Dynamic Large-Scale Logistics Networks
Working Group: | Former AWG Mathematical Modeling of Complex Systems |
Leadership: | Prof. Dr. Sergey Dashkovskiy |
Processor: | Dr. Mykhaylo Kosmykov |
Funding: | Volkswagen Stiftung |
Project partner: |
Institut für Mathematik, Universität Würzburg BIBA, Bremer Institut für Produktion und Logistik GmbH (BIBA) |
Time period: | 01.01.2008 - 31.12.2010 |
Modern logistics networks are usually geographically distributed and have a complex and large-scale structure. The dynamics of material and information flows in such networks is mostly nonlinear and is influenced by internal and external perturbations. The mathematical modelling of logistics networks facilitates the analysis and prediction of properties relevant to the economy. In this interdisciplinary research project such networks are investigated from the standpoint of stability and approximation theory, in cooperation with the Bremen Institute for Production and Logistics (BIBA) and the Institute of Mathematics, University of Würzburg. This includes as an integral part the inclusion of a scenario from the practice of a pump set manufacturer.
During the investigations various mathematical models were created for networks. These models connect the structure of the logistics network with the dynamical systems by describing dynamic processes taking place in the nodes and edges. The nodes represent individual locations of the network such as suppliers, production and distribution sites, and customers. Based on the edges between the nodes, the transport connections are shown.
Stability properties of such networks are analyzed in the framework of the so-called input-to-state stability (ISS). To this end, stability criteria for continuous systems with mixed formulation and ISS for hybrid systems have been developed. These criteria are based on the structure of the networks and were accompanied by simulation-based studies.
In addition to the stability of a logistics network, its robustness is an important property that has been studied in this project as well. In this context, the robustness is the nature and extent of the smallest disturbance that makes the network unstable.
Due to its size, the models for research are often difficult to access. Therefore, a method was developed for model reduction that preserves the original behavior of the network. Basis for the reduction are a ranking of the importance of each node for the whole network and the topology of the original network. The idea is to exclude the nodes with a small rank of the model or to aggregate them with the other nodes. The reduced models form the basis for the subsequent stability investigation. Currently is being explored the relationship between the stability properties of the reduced and original models.
Publications
- S. Dashkovskiy, M. Kosmykov.
A Lyapunov-Razumikhin approach for stability analysis of logistics networks with time-delays.
International Journal of Systems Science, 43(5), 845–853, Taylor & Francis, 2012.DOI: 10.1080/00207721.2010.528179
online at: http://www.tandfonline.com/doi/pdf/10.1080/00207721.2010.528179 - S. Dashkovskiy, M. Kosmykov, F. Wirth.
A small gain condition for interconnections of ISS systems with mixed ISS characterizations.
IEEE Transactions on Automatic Control, 56(6):1247-1258, 2011.online at: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5585718&tag=1
- B. Scholz-Reiter, F. Wirth, S. Dashkovskiy, M. Schönlein, T. Makuschewitz, M. Kosmykov.
Structure-preserving model reduction of large-scale logistics networks - applications for supply chains.
The European Physical Journal B , 84(4):501-520, Springer Verlag, 2011. - M. Kosmykov.
Hybrid dynamics in large-scale logistics networks.
Dissertationsschrift, Universität Bremen, 2011.online at: http://nbn-resolving.de/urn:nbn:de:gbv:46-00102276-18
- B. Scholz-Reiter, S. Dashkovskiy, F. Wirth, M. Schönlein, M. Kosmykov, T. Makuschewitz.
A comparison of mathematical modelling approaches for stability analysis of supply chains.
International Journal of Logistics Systems and Management, 10(2):208-223, 2011. - S. Dashkovskiy, H. Ito, F. Wirth.
On a small gain theorem for ISS networks in dissipative Lyapunov form.
European Journal of Control, 17(4):357-365, 2011.online at: http://ejc.revuesonline.com/article.jsp?articleId=16472
- S. Dashkovskiy, M. Görges, M. Kosmykov, A. Mironchenko, L. Naujok.
Modeling and stability analysis of autonomously controlled production networks.
