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Discovering the Properties of a Problem of Scheduling Battery Charging Jobs to Minimize the Total Time with the Use of Harmonic Numbers

Author

Listed:
  • Rafał Różycki

    (Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
    These authors contributed equally to this work.)

  • Zofia Walczak

    (Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
    These authors contributed equally to this work.)

  • Grzegorz Waligóra

    (Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965 Poznan, Poland
    These authors contributed equally to this work.)

Abstract

In this work, we consider a problem from the field of power-aware scheduling in which a fleet of electric vehicles have to be charged in a minimum time. Each vehicle is equipped with a lithium-ion battery of a given capacity. The initial power used for charging each battery is known, whereas it is assumed that the power drops to zero at the moment when the battery gets fully loaded. The power usage function is linear and decreasing. The charging jobs are nonpreemptable and independent, whereas the total available amount of power is limited. The objective is to minimize the schedule length. In this paper, we analyze the case of a problem with identical jobs that already cover a wide variety of practical situations. By employing inverses of natural numbers, similar to harmonic series, we prove two properties of this case, and we also discuss the phenomenon of the stabilization of the difference between the start times of two successive jobs in a schedule. We also take under examination a few special cases of the problem. Some conclusions and directions for future research are given.

Suggested Citation

  • Rafał Różycki & Zofia Walczak & Grzegorz Waligóra, 2024. "Discovering the Properties of a Problem of Scheduling Battery Charging Jobs to Minimize the Total Time with the Use of Harmonic Numbers," Energies, MDPI, vol. 17(15), pages 1-18, August.
    • Handle: RePEc:gam:jeners:v:17:y:2024:i:15:p:3843-:d:1449763
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    References listed on IDEAS

    as
    1. Pegah Alaee & Julius Bems & Amjad Anvari-Moghaddam, 2023. "A Review of the Latest Trends in Technical and Economic Aspects of EV Charging Management," Energies, MDPI, vol. 16(9), pages 1-28, April.
    2. A Janiak & M Y Kovalyov, 2012. "Scheduling jobs with position-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(7), pages 1018-1020, July.
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