This paper presents a new type of Petri nets : Batches Petri nets. This model, extension of Hybrid Petri nets, allows to integrate a formalisation of parts circpIatioa on accumulation conveyors. The Batches Petri net ir defined with the introduction of a new kind of place and of transition : the batch place and the batch transition. Evolution ruler are determined in order to do the simulation of systems composed by accumulation phenomena L INTRODUCTIONPetri nets are powerful tools, to modelise and to simulate mandacturing systems. The introduction of the notion of parts flow in a such tool, allows to define Hybrid Petri nets [ 11. This modelling tool combines the advantages of discrete Petri nets and those of the continuous petri nets. It can represent high throughput manufkming system, in which the quantity of parts is assimilated with a continuous real flow. To optimise line productivity, it is necessary to study the parts flow circulating between machines. This parts flow depends on the machines state, variations of element speed, and especially on the transient behaviour of accumulation conveyors (elements which assume transport and storage).Batches Petri nets, extension of Hybrid Petri nets, are defined, in order to represent transient behaviour of accumulation conveyors. By the notion of internal coherent batch, in other words by a set of parts with the same density of repartition, they introduce a mathematical formalisation of the parts flow circulation on accumulation conveyors. This formalisation is associated with a new kind of nodes, named batch nodes.After a brief presentation of the Hybrid Petri nets interest, Batches Petri nets are presented. The formalisation of timed Batches Petri nets is defined. The evolution rules, conditions of firing and evolution graph are described, in order to simulate the behaviour of systems composed by accumulation elements. An example is studied to show the cvolution of a Batches Petri net. INTEREST OF HYBRID PETRI NETSThe main interest of Hybrid Petri nets is that they combine the advantages of Continuous Petri nets for the representation of flows and those of Discrete Petri nets for the representation of process contrc!s (failures, decisions,. ..) [2]. In Continuous Petri nets, the number of states changing 607 to be W e d during simulation is not only, smaller than that ofthe cocresponding discrete model, but it is also minimum. It contains the necessary minimum amount of information to describe the state of the system. Their theoretical intenst is the study of the system's comportment and its simulation.The timed Hybrid Petri nets, by their discrete approach, can modelk a machine's failure with an associ8std delay, for example. Their continuous approach allows, in the case of a manufecturing system, for example, to deterrmne the input and output flows of the elements [3].Despite the advantages of Hybrid FW, they are not powerful enough to modelise the comportment of free transfer conveyors in transient behaviour.A first modelisation of conveyor belts based on thi...

This article presents a Verification and Validation approach which is used here in order to complete the classical tool box the industrial user may utilize in Enterprise Modeling and Integration domain. This approach, which has been defined independently from any application domain is based on several formal concepts and tools presented in this paper. These concepts are property concepts, property reference matrix, properties graphs, enterprise modeling domain ontology, conceptual graphs and formal reasoning mechanisms.

An efficient Binary Search-based approach used to determine the sets of human resources allowing one to reach, for an enterprise process, a given performance level is presented. It is based on an enterprise process performance methodology integrating human skill influence. In a first step, this approach is compared with algorithms such as Hybrid Taboo-Descent, Simulated Annealing and Knapsack algorithms for different performance points of view (temporal, financial, quality oriented) on limited and large complexity examples. In a second step, this approach is generalized to integrate simultaneously several viewpoints.

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The aim of this paper is to propose and apply a verification and validation approach to Enterprise Modeling that enables the user to improve the relevance and correctness, the suitability and coherence of a model by using properties specification and formal proof of properties.