Eur. Phys. J. B 84, 501-520 (2011)
https://doi.org/10.1140/epjb/e2011-10894-6

Regular Article

Structure-preserving model reduction of large-scale logistics networks

Applications for supply chains

¹ BIBA - Bremer Institut für Produktion und Logistik GmbH, University of Bremen, Hochschulring 20, 28359 Bremen, Germany
² Institute for Mathematics, University of Würzburg, Emil-Fischer-Str. 40, 97074 Würzburg, Germany
³ Department of Civil Engineering, University of Applied Sciences Erfurt, Altonaer Str. 25, 99085 Erfurt, Germany
⁴ Center of Industrial Mathematics, University of Bremen, 28334 Bremen, Germany

^a e-mail: wirth@mathematik.uni-wuerzburg.de

Received: 18 November 2010
Received in final form: 14 May 2011
Published online: 17 August 2011

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.