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MaxFlow-MinCut Duality for a Paint Shop Problem

  • Thomas Epping
  • Winfried Hochstättler
  • Marco E. Lübbecke
Conference paper
Part of the Operations Research Proceedings 2002 book series (ORP, volume 2002)

Abstract

Motivated by an application in car manufacturing we consider the following problem: How can we synthesize a given word from restricted reservoirs of colored letters with a minimal number of color changes between adjacent letters? We focus on instances in which each letter occurs exactly twice, once in each of two given colors. In this case the problem turns out to be the dual of a MinCut problem for one point extensions of a certain class of regular matroids. We discuss consequences of the MaxFlow-MinCut duality and describe algorithmic approaches.

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References

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    Epping Th., Hochstattler W. (2002) Storage and Retrieval of Car Bodies by the Use of Line Storage Systems. Technical report btu-lsgdi-001.02, BTU Cottbus, GermanyGoogle Scholar
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    Epping Th., Hochstattler W., Oertel P. (2002) Complexity Results on a Paint Shop Problem. Submitted to: Discrete Applied MathematicsGoogle Scholar
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    Golumbic, M. C. (1980) Algorithmic Graph Theory and Perfect Graphs. Academic PressGoogle Scholar
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    Seymour P. D. (1977) The Matroids with the Max-Flow Min-Cut Property. Journal of Combinatorial Theory, Series B 23, pp 189–222CrossRefGoogle Scholar
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    Spieckermann S., Vo13 S. (1996) Paint Shop Simulation in the Automotive Industry. ASIM Mitteilungen 54, pp. 367–380Google Scholar
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    Oxley,J.G.(1992)Matroid Theory.Oxford University PressGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Thomas Epping
    • 1
  • Winfried Hochstättler
    • 1
  • Marco E. Lübbecke
    • 2
  1. 1.Department of MathematicsBTU CottbusCottbusGermany
  2. 2.Department of Mathematical OptimizationTU BraunschweigGermany

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