An Alternative Modeling Approach for an Integrated Simulation and Optimization of a Class of Production Networks

  • Armin Fügenschuh
  • Simone Göttlich
  • Michael Herty


We present a new modeling approach for production networks, which can be used for both simulation and optimization. It makes use of only a few general assumptions, such that it is applicable to a variety of problems. We survey the underlying fundamentals, derive a basic model based on partial differential equations and show its relation to linear mixed-integer programming. The mixed-integer model allows for simulation and optimization of dynamic time dependent production processes, and can be solved using standard software. Computational results are presented along a realworld industrial case study.


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  1. 1.
    Armbruster D, de Beer C, Freitag M, Jagalski T, Ringhofer C (2005) Autonomous Control of Production Networks using a Pheromone Approach. Preprint, submitted to Physica.Google Scholar
  2. 2.
    Armbruster D, Degond P, Ringhofer C (2006) A Model for the Dynamics of Large Queuing Networks and Supply Chains. SIAM Journal of Applied Mathematics 66: 896–920.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baumol WJ (1970) Economic Dynamics, 3rd edition. Macmillan, New York.Google Scholar
  4. 4.
    Bixby RE, Simchi-Levi D, Martin A, Zimmermann U (2004) Mathematics in the Supply Chain. Oberwolfach Reports 1(2): 963–1036.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Forrester JW (1964) Industrial Dynamics, 3rd print. MIT Press, Massachusetts.Google Scholar
  6. 6.
    Fügenschuh A, Göttlich S, Herty M, Klar A, Martin A (2006), A Mixed-Integer Programming Approach for the Optimization of Continuous Models in Supply Chain Management, submitted to M3AS.Google Scholar
  7. 7.
    Fügenschuh A, Herty M, Klar A, Martin A (2006), Combinatorial and Continuous Models for the Optimization of Traffic Flows on Networks. SIAM Journal of Optimization 16(4): 1155–1176.zbMATHCrossRefGoogle Scholar
  8. 8.
    Fügenschuh A, Martin A (2005), Computational Integer Programming and Cutting Planes. In: K. Aardal, G. Nemhauser, R. Weissmantel (eds.), “Handbook on Discrete Optimization”, Series “Handbooks in Operations Research and Management Science”. Elsevier, 69–122.Google Scholar
  9. 9.
    Göttlich S, Herty M, Klar A (2005) Network models for supply chains. Communications in Mathematical Sciences (CMS) 3(4): 545–559.zbMATHGoogle Scholar
  10. 10.
    Göttlich S, Herty M, Klar A (2006) Modelling and optimization of supply chains on complex networks. Communications in Mathematical Sciences (CMS) 4(2): 315–330.Google Scholar
  11. 11.
    Günther HO, Mattfeld DC, Suhl L (Eds) (2005) Supply Chain Management und Logistik-Optimierung, Simulation, Decision Support. Physica-Verlag, Heidelberg.Google Scholar
  12. 12.
    Günther HO, van Beek P (Eds.) (2003) Advanced Planning and Scheduling Solutions in Process Industry. Springer, Berlin.Google Scholar
  13. 13.
    Mattheij R.M.M, Rienstra S.W, ten Thije Boonkkamp J.H.M. (2005), Partial Differential Equations — Modeling, Analysis, Computation. SIAM Monographs on Mathematical Modeling and Computation. SIAM, Philadelphia.Google Scholar
  14. 14.
    Nemhauser G, Wolsey LA. (1999) Integer and Combinatorial Optimization. Wiley-Interscience.Google Scholar
  15. 15.
    ILOG CPLEX Division, 889 Alder Avenue, Suite 200, Incline Village, NV 89451, USA. Information available at URL Scholar
  16. 16.
    Simchi-Levi D, Kaminsky P, Simchi-Levi E (2003) Managing the Supply Chain: the definitive guide for the business. McGraw-Hill, New York.Google Scholar
  17. 17.
    Wolsey L, Pochet Y (2006) Production Planning by Mixed Integer Programming. Springer Series in Operations Research and Financial Engineering. Springer, New York.zbMATHGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2007

Authors and Affiliations

  • Armin Fügenschuh
    • 1
  • Simone Göttlich
    • 2
  • Michael Herty
    • 2
  1. 1.TU DarmstadtDarmstadt
  2. 2.TU KaiserslauternKaiserslautern

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