Skip to Main content Skip to Navigation

Modélisation de conflits et calcul de bornes dans les systèmes de production par la théorie des dioïdes

Abstract : Flow-shops are manufacturing deterministic systems which can be analytically modelled in a fairly easy way, in a dioid algebraic structure. Dioids are endowed with operations mostly based on synchronisation and delay phenomenon, which leads to a linear model. Nevertheless, production systems consist of an increasing number of heterogeneous and interacting elements, which turns them into job-shops. These interactions are sometimes conflicts; therefore, an analytical model cannot be designed any more. Not considering accurately a system with conflicts, but rather thanks to its extremal behaviours, the former can be modelled in an approximated way, which turns to be linear modelling in a dioid of intervals. Provided the use of appropriate shared resources assignment rules and routing policies, we define linear models of those sections. We give an approximated model, in a dioid of intervals, of those complex systems, which allows for using dioid algebraic structure theory contributions. Besides, discrete event dynamic systems, and in particular production systems, are often depicted by Petri nets. We define in this thesis the semantics of a particular sub-class of Petri nets: timed event graphs with time uncertainties, which correspond to systems of relations expressed in a dioid of intervals. Finally, our contribution allows for the study of some job-shops, while it was only possible to study flow-shops.
Complete list of metadatas
Contributor : Olivier Boutin <>
Submitted on : Thursday, July 15, 2010 - 6:55:46 PM
Last modification on : Tuesday, May 7, 2019 - 6:30:06 PM
Long-term archiving on: : Friday, October 22, 2010 - 11:52:56 AM


  • HAL Id : tel-00502840, version 1


Olivier Boutin. Modélisation de conflits et calcul de bornes dans les systèmes de production par la théorie des dioïdes. Modélisation et simulation. Ecole Centrale de Nantes (ECN), 2009. Français. ⟨tel-00502840⟩



Record views


Files downloads