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Batch Sequencing and Cooperation

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

    (Tilburg University, Center for Economic Research)

Abstract

Game theoretic analysis of sequencing situations has been restricted to manufactur- ing systems which consist of machines that can process only one job at a time. However, in many manufacturing systems, operations are carried out by batch machines which can simultaneously process multiple jobs. This paper aims to extend the game theoretical approach to the cost allocation problems arising from sequencing situations on systems that consist of batch machines. We first consider sequencing situations with a single batch machine and analyze cooperative games arising from these situations. It is shown that these games are convex and an expression for the Shapley value of these games is provided. We also introduce an equal gain splitting rule for these sequencing situa- tions and provide an axiomatic characterization. Second, we analyze various aspects of flow-shop sequencing situations which consist of batch machines only. In particular, we provide two cases in which the cooperative game arising from the flow-shop sequencing situation is equal to the game arising from a sequencing situation that corresponds to one specific machine in the flow-shop.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2008-100.

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Date of creation: 2008
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Handle: RePEc:dgr:kubcen:2008100

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

Related research

Keywords: Sequencing situations; sequencing games; batch machines;

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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. Borm, P.E.M. & Fiestras-Janeiro, G. & Hamers, H.J.M. & Sánchez, E. & Voorneveld, M., 2002. "On the convexity of games corresponding to sequencing situations with due dates," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88223, Tilburg University.
  3. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, vol. 20(4), pages 419-27.
  4. Slikker, Marco, 2006. "Balancedness of multiple machine sequencing games revisited," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1944-1949, November.
  5. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1993. "Cooperation in one machine scheduling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154197, Tilburg University.
  6. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  7. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
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