This paper describes a fundamentally new mathematical model of the cutting stock problem - the problem at the core of paper machine deckle filling and corrugator planning. The approach does not require pre-enumeration of acceptable cutting patterns; rather it is based on pre-specification of pattern usage levels. The model takes its inspiration from the fact that with knowledge of the best patterns in the deckle fill, it is a relatively simple matter to calculate the number of sets of each pattern to satisfy the demand constraints. Alternatively if the usage levels (number of sets) are specified, even approximately, then it is relatively simple to determine the associated patterns that would be needed to satisfy the demands. The resulting integer programming model allows direct specification of numbers of patterns and even offers the prospect of applying sequencing constraints directly. The model can be successfully solved with commercial general purpose optimisation software. The paper discusses several ways in which pattern usage levels can be set so that the resulting integer programming models are simple, compact and yet include all feasible solutions.
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