Authors: Olivier Boutin, Bertrand Cottenceau, Jean Jacques Loiseau, Anne L'Anton
Addresses: IRCCyN, UMR CNRS 6597, 1 rue de la Noe, BP 92101, 44321 Nantes Cedex 03, France. ' LISA, EA 4094, 62 avenue, Notre Dame du Lac, 49000 Angers, France. ' IRCCyN, UMR CNRS 6597, 1 rue de la Noe, BP 92101, 44321 Nantes Cedex 03, France. ' IRCCyN, UMR CNRS 6597, 1 rue de la Noe, BP 92101, 44321 Nantes Cedex 03, France
Abstract: This paper deals with formal modelling of Petri nets including shared resources. These phenomena appear widely in the production management context, for the modelling of manufacturing cells. But, they usually cannot be formally represented in dioid algebraic structures based on sets of scalars. In this paper, we design a method to describe such a phenomenon in a dioid of intervals. In fact, the resource-sharing problem is turned into a time uncertainty problem, regarding the access to the shared resource. In this new problem, time uncertainties are bounded and can be described by intervals. Both bounds of the behaviours of the studied production systems can be manipulated in the scope of the ℤmax dioid, even though the original systems are not ℤmax linear by essence.
Keywords: discrete event systems; conflicts; job shops; shared resources; modelling; Petri nets; pseudo-periodic assignment policy; dioids; (max,+) linear systems; interval analysis; production management; manufacturing cells.
International Journal of Mathematics in Operational Research, 2011 Vol.3 No.2, pp.125 - 147
Available online: 06 Mar 2011 *Full-text access for editors Access for subscribers Purchase this article Comment on this article