Skip to main content
SpringerLink
Log in

A local search approach to a circle cutting problem arising in the motor cycle industry

  • Case-Oriented Paper
  • Published:
Journal of the Operational Research Society

Abstract

This paper is concerned with the development of a customized circle packing algorithm for a manufacturer of sprockets for the motor cycle industry. Practical constraints mean that the problem differs somewhat from those tackled elsewhere in the literature. In particular, the layouts need to conform to a given structure. This is achieved by using a local search algorithm with an appropriate starting solution and a series of neighbourhoods designed to preserve the layout structure. Empirical evidence based on real data shows that the quality of the resulting solutions closely matches that of cutting patterns currently produced by human experts. Computation times average around 20–30 s per order as compared to several hours for an equivalent manual solution.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4

Similar content being viewed by others

References

  • Abramson D and Dang H (1993). School timetables: a case study using simulated annealing. In: Vidal RVV (ed). Applied Simulated Annealing. LNEMS 396. Springer Verlag, Berlin, pp 104–124.

    Google Scholar 

  • Beasley JE (1985). An exact two-dimensional non-guillotine cutting tree search procedure. Opns Res 33: 49–64.

    Article  Google Scholar 

  • Bennell J and Dowsland K (2001). Hybridising tabu search with optimisation techniques for irregular stock-cutting. Mngt Sci 47: 1160–1172.

    Article  Google Scholar 

  • Birgin EG, Martinez JM and Ronconi DP (2005). Optimizing the packing of cylinders into a rectangular container: a nonlinear approach. Eur J Opl Res 160: 19–33.

    Article  Google Scholar 

  • Boll DW, Donovan J, Graham RL and Lubachevsky BD (2000). Improving dense packings of equal disks in a square. Electronic J Combin 7: R46.

    Google Scholar 

  • Burke EK, Hellier RSR, Kendall G and Whitwell G (forthcoming). A new bottom-left algorithm for the two-dimensional irregular packing problem. Opns Res (accepted for publication).

  • Burke EK, Kendall G and Whitwell G (2004). A new placement heuristic for the orthogonal stock cutting problem. Opns Res 52: 655–671.

    Article  Google Scholar 

  • Chen DZ, Hu X, Huang Y and Li Y (2001). Algorithms for congruent sphere packing and applications. In: Souvaine D (ed). Proceedings of the Seventeenth Annual Symposium on Computational Geometry, Medford, Massachusetts, United States. ACM Press, New York, pp 212–221.

    Google Scholar 

  • Collins CR and Stephenson K (2003). A circle packing algorithm. Comput Geometry: Theory Appl 25: 233–256.

    Article  Google Scholar 

  • Conway JH and Sloane NJA (1992). Sphere Packings, Lattices, and Groups, 2nd edn. Springer-Verlag: New York.

    Google Scholar 

  • Correia MH, Oliveira JF and Ferreira JS (2000). Cylinder packing by simulated annealing. Pesquisa Operacional 20: 269–286.

    Article  Google Scholar 

  • Cui Y (2005). A cutting stock problem and its solution in the manufacturing industry of large electric generators. Comput Opns Res 32: 1709–1721.

    Article  Google Scholar 

  • Dowsland KA (1991). Optimising the palletisation of cylinders in cases. OR Spektrum 13: 204–212.

    Article  Google Scholar 

  • Dowsland KA, Bennell J and Dowsland W (1998). Jostling for position—local improvement for irregular cutting patterns. J Opl Res Soc 49: 647–658.

    Article  Google Scholar 

  • Dowsland KA, Herbert E, Kendall G and Burke EK (2006). Using tree search bounds to enhance a genetic algorithm approach to two rectangle packing problems. Eur J Opl Res 168: 390–402.

    Article  Google Scholar 

  • Dowsland KA, Vaid S and Dowsland W (2002). An algorithm for polygon placement using a bottom-left strategy. Eur J Opl Res 141: 371–381.

    Article  Google Scholar 

  • Dowsland KA and Dowsland WB (1992). Packing problems. Eur J Opl Res 56: 2–14.

    Article  Google Scholar 

  • George JA, George JM and Lamar BW (1995). Packing different-sized circles into a rectangular container. Eur J Opl Res 84: 693–712.

    Article  Google Scholar 

  • Gilmore PC and Gomory RE (1961). A linear programming approach to the cutting-stock problem. Opns Res 9: 849–859.

