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On the Convexity of Step out - Step in Sequencing Games

Author

Listed:
  • Musegaas, Marieke

    (Tilburg University, Center For Economic Research)

  • Borm, Peter

    (Tilburg University, Center For Economic Research)

  • Quant, Marieke

    (Tilburg University, Center For Economic Research)

Abstract

The main result of this paper is the convexity of step out–step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas et al. (Eur J Oper Res 246:894–906, 2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an arbitrary coalition in a SoSi sequencing game. In particular, we use that in determining an optimal processing order of a coalition, the algorithm can start from the optimal processing order found for any subcoalition of smaller size and thus all information on such an optimal processing order can be used.
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Suggested Citation

  • Musegaas, Marieke & Borm, Peter & Quant, Marieke, 2016. "On the Convexity of Step out - Step in Sequencing Games," Discussion Paper 2016-043, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:f8a803f5-1f6a-4ac4-b4f6-70e0ba254979
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    References listed on IDEAS

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    1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1993. "Cooperation in one machine scheduling," Other publications TiSEM 9c5ceec5-2080-4b5c-98d5-0, Tilburg University, School of Economics and Management.
    2. 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.
    3. 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.
    4. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    5. Bas van Velzen & Herbert Hamers, 2003. "On the balancedness of relaxed sequencing games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 287-297, May.
    6. Marco Slikker, 2006. "Relaxed sequencing games have a nonempty core," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 235-242, June.
    7. 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. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    3. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    4. Ata Atay & Christian Trudeau, 2022. "Queueing games with an endogenous number of machines," Working Papers 2202, University of Windsor, Department of Economics.

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    More about this item

    Keywords

    relaxed sequencing games; convexity;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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