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Job sequencing and tool switching problem with non-identical parallel machines: mathematical formulations and modeling improvements

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  • Hadj Salem, Khadija
  • Kramer, Arthur
  • Robbes, Alexis

Abstract

The job sequencing and tool switching problem with non-identical parallel machines (SSP-NPM) is a generalization of the job sequencing and tool switching problem (SSP), which is known to be an NP-hard optimization problem. SSP-NPM involves scheduling jobs on non-identical parallel machines while determining the associated tool sequences to minimize the makespan. In this paper, we propose an improved version of the existing position-based MILP model introduced in Calmels (2022a). Building on this, we develop a position-based arc flow model. In addition, we introduce a novel MILP formulation based on a job group representation of the problem, as used in Akhundov and Ostrowski (2024) for the SSP, which we extend to derive a job group based arc flow model. Several valid inequalities and symmetry-breaking constraints were considered to improve the proposed approaches. Lower and upper bounds were also developed to improve the proposed approaches. Computational experiments were performed using available literature and randomly generated instances to evaluate the effectiveness of the proposed approaches.

Suggested Citation

  • Hadj Salem, Khadija & Kramer, Arthur & Robbes, Alexis, 2026. "Job sequencing and tool switching problem with non-identical parallel machines: mathematical formulations and modeling improvements," European Journal of Operational Research, Elsevier, vol. 330(2), pages 416-426.
    • Handle: RePEc:eee:ejores:v:330:y:2026:i:2:p:416-426
    DOI: 10.1016/j.ejor.2025.09.026
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    References listed on IDEAS

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    1. Dorothea Calmels & Chandrasekharan Rajendran & Hans Ziegler, 2019. "Heuristics for Solving the Job Sequencing and Tool Switching Problem with Non-identical Parallel Machines," Operations Research Proceedings, in: Bernard Fortz & Martine Labbé (ed.), Operations Research Proceedings 2018, pages 459-465, Springer.
    2. Christopher S. Tang & Eric V. Denardo, 1988. "Models Arising from a Flexible Manufacturing Machine, Part I: Minimization of the Number of Tool Switches," Operations Research, INFORMS, vol. 36(5), pages 767-777, October.
    3. Christopher S. Tang & Eric V. Denardo, 1988. "Models Arising from a Flexible Manufacturing Machine, Part II: Minimization of the Number of Switching Instants," Operations Research, INFORMS, vol. 36(5), pages 778-784, October.
    4. Dorothea Calmels, 2019. "The job sequencing and tool switching problem: state-of-the-art literature review, classification, and trends," International Journal of Production Research, Taylor & Francis Journals, vol. 57(15-16), pages 5005-5025, August.
    5. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    6. Tiago Tiburcio da Silva & Antônio Augusto Chaves & Horacio Hideki Yanasse, 2021. "A new multicommodity flow model for the job sequencing and tool switching problem," International Journal of Production Research, Taylor & Francis Journals, vol. 59(12), pages 3617-3632, June.
    7. Van Hop, Nguyen & Nagarur, Nagendra N., 2004. "The scheduling problem of PCBs for multiple non-identical parallel machines," European Journal of Operational Research, Elsevier, vol. 158(3), pages 577-594, November.
    8. Akhundov, Najmaddin & Ostrowski, James, 2024. "Exploiting symmetry for the job sequencing and tool switching problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 976-987.
    9. Calmels, Dorothea, 2022. "An iterated local search procedure for the job sequencing and tool switching problem with non-identical parallel machines," European Journal of Operational Research, Elsevier, vol. 297(1), pages 66-85.
    10. Burak Gökgür & Brahim Hnich & Selin Özpeynirci, 2018. "Parallel machine scheduling with tool loading: a constraint programming approach," International Journal of Production Research, Taylor & Francis Journals, vol. 56(16), pages 5541-5557, August.
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