Abstract
The paper deals with a parallel machines scheduling problem with dedicated tasks with sequence-dependent setup times that are subject to the non-overlapping constraint. This problem emerges in the productions where only one machine setter is available on the shop floor. We consider that setups are performed by a single person who cannot serve more than one machine at the same moment, i.e., the setups must not overlap in time. We show that the problem remains \(\mathcal {NP}\)-hard under the fixed sequence of tasks on each machine. To solve the problem, we propose an Integer Linear Programming formulation, five Constraint Programming models, and a hybrid heuristic algorithm LOFAS that leverages the strength of Integer Linear Programming for the Traveling Salesperson Problem (TSP) and the efficiency of Constraint Programming at sequencing problems minimizing makespan. Furthermore, we investigate the impact of the TSP solution quality on the overall objective value. The results show that LOFAS with a heuristic TSP solver achieves on average 10.5% worse objective values but it scales up to 5000 tasks with 5 machines.
This work was funded by Ministry of Education, Youth and Sport of the Czech Republic within the project Cluster 4.0 number CZ.02.1.01/0.0/0.0/16_026/0008432.
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Notes
- 1.
Note that in the IBM CP Optimizer, the function TypeOfNext is used.
- 2.
Again, in the IBM CP Optimizer, the function TypeOfNext is used.
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We would like to thank Philippe Laborie for his help with the design of CP4 model.
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Vlk, M., Novak, A., Hanzalek, Z., Malapert, A. (2020). Non-overlapping Sequence-Dependent Setup Scheduling with Dedicated Tasks. In: Parlier, G., Liberatore, F., Demange, M. (eds) Operations Research and Enterprise Systems. ICORES 2019. Communications in Computer and Information Science, vol 1162. Springer, Cham. https://doi.org/10.1007/978-3-030-37584-3_2
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