traditionally, the goal of this problem is to find an assignment that minimizes or maximizes a measure of efficiency, such as maximization of utility or minimization of cost. Lately, the interest in incorporating a measure of fairness in addition to efficiency has gained importance. This paper studies how to incorporate these two criteria in an integer assignment, using the Jain’s index as a measure of fairness. The original formulation of the assignment problem with this index involves a non-concave function, which renders a non-linear non-convex problem, usually hard to solve. To this aim, we develop two reformulations, where one is based on a quadratic objective function and the other one is based on integer second-order cone programming. We explore the performance of these reformulations in instances of real-world data derived from an application of assigning personnel to projects, and also in instances of randomly generated data. In terms of solution quality, all formulations prove to be effective in finding solutions capturing both efficiency and fairness criteria, with some slight differences depending on the type of instance. In terms of solving time, however, the performances of the formulations differ considerably. In particular, the integer quadratic approach proves to be much faster in finding optimal solutions.

Suggested Citation

  • Nahid Rezaeinia & Julio C. Góez & Mario Guajardo, 2023. "On efficiency and the Jain’s fairness index in integer assignment problems," Computational Management Science, Springer, vol. 20(1), pages 1-23, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00477-9
    DOI: 10.1007/s10287-023-00477-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-023-00477-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-023-00477-9?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.
    Full references (including those not matched with items on IDEAS)

    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. Jamie Fairbrother & Konstantinos G. Zografos & Kevin D. Glazebrook, 2020. "A Slot-Scheduling Mechanism at Congested Airports that Incorporates Efficiency, Fairness, and Airline Preferences," Transportation Science, INFORMS, vol. 54(1), pages 115-138, January.
    2. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    3. Nahid Rezaeinia & Julio César Góez & Mario Guajardo, 2022. "Efficiency and fairness criteria in the assignment of students to projects," Annals of Operations Research, Springer, vol. 319(2), pages 1717-1735, December.
    4. Gur, Yonatan & Iancu, Dan & Warnes, Xavier, 2020. "Value Loss in Allocation Systems with Provider Guarantees," Research Papers 3813, Stanford University, Graduate School of Business.
    5. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    6. Pan, Xunzhang & Teng, Fei & Wang, Gehua, 2014. "A comparison of carbon allocation schemes: On the equity-efficiency tradeoff," Energy, Elsevier, vol. 74(C), pages 222-229.
    7. Rachmilevitch, Shiran, 2015. "Nash bargaining with (almost) no rationality," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 107-109.
    8. Chen, Violet Xinying & Hooker, J.N., 2022. "Combining leximax fairness and efficiency in a mathematical programming model," European Journal of Operational Research, Elsevier, vol. 299(1), pages 235-248.
    9. Spencer Leitch & Zhiyuan Wei, 2024. "Improving spatial access to healthcare facilities: an integrated approach with spatial analysis and optimization modeling," Annals of Operations Research, Springer, vol. 341(2), pages 1057-1074, October.
    10. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    11. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    12. Alexandre Jacquillat & Vikrant Vaze, 2018. "Interairline Equity in Airport Scheduling Interventions," Transportation Science, INFORMS, vol. 52(4), pages 941-964, August.
    13. Emin Karagözoğlu & Kerim Keskin, 2015. "A Tale of Two Bargaining Solutions," Games, MDPI, vol. 6(2), pages 1-14, June.
    14. Claus-Jochen Haake & Cheng-Zhong Qin, 2018. "On unification of solutions to the bargaining problem," Working Papers CIE 113, Paderborn University, CIE Center for International Economics.
    15. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy, 2022. "On the Fair Division of a Random Object," Management Science, INFORMS, vol. 68(2), pages 1174-1194, February.
    16. Philippe Ezran & Yoram Haddad & Mérouane Debbah, 2019. "Allais’ paradox and resource allocation in telecommunication networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 70(3), pages 337-348, March.
    17. Ignacio A. Sepúlveda & Maichel M. Aguayo & Rodrigo De la Fuente & Guillermo Latorre-Núñez & Carlos Obreque & Camila Vásquez Orrego, 2024. "Scheduling mobile dental clinics: A heuristic approach considering fairness among school districts," Health Care Management Science, Springer, vol. 27(1), pages 46-71, March.
    18. Ye, Qing Chuan & Zhang, Yingqian & Dekker, Rommert, 2017. "Fair task allocation in transportation," Omega, Elsevier, vol. 68(C), pages 1-16.
    19. Hongzhe Zhang & Xiaohang Zhao & Xiao Fang & Bintong Chen, 2024. "Proactive Resource Request for Disaster Response: A Deep Learning-Based Optimization Model," Information Systems Research, INFORMS, vol. 35(2), pages 528-550, June.
    20. Lessan, Javad & Fu, Liping & Bachmann, Chris, 2020. "Towards user-centric, market-driven mobility management of road traffic using permit-based schemes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).

    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:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00477-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.