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Trade tolerance and exact solutions in the cutting stock problem

Adolf Diegel (Cutline Research), Olaf Diegel (Auckland University of Technology), Edouard Montocchio and Sias van Schalkwyk (Mondi Business Paper South Africa, Durban and Richards Bay),

George Pritchard (Mondi Packaging South Africa)


Deckling or cutting stock problems involve large units to be split into small ones. We aim to reduce stock usage and setups, favour long runs, surplus over waste, low pattern loss, few order splits and prompt delivery. We may also have to respect trade tolerance or keep pattern loss within the width of a disposal chute. Finally, when sheets are to be made or reels too narrow for a winder's knife settings, for the winder we generate parent reels or cutreels, to be deckled again on a second cutter or re-reeler, "two-stage", involving two machines.

Compact Linear Programming and dynamic pattern generation guaranty low stock usage, yet early formulations prevented deficit only, not surplus. Now we can set limits on deficit or surplus, including zero tolerance to fill demand exactly. We may also admit extra stock to allow longer runs, fixed pattern multiples or to improve other aspects of a plan.

We explore this topic and define comparative advantage to explain why positive tolerance favours some sizes and keeps others at their lowest level. With zero tolerance, if an exact plan does not emerge by default, loss is maximal, turning surplus into broke and impairing run length or setups: zero tolerance is the worst policy.

Keywords: Deckling, Cutting stock, Trim loss problem, Trade tolerance, Run length

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