Mathematical models for the cutting stock with limited open stacks problem

This research is focused on solving the Cutting Stock with Limited Open Stacks Problem (CS-LOSP). The CS-LOSP is an optimization problem which consists of the classical Cutting Stock Problem (CSP) paired with the additional constraint that the maximum number of open stacks from the sequencing of the cutting patterns obtained from the CSP solution is equal or lower than a preset limit. Despite being a problem with great practical importance, the literature lacks models for this problem, and only one-dimensional problems are addressed. In this paper, we propose two integer linear programming formulations for the CS-LOSP that are valid for solving instances of the CSP of any dimension. In order to eliminate symmetrical solutions to the problem, the proposed formulations sequence sets of cutting patterns instead of sequencing the cutting patterns individually, thus, the search space for solutions is reduced. A set of randomly generated instances for the two-dimensional problem is used to perform computational experiments in order to validate the proposed mathematical formulations.