Sequencing games with repeated players |
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Authors: | Arantza Estévez-Fernández Peter Borm Pedro Calleja Herbert Hamers |
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Institution: | (1) Department of Econometrics and OR, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands;(2) P.O. Box 90153, 5000 LE Tilburg, The Netherlands;(3) Department of Economic, Financial, and Actuarial Mathematics, University of Barcelona, Av. Diagonal 690, 08034 Barcelona, Spain |
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Abstract: | Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a
player may have more than one job to be processed, so called RP(repeated player) sequencing situations. In max-RP sequencing
situations it is assumed that each player’s cost function is linear with respect to the maximum completion time of his jobs,
whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both
classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all
players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing
games. Moreover, it is seen that min-RP sequencing games are convex.
We thank two referees for their valuable suggestions for improvement.
Financial support for P. Calleja has been given by the Ministerio de Educación y Ciencia and FEDER under grant SEJ2005-02443/ECON,
and by the Generalitat de Catalunya through a BE grant from AGAUR and grant 2005SGR00984. |
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Keywords: | Cooperative game theory Sequencing Equal gain splitting Core Convexity |
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