A new model for complete solutions to one-dimensional cutting stock problems

This new model resolves the non-linearity in the one-dimensional cutting stock problem, between pattern variables and pattern run lengths, by a novel use of 0–1 variables. The model does not require pre-specification of cutting patterns. It explicitly includes practical constraints such as pattern cardinality constraints, minimum run length constraints and sequence related constraints. The resultant MIP is relatively compact and its application to four problem instances using a commercial MIP package is presented.