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Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates

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  • Kedad-Sidhoum, Safia
  • Solis, Yasmin Rios
  • Sourd, Francis

Abstract

This paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs. New lower bounds are proposed for the problem, they can be classed into two families. First, two assignment-based lower bounds for the one-machine problem are generalized for the parallel machine case. Second, a time-indexed formulation of the problem is investigated in order to derive efficient lower bounds throught column generation or Lagrangean relaxation. A simple local search algorithm is also presented in order to derive an upper bound. Computational experiments compare these bounds for both the one machine and parallel machine problems and show that the gap between upper and lower bounds is about 1.5%.

Suggested Citation

  • Kedad-Sidhoum, Safia & Solis, Yasmin Rios & Sourd, Francis, 2008. "Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1305-1316, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1305-1316
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    Cited by:

    1. Halil Şen & Kerem Bülbül, 2015. "A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 135-150, February.
    2. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
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    5. Alves de Queiroz, Thiago & Iori, Manuel & Kramer, Arthur & Kuo, Yong-Hong, 2023. "Dynamic scheduling of patients in emergency departments," European Journal of Operational Research, Elsevier, vol. 310(1), pages 100-116.
    6. Detienne, Boris & Pinson, Éric & Rivreau, David, 2010. "Lagrangian domain reductions for the single machine earliness-tardiness problem with release dates," European Journal of Operational Research, Elsevier, vol. 201(1), pages 45-54, February.
    7. Zhang, Hanxiao & Li, Yan-Fu, 2022. "Integrated optimization of test case selection and sequencing for reliability testing of the mainboard of Internet backbone routers," European Journal of Operational Research, Elsevier, vol. 299(1), pages 183-194.
    8. Yunpeng Pan & Zhe Liang, 2017. "Dual relaxations of the time-indexed ILP formulation for min–sum scheduling problems," Annals of Operations Research, Springer, vol. 249(1), pages 197-213, February.
    9. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    10. Kerem Bülbül & Halil Şen, 2017. "An exact extended formulation for the unrelated parallel machine total weighted completion time problem," Journal of Scheduling, Springer, vol. 20(4), pages 373-389, August.

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