• Application of an optimization...

Treffer: Application of an optimization problem in Max-Plus algebra to scheduling problems

Title:
Application of an optimization problem in Max-Plus algebra to scheduling problems
Authors:
BOUQUARD, J.-L, LENTE, C, BILLAUT, J.-C
Source:
International Symposium on Combinatorial Optimization CO'02Discrete applied mathematics. 154(15):2064-2079
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 25 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Sciences appliquees, Applied sciences, Recherche operationnelle. Gestion, Operational research. Management science, Recherche opérationnelle et modèles formalisés de gestion, Operational research and scientific management, Optimisation. Problèmes de recherche, Optimization. Search problems, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Logiciel, Software, Performances des systèmes informatiques. Fiabilité, Computer systems performance. Reliability, Algèbre max plus, Max plus algebra, Algebra max plus, Borne inférieure, Lower bound, Cota inferior, Borne supérieure, Upper bound, Cota superior, Informatique théorique, Computer theory, Informática teórica, Machine unique, Single machine, Máquina única, Matrice triangulaire, Triangular matrix, Matriz triangular, Méthode optimisation, Optimization method, Método optimización, Ordonnancement, Scheduling, Reglamento, Problème NP difficile, NP hard problem, Problema NP duro, Temps polynomial, Polynomial time, Tiempo polinomial, Algorithme polynomial, Algorithme test, Flow shop, Max-Plus algebra, Optimization
Document Type:
Konferenz Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Laboratoire d'Informatique, Université François Rabelais de Tours, Ecole Polytechnique de l'Université de Tours, 64 avenue Jean Portalis, 37200 Tours, France
ISSN:
0166-218X
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18159566
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics

Operational research. Management
Accession Number:
edscal.18159566
Database:
PASCAL Archive

Weitere Informationen

The problem tackled in this paper deals with products of a finite number of triangular matrices in Max-Plus algebra, and more precisely with an optimization problem related to the product order. We propose a polynomial time optimization algorithm for 2 × 2 matrices products. We show that the problem under consideration generalizes numerous scheduling problems, like single machine problems or two-machine flow shop problems. Then, we show that for 3 x 3 matrices, the problem is NP-hard and we propose a branch-and-bound algorithm, lower bounds and upper bounds to solve it. We show that an important number of results in the literature can be obtained by solving the presented problem, which is a generalization of single machine problems, two- and three-machine flow shop scheduling problems. The branch-and-bound algorithm is tested in the general case and for a particular case and some computational experiments are presented and discussed.