Logistics Research, 3(2):145-157, Springer Verlag, 2011.DOI: 10.1007/s12159-011-0049-6
online at: http://www.springerlink.com/content/12nm645q18k27673/ - B. Scholz-Reiter, M. Schönlein, M. Kosmykov, T. Makuschewitz.
A comparison of mathematical modelling approaches for stability analysis of supply chains.
International Conference on Industrial Logistics "Logistics and Sustainability", 08.03.-11.03.2010, Rio de Janeiro, Brazil.
Proceedings of the ICIL 2010, pp. 297-305, 2010. - S. Dashkovskiy, M. Kosmykov.
Input-to-state stability of interconnected hybrid systems.
Zur Veröffentlichung eingereicht. - S. Dashkovskiy, M. Kosmykov, A. Mironchenko, L. Naujok.
Application of the LISS Lyapunov-Krasovskii small-gain theorem to autonomously controlled production networks with time-delays.
Conference on Control and Fault-Tolerant Systems, 06.10.-08.10.2010, Nice, France.
Proceedings of the Conference on Control and Fault-Tolerant Systems, pp. 765-770, 2010. - S. Dashkovskiy, M. Kosmykov, L. Naujok.
ISS of interconnected impulsive systems with and without time-delays.
8th IFAC Symposium on Nonlinear Control Systems, 01.09.-03.09.2010, Bologna, Italy.
Proceedings of the 8th IFAC Symposium on Nonlinear Control Systems, pp. 831-836, 2010. - B. Scholz-Reiter, F. Wirth, S. Dashkovskiy, M. Kosmykov, T. Makuschewitz, M. Schönlein.
Some remarks on stability and robustness of production networks based on fluid models.
2nd International Conference on Dynamics in Logistics, 17.08.-21.08.2009, Bremen, Germany.
To appear in Proceedings of the 2nd International Conference on Dynamics in Logistics, Springer Verlag.online at: http://www.math.uni-bremen.de/zetem/cms/media.php/256/2009-LDIC-fluid.pdf
- S. Dashkovskiy, M. Kosmykov.
Stability of networks of hybrid ISS Systems.
48th IEEE Conference on Decision and Control, 16.12.-18.12.2009, Shanghai, China.
Proceedings of the 48th IEEE Conference on Decision and Control, pp. 3870-3875, 2009.online at: http://www.math.uni-bremen.de/~kosmykov/Publications/2009_CDC_DaKo.pdf
- S. Dashkovskiy, M. Kosmykov, F. Wirth.
A small gain condition for interconnections of ISS systems with mixed ISS characterizations.
European Control Conference 2009, 23.08.-26.08.2009, Budapest, Hungary.
Proceedings of the European Control Conference 2009, pp. 1083-1088, 2009.online at: http://www.math.uni-bremen.de/~dsn/Publications/2009-ECC-DKW-mixed_iss-final.pdf
- B. Scholz-Reiter, F. Wirth, S. Dashkovskiy, M. Kosmykov, T. Makuschewitz, M. Schönlein.
An approach to model reduction of logistic networks based on ranking.
2nd International Conference on Dynamics in Logistics, 17.08.-21.08.2009, Bremen, Germany.
To appear in Proceedings of the 2nd International Conference on Dynamics in Logistics, Springer Verlag.online at: http://www.math.uni-bremen.de/zetem/cms/media.php/256/2009-LDIC-RWDKMS.pdf
- B. Scholz-Reiter, M. Schönlein, F. Wirth, S. Dashkovskiy, T. Makuschewitz, M. Kosmykov.
Application of the PageRank algorithm for ranking locations of a production network.
42nd CIRP Conference on Manufacturing Systems , 03.06.-05.06.2009, Grenoble, France.
Proceedings of the 42nd CIRP Conference on Manufacturing Systems, 2009.online at: http://www.math.uni-bremen.de/zetem/cms/media.php/256/2009-CIRP-RWDMKS.pdf
- S. Dashkovskiy, M. Kosmykov.
Stability analysis of logistics networks with time-delays.
Erscheint in Production Planning & ControlDOI: 10.1080/09537287.2012.659867
online at: http://www.tandfonline.com/doi/abs/10.1080/09537287.2012.659867