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Envy-Free Allocation by Sperner’s Lemma Adapted to Rotation Shifts in a Company

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  • Sagrario Lantarón

    (Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain)

  • Mariló López

    (Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain)

  • Susana Merchán

    (Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain)

  • Javier Rodrigo

    (Departamento de Matemática Aplicada, ICAI, Universidad Pontificia Comillas, 28040 Madrid, Spain)

  • José Samuel Rodríguez

    (Departamento de Didáctica de las Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain)

Abstract

This article discusses a theoretical construction based on the graph theory to rework the space of potential partitions in envy-free distribution. This work has the objective of applying Sperner’s lemma to the distribution of three rotating shifts for three workers who are to cover a 24 h job position in a company. As a novel feature, worker’s preferences have been modeled as functions of probability for the three shifts, according to salary offers for said shifts. Envy-free allocation was achieved, since each worker received their preferred shift without the need for negotiation between agents in conflict. Adaptation to the type of dynamic situations that arise with rotating shifts, as well as the consideration of probabilistic preferences by workers are some of the main novelties of this work.

Suggested Citation

  • Sagrario Lantarón & Mariló López & Susana Merchán & Javier Rodrigo & José Samuel Rodríguez, 2021. "Envy-Free Allocation by Sperner’s Lemma Adapted to Rotation Shifts in a Company," Mathematics, MDPI, vol. 9(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1015-:d:546829
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    References listed on IDEAS

    as
    1. Cloutier, John & Nyman, Kathryn L. & Su, Francis Edward, 2010. "Two-player envy-free multi-cake division," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 26-37, January.
    2. Xiaotie Deng & Qi Qi & Amin Saberi, 2012. "Algorithmic Solutions for Envy-Free Cake Cutting," Operations Research, INFORMS, vol. 60(6), pages 1461-1476, December.
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