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Family Sequencing and Cooperation

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  • Grundel, S.
  • Ciftci, B.B.
  • Borm, P.E.M.
  • Hamers, H.J.M.

    (Tilburg University, Center for Economic Research)

Abstract

To analyze the allocation problem of the maximal cost savings of the whole group of jobs, we define and analyze a so-called corresponding cooperative family sequencing game which explicitly takes into account the maximal cost savings for any coalition of jobs. Using nonstandard techniques we prove that each family sequencing game has a non-empty core by showing that a particular marginal vector belongs to the core. Finally, we specifically analyze the case in which the initial order is family ordered.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-040.

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Date of creation: 2012
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Handle: RePEc:dgr:kubcen:2012040

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Web page: http://center.uvt.nl

Related research

Keywords: Single-machine scheduling; Family scheduling model; Setup times; Cooperative Game; Core; Marginal Vector.;

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References

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  1. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
  2. Hamers, H.J.M. & Klijn, F. & Velzen, S. van, 2002. "On the Convexity of Precedence Sequencing Games," Discussion Paper 2002-112, Tilburg University, Center for Economic Research.
  3. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
  4. 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.
  5. Flip Klijn & Estela S?chez, 2004. "Sequencing Games without Initial Order," UFAE and IAE Working Papers 622.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. 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.
  7. 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.
  8. Hamers, H.J.M. & Borm, P.E.M. & Tijs, S.H., 1995. "On games corresponding to sequencing situations with ready times," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86378, Tilburg University.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  14. 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.
  15. 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.
  16. 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.
  17. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
  18. 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.
  19. 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.
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Cited by:
  1. Chun, Youngsub & Mitra, Manipushpak, 2014. "Subgroup additivity in the queueing problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 281-289.

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