Two approaches to handle the dynamism in a scheduling problem with sequence-dependent setup times

Abstract

In this work we address the minimization of the makespan in a scheduling problem where the machine setup times are sequence-dependent. The jobs, which arrive throughout the production process, has a release time that is unknown in advance. Considering both, dynamic environments and sequence-dependent setup times, make the problem more realistic, but also more challenging from an algorithmic and modeling point of view. To deal with the addressed problem, we implement the continuous and periodic rescheduling approaches, providing them with the same re-optimization methods. To implement the re-optimization methods, we design two insertion procedures for adding the new released jobs in the processing sequence, as well as improvement procedures, based on Iterated Greedy strategies, to reduce the sequence makespan. In the improvement phase of the Iterated Greedy strategies we implement three improvement methods that combine four local searches. The developed algorithms are assessed based on the quality of the solutions they find and the CPU time they consume to reach these solutions. We use instances from the literature and larger instances generated in this work. The three algorithm versions showed quality solutions when compared with optimal solutions for the static problem and with solutions of the Perfect Information Model for the dynamic problem. Additionally, they showed a good performance for both the continuous and periodic approach. When these two approaches are compared, results indicate that the continuous approach would be the most appropriate when the proportion of dynamic jobs is low, while when the proportion is high, it would seem more advisable to use the periodic approach, appropriately selecting the frequency of re-optimization processes.