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The European Physical Journal B

, Volume 84, Issue 4, pp 501–520 | Cite as

Structure-preserving model reduction of large-scale logistics networks

Applications for supply chains
  • B. Scholz-Reiter
  • F. WirthEmail author
  • S. Dashkovskiy
  • T. Makuschewitz
  • M. Schönlein
  • M. Kosmykov
Regular Article Focus Section on Frontiers in Network Science: Advances and Applications

Abstract

We investigate the problem of model reduction with a view to large-scale logistics networks, specifically supply chains. Such networks are modeled by means of graphs, which describe the structure of material flow. An aim of the proposed model reduction procedure is to preserve important features within the network. As a new methodology we introduce the LogRank as a measure for the importance of locations, which is based on the structure of the flows within the network. We argue that these properties reflect relative importance of locations. Based on the LogRank we identify subgraphs of the network that can be neglected or aggregated. The effect of this is discussed for a few motifs. Using this approach we present a meta algorithm for structure-preserving model reduction that can be adapted to different mathematical modeling frameworks. The capabilities of the approach are demonstrated with a test case, where a logistics network is modeled as a Jackson network, i.e., a particular type of queueing network.

Keywords

Arrival Rate Model Reduction Vertex Versus Logistics Network Candidate List 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • B. Scholz-Reiter
    • 1
  • F. Wirth
    • 2
    Email author
  • S. Dashkovskiy
    • 3
  • T. Makuschewitz
    • 1
  • M. Schönlein
    • 2
  • M. Kosmykov
    • 4
  1. 1.BIBA — Bremer Institut für Produktion und Logistik GmbHUniversity of BremenBremenGermany
  2. 2.Institute for MathematicsUniversity of WürzburgWürzburgGermany
  3. 3.Department of Civil EngineeringUniversity of Applied Sciences ErfurtErfurtGermany
  4. 4.Center of Industrial MathematicsUniversity of BremenBremenGermany

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