Skip to main content
Log in

Balancedness of Sequencing Games with Multiple Parallel Machines

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We provide simple constructive proofs of balancedness of classes of m-PS (m-Parallel Sequencing) games, which arise from sequencing situations with m parallel machines. This includes the setting that is studied by Calleja et al. (2001) and Calleja et al. (2002), who provided a complex constructive proof and a simple non-constructive proof of balancedness of a restricted class of 2-PS games, respectively. Furthermore, we provide a counterexample to illustrate that our balancedness results cannot be extended to a general setting.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bondareva, O. (1963). “Certain Applications of the Methods of Linear Programming to the Theory of Cooperative Games (In Russian).” Problemy Kibernetiki 10, 119–139.

    Google Scholar 

  • Calleja, P., P. Borm, H. Hamers, and F. Klijn. (2001). “On a New Class of Parallel Sequencing Situations and Related Games.”CentER Discussion Paper 2001-03, Tilburg University, Tilburg, The Netherlands.

  • Calleja, P., P. Borm, H. Hamers, F. Klijn, and M. Slikker. (2002). “On a New Class of Parallel Sequencing Situations and Related Games.” Annals of Operations Research 109, 265–277.

    Article  Google Scholar 

  • Curiel, I., H. Hamers, and F. Klijn. (2002). “Sequencing Games: A Survey.” In Borm, P. and Peters, H., (eds.), Chapters in Game Theory (In Honor of Stef Tijs) Kluwer Academic Publishers, Boston, pp. 27–50.

    Google Scholar 

  • Curiel, I., G. Pederzoli, and S. Tijs. (1989). “Sequencing Games.” European Journal of Operational Research 40, 344–351.

    Article  Google Scholar 

  • Curiel, I., J. Potters, V. Rajendra Prassad, S. Tijs, and B. Veltman. (1993). “Cooperation in One-Machine Scheduling.”Zeitschrift für Operations Research 38, 113–129.

    Google Scholar 

  • Curiel, I., J. Potters, V. Rajendra Prassad, S. Tijs, and B. Veltman. (1994). “Sequencing and Cooperation.“ Operations Research 42, 566–568.

    Article  Google Scholar 

  • Hamers, H., F. Klijn, and J. Suijs. (1999). “On the Balancedness of Multiple Machine Sequencing Games.” European Journal of Operational Research 119, 678–691.

    Article  Google Scholar 

  • Hamers, H. and M. Slikker. (1995). “The PEGS-Rule for Probabilistic Sequencing Situations.” Cahiers du Centre dÉtudes de Recherche Opérationelle 37, 109–119.

    Google Scholar 

  • Pritsker, A., L. Miller, and R. Zinkl. (1971). “Sequencing n Products Involving m Independent Jobs on m Machines.” A.I.I.E. Transactions 3, 49–60.

    Google Scholar 

  • Shapley, L. (1967). “On Balanced Sets and Cores. “Naval Research Logistics Quarterly 14, 453– 460.

    Google Scholar 

  • Slikker, M. (2003). “An m-Sequencing Game with an Empty Core.” BETA Working Paper 94, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.

  • van den Nouweland, A., M. Krabbenborg, and J. Potters. (1992). “Flow-Shops with a Dominant Machine.” European Journal of Operational Research 62, 38–46.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Slikker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Slikker, M. Balancedness of Sequencing Games with Multiple Parallel Machines. Ann Oper Res 137, 177–189 (2005). https://doi.org/10.1007/s10479-005-2253-8

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-005-2253-8

Keywords

Navigation