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Networks and Heterogeneous Media

2006, Volume 1, Issue 4: 675-688. doi: 10.3934/nhm.2006.1.675
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Optimal control for continuous supply network models

  • 1.
    Technische Universität Kaiserslautern, Fachbereich Mathematik, Postfach 3049, D-67653 Kaiserslautern
  • 2.
    Fraunhofer Institute ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern
  • Received: 01 September 2006

  • Primary: 90B10.

  • We consider a supply network where the flow of parts can be controlled at the vertices of the network. Based on a coarse grid discretization provided in [6] we derive discrete adjoint equations which are subsequently validated by the continuous adjoint calculus. Moreover, we present numerical results concerning the quality of approximations and computing times of the presented approaches.

    Citation: Claus Kirchner, Michael Herty, Simone Göttlich, Axel Klar. Optimal control for continuous supply network models[J]. Networks and Heterogeneous Media, 2006, 1(4): 675-688. doi: 10.3934/nhm.2006.1.675

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  • We consider a supply network where the flow of parts can be controlled at the vertices of the network. Based on a coarse grid discretization provided in [6] we derive discrete adjoint equations which are subsequently validated by the continuous adjoint calculus. Moreover, we present numerical results concerning the quality of approximations and computing times of the presented approaches.


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    1. C. D'Apice, R. Manzo, B. Piccoli, Numerical Schemes for the Optimal Input Flow of a Supply Chain, 2013, 51, 0036-1429, 2634, 10.1137/120889721
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    6. D.B. Work, A.M. Bayen, Convex Formulations of Air Traffic Flow Optimization Problems, 2008, 96, 0018-9219, 2096, 10.1109/JPROC.2008.2006150
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    9. Khaled A.A.A. Othman, Thomas Meurer, Demand Tracking Control in Manufacturing Systems, 2020, 53, 24058963, 11219, 10.1016/j.ifacol.2020.12.334
    10. Simone Göttlich, Michael Herty, Optimal control for supply network models: Mixed integer programming, 2007, 7, 16177061, 2060051, 10.1002/pamm.200700618
    11. Alfredo Cutolo, Benedetto Piccoli, Luigi Rarità, An Upwind-Euler Scheme for an ODE-PDE Model of Supply Chains, 2011, 33, 1064-8275, 1669, 10.1137/090767479
    12. Ciro D'Apice, Peter I. Kogut, Rosanna Manzo, On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms, 2010, 2010, 1687-5249, 1, 10.1155/2010/982369
    13. Michael N. Jung, Christian Kirches, Sebastian Sager, Susanne Sass, Computational Approaches for Mixed Integer Optimal Control Problems with Indicator Constraints, 2018, 46, 2305-221X, 1023, 10.1007/s10013-018-0313-z
    14. Khaled A.A.A. Othman, Thomas Meurer, Optimal Boundary Control for the Backlog Problem in Production Systems, 2022, 55, 24058963, 511, 10.1016/j.ifacol.2022.09.146
    15. Tanmay Sarkar, A numerical study on a nonlinear conservation law model pertaining to manufacturing system, 2016, 47, 0019-5588, 655, 10.1007/s13226-016-0199-y
    16. Agnes Dittel, Simone Göttlich, Ute Ziegler, Optimal design of capacitated production networks, 2011, 12, 1389-4420, 583, 10.1007/s11081-010-9123-1
    17. A. Fügenschuh, S. Göttlich, M. Herty, C. Kirchner, A. Martin, Efficient reformulation and solution of a nonlinear PDE-controlled flow network model, 2009, 85, 0010-485X, 245, 10.1007/s00607-009-0038-7
    18. A. Fügenschuh, S. Göttlich, M. Herty, A. Klar, A. Martin, A Discrete Optimization Approach to Large Scale Supply Networks Based on Partial Differential Equations, 2008, 30, 1064-8275, 1490, 10.1137/060663799
    19. Oliver Kolb, Simone Göttlich, A continuous buffer allocation model using stochastic processes, 2015, 242, 03772217, 865, 10.1016/j.ejor.2014.10.065
    20. Ciro D'Apice, Peter I. Kogut, Rosanna Manzo, On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains, 2014, 9, 1556-181X, 501, 10.3934/nhm.2014.9.501
    21. Simone Göttlich, Michael Herty, Claus Kirchner, Optimal control for supply network models: adjoint calculus, 2007, 7, 16177061, 2060053, 10.1002/pamm.200700624
    22. Simone Göttlich, Axel Klar, 2013, Chapter 8, 978-3-642-32159-7, 395, 10.1007/978-3-642-32160-3_8
    23. Ingenuin Gasser, Martin Rybicki, Winnifried Wollner, Optimal control of the temperature in a catalytic converter, 2014, 67, 08981221, 1521, 10.1016/j.camwa.2014.02.006
    24. Simone Göttlich, Sebastian Kühn, Jan Peter Ohst, Stefan Ruzika, Markus Thiemann, Evacuation dynamics influenced by spreading hazardous material, 2011, 6, 1556-181X, 443, 10.3934/nhm.2011.6.443
    25. P. Degond, C. Ringhofer, Stochastic Dynamics of Long Supply Chains with Random Breakdowns, 2007, 68, 0036-1399, 59, 10.1137/060674302
    26. S. Göttlich, S. Kühn, J. A. Schwarz, R. Stolletz, Approximations of time-dependent unreliable flow lines with finite buffers, 2016, 83, 1432-2994, 295, 10.1007/s00186-015-0529-6
    27. Simone Göttlich, Oliver Kolb, Sebastian Kühn, Optimization for a special class of traffic flow models: Combinatorial and continuous approaches, 2014, 9, 1556-181X, 315, 10.3934/nhm.2014.9.315
    28. Sebastian Sager, 2012, Chapter 22, 978-1-4614-1926-6, 631, 10.1007/978-1-4614-1927-3_22
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  • © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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