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Généralisation Max-Plus des bornesde Lageweg, Lenstra et Rinnooy Kan

Published online by Cambridge University Press:  15 March 2004

Christophe Lenté
Affiliation:
Laboratoire d'Informatique de l'Université de Tours, Polytecth'Tours/DI.
Jean-Louis Bouquard
Affiliation:
Laboratoire d'Informatique de l'Université de Tours, Polytecth'Tours/DI.
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Abstract

Le traditionnel problème d'ordonnancement de type flowshop se généralise en un problème d'optimisation matricielle dansl'algèbre Max-Plus. Une famille de bornes inférieures est présentée pour ce nouveau problème et la preuve est apportée que ces bornes généralisent les bornes de Lageweg et al.

Type
Research Article
Copyright
© EDP Sciences, 2003

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References

F. Baccelli, G. Cohen, G. Olsder and J.P. Quadrat, Synchronisation and Linearity: An Algebra for Discrete Event Systems. John Wiley and Sons, New York (1992).
Baker, K.R., Scheduling groups of jobs in the two machine flow shop. Math. Comput. Modeling 13 (1990) 29-36. CrossRef
Blyth, T.S., Matrices over ordered algebraic structures. J. Lond. Math. Soc. 39 (1964) 427-432 . CrossRef
T.S. Blyth and M.F. Janowitz, Residuation Theory. Pergamon Press (1972).
Cetinkaya, F.C., Lot streaming in a two stage flow shop with setup, processing and removal times separated. J. Oper. Res. Soc. 45 (1994) 1445-1455. CrossRef
Cohen, G., Dubois, D., Quadrat, J.P. and Viot, M., A linear system-theoretic view of discret-event processes and its use for performance evaluation in manufacturing. IEEE Trans. Autom. Control 30 (1985) 210-220 . CrossRef
Dar-Li, Y. and Maw-Sheng, C., Two-machine flowshop group scheduling problem. Comput. Oper. Res. 27 (2000) 75-985.
Garey, M.R., Johnson, D.S. and Sethi, R., The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1 (1976) 117-129 . CrossRef
S. Gaubert, Théorie des systèmes linéaires dans les dioïdes. Thèse de doctorat, École des mines de Paris (1992).
Gaubert, S. and Mairesse, J., Modeling and analysis of timed petri nets using heaps of pieces. IEEE Trans. Autom. Control 44 (1999) 683-698 . CrossRef
B. Giffler, Schedule algebras and their use in formulating general systems simulations, in Industrial scheduling. Muth and Thompson, Prentice Hall, New Jersey, USA (1963).
M. Gondran and M. Minoux, Graphes et algorithmes. Eyrolles, Paris, 3 e edn. (1995).
J. Gunawardena, Idempotency. Publications of the Newton Institute, Cambridge University Press (1998).
C. Hanen and A. Munier, Cyclic scheduling on parallel processors: An overview, in Scheduling Theory and its Applications, edited by P. Chretienne, E. Coffman, J. Lenstra and Z. Liu. John Wiley (1995) 193-226.
Jackson, J.R., An extention of johnson's results on job-lot scheduling. Naval Res. Log. Quart. 3 (1956) 201-203. CrossRef
Johnson, S.M., Optimal two- and three-stage production schedules with setup times included. Naval Res. Log. Quart. 1 (1954) 61-68. CrossRef
Lageweg, B.J., Lenstra, J.K. and Rinnooy Kan, A.H.G., A general bounding scheme for the flow-shop problem. Oper. Res. 26 (1978) 53-67. CrossRef
C. Lenté, Analyse Max-Plus de problèmes d'ordonnancement de type Flowshop. Thèse de doctorat, Université François Rabelais, Tours (novembre 2001).
C. Lenté and J.C. Billaut, Une application des algèbres tropicales aux problèmes d'ordonnancement de type flowshop, in MOSIM'99, Annecy, France (octobre 1999) 177-182.
C. Lenté, J.C. Billaut and J.L. Bouquard, Modélisation unifiée de flowshops à deux machines, in conférence francophone de modélisation et simulation, (MOSIM'01), Troyes, France (avril 2001) 599-603.
C. Lenté, J.C. Billaut and J.L. Bouquard, Max-plus generalization of a flowshop problem lower and upper bounds, in (INCOM'01), Vienne, Autriche (sept. 2001).
C. Lenté, F. Chevaleyre and N. Neel, Flowshops et minimisation de produits matriciels max+, in 3 e journées francophone de recherche opérationnelle, (FRANCORO'01), l'aide à la décision pour l'amélioration de la performance, Québec, Canada (mai 2001) 599-603.
Mitten, L.G., Sequencing n jobs on two machines with arbitrary time lags. Manage. Sci. 5 (1959) 293-298 . CrossRef
I. Nabeshima and S. Maruyama, A note on the two-machine flow shop scheduling problem with separated setup and cleanup times, time lags and transportation times. Rep. Univ. Electro-com 34 (1983).
Sequencing, D.R. Sule n jobs on two machines with setup, processing and removal times separated. Naval Res. Log. Quart. 29 (1982) 517-519.
Yoshida, T. and Hitomi, K., Optimal two-stage production scheduling with setup times separated. AIIE Transactions 11 (1979) 261-263. CrossRef