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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. Rajendran, Chandrasekharan, 1995. "Heuristics for scheduling in flowshop with multiple objectives," European Journal of Operational Research, Elsevier, vol. 82(3), pages 540-555, May.
    9. Brian Thomas Eck & Michael Pinedo, 1993. "On the Minimization of the Makespan Subject to Flowtime Optimality," Operations Research, INFORMS, vol. 41(4), pages 797-801, August.
    10. Gupta, Jatinder N. D. & Neppalli, Venkata R. & Werner, Frank, 2001. "Minimizing total flow time in a two-machine flowshop problem with minimum makespan," International Journal of Production Economics, Elsevier, vol. 69(3), pages 323-338, February.
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    Cited by:

    1. 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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