A PageRank-based heuristic for the minimization of open stacks problem.

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.