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Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time

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  • Jiang, Xiaojuan
  • Lee, Kangbok
  • Pinedo, Michael L.

Abstract

We consider bicriteria scheduling problems with identical machines in parallel and two popular but conflicting objectives, namely, the makespan and the total completion time. Assuming no prioritization of the two objectives, we are interested in the simultaneous optimization of the two objectives and approximation algorithms relative to an ideal schedule – which may not exist – that has both objectives at their minimum. For the problem with a given number of machines, we propose a fast (ρ1,ρ2)-approximation algorithm where ρ1 and ρ2 represent approximation ratios with regard to the makespan and the total completion time, respectively. We also analyze the problem’s inapproximability by proposing a lower bound of the approximation ratio, which cannot be improved by any algorithm.

Suggested Citation

  • Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2023. "Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time," European Journal of Operational Research, Elsevier, vol. 305(2), pages 594-607.
    • Handle: RePEc:eee:ejores:v:305:y:2023:i:2:p:594-607
    DOI: 10.1016/j.ejor.2022.06.021
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    References listed on IDEAS

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    1. Lee, Kangbok & Leung, Joseph Y-T. & Jia, Zhao-hong & Li, Wenhua & Pinedo, Michael L. & Lin, Bertrand M.T., 2014. "Fast approximation algorithms for bi-criteria scheduling with machine assignment costs," European Journal of Operational Research, Elsevier, vol. 238(1), pages 54-64.
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    8. J N D Gupta & J C Ho & S Webster, 2000. "Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(11), pages 1330-1339, November.
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    Cited by:

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    2. Li, Weidong & Ou, Jinwen, 2024. "Approximation algorithms for scheduling parallel machines with an energy constraint in green manufacturing," European Journal of Operational Research, Elsevier, vol. 314(3), pages 882-893.
    3. David Fischer & Péter Györgyi, 2023. "Approximation algorithms for coupled task scheduling minimizing the sum of completion times," Annals of Operations Research, Springer, vol. 328(2), pages 1387-1408, September.

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