Title: Shared resources in production systems: (max,+) analysis

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 ℤ_max dioid, even though the original systems are not ℤ_max 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.

DOI: 10.1504/IJMOR.2011.038907

International Journal of Mathematics in Operational Research, 2011 Vol.3 No.2, pp.125 - 147

Published online: 12 Feb 2015 *

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