Abstract
The minimization of open stacks problem (MOSP) aims to determine the ideal production sequence to optimize the occupation of physical space in manufacturing settings. Most of current methods for solving the MOSP were not designed to work with large instances, precluding their use in specific cases of similar modeling problems. We therefore propose a PageRank-based heuristic to solve large instances modeled in graphs. In computational experiments, both data from the literature and new datasets up to 25 times fold larger in input size than current datasets, totaling 1330 instances, were analyzed to compare the proposed heuristic with state-of-the-art methods. The results showed the competitiveness of the proposed heuristic in terms of quality, as it found optimal solutions in several cases, and in terms of shorter run times compared with the fastest available method. Furthermore, based on specific graph densities, we found that the difference in the value of solutions between methods was small, thus justifying the use of the fastest method. The proposed heuristic is scalable and is more affected by graph density than by size.
Highlights
The cutting-stock problem occurs in industrial settings in which smaller objects of different sizes and shapes are manufactured to meet customer demands from larger objects of predefined size, such as wood panels, paper or steel rolls and flat glass
The column D is the minimization of open stacks problem (MOSP) graph density, OPT is the value of the optimal solution in maximum number of open stacks (MNOS), Table 2
In the GP dataset, all non-optimal results obtained by PieceRank opened only 1 stack more than the optimal solution, and the worst solutions were observed in the SP dataset, with 15% and 17% gaps
Summary
The cutting-stock problem occurs in industrial settings in which smaller objects of different sizes and shapes are manufactured to meet customer demands from larger objects of predefined size, such as wood panels, paper or steel rolls and flat glass. At each stage of the production process, a pattern is processed, and the resulting pieces are added to specific stacks close to the machine that produced them. In this case, physical constraints prevent the allocation of space for the simultaneous accommodation of stacks of all requested pieces.
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