Commande sous contraintes temporelles des réseaux de graphes d'événements temporisés en conflit

International audienceDans ce papier, nous abordons le problème de modélisation et de commande des systèmesàévénements discrets avec des ressources partagées représentés par une classe particulière des réseaux de Petri temporisés. Précisément, nous considérons des Réseaux de Graphes d'Evénements Temporisés en Conflit (RGETC) soumisà des contraintes tem-porelles strictes. Premièrement, une formalisation algébrique en termes de systèmesà com-mutation Max-Plus est proposée pour décrire le comportement dynamique des RGETCs. Deuxièmement, des lois de commande en boucle fermée sont calculées pour garantir le respect de ces contraintes de temps imposéesà certaines places du réseau. Des conditions suffisantes pour l'existence de telles lois de commande ontété fournies. Finalement, nous appliquons les résultats théoriques développés précédemment pour contrôler un système ferroviaire de croisement de trainà temps critique

Manufacturing Systems Line Balancing using Max-Plus Algebra

In today\u27s dynamic environment, particularly the manufacturing sector, the necessity of being agile, and flexible is far greater than before. Decision makers should be equipped with effective tools, methods, and information to respond to the market\u27s rapid changes. Modelling a manufacturing system provides unique insight into its behavior and allows simulating all crucial elements that have a role in the system performance. Max-Plus Algebra is a mathematical tool that can model a Discrete Event Dynamic System in the form of linear equations. Whereas Max-Plus Algebra was introduced after the 1980s, the number of studies regarding this tool and its applications is fewer than regarding Petri Nets, Automata, Markov process, Discrete Even Simulation and Queuing models. Consequently, Max-Plus Algebra needs to be applied and tested in many systems in order to explore hidden aspects of its function and capabilities. To work effectively; the production/assembly line should be balanced. Line balancing is one of the manufacturing functions that tries to divide work equally across the production flow. Car Headlight Manufacturing Line as a Discrete Manufacturing System is considered which is a combination of manufacturing and assembly lines composed of different stations. Seven system scenarios were modeled and analyzed using Max-Plus to balance the car headlights production line. Key Performance Indicators (KPIs) are used to compare the various scenarios including Cycle Time, Average Deliver Rate, Total Processing Lead Time, Stations\u27 Utilization Rate, Idle Time, Efficiency, and Financial Analysis. FlexSim simulation software is used to validate the Max-Plus models results and its advantages and drawbacks compared with Max-Plus Algebra. This study is a unique application of Max-Plus Algebra in line balancing of a manufacturing system. Moreover, the problem size of the considered model is at least twice (12 stations) that of previous studies. In the matter of complexity, seven different scenarios are developed through the combination of parallel stations and buffers. Due to that the last scenario is included four parallel stations plus two buffers Based on the findings, the superiority of scenario 7 compared to other scenarios is proved due to its lowest system delivering first output time (14 seconds), best average delivery rate (24.5 seconds), shortest cycle time (736 seconds), shortest total processing lead time (11,534 seconds), least percentage of idle time (12%), lowest unit cost ($6.9), and highest efficiency (88%). However, Scenario 4 has the best utilization rate at 75%