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Bicriteria scheduling of equal length jobs on uniform parallel machines

Author

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  • Qiulan Zhao

    (Nanjing University)

  • Jinjiang Yuan

    (Zhengzhou University)

Abstract

We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i-th position will be assigned the i-th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:3:d:10.1007_s10878-019-00507-w
    DOI: 10.1007/s10878-019-00507-w
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    References listed on IDEAS

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    1. 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.
    2. Subhash C. Sarin & Divya Prakash, 2004. "Equal Processing Time Bicriteria Scheduling on Parallel Machines," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 227-240, September.
    3. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    4. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    5. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    6. 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.
    7. Oron, Daniel & Shabtay, Dvir & Steiner, George, 2015. "Single machine scheduling with two competing agents and equal job processing times," European Journal of Operational Research, Elsevier, vol. 244(1), pages 86-99.
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    Cited by:

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    3. Qi Feng & Shisheng Li, 2022. "Algorithms for Multi-Customer Scheduling with Outsourcing," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
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    5. Yuan Gao & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2022. "Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost," 4OR, Springer, vol. 20(2), pages 273-287, June.
    6. Ruyan He & Jinjiang Yuan & C. T. Ng & T. C. E. Cheng, 2021. "Two-agent preemptive Pareto-scheduling to minimize the number of tardy jobs and total late work," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 504-525, February.

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