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Sequencing games without initial order

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  • Flip Klijn
  • Estela Sánchez

Abstract

In this note we study uncertainty sequencing situations, i.e., one-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (Eur J Oper Res 40:344–351, 1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times. Copyright Springer-Verlag 2006

Suggested Citation

  • Flip Klijn & Estela Sánchez, 2006. "Sequencing games without initial order," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 53-62, February.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:1:p:53-62
    DOI: 10.1007/s00186-005-0012-x
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    References listed on IDEAS

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    1. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    2. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Citations

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    Cited by:

    1. van Beek, Andries, 2023. "Solutions in multi-actor projects with collaboration and strategic incentives," Other publications TiSEM 3739c498-5edb-442f-87d8-c, Tilburg University, School of Economics and Management.
    2. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
    3. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2021. "Cooperation and Competition in Linear Production and Sequencing Processes," Other publications TiSEM fd7a301b-7ef3-4142-835d-a, Tilburg University, School of Economics and Management.
    4. Grundel, Soesja & Çiftçi, Barış & Borm, Peter & Hamers, Herbert, 2013. "Family sequencing and cooperation," European Journal of Operational Research, Elsevier, vol. 226(3), pages 414-424.
    5. Debasis Mishra & Bharath Rangarajan, 2007. "Cost sharing in a job scheduling problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 369-382, October.
    6. Moulin, Herve, 2004. "On Scheduling Fees to Prevent Merging, Splitting and Transferring of Jobs," Working Papers 2004-04, Rice University, Department of Economics.
    7. Musegaas, M. & Borm, P.E.M. & Quant, M., 2015. "Step out–Step in sequencing games," European Journal of Operational Research, Elsevier, vol. 246(3), pages 894-906.
    8. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    9. Saavedra-Nieves, Alejandro & Schouten, Jop & Borm, Peter, 2020. "On interactive sequencing situations with exponential cost functions," European Journal of Operational Research, Elsevier, vol. 280(1), pages 78-89.
    10. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s021919891850007x is not listed on IDEAS
    11. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2019. "Games in sequencing situations with externalities," European Journal of Operational Research, Elsevier, vol. 278(2), pages 699-708.
    12. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2023. "Competition and cooperation in linear production and sequencing processes," Games and Economic Behavior, Elsevier, vol. 139(C), pages 117-132.

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    More about this item

    Keywords

    Sequencing; Cooperative games; C71; C78;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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