Abstract
Cyclic manufacturing systems can be modeled by marked graphs, which are an elementary class of Petri nets. To model systems with bulk services and arrivals and to reduce the size of the model, weighted marked graphs can be used. An important step when designing these systems is the definition of the number of manufacturing resources to be used in order to reach a given productivity. In terms of timed Petri nets, this is known as the marking optimization problem and consists of reaching a given average cycle time while minimizing a linear combination of markings. In this paper, a necessary and sufficient condition to obtain a feasible solution of the marking optimization problem of weighted marked graphs with deterministic times is established. A fast heuristic solution, based on an iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Campos, J., Chiola, 0., and Silva, M. 1991. Ergodicity and throughput bounds of Petri nets with unique consistent firing count vector. IEEE Trans. on Software Engineering 17(2): 117—125.
Chao, D. T., Zhou, M., and Wang, D. T. 1993. Multiple-weighted marked graphs. Proc. IFAC 12th Triennial World Congress, Australia: Sydney. pp. 371—374.
Chrzastowski-Wachtel. P., and Raczunas, M. 1995. Orbits, half-frozen tokens and the liveness of weighted circuits. 'Workshop on structure in concurrency theory and works/sop in computing. Berlin: Springer Verlag, pp. 116—128.
Gaubert, S. 1990. An algebraic method for optimizing resources in timed event graphs, Lecture Notes in Control amid information Sciences, No. 144, Springer Verlag, pp. 957—966.
Laftit, S. Proth, J. M., and Xie, X. 1992. Optimization of semiflow criteria for event graphs. IEEE Trans. on Automatic Control37(5): 547—555.
Munier, A. 1993. Régime asymptotique optimal dun graphe d'événements temporisé genéralisé—Applicatton un problème d'assemblage. RAIRO 27: 487—513.
Munier, A. 1996. The basic cyclic scheduling problem with linear precedence constraints. Discrete Applied Mathematics 64: 219—238.
Murata, T. 1989. Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4): 541—580.
Proth, E. M., Sauer, N., Wardi, Y., and Xie, X. 1996. Marking optimization of stochastic timed event graphs using WA. Discrete Es'ent Dynamic Systems 6: 221—239.
Proth, J. M., Sauer, N., and Xie. X. 1997a. Optimization of the number of transportation devices in a flexible manufacturing system using event graphs. IEEE Traits, on Industrial Electronics 44(3): 298—306.
Proth, J. M., and Xie, X. 1997b. Petri Nets: A tool for design and nianagement of manufacturing systems. John Wiley & Son (Ed.).
Silva, M. Ed Valette, R. 1989. Petri nets and flexible manufacturing. Advances in Petri Nets 1989. G. Rozenberg (ed.), Lecture Notes of Computer Science, Spnnger Verlag, pp. 374—417.
Teruel. E., Chrzastowski. P., olom, E. M., and Silva. M. 1992. On Weighted T-Systems. Lecture Notes in Computer Science, 616, 13th International Conference on Applications and Theory of Petri Nets. Sheffield, 348—367.
Valentin, C. 1994. Modeling and analysis methods for i class of hybnd dynamic systems. Proc. of Syniposiunim ADP-22294, Brussels, 22 1—226.
Xie, X. L. 1993. On the impact of randomness in production lines controlled by kanbans. Proc. of the Seond European Control C'onference, The Netherlands: Groningen, 158—163.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sauer, N. Marking Optimization of Weighted Marked Graphs. Discrete Event Dynamic Systems 13, 245–262 (2003). https://doi.org/10.1023/A:1024055724914
Issue Date:
DOI: https://doi.org/10.1023/A:1024055724914