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Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

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  • Bartłomiej Przybylski

    (Adam Mickiewicz University)

Abstract

We consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

Suggested Citation

  • Bartłomiej Przybylski, 2022. "Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 207-222, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00821-2
    DOI: 10.1007/s10878-021-00821-2
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    References listed on IDEAS

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    1. Li Sun & Lei Ning & Jia-zhen Huo, 2020. "Group Scheduling Problems with Time-Dependent and Position-Dependent DeJong’s Learning Effect," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, February.
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    4. G Mosheiov, 2008. "Minimizing total absolute deviation of job completion times: extensions to position-dependent processing times and parallel identical machines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(10), pages 1422-1424, October.
    5. Biskup, Dirk, 1999. "Single-machine scheduling with learning considerations," European Journal of Operational Research, Elsevier, vol. 115(1), pages 173-178, May.
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    7. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Rate-Modifying Activities," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 317-331, Springer.
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