Cutting aluminium coils with high length variabilities

Abstract

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.