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On the Convexity of Precedence Sequencing Games

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  • Herbert Hamers
  • Flip Klijn
  • Bas Velzen

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. We show that these sequencing games are convex if the initial order of the jobs is a concatenation of chains. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Herbert Hamers & Flip Klijn & Bas Velzen, 2005. "On the Convexity of Precedence Sequencing Games," Annals of Operations Research, Springer, vol. 137(1), pages 161-175, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:161-175:10.1007/s10479-005-2252-9
    DOI: 10.1007/s10479-005-2252-9
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    References listed on IDEAS

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    1. 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.
    2. Imma Curiel & Jos Potters & Rajendra Prasad & Stef Tijs & Bart Veltman, 1994. "Sequencing and Cooperation," Operations Research, INFORMS, vol. 42(3), pages 566-568, June.
    3. 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.
    4. 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.
    5. 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.
    6. van den Nouweland, Anne & Krabbenborg, Marc & Potters, Jos, 1992. "Flow-shops with a dominant machine," European Journal of Operational Research, Elsevier, vol. 62(1), pages 38-46, October.
    7. 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.
    8. 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.
    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," Other publications TiSEM 14e21ac6-26af-438e-943b-9, Tilburg University, School of Economics and Management.
    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.
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    More about this item

    Keywords

    cooperative games; sequencing situations;

    JEL classification:

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

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