1. Proceedings
  2. I3M
  3. 2018
  4. MAS
  5. 10.46354/i3m.2018.mas.011

Categoric simulation of production flows

  • a David Kruml , 
  • b  Jan Paseka   
  • a,b Department of Mathematics and Statistics, Masaryk University Kotlárská 2, 611 37 Brno, Czech Republic
Cite as
Kruml D., Paseka J. (2018). Categoric simulation of production flows. Proceedings of the 17th International Conference on Modeling & Applied Simulation (MAS 2018), pp. 68-75. DOI: https://doi.org/10.46354/i3m.2018.mas.011

Abstract

We develop a notion of categoric simulation of production flows. The flowis geometrically depicted as a certain subset in three modes (dimensions)—mass, space, and time. Each of the modes could be organized to a tree structure. We want to see the modes by means of an abstract mathematical notion—a category—which naturally captures the hierarchical/net structure of a mode even that it could be very complex. As a highly abstract notion, categoric simulation provides a broad perspective on simulation as something that can be developed and changed and thus has the ability to be a fundamental method of representing flows. We argue that this methodology has the potential of providing elegant, simple, and efficient solutions to problems arising in the manufacturing, as well as other applications concerning multivalued or varying flows in nets.

References

  1. Abramsky S., Coecke B., 2004. A Categorical Semantics of Quantum Protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415–425. 17-17 July 2004, Turku (Finland).
  2. Al-Turki O., Ayar T., Yilbas B. S., Sahin A. Z., 2014. Integrated Maintenance Planning in Manufacturing Systems. Cham: Springer International Publishing.
  3. Birkhoff G., von Neumann J., 1936. The logic of quantum mechanics. The Annals of Mathematics, 37 (2), 823–843.
  4. Baez J.C., Fong B., 2016. A compositional framework for passive linear networks. arXiv preprint arXiv:1504.05625. Available from: https://arxiv.org/pdf/1504.05625.
  5. Bonchi F., Sobocinski P., Zanasi F., 2017. The Calculus of Signal Flow Diagrams I: Linear relations on streams. Information and Computation 252, 2–29.
  6. Cazanescu V.-E., Stefanescu G., 1990. Towards a new algebraic foundation of flowchart scheme theory. Fundamenta Informaticae 13, 171–210.
  7. Choi B. K., Kang D., 2013. Modeling and Simulation of Discrete-Event Systems. Hoboken, New Jersey: John Wiley & Sons, Inc.
  8. Coecke B., Paquette É. O., 2011. Categories for the practising physicist. In: Coecke B., ed. New Structures for Physics. Berlin: Springer, Lecture Notes in Physics, vol. 813, 173–286.
  9. Meseguer J., Montanari U., 1990. Petri nets are monoids. Information and Computation 88, 105–155.
  10. Negahban A., Smith J., 2014. Simulation for manufacturing system design and operation: Literature review and analysis. Journal of Manufacturing Systems 33 (2), 241–261.
  11. Shanker K., Srinivasulu A., 1989. Some solution methodologies for loading problems in a flexible manufacturing system. International Journal of Production Research 27 (6), 1019-1034.
  12. Tanchoco J., 1994. Material flow systems in manufacturing. Dordrecht: Springer.