Modeling and solving the endpoint cutting problem

The material cutting process consists of two NP-hard problems: first, it is necessary to find the optimal cutting pattern to minimize the waste area. Second, it is necessary to find the cutting sequence over the plate to extract the pieces in the shortest possible time. The structure of the cutting path problem can vary according to the technology used in the process. In industries where material can be considered a commodity, the cutting path is decisive due to the need to operate economically and efficiently. These types of minimization demand exact models that use nonconventional formulation techniques in search of computational efficiency and for heuristic processes to be specialized so that a good solution is guaranteed. In this paper, three different approaches were proposed. First, a novel and accurate formulation was presented based on a network flow structure. Second, a reactive GRASP algorithm with solution filtering was designed, using seven operators executed under two randomly selected local search philosophies. Finally, four warm-start variants were designed hybridizing the GRASP algorithm subprocedures with the exact model. The approaches are compared through benchmarking; for this, a set of instances composed of cutting patterns taken from the solution of classical instances of the two-dimensional cutting problem was created and made available. The obtained results show that all three approaches solve the problem successfully. Additionally, the computing time is analyzed, illustrating the pros and cons of each approach. Given the cutting path, including the quality of the pieces is left as a future work proposal.