Skip to main content
Log in

Cutting aluminium coils with high length variabilities

  • Published:
Annals of Operations Research Aims and scope Submit manuscript


A case study of a cutting stock problem in an aluminium mill is presented. Orders have release dates, due dates, a total length and may be delivered in any number of coils, the length of the coils being bounded from below and above. A variety of different cutting machines is available, hierarchical cuts may be necessary to produce small widths. The mill is capable of producing custom-made coils within certain bounds but there is a declared preference for standard widths. The task is to group the orders into coils which can be produced by the mill and slit by the machines. Waste should be minimized, the dates should be obeyed, the load of the machines should be balanced. In spite of the fact that column generation is not possible, the problem is solved efficiently in practice by a multi-pattern approach using linear programming.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others


  1. H. Dyckhoff and U. Finke,Cutting and Packing in Production and Distribution (Physica Verlag, Heidelberg, 1992).

    Google Scholar 

  2. P.C. Gilmore and R.E. Gomory, A linear programming approach to the cutting-stock problem, Oper. Res. 9(1961)849–859.

    Google Scholar 

  3. P.C. Gilmore and R.E. Gomory, A linear programming approach to the cutting-stock problem—Part II, Oper. Res. 11(1963)863–888.

    Google Scholar 

  4. P.C. Gilmore and R.E. Gomory, Multistage cutting stock problems, Oper. Res. 13(1965)94–120.

    Google Scholar 

  5. G. Meier, Heuristische Walztafelkombination für ein Blechwalzwerk, Fallstudien Oper. Res. 1(1978)119–133.

    Google Scholar 

  6. K. Richter, Solving sequential interval cutting problems via dynamic programming, Euro. J. Oper. Res. 57(1992)332–338.

    Google Scholar 

  7. J. Terno, R. Lindemann and G. Scheithauer,Zuschnittprobleme und ihre praktische Lösung (Harri Deutsch, Thun/Frankfurt am Main, 1987).

    Google Scholar 

  8. G. Wäscher, P. Carow and H. Müller, Entwicklung eines flexiblen Verfahrens für Zuschneideprobleme in einem Kaltwalzwerk, Oper. Res. 29(1985)B 209-B 230.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Helmberg, C. Cutting aluminium coils with high length variabilities. Ann Oper Res 57, 175–189 (1995).

Download citation

  • Issue Date:

  • DOI: