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On Games corresponding to Sequencing Situations with Precedence Relations

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Abstract

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs. It is shown that these sequencing games are convex.

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  • Herbert Hamers & Flip Klijn & Bas van Velzen, 2002. "On Games corresponding to Sequencing Situations with Precedence Relations," UFAE and IAE Working Papers 553.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:553.02
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    1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Other publications TiSEM be67f9e9-7a4a-47f1-9fb9-7, Tilburg University, School of Economics and Management.
    2. Pedro Calleja & Peter Borm & Herbert Hamers & Flip Klijn & Marco Slikker, 2002. "On a New Class of Parallel Sequencing Situations and Related Games," Annals of Operations Research, Springer, vol. 109(1), pages 265-277, January.
    3. Hamers, H.J.M. & Borm, P.E.M. & Tijs, S.H., 1993. "On games corresponding to sequencing situations with ready times," Other publications TiSEM 8e2af556-5430-4f98-9334-c, Tilburg University, School of Economics and Management.
    4. Imma Curiel & Jos Potters & Rajendra Prasad & Stef Tijs & Bart Veltman, 1994. "Sequencing and Cooperation," Operations Research, INFORMS, vol. 42(3), pages 566-568, June.
    5. 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.
    6. Hamers, Herbert & Suijs, Jeroen & Tijs, Stef & Borm, Peter, 1996. "The Split Core for Sequencing Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 165-176, August.
    7. Hamers, Herbert & Klijn, Flip & Suijs, Jeroen, 1999. "On the balancedness of multiple machine sequencing games," European Journal of Operational Research, Elsevier, vol. 119(3), pages 678-691, December.
    8. van Velzen, S. & Hamers, H.J.M., 2002. "On the Balancedness of Relaxed Sequencing Games," Other publications TiSEM 14e21ac6-26af-438e-943b-9, Tilburg University, School of Economics and Management.
    9. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    10. van Velzen, S. & Hamers, H.J.M., 2002. "On the Balancedness of Relaxed Sequencing Games," Discussion Paper 2002-49, Tilburg University, Center for Economic Research.
    11. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    12. 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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    Cited by:

    1. Atay, Ata & Calleja, Pedro & Soteras, Sergio, 2021. "Open shop scheduling games," European Journal of Operational Research, Elsevier, vol. 295(1), pages 12-21.
    2. Jesús Getán & Josep Izquierdo & Jesús Montes & Carles Rafels, 2015. "The bargaining set for almost-convex games," Annals of Operations Research, Springer, vol. 225(1), pages 83-89, February.
    3. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    4. Lohmann, E.R.M.A. & Borm, P.E.M. & Slikker, M., 2010. "Preparation Sequencing Situations and Related Games," Discussion Paper 2010-31, Tilburg University, Center for Economic Research.
    5. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Other publications TiSEM 3e1db5c9-0f77-4f91-a075-c, Tilburg University, School of Economics and Management.
    6. 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.
    7. van Velzen, S. & Hamers, H.J.M., 2002. "On the Balancedness of Relaxed Sequencing Games," Discussion Paper 2002-49, Tilburg University, Center for Economic Research.
    8. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Discussion Paper 2020-006, Tilburg University, Center for Economic Research.
    9. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Discussion Paper 2008-100, Tilburg University, Center for Economic Research.
    10. Edwin Lohmann & Peter Borm & Marco Slikker, 2014. "Sequencing situations with Just-in-Time arrival, and related games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 285-305, December.
    11. Ozen, U. & Norde, H.W. & Slikker, M., 2005. "On the Convexity of News Vendor Games," Other publications TiSEM 2faeeb88-8d0b-4c36-9b08-5, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    cooperative games; sequencing situations; convexity;
    All these keywords.

    JEL classification:

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

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