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Scheduling identical jobs on uniform parallel machines

Author

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  • M.I. Dessouky
  • B.J. Lageweg
  • J.K. Lenstra
  • S.L. van de Velde

Abstract

We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O(n3) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O(n2) time. We present faster algorithms, requiring only O(n+mlog m) time for minimizing makespan and total completion time, O(nlogn) time for minimizing total weighted completion time, maximum lateness, total tardiness and the weighted number of tardy jobs, and O(nlog2n) time for maximum weighted tardiness. In the case of release dates, we propose an O(nlogn) algorithm for minimizing makespan, and an O(mn2m+1) time dynamic programming algorithm for minimizing total completion time.

Suggested Citation

  • M.I. Dessouky & B.J. Lageweg & J.K. Lenstra & S.L. van de Velde, 1990. "Scheduling identical jobs on uniform parallel machines," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 44(3), pages 115-123, September.
    • Handle: RePEc:bla:stanee:v:44:y:1990:i:3:p:115-123
    DOI: 10.1111/j.1467-9574.1990.tb01276.x
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    Citations

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    Cited by:

    1. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    2. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    3. Janiak, Adam & Krysiak, Tomasz & Pappis, Costas P. & Voutsinas, Theodore G., 2009. "A scheduling problem with job values given as a power function of their completion times," European Journal of Operational Research, Elsevier, vol. 193(3), pages 836-848, March.
    4. Dessouky, Maged M. & Dessouky, Mohamed I. & Verma, Sushil K., 1998. "Flowshop scheduling with identical jobs and uniform parallel machines," European Journal of Operational Research, Elsevier, vol. 109(3), pages 620-631, September.
    5. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    6. Baptiste, Philippe, 2003. "On minimizing the weighted number of late jobs in unit execution time open-shops," European Journal of Operational Research, Elsevier, vol. 149(2), pages 344-354, September.
    7. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
    8. Jun-Ho Lee & Hoon Jang, 2019. "Uniform Parallel Machine Scheduling with Dedicated Machines, Job Splitting and Setup Resources," Sustainability, MDPI, vol. 11(24), pages 1-23, December.
    9. Donatas Elvikis & Vincent T’kindt, 2014. "Two-agent scheduling on uniform parallel machines with min-max criteria," Annals of Operations Research, Springer, vol. 213(1), pages 79-94, February.
    10. Arbib, Claudio & Felici, Giovanni & Servilio, Mara, 2019. "Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs," Omega, Elsevier, vol. 84(C), pages 18-30.
    11. Nodari Vakhania & Frank Werner, 2021. "Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines," Mathematics, MDPI, vol. 9(6), pages 1-18, March.
    12. Cheng, T. C. Edwin & Gordon, Valery S. & Kovalyov, Mikhail Y., 1996. "Single machine scheduling with batch deliveries," European Journal of Operational Research, Elsevier, vol. 94(2), pages 277-283, October.
    13. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    14. Peter Brucker & Natalia V. Shakhlevich, 2016. "Necessary and sufficient optimality conditions for scheduling unit time jobs on identical parallel machines," Journal of Scheduling, Springer, vol. 19(6), pages 659-685, December.
    15. Qiulan Zhao & Jinjiang Yuan, 2020. "Bicriteria scheduling of equal length jobs on uniform parallel machines," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 637-661, April.

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