Optimization and Engineering

, Volume 19, Issue 1, pp 71–96 | Cite as

Optimal packing of material flow on conveyor belts

  • Markus Erbrich
  • Simone GöttlichEmail author
  • Marion Pfirsching


We are interested in an optimal packing density problem for material flows on conveyor belts in two spatial dimensions. The control problem is concerned with the initial configuration of parts on the belt to ensure a high overall flow rate and to further reduce congestion. An adjoint approach is used to compare the optimization results from the microscopic model based on a system of ordinary differential equations with the corresponding macroscopic model relying on a hyperbolic conservation law. Computational results highlight similarities and differences of both optimization models and emphasize the benefits of the macroscopic approach.


Optimal packing Material flow Multiscale models Numerical studies 

Mathematics Subject Classification

49J15 49J20 65Kxx 



This work was financially supported by the German Research Foundation (DFG), Grant OptiFlow (Project-ID GO 1920/3-1).


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Markus Erbrich
    • 1
  • Simone Göttlich
    • 1
    Email author
  • Marion Pfirsching
    • 1
  1. 1.Department of MathematicsUniversity of MannheimMannheimGermany

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