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Proportionate flow shop games

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Author Info
Estevez-Fernandez, Arantza
Mosquera, Manuel A.
Borm, Peter
Hamers, Herbert (Tilburg University, Center for Economic Research)

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

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

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

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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. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Hamers, H. & Borm, P. & Tijs, S., 1993. "A Games Corresponding to Sequencing Situations with Ready Times," Papers 9316, Tilburg - Center for Economic Research.
  4. Hamers, H. & Klijn, F. & Suijs, J., 1998. "On the balancedness of m-sequencing games," Discussion Paper 17, Tilburg University, Center for Economic Research. [Downloadable!]
  5. Estevez-Fernandez, & Borm, P.E.M. & Calleja, P. & Hamers, H.J.M., 2004. "Sequencing games with repeated players," Discussion Paper 128, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Calleja, P. & Borm, P. & Hamers, H., 2001. "On a new class of parallel sequencing situations and related games," Discussion Paper 3, Tilburg University, Center for Economic Research. [Downloadable!]
  7. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June. [Downloadable!] (restricted)
  8. Calleja, P. & Estevez-Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2004. "Job scheduling, cooperation, and control," Discussion Paper 65, Tilburg University, Center for Economic Research. [Downloadable!]
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