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@PHDTHESIS{Ziegler:210495,
      author       = {Ziegler, Ute},
      othercontributors = {Herty, Michael},
      title        = {{M}athematical modelling, simulation and optimisation of
                      dynamic transportation networks : with applications in
                      production and traffic},
      address      = {Aachen},
      publisher    = {Publikationsserver der RWTH Aachen University},
      reportid     = {RWTH-CONV-143622},
      pages        = {IV, 172 S. : graph. Darst.},
      year         = {2012},
      note         = {Prüfungsjahr: 2012. - Publikationsjahr: 2013; Aachen,
                      Techn. Hochsch., Diss., 2012},
      abstract     = {In this work we provide a general classification of dynamic
                      transportation networks (DTNs), which represent macroscopic
                      PDE/ODE-based descriptions of network flow problems. There
                      is a broad variety of versions depending on the application;
                      for example it is possible to model buffers, where particles
                      can be stored. Furthermore, we can describe the evolution of
                      density by conservation laws and model different kinds of
                      coupling conditions. Afterwards we consider optimisation
                      techniques. We discuss the advantages of mixed integer
                      optimisation and presented a general strategy how DTNs can
                      be transformed into linear mixed-integer optimization
                      Problems (short MIPs). Furthermore, we show how the
                      knowledge of the problem structure can be used to introduce
                      bounding heuristics which are extremely efficient to speed
                      up the optimisation procedure. Within this frame, we present
                      specific models with application in production and traffic.
                      The first is a novel production model for the time-changing
                      repair worker assignment. The main idea is to keep the
                      system performance optimal whenever machines have failed and
                      must be repaired. In general, available workers are limited
                      and therefore a decision has to be made on which machines
                      are repaired first. The resulting optimisation question is
                      how the optimal worker schedule looks like to maximise the
                      production flow. This issue is intensively analysed and
                      numerical case studies comparing fixed and time-changing
                      schedules are presented. The numerical results show the
                      different opportunities of our modelling approach. With
                      respect to the second application, we consider the LWR-based
                      traffic flow network model. We show how coupling conditions
                      of several junction types can be transformed into easily
                      linearisable min-terms. We introduce a numerical framework
                      for the Hamilton-Jacobi formulation of traffic flow and show
                      how this correctly resolves the dynamics at the junction. We
                      present simulations for a roundabout and compare them with
                      existing results and computed travel times for certain
                      routes through the network depending on the starting time of
                      the travel. Moreover, we model traffic light settings for
                      LWR-based traffic flow networks that can easily be adapted
                      to arbitrary junction types and network topologies and
                      discuss requirements for secure traffic light settings. We
                      show the necessity of additional requirements on the
                      switching time rate to avoid inapplicably frequent
                      fluctuations which appear when mixed integer optimisation
                      techniques are used, and solve this problem with previously
                      derived techniques. Furthermore, we use the knowledge of the
                      problem structure to develop bounding heuristics to speed up
                      the optimisation process by providing feasible solutions for
                      the subproblems within the $Branch\&Bound$ procedure. The
                      resulting improvements for the optimisation procedure are
                      remarkable and indicate the potential of combining
                      simulation techniques with Branch $\&$ Bound procedures.},
      keywords     = {Gemischt-ganzzahlige Optimierung (SWD) / Netzwerk (SWD) /
                      Dynamik (SWD) / Mathematische Modellierung (SWD) / Heuristik
                      (SWD)},
      cin          = {110000 / 114620},
      ddc          = {510},
      cid          = {$I:(DE-82)110000_20140620$ / $I:(DE-82)114620_20140620$},
      shelfmark    = {35R02 * 90B20 * 90B30 * 35Q93 * 90C57},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-opus-44522},
      url          = {https://publications.rwth-aachen.de/record/210495},
}