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Proportionate Flow Shop Games

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  • Estevez Fernandez, M.A.
  • Mosquera, M.A.
  • Borm, P.E.M.
  • Hamers, H.J.M.

    (Tilburg University, Center for Economic Research)

Abstract

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-63.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:200663

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Keywords: Proportionate flow shop problems; core; convexity;

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  1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
  2. Borm, P.E.M. & Fiestras-Janeiro, G. & Hamers, H.J.M. & Sánchez, E. & Voorneveld, M., 1999. "On the Convexity of Games Corresponding to Sequencing Situations with Due Dates," Discussion Paper 1999-49, Tilburg University, Center for Economic Research.
  3. Estevez Fernandez, M.A. & Borm, P.E.M. & Calleja, P. & Hamers, H.J.M., 2008. "Sequencing games with repeated players," Open Access publications from Tilburg University urn:nbn:nl:ui:12-195639, Tilburg University.
  4. Hamers, H.J.M. & Klijn, F. & Suijs, J.P.M., 1998. "On the Balancedness of M-Sequencing Games," Discussion Paper 1998-17, Tilburg University, Center for Economic Research.
  5. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  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. Borm, P.E.M. & Calleja, P. & Hamers, H.J.M. & Klijn, F. & Slikker, M., 2002. "On a new class of parallel sequencing situations and related games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-90187, Tilburg University.
  8. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  9. Calleja, P. & Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2004. "Job Scheduling, Cooperation and Control," Discussion Paper 2004-65, Tilburg University, Center for Economic Research.
  10. 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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