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Bilevel integer linear models for ranking items and sets

Author

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  • Labbé, Martine
  • Landete, Mercedes
  • Monge, Juan F.

Abstract

Item and set orderings help with data management. Depending on the context, it is just as important to order a list of items (customers from different provinces, companies from different sectors, players from different teams) as it is to order a list of sets of these items (provinces, sectors, teams). It is evident that the order that is chosen for the items is not independent of the order that is chosen for the sets. It is possible that several set orders are sensible for the same item order and vice versa, that several item orders are sensible for the same set order. In this work, we propose a bilevel model to calculate an adequate order of items when an order of sets is available and another bilevel model to calculate an adequate order of sets when an order of items is available. In addition, it is shown how to reduce both bilevel models to single level models. Two illustrative computational studies are presented, the first with collected on 25 tennis players and ATP statistics and the second with Biomedical data. Both examples illustrate the good behavior of the models and the interest of their application in a real case scenario

Suggested Citation

  • Labbé, Martine & Landete, Mercedes & Monge, Juan F., 2023. "Bilevel integer linear models for ranking items and sets," Operations Research Perspectives, Elsevier, vol. 10(C).
    • Handle: RePEc:eee:oprepe:v:10:y:2023:i:c:s2214716023000064
    DOI: 10.1016/j.orp.2023.100271
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    References listed on IDEAS

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    1. Aledo, Juan A. & Gámez, Jose A. & Molina, David, 2016. "Using extension sets to aggregate partial rankings in a flexible setting," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 208-223.
    2. Javier Alcaraz & Eva M. García-Nové & Mercedes Landete & Juan F. Monge, 2020. "The linear ordering problem with clusters: a new partial ranking," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 646-671, October.
    3. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    4. Juan Aparicio & Mercedes Landete & Juan F. Monge, 2020. "A linear ordering problem of sets," Annals of Operations Research, Springer, vol. 288(1), pages 45-64, May.
    5. Javier Alcaraz & Mercedes Landete & Juan F. Monge, 2022. "Rank Aggregation: Models and Algorithms," Springer Books, in: Saïd Salhi & John Boylan (ed.), The Palgrave Handbook of Operations Research, chapter 0, pages 153-178, Springer.
    6. Andreas Darmann & Christian Klamler, 2019. "Using the Borda rule for ranking sets of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 399-414, October.
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