Minimizing saw cycles on the cutting stock problem with processing times depending on the cutting pattern

In this paper the cutting stock problem minimizing saw cycles is considered. In this context where objects can be cut simultaneously the trade-off between raw material and machine utilization costs is of major interest. Different processing times for each cutting pattern are considered, according to the number of items on it, different from previous works of the literature. The optimization aims to minimize both machine utilization costs due to the saw cycles and raw material usage costs. An integer mathematical formulation is proposed, and a solution method based on a column generation procedure is used. Computational tests were performed to assess the impact on costs for illustrative and real industry instances. A set of instances were also randomly generated to analyse the behaviour of the outcome of the problem in face of different technical parameters.