Skip to main content
SpringerLink
Log in
Book cover

Optimization Methods and Applications pp 183–216Cite as

Linear Assignment Problems in Combinatorial Optimization

  • Chapter
  • First Online:

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 130))

Abstract

In this chapter we introduce the notion of a “pattern” in the Linear Assignment Problem and show that patterns may be useful to create new insights and approaches for many combinatorial optimization problems defined on a rectangular input matrix. We define a pattern as a specific collection of cells in the rectangular matrix reflecting the structure of an optimal solution to the original combinatorial optimization problem (COP). We illustrate the notion of pattern by means of some well-known problems in combinatorial optimization, including the variations of the Linear Ordering Problem, the Cell Formation Problem, and some others. Then, we give a detailed consideration to pattern-based solution approaches for the two mentioned problems.

This is a preview of subscription content, log in via an institution.

Notes

  1. 1.

    See http://www.iwr.uni-heidelberg.de/iwr/comopt/soft/LOLIB/LOLIB.html.

References

  1. Ballakur, A., Steudel, H.J.: A within cell utilization based heuristic for designing cellular manufacturing systems. Int. J. Prod. Res. 25, 639–655 (1987)

    Article  Google Scholar 

  2. Bekker, H., Braad, E.P., Goldengorin, B.: Using bipartite and multidimensional matching to select the roots of a system of polynomial equations. Lect. Notes Comput. Sci. 3483, 397–406 (2003)

    Article  Google Scholar 

  3. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  4. Goldengorin, B., Krushinsky, D., Slomp, J.: Flexible PMP approach for large-size cell formation. Oper. Res. 60(5), 1157–1166 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldengorin, B., Krushinsky, D., Pardalos, P.: Cell Formation in Industrial Engineering. Springer, New York (2013)

    Book  MATH  Google Scholar 

  6. Goncalves, J.F., Resende, M.C.G.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)

    Article  Google Scholar 

  7. Jünger, M.: Polyhedral Combinatorics and the Acyclic Subdigraph Problem. Heldermann Verlag, Berlin (1985)

    MATH  Google Scholar 

  8. Krishnamoorthy, M.S.: An NP-hard problem in bipartite graphs. SIGACT News 7(1), 26 (1975)

    Article  Google Scholar 

  9. Kuhn, H.W.: The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2, 83–97 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  10. McCormick, W.T., Schweitzer, P.J., White, T.W.: Problem decomposition and data reorganization by a clustering technique. Oper. Res. 20(5), 993–1009 (1972)

    Article  MATH  Google Scholar 

  11. Nering, E.D., Tucker, A.W.: Linear Programs and related Problems. Academic, San Diego (1993)

    Google Scholar 

  12. Reinelt, G.: The Linear Ordering Problem. Heldermann Verlag, Berlin (1985)

    MATH  Google Scholar 

  13. Waghodekar, P.H., Sahu, S.: Machine-component cell formation in group technology: MACE. Int. J. Prod. Res. 22(6), 937–948 (1984)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ohio University, Athens, OH, USA

    Boris Goldengorin

  2. University of Florida, Gainesville, FL, USA

    Boris Goldengorin

  3. Wageningen University and Research, Wageningen, The Netherlands

    Dmitry Krushinsky

Authors
  1. Boris Goldengorin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dmitry Krushinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry Krushinsky .

Editor information

Editors and Affiliations

  1. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Methods of Discrete Optimization, V.M. Glushkov Institute of Cybernetics, Kyiv, Ukraine

    Volodymyr Shylo

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Goldengorin, B., Krushinsky, D. (2017). Linear Assignment Problems in Combinatorial Optimization. In: Butenko, S., Pardalos, P., Shylo, V. (eds) Optimization Methods and Applications . Springer Optimization and Its Applications, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-68640-0_9

Download citation

Publish with us

Policies and ethics

Search

Navigation