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Changeover formulations for discrete-time mixed-integer programming scheduling models

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  • Velez, Sara
  • Dong, Yachao
  • Maravelias, Christos T.

Abstract

Changeover times can have a significant impact on the scheduling of manufacturing operations. Unfortunately, accounting for changeovers in mixed-integer programming (MIP) scheduling formulations makes the resulting models computationally more expensive. We propose five new formulations for sequence-dependent changeovers, applicable to a wide range of scheduling problems. We generate constraints for different sets of time points and sets of tasks. We also propose valid inequalities for makespan minimization. Furthermore, we prove results regarding the relative tightness of each formulation. Finally, we perform a computational study. Interestingly, we find that tighter formulations do not always lead to faster solution times, and we show that some of the new formulations perform better than the previously proposed ones.

Suggested Citation

  • Velez, Sara & Dong, Yachao & Maravelias, Christos T., 2017. "Changeover formulations for discrete-time mixed-integer programming scheduling models," European Journal of Operational Research, Elsevier, vol. 260(3), pages 949-963.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:949-963
    DOI: 10.1016/j.ejor.2017.01.004
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    References listed on IDEAS

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    Cited by:

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    2. Castro, Pedro M. & Harjunkoski, Iiro & Grossmann, Ignacio E., 2019. "Discrete and continuous-time formulations for dealing with break periods: Preemptive and non-preemptive scheduling," European Journal of Operational Research, Elsevier, vol. 278(2), pages 563-577.
    3. Hao, Jun & Li, Jianping & Wu, Dengsheng & Sun, Xiaolei, 2020. "Portfolio optimisation of material purchase considering supply risk – A multi-objective programming model," International Journal of Production Economics, Elsevier, vol. 230(C).
    4. Kramer, Arthur & Iori, Manuel & Lacomme, Philippe, 2021. "Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization," European Journal of Operational Research, Elsevier, vol. 289(3), pages 825-840.

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