Jahresbericht 2009 - Biba - Universität Bremen

Stability, Robustness and Approximation of DynamicLarge-Scale Networks – Theory and Applications inLogistics NetworksMore people than ever beforetravel in our global world to far awayplaces in less time. This continuouslinking leads to transportation networksthat benefit the worldwideflow of commodities as well. Oftenproducts pass manufacturing sites indifferent countries and travel severalthousand kilometres, before reachingtheir client. On their journey theymove in complex logistics networks.Job of these networks is to procureraw materials worldwide, to openlocal cost advantages by distributedproduction and assembly sites,to integrate partners with excellentexpertises and to finally deliver theproducts to the customer. The mostimportant aspect, however, is thecreation of a sustainable and competitiveoperation.The control of the dynamics of acomplex, large-scale logistics networkposes a challenging job. For instance,not kept transportation timeslead to late pickup or delivery dates.One reason for this is traffic congestion.Traffic jams and building sitesmake it necessary to chose longeralternative routes or generate waitingtimes. On the other hand, perturbationsof production processes canalso negatively affect the whole logisticssystem. More and more complicatedand specified machines leadto a high dependence on single resources.Due to this dependence anunscheduled repair of a single resourcecan lead to delays of the supplydates of customer orders as well asto delays in transportation. Nevertheless,supply difficulties are alsocaused by an astonishing increaseof customer demands for a product.A successful advertising campaignor political decisions can be thetrigger. Thus an upcoming increasein the value added tax animatespeople to hamster purchases. Asidefrom transport and production processes,the structure is also subjectto dynamic influences. Experiencedpartners might leave the networkand new partners join it.In many respects, methods andtools for stability analysis and controlare missing. This deficit is addressedby the interdisciplinary research project„ Stability, Robustness and Approximationof Dynamic Large-ScaleNetworks – Theory and Applicationsin Logistics Networks” The engineeringsciences are represented by theworking group around Prof. Dr.-Ing.Scholz-Reiter at BIBA and mathematicsby two working groups of Prof.Dr. Fabian Wirth at the University ofWürzburg and Dr. Sergey Dashkovskiyfrom the centre of industrial mathematicsat the University of Bremen.The interdisciplinary approach to thebasic research project permits lookingat the problems from a quantitativeand qualitative point of view.In order to carry out stabilityanalysis, suitable modelling methodsare created. Large-scalelogistics networks can be modelledas directed graphs. In this case,nodes and edges are characterisedby individual dynamics. Due to theirlarge size, these comprehensivemodels are quite hard to analyseand often hardly accessible to investigations.For this reason, a methodfor model reduction will be developedthat preserves the behaviourof the original network. The modelreduction is based on a ranking ofimportance of single locations forthe entire network as well as on thetopology of the original network. Thereduced models form the basis forthe following stability analysis. For thispurpose, stability criteria for nominaland disturbed networks are developed.This process is accompaniedby simulation-based investigations.Not only is the stability of a logisticsnetwork important, but also its robustness.In this context, robustness definesthe kind and the magnitude ofthe smallest disturbance that leadsto an unstable state of the network.On the basis of the obtained results,different management principles willbe developed. These should help inavoiding vulnerable network structures,to carry out suitable capacityallocations and to control any perturbations.Thomas Makuschewitz23