    Article  Google Scholar 

  • Glover F and Laguna M (1997). Tabu Search. Kluwer Academic Publishers: Boston, USA.

    Book  Google Scholar 

  • Glover FW and Kochenberger GA (2003). Handbook of Metaheuristics. Kluwer Academic Publishers: Boston, USA.

    Book  Google Scholar 

  • Graham RL and Lubachevsky BD (1996). Repeated patterns of dense packings of equal disks in a square. Electronic J Combin 3: R16.

    Google Scholar 

  • Huang WQ, Li Y and Xu RC (2001). Local search based on a physical model for solving a circle packing problem. In: de Sousa JP (ed). Proceedings of the fourth Metaheuristics International Conference 2001 (MIC’2001), July 2001. Kluwer, Boston, pp 455–459.

    Google Scholar 

  • Huang WQ, Li Y, Akeb H and Li CM (2005). Greedy algorithms for packing unequal circles into a rectangular container. J Opl Res Soc 56: 539–548.

    Article  Google Scholar 

  • Huang WQ, Li Y, Jurkowiak B, Li CM and Xu RC (2003). A two-level search strategy for packing unequal circles into a circle container. In: Rossi F (ed). Proceedings of the Ninth International Conference on Principles and Practice of Constraint Programming (CP’03), Kinsale, Ireland. Lecture Notes in Computer Science 2833. Springer Verlag, Berlin, pp 868–872.

    Google Scholar 

  • Kantorovitch LV (1939, 1960). Mathematical methods of organising and planning production. Mngt Sci 6: 366–422.

    Article  Google Scholar 

  • Koebe P (1936). Kontaktprobleme der Konformen Addildung, Abh. Sächs. Akad. Wiss. Leipzig. Math. Natur. Kl. 88: 141–164.

    Google Scholar 

  • Kravitz S (1967). Packing cylinders into cylindrical containers. Math Magazine 40: 65–70.

    Article  Google Scholar 

  • Lodi A, Martello S and Monaci M (2002). Two-dimensional packing problems: a survey. Eur J Opl Res 141: 241–252.

    Article  Google Scholar 

  • Nurmela KJ and Östergård PRJ (1997). Packing up to 50 Equal Circles in a square. Discrete Comput Geometry 18: 111–120.

    Article  Google Scholar 

  • Reeves C (1993). Modern Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Press: Oxford, UK.

    Google Scholar 

  • Steinhaus H (1999). Mathematical Snapshots, 3rd edn. Dover: New York, p 202.

    Google Scholar 

  • Stephenson K (2003). Circle packing: a mathematical tale. Notices—Am Math Soc 50: 1376–1388.

    Google Scholar 

  • Stoyan YG and Yas'kov G (2004). A mathematical model and a solution method for the problem of placing various-sized circles into a strip. Eur J Opl Res 156: 590–600.

    Article  Google Scholar 

  • Sweeney E and Paternoster RE (1992). Cutting and packing problems: a categorized, application-orientated research bibliography. J Opl Res Soc 43: 691–706.

    Article  Google Scholar 

  • Wang H, Huang W, Zhang Q and Xu D (2002). An improved algorithm for the packing of unequal circles within a larger containing circle. Eur J Opl Res 141: 440–453.

    Article  Google Scholar 

  • Wells D (1991). The Penguin Dictionary of Curious and Interesting Geometry. Penguin: London, pp 30–31.

    Google Scholar 

  • Wildemuth BM (2004). The effects of domain knowledge on search tactic formulation. J Am Soc Inform Sci Technol 55: 246–258.

    Article  Google Scholar 

  • Williams R (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications: New York, pp 34–47.

    Google Scholar 

  • Wright MB (1991). Scheduling English cricket umpires. J Opl Res Soc 42: 447–452.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Nottingham, Nottingham, UK

    K A Dowsland & G Kendall

  2. Gower Optimal Algorithms Ltd, Swansea, UK

    K A Dowsland

  3. Kitcross, Presles, Belgium

    M Gilbert

Authors
  1. K A Dowsland
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M Gilbert
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G Kendall
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K A Dowsland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dowsland, K., Gilbert, M. & Kendall, G. A local search approach to a circle cutting problem arising in the motor cycle industry. J Oper Res Soc 58, 429–438 (2007). https://doi.org/10.1057/palgrave.jors.2602170

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/palgrave.jors.2602170

Keywords

Search

Navigation