Computing upper and lower bounds on textile nesting problems

  • Ralf Heckmann
  • Thomas Lengauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)

Abstract

We consider an industrial cutting problem in textile manufacturing and report on heuristics for computing cutting images and lower bounds on waste for this problem. For the upper bounds we use greedy strategies based on hodographs and global optimization based on simulated annealing. For the lower bounds we use branch-and-bound methods for computing optimal solutions of placement subproblems that determine the performance of the overall subproblem. The upper bounds are computed in less than an hour on a common-day workstation and are competitive in quality with results obtained by human nesters. The lower bounds take a few hours to compute and are within 0.4% of the upper bound for certain types of clothing (e.g., for pants).

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References

  1. 1.
    C. Amaral, J. Bernardo, and J. Jorge. “Marker-making using automatic placement of irregular shapes for the garment industry”. Computer & Graphics, Vol 14 No. 1:41–46, 1990.Google Scholar
  2. 2.
    C. Bounsaythip, S. Maouche, and G. Roussel. “Algorithms for a marker making system: ε-admissible resolution”. 12th International Conference on Systems Science, Wroclaw (Poland), 1995.Google Scholar
  3. 3.
    J. Chung, D. J. Hillman, and D. Scott. “An intelligent nesting system on 2-D highly irregular resources”. In Applications of Artificial Intelligence VIII — Proceedings of the 8th International Conference of the International Society for Optical Engineering (SPIE), pages 472–483, 1990. Vol. 1293.Google Scholar
  4. 4.
    R. Cuninghame-Green. ”Geometry, shoemaking and the milk tray problem”. New Scientist, No. 12:50–53, 1989.Google Scholar
  5. 5.
    R. Cuninghame-Green. ”Cut out waste!”. OR Insight, Vol. 5, No. 3:4–7, 1992.Google Scholar
  6. 6.
    K. Daniels, Z. Li, and V. Milenkovic. “Automatic marker making”. In T. Shermer, editor, Proceedings of the Third Canadian Conference on Computational Geometry, August 1991.Google Scholar
  7. 7.
    K. Daniels, Z. Li, and V. Milenkovic. “Placement and compaction of non-convex polygons for clothing manufacture”. In C. Wang, editor, Proceedings of the Fourth Canadian Conference on Computational Geometry, August 1992.Google Scholar
  8. 8.
    K. Daniels and V. Milenkovic. “Multiple translational containment: Approximate and exact algorithms”. Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 205–214, 1995.Google Scholar
  9. 9.
    K. Daniels and V. Milenkovic. “Translational polygon containment and minimal enclosure using geometric algorithms and mathematical programming”. 36th Annual IEEE Conference on Foundations of Computer Science, 1995.Google Scholar
  10. 10.
    K. A. Dowsland and W. B. Dowsland. “Packing problems”. European Journal of Operational Research (EJOR), Vol. 56, No. 1:2–14, 1992.Google Scholar
  11. 11.
    K. A. Dowsland and W. B. Dowsland. “Solution approaches to irregular nesting problems”. Working paper EBMS/1994/18, European Business Management School, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, UK, 1994.Google Scholar
  12. 12.
    H. Dyckhoff and U. Finke. “Cutting and Packing in Production and Distribution”. Physica-Verlag, Heidelberg, Germany, 1992.Google Scholar
  13. 13.
    R. J. Fowler, M. S. Paterson, and S. L. Tanimoto. “Optimal packing and covering in the plane are NP-complete”. Information Processing Letters (IPL), Vol. 12, No. 3:133–137, 1981.Google Scholar
  14. 14.
    R. Heckmann and T. Lengauer. “A simulated annealing approach to the nesting problem in the textile manufacturing industry”. In R. E. Burkard, P. L. Hammer, T. Ibaraki, and M. Queyranne, editors, Annals of Operations Research, volume No. 57, pages 103–133. J.C. Baltzer AG Science Publishers, Amsterdam, 1995.Google Scholar
  15. 15.
    J. Heistermann and T. Lengauer. “Efficient automatic part nesting on irregular and inhomogeneous surfaces”. In Proceedings of the Fourth ACM-SIAM Symposium on Discrete Algorithms (SODA '93), pages 251–259, Austin, Texas, USA, January 1993.Google Scholar
  16. 16.
    J. Heistermann and T. Lengauer. “The nesting problem in the leather manufacturing industry”. In R. E. Burkard, P. L. Hammer, T. Ibaraki, and M. Queyranne, editors, Annals of Operations Research, volume No. 57, pages 147–173. J.C. Baltzer AG Science Publishers, Amsterdam, 1995.Google Scholar
  17. 17.
    Z. Li and V. Milenkovic. “A compaction algorithm for non-convex polygons and its application”. In Proceedings of the Ninth Annual ACM Symposium on Computational Geometry, May 1993.Google Scholar
  18. 18.
    S. Maouche and G. Roussel. “Intelligent lay-planning system for irregular shapes and sheet with patterns and flaws. resolution by ε-admissible tree search”. 24th International Symposium on Industrial Robots (ISIR), Tokyo, 1993.Google Scholar
  19. 19.
    V. Milenkovic. “Multiple translational containment, Part II: Exact algorithms”. Extended abstract, Aiken Computation Laboratory, Harvard University, Cambridge, MA 02138, 1994.Google Scholar
  20. 20.
    C. E. Pfefferkorn. “A heuristic problem solving design system for equipment or furniture layouts”. Communications of the ACM, Vol. 18, No. 5:286–297, 1975.Google Scholar
  21. 21.
    E. Ridenour Paternoster and P. E. Sweeney. “Cutting and packing problems: A categorized application-orientated research bibliography”. Journal of the Operational Research Society, Vol. 43, No. 7:691–706, 1992.Google Scholar
  22. 22.
    S. Roberts. “Application of heuristic techniques to the cutting-stock problem for worktops”. Journal of the Operational Research Society, Vol. 35, No. 5:369–377, 1984.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Ralf Heckmann
    • 1
  • Thomas Lengauer
    • 1
    • 2
  1. 1.Institute for Algorithms and Scientific ComputingGerman National Research Center for Information Technology (GMD)Sankt AugustinGermany
  2. 2.Department of Computer ScienceUniversity of BonnBonnGermany

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