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Family sequencing and cooperation

Author

Listed:
  • Grundel, Soesja
  • Çiftçi, Barış
  • Borm, Peter
  • Hamers, Herbert

Abstract

This paper analyzes a single-machine scheduling problem with family setup times both from an optimization and a cost allocation perspective. In a family sequencing situation jobs are processed on a single machine, there is an initial processing order on the jobs, and every job within a family has an identical cost function that depends linearly on its completion time. Moreover, a job does not require a setup when preceded by another job from the same family while a family specific setup time is required when a job follows a member of some other family.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:226:y:2013:i:3:p:414-424
    DOI: 10.1016/j.ejor.2012.11.060
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    References listed on IDEAS

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    1. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
    2. Wan, Guohua & Yen, Benjamin P.-C., 2009. "Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 195(1), pages 89-97, May.
    3. Mosheiov, Gur & Oron, Daniel, 2008. "A single machine batch scheduling problem with bounded batch size," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1069-1079, June.
    4. Ocetkiewicz, Krzysztof M., 2010. "A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem," European Journal of Operational Research, Elsevier, vol. 203(2), pages 316-320, June.
    5. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
    6. Hamers, H. & Borm, P. & Tijs, S., 1993. "A Games Corresponding to Sequencing Situations with Ready Times," Papers 9316, Tilburg - Center for Economic Research.
    7. Liaee, Mohammad Mehdi & Emmons, Hamilton, 1997. "Scheduling families of jobs with setup times," International Journal of Production Economics, Elsevier, vol. 51(3), pages 165-176, September.
    8. 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.
    9. Allahverdi, Ali & Gupta, Jatinder N. D. & Aldowaisan, Tariq, 1999. "A review of scheduling research involving setup considerations," Omega, Elsevier, vol. 27(2), pages 219-239, April.
    10. Gordon, Valery S. & Strusevich, Vitaly A., 2009. "Single machine scheduling and due date assignment with positionally dependent processing times," European Journal of Operational Research, Elsevier, vol. 198(1), pages 57-62, October.
    11. 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.
    12. Gregory Dobson & Uday S. Karmarkar & Jeffrey L. Rummel, 1987. "Batching to Minimize Flow Times on One Machine," Management Science, INFORMS, vol. 33(6), pages 784-799, June.
    13. 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.
    14. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
    15. 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.
    16. repec:spr:compst:v:63:y:2006:i:1:p:53-62 is not listed on IDEAS
    17. Koulamas, Christos & Gupta, Sushil & Kyparisis, George J., 2010. "A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times," European Journal of Operational Research, Elsevier, vol. 205(2), pages 479-482, September.
    18. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    19. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    20. 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. 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.
    2. repec:eee:ejores:v:262:y:2017:i:2:p:411-423 is not listed on IDEAS
    3. Chun, Youngsub & Mitra, Manipushpak, 2014. "Subgroup additivity in the queueing problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 281-289.

    More about this item

    Keywords

    Single-machine scheduling; Family scheduling model; Setup times; Cooperative game; Core; Marginal vector;

    JEL classification:

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

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