Encyclopedia of Optimization

2009 Edition
| Editors: Christodoulos A. Floudas, Panos M. Pardalos

MINLP: Trim-loss Problem

  • Iiro Harjunkoski
  • Ray Pörn
  • Tapio Westerlund
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-74759-0_387

Article Outline

Keywords

Problem Formulation

Linear Transformations

Parameterization Methods

Convex Transformations

  Exponential Transformation

  Square-Root Transformation

  Logarithmic and Square-Root Transformation

  Inverted Transformation

  Modified Square-Root Transformation

Example: A Numerical Problem

Conclusions

Notation

See also

References

Keywords

Scheduling Paper converting Trim-loss problem Bilinear Convex transformation 
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References

  1. 1.
    Adjiman CS, Androulakis IP, Floudas CA (1997) Global optimization of MINLP problems in process synthesis and design. Comput Chem Eng 21:S445–S450Google Scholar
  2. 2.
    Dakin RJ (1965) A tree search algorithm for mixed integer programming problems. Comput J 8:250–255MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Gilmore PC, Gomory RE (1961) A linear programming approach to the cutting-stock problem. Oper Res 9:849–859MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Haessler RW (1971) A heuristic programming solution to a non-linear cutting stock problem. Managem Sci 17:B793–B802Google Scholar
  5. 5.
    Harjunkoski I, Pörn R, Westerlund T, Skrifvars H (1997) Different strategies for solving bilinear integer problems with convex transformations. Comput Chem Eng 21:S487–S492Google Scholar
  6. 6.
    Harjunkoski I, Westerlund T, Isaksson J, Skrifvars H (1996) Different formulations for solving trim-loss problems in a paper converting mill with ILP. Comput Chem Eng 20:S121–S126CrossRefGoogle Scholar
  7. 7.
    Hinxman AI (1980) The trim-loss and assortment problems: A survey. Europ J Oper Res 5:8–18MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Johnston RE (1986) Rounding algorithms for cutting stock problems. Asia–Pacific J Oper Res 3:166–171MATHGoogle Scholar
  9. 9.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetCrossRefGoogle Scholar
  10. 10.
    Skrifvars H, Harjunkoski I, Westerlund T, Kravanja Z, Pörn R (1996) Comparison of different MINLP methods applied on certain chemical engineering problems. Comput Chem Eng 20:S333–S338CrossRefGoogle Scholar
  11. 11.
    Smith EMB, Pantelides CC (1997) Global optimization of nonconvex MINLPs. Comput Chem Eng 21:S791–S796Google Scholar
  12. 12.
    Westerlund T, Pettersson F (1995) An extended cutting plane method for solving convex MINLP problems. Comput Chem Eng 19:S131–S136CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Iiro Harjunkoski
    • 1
  • Ray Pörn
    • 2
  • Tapio Westerlund
    • 3
  1. 1.Process Design Lab.Åbo Akad. UniversityTurkuFinland
  2. 2.Department Math.Åbo Akad. UniversityTurkuFinland
  3. 3.Process Design Lab.Åbo Akad. UniversityÅboFinland