Treffer: On formulations for the one-dimensional cutting stock with a limited number of open stacks problem.

This paper addresses the one-dimensional cutting stock with a limited number of open stacks problem (CS-LOSP). The CS-LOSP is an optimisation problem derived from the classical cutting stock problem. It incorporates an additional scheduling constraint that limits the maximum number of simultaneously open stacks resulting from cutting large objects. Despite its significant practical relevance, there are few models addressing this problem in the literature. To fully model and solve the problem, we propose two integer linear programming (ILP) formulations for the CS-LOSP. The first formulation relies on sequencing sets of predefined cutting patterns, while the second is an improved arc-flow formulation. We conducted computational experiments using a general-purpose ILP solver, demonstrating that our models surpassed or were competitive with the current state-of-the-art formulation for several problem instances. Our models stand out in scenarios where the large objects have greater length or the limit on the maximum number of simultaneously open stacks is less restrictive. [ABSTRACT FROM AUTHOR]

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